Semiclassical initial value representation for the quantum propagator in the Heisenberg interaction representation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Petersen, Jakob; Pollak, Eli, E-mail: eli.pollak@weizmann.ac.il

2015-12-14

One of the challenges facing on-the-fly ab initio semiclassical time evolution is the large expense needed to converge the computation. In this paper, we suggest that a significant saving in computational effort may be achieved by employing a semiclassical initial value representation (SCIVR) of the quantum propagator based on the Heisenberg interaction representation. We formulate and test numerically a modification and simplification of the previous semiclassical interaction representation of Shao and Makri [J. Chem. Phys. 113, 3681 (2000)]. The formulation is based on the wavefunction form of the semiclassical propagation instead of the operator form, and so is simpler andmore » cheaper to implement. The semiclassical interaction representation has the advantage that the phase and prefactor vary relatively slowly as compared to the “standard” SCIVR methods. This improves its convergence properties significantly. Using a one-dimensional model system, the approximation is compared with Herman-Kluk’s frozen Gaussian and Heller’s thawed Gaussian approximations. The convergence properties of the interaction representation approach are shown to be favorable and indicate that the interaction representation is a viable way of incorporating on-the-fly force field information within a semiclassical framework.« less

A holographic model for black hole complementarity

DOE PAGES

Lowe, David A.; Thorlacius, Larus

2016-12-07

Here, we explore a version of black hole complementarity, where an approximate semiclassical effective field theory for interior infalling degrees of freedom emerges holo-graphically from an exact evolution of exterior degrees of freedom. The infalling degrees of freedom have a complementary description in terms of outgoing Hawking radiation and must eventually decohere with respect to the exterior Hamiltonian, leading to a breakdown of the semiclassical description for an infaller. Trace distance is used to quantify the difference between the complementary time evolutions, and to define a decoherence time. We propose a dictionary where the evolution with respect to the bulkmore » effective Hamiltonian corresponds to mean field evolution in the holographic theory. In a particular model for the holographic theory, which exhibits fast scrambling, the decoherence time coincides with the scrambling time. The results support the hypothesis that decoherence of the infalling holographic state and disruptive bulk effects near the curvature singularity are comple-mentary descriptions of the same physics, which is an important step toward resolving the black hole information paradox.« less

Symmetry and conservation laws in semiclassical wave packet dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ohsawa, Tomoki, E-mail: tomoki@utdallas.edu

2015-03-15

We formulate symmetries in semiclassical Gaussian wave packet dynamics and find the corresponding conserved quantities, particularly the semiclassical angular momentum, via Noether’s theorem. We consider two slightly different formulations of Gaussian wave packet dynamics; one is based on earlier works of Heller and Hagedorn and the other based on the symplectic-geometric approach by Lubich and others. In either case, we reveal the symplectic and Hamiltonian nature of the dynamics and formulate natural symmetry group actions in the setting to derive the corresponding conserved quantities (momentum maps). The semiclassical angular momentum inherits the essential properties of the classical angular momentum asmore » well as naturally corresponds to the quantum picture.« less

Semiclassical approaches to nuclear dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Magner, A. G., E-mail: magner@kinr.kiev.ua; Gorpinchenko, D. V.; Bartel, J.

The extended Gutzwiller trajectory approach is presented for the semiclassical description of nuclear collective dynamics, in line with the main topics of the fruitful activity of V.G. Solovjov. Within the Fermi-liquid droplet model, the leptodermous effective surface approximation was applied to calculations of energies, sum rules, and transition densities for the neutron–proton asymmetry of the isovector giant-dipole resonance and found to be in good agreement with the experimental data. By using the Strutinsky shell correction method, the semiclassical collective transport coefficients, such as nuclear inertia, friction, stiffness, and moments of inertia, can be derived beyond the quantum perturbation approximation ofmore » the response function theory and the cranking model. The averaged particle-number dependences of the low-lying collective vibrational states are described in good agreement with the basic experimental data, mainly due to the enhancement of the collective inertia as compared to its irrotational flow value. Shell components of the moment of inertia are derived in terms of the periodic-orbit free-energy shell corrections. A good agreement between the semiclassical extended Thomas–Fermi moments of inertia with shell corrections and the quantum results is obtained for different nuclear deformations and particle numbers. Shell effects are shown to be exponentially dampted out with increasing temperature in all the transport coefficients.« less

Simple model dielectric functions for insulators

NASA Astrophysics Data System (ADS)

Vos, Maarten; Grande, Pedro L.

2017-05-01

The Drude dielectric function is a simple way of describing the dielectric function of free electron materials, which have an uniform electron density, in a classical way. The Mermin dielectric function describes a free electron gas, but is based on quantum physics. More complex metals have varying electron densities and are often described by a sum of Drude dielectric functions, the weight of each function being taken proportional to the volume with the corresponding density. Here we describe a slight variation on the Drude dielectric functions that describes insulators in a semi-classical way and a form of the Levine-Louie dielectric function including a relaxation time that does the same within the framework of quantum physics. In the optical limit the semi-classical description of an insulator and the quantum physics description coincide, in the same way as the Drude and Mermin dielectric function coincide in the optical limit for metals. There is a simple relation between the coefficients used in the classical and quantum approaches, a relation that ensures that the obtained dielectric function corresponds to the right static refractive index. For water we give a comparison of the model dielectric function at non-zero momentum with inelastic X-ray measurements, both at relative small momenta and in the Compton limit. The Levine-Louie dielectric function including a relaxation time describes the spectra at small momentum quite well, but in the Compton limit there are significant deviations.

Entropy, temperature and internal energy of trapped gravitons and corrections to the Black Hole entropy

NASA Astrophysics Data System (ADS)

Viaggiu, Stefano

2017-12-01

In this paper we study the proposal present in Viaggiu (2017) concerning the statistical description of trapped gravitons and applied to derive the semi-classical black hole (BH) entropy SBH. We study the possible configurations depending on physically reasonable expressions for the internal energy U. In particular, we show that expressions for U ∼Rk , k ≥ 1, with R the radius of the confining spherical box, can have a semi-classical description, while behaviors with k < 1 derive from thermodynamic or quantum fluctuations. There, by taking a suitable physically motivated expression for U(R) , we obtain the well known logarithmic corrections to the BH entropy, with the usual behaviors present in the literature of BH entropy. Moreover, a phase transition emerges with a positive specific heat C at Planckian lengths instead of the usual negative one at non-Planckian scales, in agreement with results present in the literature. Finally, we show that evaporation stops at a radius R of the order of the Planck length.

Semiclassical approach to finite-temperature quantum annealing with trapped ions

NASA Astrophysics Data System (ADS)

Raventós, David; Graß, Tobias; Juliá-Díaz, Bruno; Lewenstein, Maciej

2018-05-01

Recently it has been demonstrated that an ensemble of trapped ions may serve as a quantum annealer for the number-partitioning problem [Nat. Commun. 7, 11524 (2016), 10.1038/ncomms11524]. This hard computational problem may be addressed by employing a tunable spin-glass architecture. Following the proposal of the trapped-ion annealer, we study here its robustness against thermal effects; that is, we investigate the role played by thermal phonons. For the efficient description of the system, we use a semiclassical approach, and benchmark it against the exact quantum evolution. The aim is to understand better and characterize how the quantum device approaches a solution of an otherwise difficult to solve NP-hard problem.

Impact of built-in fields and contact configuration on the characteristics of ultra-thin GaAs solar cells

DOE Office of Scientific and Technical Information (OSTI.GOV)

Aeberhard, Urs, E-mail: u.aeberhard@fz-juelich.de

2016-07-18

We discuss the effects of built-in fields and contact configuration on the photovoltaic characteristics of ultra-thin GaAs solar cells. The investigation is based on advanced quantum-kinetic simulations reaching beyond the standard semi-classical bulk picture concerning the consideration of charge carrier states and dynamics in complex potential profiles. The thickness dependence of dark and photocurrent in the ultra-scaled regime is related to the corresponding variation of both, the built-in electric fields and associated modification of the density of states, and the optical intensity in the films. Losses in open-circuit voltage and short-circuit current due to the leakage of electronically and opticallymore » injected carriers at minority carrier contacts are investigated for different contact configurations including electron and hole blocking barrier layers. The microscopic picture of leakage currents is connected to the effect of finite surface recombination velocities in the semi-classical description, and the impact of these non-classical contact regions on carrier generation and extraction is analyzed.« less

Coupled forward-backward trajectory approach for nonequilibrium electron-ion dynamics

NASA Astrophysics Data System (ADS)

Sato, Shunsuke A.; Kelly, Aaron; Rubio, Angel

2018-04-01

We introduce a simple ansatz for the wave function of a many-body system based on coupled forward and backward propagating semiclassical trajectories. This method is primarily aimed at, but not limited to, treating nonequilibrium dynamics in electron-phonon systems. The time evolution of the system is obtained from the Euler-Lagrange variational principle, and we show that this ansatz yields Ehrenfest mean-field theory in the limit that the forward and backward trajectories are orthogonal, and in the limit that they coalesce. We investigate accuracy and performance of this method by simulating electronic relaxation in the spin-boson model and the Holstein model. Although this method involves only pairs of semiclassical trajectories, it shows a substantial improvement over mean-field theory, capturing quantum coherence of nuclear dynamics as well as electron-nuclear correlations. This improvement is particularly evident in nonadiabatic systems, where the accuracy of this coupled trajectory method extends well beyond the perturbative electron-phonon coupling regime. This approach thus provides an attractive route forward to the ab initio description of relaxation processes, such as thermalization, in condensed phase systems.

Quantum Dynamics and a Semiclassical Description of the Photon.

ERIC Educational Resources Information Center

Henderson, Giles

1980-01-01

Uses computer graphics and nonstationary, superposition wave functions to reveal the dynamic quantum trajectories of several molecular and electronic transitions. These methods are then coupled with classical electromagnetic theory to provide a conceptually clear picture of the emission process and emitted radiation localized in time and space.…

Semiclassical theory of Landau levels and magnetic breakdown in topological metals

NASA Astrophysics Data System (ADS)

Alexandradinata, A.; Glazman, Leonid

2018-04-01

The Bohr-Sommerfeld quantization rule lies at the heart of the semiclassical theory of a Bloch electron in a magnetic field. This rule is predictive of Landau levels and de Haas-van Alphen oscillations for conventional metals, as well as for a host of topological metals which have emerged in the recent intercourse between band theory, crystalline symmetries, and topology. The essential ingredients in any quantization rule are connection formulas that match the semiclassical (WKB) wave function across regions of strong quantum fluctuations. Here, we propose (a) a multicomponent WKB wave function that describes transport within degenerate-band subspaces, and (b) the requisite connection formulas for saddle points and type-II Dirac points, where tunneling respectively occurs within the same band, and between distinct bands. (a) and (b) extend previous works by incorporating phase corrections that are subleading in powers of the field; these corrections include the geometric Berry phase, and account for the orbital magnetic moment and the Zeeman coupling. A comprehensive symmetry analysis is performed for such phase corrections occurring in closed orbits, which is applicable to solids in any (magnetic) space group. We have further formulated a graph-theoretic description of semiclassical orbits. This allows us to systematize the construction of quantization rules for a large class of closed orbits (with or without tunneling), as well as to formulate the notion of a topological invariant in semiclassical magnetotransport—as a quantity that is invariant under continuous deformations of the graph. Landau levels in the presence of tunneling are generically quasirandom, i.e., disordered on the scale of nearest-neighbor level spacings but having longer-ranged correlations; we develop a perturbative theory to determine Landau levels in such quasirandom spectra.

Semiclassical evaluation of quantum fidelity

NASA Astrophysics Data System (ADS)

Vanicek, Jiri

2004-03-01

We present a numerically feasible semiclassical method to evaluate quantum fidelity (Loschmidt echo) in a classically chaotic system. It was thought that such evaluation would be intractable, but instead we show that a uniform semiclassical expression not only is tractable but it gives remarkably accurate numerical results for the standard map in both the Fermi-golden-rule and Lyapunov regimes. Because it allows a Monte-Carlo evaluation, this uniform expression is accurate at times where there are 10^70 semiclassical contributions. Remarkably, the method also explicitly contains the ``building blocks'' of analytical theories of recent literature, and thus permits a direct test of approximations made by other authors in these regimes, rather than an a posteriori comparison with numerical results. We explain in more detail the extended validity of the classical perturbation approximation and thus provide a ``defense" of the linear response theory from the famous Van Kampen objection. We point out the potential use of our uniform expression in other areas because it gives a most direct link between the quantum Feynman propagator based on the path integral and the semiclassical Van Vleck propagator based on the sum over classical trajectories. Finally, we test the applicability of our method in integrable and mixed systems.

Symplectic semiclassical wave packet dynamics II: non-Gaussian states

NASA Astrophysics Data System (ADS)

Ohsawa, Tomoki

2018-05-01

We generalize our earlier work on the symplectic/Hamiltonian formulation of the dynamics of the Gaussian wave packet to non-Gaussian semiclassical wave packets. We find the symplectic forms and asymptotic expansions of the Hamiltonians associated with these semiclassical wave packets, and obtain Hamiltonian systems governing their dynamics. Numerical experiments demonstrate that the dynamics give a very good approximation to the short-time dynamics of the expectation values computed by a method based on Egorov’s theorem or the initial value representation.

Frozen Gaussian approximation based domain decomposition methods for the linear Schrödinger equation beyond the semi-classical regime

NASA Astrophysics Data System (ADS)

Lorin, E.; Yang, X.; Antoine, X.

2016-06-01

The paper is devoted to develop efficient domain decomposition methods for the linear Schrödinger equation beyond the semiclassical regime, which does not carry a small enough rescaled Planck constant for asymptotic methods (e.g. geometric optics) to produce a good accuracy, but which is too computationally expensive if direct methods (e.g. finite difference) are applied. This belongs to the category of computing middle-frequency wave propagation, where neither asymptotic nor direct methods can be directly used with both efficiency and accuracy. Motivated by recent works of the authors on absorbing boundary conditions (Antoine et al. (2014) [13] and Yang and Zhang (2014) [43]), we introduce Semiclassical Schwarz Waveform Relaxation methods (SSWR), which are seamless integrations of semiclassical approximation to Schwarz Waveform Relaxation methods. Two versions are proposed respectively based on Herman-Kluk propagation and geometric optics, and we prove the convergence and provide numerical evidence of efficiency and accuracy of these methods.

Semiclassical states on Lie algebras

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsobanjan, Artur, E-mail: artur.tsobanjan@gmail.com

2015-03-15

The effective technique for analyzing representation-independent features of quantum systems based on the semiclassical approximation (developed elsewhere) has been successfully used in the context of the canonical (Weyl) algebra of the basic quantum observables. Here, we perform the important step of extending this effective technique to the quantization of a more general class of finite-dimensional Lie algebras. The case of a Lie algebra with a single central element (the Casimir element) is treated in detail by considering semiclassical states on the corresponding universal enveloping algebra. Restriction to an irreducible representation is performed by “effectively” fixing the Casimir condition, following themore » methods previously used for constrained quantum systems. We explicitly determine the conditions under which this restriction can be consistently performed alongside the semiclassical truncation.« less

Regular black holes from semi-classical down to Planckian size

NASA Astrophysics Data System (ADS)

Spallucci, Euro; Smailagic, Anais

In this paper, we review various models of curvature singularity free black holes (BHs). In the first part of the review, we describe semi-classical solutions of the Einstein equations which, however, contains a “quantum” input through the matter source. We start by reviewing the early model by Bardeen where the metric is regularized by-hand through a short-distance cutoff, which is justified in terms of nonlinear electro-dynamical effects. This toy-model is useful to point-out the common features shared by all regular semi-classical black holes. Then, we solve Einstein equations with a Gaussian source encoding the quantum spread of an elementary particle. We identify, the a priori arbitrary, Gaussian width with the Compton wavelength of the quantum particle. This Compton-Gauss model leads to the estimate of a terminal density that a gravitationally collapsed object can achieve. We identify this density to be the Planck density, and reformulate the Gaussian model assuming this as its peak density. All these models, are physically reliable as long as the BH mass is big enough with respect to the Planck mass. In the truly Planckian regime, the semi-classical approximation breaks down. In this case, a fully quantum BH description is needed. In the last part of this paper, we propose a nongeometrical quantum model of Planckian BHs implementing the Holographic Principle and realizing the “classicalization” scenario recently introduced by Dvali and collaborators. The classical relation between the mass and radius of the BH emerges only in the classical limit, far away from the Planck scale.

Semiclassical Monte Carlo: A first principles approach to non-adiabatic molecular dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

White, Alexander J.; Center for Nonlinear Studies; Gorshkov, Vyacheslav N.

2014-11-14

Modeling the dynamics of photophysical and (photo)chemical reactions in extended molecular systems is a new frontier for quantum chemistry. Many dynamical phenomena, such as intersystem crossing, non-radiative relaxation, and charge and energy transfer, require a non-adiabatic description which incorporate transitions between electronic states. Additionally, these dynamics are often highly sensitive to quantum coherences and interference effects. Several methods exist to simulate non-adiabatic dynamics; however, they are typically either too expensive to be applied to large molecular systems (10's-100's of atoms), or they are based on ad hoc schemes which may include severe approximations due to inconsistencies in classical and quantummore » mechanics. We present, in detail, an algorithm based on Monte Carlo sampling of the semiclassical time-dependent wavefunction that involves running simple surface hopping dynamics, followed by a post-processing step which adds little cost. The method requires only a few quantities from quantum chemistry calculations, can systematically be improved, and provides excellent agreement with exact quantum mechanical results. Here we show excellent agreement with exact solutions for scattering results of standard test problems. Additionally, we find that convergence of the wavefunction is controlled by complex valued phase factors, the size of the non-adiabatic coupling region, and the choice of sampling function. These results help in determining the range of applicability of the method, and provide a starting point for further improvement.« less

Reply to ``Comment on `Quantum time-of-flight distribution for cold trapped atoms' ''

NASA Astrophysics Data System (ADS)

Ali, Md. Manirul; Home, Dipankar; Majumdar, A. S.; Pan, Alok K.

2008-02-01

In their comment Gomes [Phys. Rev. A 77, 026101 (2008)] have questioned the possibility of empirically testable differences existing between the semiclassical time of flight distribution for cold trapped atoms and a quantum distribution discussed by us recently [Ali , Phys. Rev. A 75, 042110 (2007).]. We argue that their criticism is based on a semiclassical treatment having restricted applicability for a particular trapping potential. Their claim does not preclude, in general, the possibility of differences between the semiclassical calculations and fully quantum results for the arrival time distribution of freely falling atoms.

Reply to 'Comment on 'Quantum time-of-flight distribution for cold trapped atoms''

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ali, Md. Manirul; Home, Dipankar; Pan, Alok K.

2008-02-15

In their comment Gomes et al. [Phys. Rev. A 77, 026101 (2008)] have questioned the possibility of empirically testable differences existing between the semiclassical time of flight distribution for cold trapped atoms and a quantum distribution discussed by us recently [Ali et al., Phys. Rev. A 75, 042110 (2007).]. We argue that their criticism is based on a semiclassical treatment having restricted applicability for a particular trapping potential. Their claim does not preclude, in general, the possibility of differences between the semiclassical calculations and fully quantum results for the arrival time distribution of freely falling atoms.

Semiclassical propagator of the Wigner function.

PubMed

Dittrich, Thomas; Viviescas, Carlos; Sandoval, Luis

2006-02-24

Propagation of the Wigner function is studied on two levels of semiclassical propagation: one based on the Van Vleck propagator, the other on phase-space path integration. Leading quantum corrections to the classical Liouville propagator take the form of a time-dependent quantum spot. Its oscillatory structure depends on whether the underlying classical flow is elliptic or hyperbolic. It can be interpreted as the result of interference of a pair of classical trajectories, indicating how quantum coherences are to be propagated semiclassically in phase space. The phase-space path-integral approach allows for a finer resolution of the quantum spot in terms of Airy functions.

An application of the Maslov complex germ method to the one-dimensional nonlocal Fisher-KPP equation

NASA Astrophysics Data System (ADS)

Shapovalov, A. V.; Trifonov, A. Yu.

A semiclassical approximation approach based on the Maslov complex germ method is considered in detail for the one-dimensional nonlocal Fisher-Kolmogorov-Petrovskii-Piskunov (Fisher-KPP) equation under the supposition of weak diffusion. In terms of the semiclassical formalism developed, the original nonlinear equation is reduced to an associated linear partial differential equation and some algebraic equations for the coefficients of the linear equation with a given accuracy of the asymptotic parameter. The solutions of the nonlinear equation are constructed from the solutions of both the linear equation and the algebraic equations. The solutions of the linear problem are found with the use of symmetry operators. A countable family of the leading terms of the semiclassical asymptotics is constructed in explicit form. The semiclassical asymptotics are valid by construction in a finite time interval. We construct asymptotics which are different from the semiclassical ones and can describe evolution of the solutions of the Fisher-KPP equation at large times. In the example considered, an initial unimodal distribution becomes multimodal, which can be treated as an example of a space structure.

Entropy evolution of moving mirrors and the information loss problem

NASA Astrophysics Data System (ADS)

Chen, Pisin; Yeom, Dong-han

2017-07-01

We investigate the entanglement entropy and the information flow of two-dimensional moving mirrors. Here we point out that various mirror trajectories can help to mimic different candidate resolutions to the information loss paradox following the semiclassical quantum field theory: (i) a suddenly stopping mirror corresponds to the assertion that all information is attached to the last burst, (ii) a slowly stopping mirror corresponds to the assertion that thermal Hawking radiation carries information, and (iii) a long propagating mirror corresponds to the remnant scenario. Based on such analogy, we find that the last burst of a black hole cannot contain enough information, while slowly emitting radiation can restore unitarity. For all cases, there is an apparent inconsistency between the picture based on quantum entanglements and that based on the semiclassical quantum field theory. Based on the quantum entanglement theory, a stopping mirror will generate a firewall-like violent emission which is in conflict with notions based on the semiclassical quantum field theory.

Identical superdeformed bands in yrast 152Dy: a systematic description

NASA Astrophysics Data System (ADS)

Dadwal, Anshul; Mittal, H. M.

2018-06-01

The nuclear softness (NS) formula, semiclassical particle rotor model (PRM) and modified exponential model with pairing attenuation are used for the systematic study of the identical superdeformed bands in the A ∼ 150 mass region. These formulae/models are employed to study the identical superdeformed bands relative to the yrast SD band 152Dy(1), {152Dy(1), 151Tb(2)}, {152Dy(1), 151Dy(4)} (midpoint), {152Dy(1), 153Dy(2)} (quarter point), {152Dy(1), 153Dy(3)} (three-quarter point). The parameters, baseline moment of inertia ({{I}}0), alignment (i) and effective pairing parameter (Δ0) are calculated using the least-squares fitting of the γ-ray transitions energies in the NS formula, semiclassical-PRM and modified exponential model with pairing attenuation, respectively. The calculated parameters are found to depend sensitively on the proposed baseline spin (I 0).

Quantized mode of a leaky cavity

NASA Astrophysics Data System (ADS)

Dutra, S. M.; Nienhuis, G.

2000-12-01

We use Thomson's classical concept of mode of a leaky cavity to develop a quantum theory of cavity damping. This theory generalizes the conventional system-reservoir theory of high-Q cavity damping to arbitrary Q. The small system now consists of damped oscillators corresponding to the natural modes of the leaky cavity rather than undamped oscillators associated with the normal modes of a fictitious perfect cavity. The formalism unifies semiclassical Fox-Li modes and the normal modes traditionally used for quantization. It also lays the foundations for a full quantum description of excess noise. The connection with Siegman's semiclassical work is straightforward. In a wider context, this theory constitutes a radical departure from present models of dissipation in quantum mechanics: unlike conventional models, system and reservoir operators no longer commute with each other. This noncommutability is an unavoidable consequence of having to use natural cavity modes rather than normal modes of a fictitious perfect cavity.

Semiclassical description of photoionization microscopy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bordas, Ch.; Lepine, F.; Nicole, C.

2003-07-01

Recently, experiments have been reported where a geometrical interference pattern was observed when photoelectrons ejected in the threshold photoionization of xenon were detected in a velocity-map imaging apparatus [C. Nicole et al., Phys. Rev. Lett. 88, 133001 (2002)]. This technique, called photoionization microscopy, relies on the existence of interferences between various trajectories by which the electron moves from the atom to the plane of observation. Unlike previous predictions relevant to the hydrogenic case, the structure of the interference pattern evolves smoothly with the excess energy above the saddle point and is only weakly affected by the presence of continuum Starkmore » resonances. In this paper, we describe a semiclassical analysis of this process and present numerical simulations in excellent agreement with the experimental results. It is shown that the background contribution dominates in the observations, as opposed to the behavior expected for hydrogenic systems where the interference pattern is qualitatively different on quasidiscrete Stark resonances.« less

Semiclassics for matrix Hamiltonians: The Gutzwiller trace formula with applications to graphene-type systems

NASA Astrophysics Data System (ADS)

Vogl, M.; Pankratov, O.; Shallcross, S.

2017-07-01

We present a tractable and physically transparent semiclassical theory of matrix-valued Hamiltonians, i.e., those that describe quantum systems with internal degrees of freedoms, based on a generalization of the Gutzwiller trace formula for a n ×n dimensional Hamiltonian H (p ̂,q ̂) . The classical dynamics is governed by n Hamilton-Jacobi (HJ) equations that act in a phase space endowed with a classical Berry curvature encoding anholonomy in the parallel transport of the eigenvectors of H (p ,q ) ; these vectors describe the internal structure of the semiclassical particles. At the O (ℏ1) level and for nondegenerate HJ systems, this curvature results in an additional semiclassical phase composed of (i) a Berry phase and (ii) a dynamical phase resulting from the classical particles "moving through the Berry curvature". We show that the dynamical part of this semiclassical phase will, generally, be zero only for the case in which the Berry phase is topological (i.e., depends only on the winding number). We illustrate the method by calculating the Landau spectrum for monolayer graphene, the four-band model of AB bilayer graphene, and for a more complicated matrix Hamiltonian describing the silicene band structure. Finally, we apply our method to an inhomogeneous system consisting of a strain engineered one-dimensional moiré in bilayer graphene, finding localized states near the Dirac point that arise from electron trapping in a semiclassical moiré potential. The semiclassical density of states of these localized states we show to be in perfect agreement with an exact quantum mechanical calculation of the density of states.

Effective field theory models for nonviolent information transfer from black holes

NASA Astrophysics Data System (ADS)

Giddings, Steven B.; Shi, Yinbo

2014-06-01

Transfer of quantum information from the interior of a black hole to its atmosphere is described, in models based on effective field theory. This description illustrates that such transfer need not be violent to the semiclassical geometry or to infalling observers, and in particular can avoid producing a singular horizon or "firewall". One can specifically quantify the rate of information transfer and show that a rate necessary to unitarize black hole evaporation produces a relatively mild modification to the stress tensor near the horizon. In an exterior description of the transfer, the new interactions responsible for it are approximated by "effective sources" acting on fields in the black hole atmosphere. If the necessary interactions couple to general modes in the black hole atmosphere, one also finds a straightforward mechanism for information transfer rates to increase when a black hole is mined, avoiding paradoxical behavior. Correspondence limits are discussed, in the presence of such new interactions, for both small black holes and large ones; the near-horizon description of the latter is approximately that of Rindler space.

A quantum relaxation-time approximation for finite fermion systems

NASA Astrophysics Data System (ADS)

Reinhard, P.-G.; Suraud, E.

2015-03-01

We propose a relaxation time approximation for the description of the dynamics of strongly excited fermion systems. Our approach is based on time-dependent density functional theory at the level of the local density approximation. This mean-field picture is augmented by collisional correlations handled in relaxation time approximation which is inspired from the corresponding semi-classical picture. The method involves the estimate of microscopic relaxation rates/times which is presently taken from the well established semi-classical experience. The relaxation time approximation implies evaluation of the instantaneous equilibrium state towards which the dynamical state is progressively driven at the pace of the microscopic relaxation time. As test case, we consider Na clusters of various sizes excited either by a swift ion projectile or by a short and intense laser pulse, driven in various dynamical regimes ranging from linear to strongly non-linear reactions. We observe a strong effect of dissipation on sensitive observables such as net ionization and angular distributions of emitted electrons. The effect is especially large for moderate excitations where typical relaxation/dissipation time scales efficiently compete with ionization for dissipating the available excitation energy. Technical details on the actual procedure to implement a working recipe of such a quantum relaxation approximation are given in appendices for completeness.

X-ray phase-contrast imaging: the quantum perspective

NASA Astrophysics Data System (ADS)

Slowik, J. M.; Santra, R.

2013-08-01

Time-resolved phase-contrast imaging using ultrafast x-ray sources is an emerging method to investigate ultrafast dynamical processes in matter. Schemes to generate attosecond x-ray pulses have been proposed, bringing electronic timescales into reach and emphasizing the demand for a quantum description. In this paper, we present a method to describe propagation-based x-ray phase-contrast imaging in nonrelativistic quantum electrodynamics. We explain why the standard scattering treatment via Fermi’s golden rule cannot be applied. Instead, the quantum electrodynamical treatment of phase-contrast imaging must be based on a different approach. It turns out that it is essential to select a suitable observable. Here, we choose the quantum-mechanical Poynting operator. We determine the expectation value of our observable and demonstrate that the leading order term describes phase-contrast imaging. It recovers the classical expression of phase-contrast imaging. Thus, it makes the instantaneous electron density of non-stationary electronic states accessible to time-resolved imaging. Interestingly, inelastic (Compton) scattering does automatically not contribute in leading order, explaining the success of the semiclassical description.

Low-Dimensional Nanostructures and a Semiclassical Approach for Teaching Feynman's Sum-over-Paths Quantum Theory

ERIC Educational Resources Information Center

Onorato, P.

2011-01-01

An introduction to quantum mechanics based on the sum-over-paths (SOP) method originated by Richard P. Feynman and developed by E. F. Taylor and coworkers is presented. The Einstein-Brillouin-Keller (EBK) semiclassical quantization rules are obtained following the SOP approach for bounded systems, and a general approach to the calculation of…

Semiclassical propagation of Wigner functions.

PubMed

Dittrich, T; Gómez, E A; Pachón, L A

2010-06-07

We present a comprehensive study of semiclassical phase-space propagation in the Wigner representation, emphasizing numerical applications, in particular as an initial-value representation. Two semiclassical approximation schemes are discussed. The propagator of the Wigner function based on van Vleck's approximation replaces the Liouville propagator by a quantum spot with an oscillatory pattern reflecting the interference between pairs of classical trajectories. Employing phase-space path integration instead, caustics in the quantum spot are resolved in terms of Airy functions. We apply both to two benchmark models of nonlinear molecular potentials, the Morse oscillator and the quartic double well, to test them in standard tasks such as computing autocorrelation functions and propagating coherent states. The performance of semiclassical Wigner propagation is very good even in the presence of marked quantum effects, e.g., in coherent tunneling and in propagating Schrodinger cat states, and of classical chaos in four-dimensional phase space. We suggest options for an effective numerical implementation of our method and for integrating it in Monte-Carlo-Metropolis algorithms suitable for high-dimensional systems.

Semiclassical excited-state signatures of quantum phase transitions in spin chains with variable-range interactions

NASA Astrophysics Data System (ADS)

Gessner, Manuel; Bastidas, Victor Manuel; Brandes, Tobias; Buchleitner, Andreas

2016-04-01

We study the excitation spectrum of a family of transverse-field spin chain models with variable interaction range and arbitrary spin S , which in the case of S =1 /2 interpolates between the Lipkin-Meshkov-Glick and the Ising model. For any finite number N of spins, a semiclassical energy manifold is derived in the large-S limit employing bosonization methods, and its geometry is shown to determine not only the leading-order term but also the higher-order quantum fluctuations. Based on a multiconfigurational mean-field ansatz, we obtain the semiclassical backbone of the quantum spectrum through the extremal points of a series of one-dimensional energy landscapes—each one exhibiting a bifurcation when the external magnetic field drops below a threshold value. The obtained spectra become exact in the limit of vanishing or very strong external, transverse magnetic fields. Further analysis of the higher-order corrections in 1 /√{2 S } enables us to analytically study the dispersion relations of spin-wave excitations around the semiclassical energy levels. Within the same model, we are able to investigate quantum bifurcations, which occur in the semiclassical (S ≫1 ) limit, and quantum phase transitions, which are observed in the thermodynamic (N →∞ ) limit.

Universal functions of nuclear proximity potential for Skyrme nucleus-nucleus interaction in a semiclassical approach

NASA Astrophysics Data System (ADS)

Gupta, Raj K.; Singh, Dalip; Kumar, Raj; Greiner, Walter

2009-07-01

The universal function of the nuclear proximity potential is obtained for the Skyrme nucleus-nucleus interaction in the semiclassical extended Thomas-Fermi (ETF) approach. This is obtained as a sum of the spin-orbit-density-independent and spin-orbit-density-dependent parts of the Hamiltonian density, since the two terms behave differently, the spin-orbit-density-independent part mainly attractive and the spin-orbit-density-dependent part mainly repulsive. The semiclassical expansions of kinetic energy density and spin-orbit density are allowed up to second order, and the two-parameter Fermi density, with its parameters fitted to experiments, is used for the nuclear density. The universal functions or the resulting nuclear proximity potential reproduce the 'exact' Skyrme nucleus-nucleus interaction potential in the semiclassical approach, within less than ~1 MeV of difference, both at the maximum attraction and in the surface region. An application of the resulting interaction potential to fusion excitation functions shows clearly that the parameterized universal functions of nuclear proximity potential substitute completely the 'exact' potential in the Skyrme energy density formalism based on the semiclassical ETF method, including also the modifications of interaction barriers at sub-barrier energies in terms of modifying the constants of the universal functions.

Semiclassical theory of electronically nonadiabatic transitions in molecular collision processes

NASA Technical Reports Server (NTRS)

Lam, K. S.; George, T. F.

1979-01-01

An introductory account of the semiclassical theory of the S-matrix for molecular collision processes is presented, with special emphasis on electronically nonadiabatic transitions. This theory is based on the incorporation of classical mechanics with quantum superposition, and in practice makes use of the analytic continuation of classical mechanics into the complex space of time domain. The relevant concepts of molecular scattering theory and related dynamical models are described and the formalism is developed and illustrated with simple examples - collinear collision of the A+BC type. The theory is then extended to include the effects of laser-induced nonadiabatic transitions. Two bound continuum processes collisional ionization and collision-induced emission also amenable to the same general semiclassical treatment are discussed.

Semi-classical statistical description of Fröhlich condensation.

PubMed

Preto, Jordane

2017-06-01

Fröhlich's model equations describing phonon condensation in open systems of biological relevance are reinvestigated within a semi-classical statistical framework. The main assumptions needed to deduce Fröhlich's rate equations are identified and it is shown how they lead us to write an appropriate form for the corresponding master equation. It is shown how solutions of the master equation can be numerically computed and can highlight typical features of the condensation effect. Our approach provides much more information compared to the existing ones as it allows to investigate the time evolution of the probability density function instead of following single averaged quantities. The current work is also motivated, on the one hand, by recent experimental evidences of long-lived excited modes in the protein structure of hen-egg white lysozyme, which were reported as a consequence of the condensation effect, and, on the other hand, by a growing interest in investigating long-range effects of electromagnetic origin and their influence on the dynamics of biochemical reactions.

Thermoelectric properties of AgSbTe₂ from first-principles calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rezaei, Nafiseh; Akbarzadeh, Hadi; Hashemifar, S. Javad, E-mail: hashemifar@cc.iut.ac.ir

2014-09-14

The structural, electronic, and transport properties of AgSbTe₂ are studied by using full-relativistic first-principles electronic structure calculation and semiclassical description of transport parameters. The results indicate that, within various exchange-correlation functionals, the cubic Fd3⁻m and trigonal R3⁻m structures of AgSbTe₂ are more stable than two other considered structures. The computed Seebeck coefficients at different values of the band gap and carrier concentration are accurately compared with the available experimental data to speculate a band gap of about 0.1–0.35 eV for AgSbTe₂ compound, in agreement with our calculated electronic structure within the hybrid HSE (Heyd-Scuseria-Ernzerhof) functional. By calculating the semiclassical Seebeckmore » coefficient, electrical conductivity, and electronic part of thermal conductivity, we present the theoretical upper limit of the thermoelectric figure of merit of AgSbTe₂ as a function of temperature and carrier concentration.« less

Coherence penalty functional: A simple method for adding decoherence in Ehrenfest dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Akimov, Alexey V., E-mail: alexvakimov@gmail.com, E-mail: oleg.prezhdo@rochester.edu; Chemistry Department, Brookhaven National Laboratory, Upton, New York 11973; Long, Run

2014-05-21

We present a new semiclassical approach for description of decoherence in electronically non-adiabatic molecular dynamics. The method is formulated on the grounds of the Ehrenfest dynamics and the Meyer-Miller-Thoss-Stock mapping of the time-dependent Schrödinger equation onto a fully classical Hamiltonian representation. We introduce a coherence penalty functional (CPF) that accounts for decoherence effects by randomizing the wavefunction phase and penalizing development of coherences in regions of strong non-adiabatic coupling. The performance of the method is demonstrated with several model and realistic systems. Compared to other semiclassical methods tested, the CPF method eliminates artificial interference and improves agreement with the fullymore » quantum calculations on the models. When applied to study electron transfer dynamics in the nanoscale systems, the method shows an improved accuracy of the predicted time scales. The simplicity and high computational efficiency of the CPF approach make it a perfect practical candidate for applications in realistic systems.« less

Polariton-acoustic-phonon interaction in a semiconductor microcavity

NASA Astrophysics Data System (ADS)

Cassabois, G.; Triques, A. L. C.; Bogani, F.; Delalande, C.; Roussignol, Ph.; Piermarocchi, C.

2000-01-01

The broadening of polariton lines by acoustic phonons is investigated in a semiconductor microcavity by means of interferometric correlation measurements with subpicosecond resolution. A decrease of the polariton-acoustic phonon coupling is clearly observed for the lower polariton branch as one approaches the resonance between exciton and photon states. This behavior cannot be explained in terms of a semiclassical linear dispersion theory but requires a full quantum description of the microcavity in the strong-coupling regime.

Semiclassical modelling of finite-pulse effects on non-adiabatic photodynamics via initial condition filtering: The predissociation of NaI as a test case

DOE Office of Scientific and Technical Information (OSTI.GOV)

Martínez-Mesa, Aliezer; Institut für Chemie, Universität Potsdam, Karl-Liebknecht-Strasse 24-25, D-14476 Potsdam-Golm; Saalfrank, Peter

2015-05-21

Femtosecond-laser pulse driven non-adiabatic spectroscopy and dynamics in molecular and condensed phase systems continue to be a challenge for theoretical modelling. One of the main obstacles is the “curse of dimensionality” encountered in non-adiabatic, exact wavepacket propagation. A possible route towards treating complex molecular systems is via semiclassical surface-hopping schemes, in particular if they account not only for non-adiabatic post-excitation dynamics but also for the initial optical excitation. One such approach, based on initial condition filtering, will be put forward in what follows. As a simple test case which can be compared with exact wavepacket dynamics, we investigate the influencemore » of the different parameters determining the shape of a laser pulse (e.g., its finite width and a possible chirp) on the predissociation dynamics of a NaI molecule, upon photoexcitation of the A(0{sup +}) state. The finite-pulse effects are mapped into the initial conditions for semiclassical surface-hopping simulations. The simulated surface-hopping diabatic populations are in qualitative agreement with the quantum mechanical results, especially concerning the subpicosend photoinduced dynamics, the main deviations being the relative delay of the non-adiabatic transitions in the semiclassical picture. Likewise, these differences in the time-dependent electronic populations calculated via the semiclassical and the quantum methods are found to have a mild influence on the overall probability density distribution. As a result, the branching ratios between the bound and the dissociative reaction channels and the time-evolution of the molecular wavepacket predicted by the semiclassical method agree with those computed using quantum wavepacket propagation. Implications for more challenging molecular systems are given.« less

On-the-Fly ab Initio Semiclassical Calculation of Glycine Vibrational Spectrum

PubMed Central

2017-01-01

We present an on-the-fly ab initio semiclassical study of vibrational energy levels of glycine, calculated by Fourier transform of the wavepacket correlation function. It is based on a multiple coherent states approach integrated with monodromy matrix regularization for chaotic dynamics. All four lowest-energy glycine conformers are investigated by means of single-trajectory semiclassical spectra obtained upon classical evolution of on-the-fly trajectories with harmonic zero-point energy. For the most stable conformer I, direct dynamics trajectories are also run for each vibrational mode with energy equal to the first harmonic excitation. An analysis of trajectories evolved up to 50 000 atomic time units demonstrates that, in this time span, conformers II and III can be considered as isolated species, while conformers I and IV show a pretty facile interconversion. Therefore, previous perturbative studies based on the assumption of isolated conformers are often reliable but might be not completely appropriate in the case of conformer IV and conformer I for which interconversion occurs promptly. PMID:28489368

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berenstein, David; Kavli Institute for Theoretical Physics, University of California at Santa Barbara, California 93106; Correa, Diego H.

We study an XXX open spin chain with variable number of sites, where the variability is introduced only at the boundaries. This model arises naturally in the study of giant gravitons in the anti-de Sitter-space/conformal field-theory correspondence. We show how to quantize the spin chain by mapping its states to a bosonic lattice of finite length with sources and sinks of particles at the boundaries. Using coherent states, we show how the Hamiltonian for the bosonic lattice gives the correct description of semiclassical open strings ending on giant gravitons.

Semiclassical propagation: Hilbert space vs. Wigner representation

NASA Astrophysics Data System (ADS)

Gottwald, Fabian; Ivanov, Sergei D.

2018-03-01

A unified viewpoint on the van Vleck and Herman-Kluk propagators in Hilbert space and their recently developed counterparts in Wigner representation is presented. Based on this viewpoint, the Wigner Herman-Kluk propagator is conceptually the most general one. Nonetheless, the respective semiclassical expressions for expectation values in terms of the density matrix and the Wigner function are mathematically proven here to coincide. The only remaining difference is a mere technical flexibility of the Wigner version in choosing the Gaussians' width for the underlying coherent states beyond minimal uncertainty. This flexibility is investigated numerically on prototypical potentials and it turns out to provide neither qualitative nor quantitative improvements. Given the aforementioned generality, utilizing the Wigner representation for semiclassical propagation thus leads to the same performance as employing the respective most-developed (Hilbert-space) methods for the density matrix.

Modification of Schrödinger-Newton equation due to braneworld models with minimal length

NASA Astrophysics Data System (ADS)

Bhat, Anha; Dey, Sanjib; Faizal, Mir; Hou, Chenguang; Zhao, Qin

2017-07-01

We study the correction of the energy spectrum of a gravitational quantum well due to the combined effect of the braneworld model with infinite extra dimensions and generalized uncertainty principle. The correction terms arise from a natural deformation of a semiclassical theory of quantum gravity governed by the Schrödinger-Newton equation based on a minimal length framework. The two fold correction in the energy yields new values of the spectrum, which are closer to the values obtained in the GRANIT experiment. This raises the possibility that the combined theory of the semiclassical quantum gravity and the generalized uncertainty principle may provide an intermediate theory between the semiclassical and the full theory of quantum gravity. We also prepare a schematic experimental set-up which may guide to the understanding of the phenomena in the laboratory.

Semiclassical matrix model for quantum chaotic transport with time-reversal symmetry

DOE Office of Scientific and Technical Information (OSTI.GOV)

Novaes, Marcel, E-mail: marcel.novaes@gmail.com

2015-10-15

We show that the semiclassical approach to chaotic quantum transport in the presence of time-reversal symmetry can be described by a matrix model. In other words, we construct a matrix integral whose perturbative expansion satisfies the semiclassical diagrammatic rules for the calculation of transport statistics. One of the virtues of this approach is that it leads very naturally to the semiclassical derivation of universal predictions from random matrix theory.

Non-adiabatic molecular dynamics by accelerated semiclassical Monte Carlo

DOE PAGES

White, Alexander J.; Gorshkov, Vyacheslav N.; Tretiak, Sergei; ...

2015-07-07

Non-adiabatic dynamics, where systems non-radiatively transition between electronic states, plays a crucial role in many photo-physical processes, such as fluorescence, phosphorescence, and photoisomerization. Methods for the simulation of non-adiabatic dynamics are typically either numerically impractical, highly complex, or based on approximations which can result in failure for even simple systems. Recently, the Semiclassical Monte Carlo (SCMC) approach was developed in an attempt to combine the accuracy of rigorous semiclassical methods with the efficiency and simplicity of widely used surface hopping methods. However, while SCMC was found to be more efficient than other semiclassical methods, it is not yet as efficientmore » as is needed to be used for large molecular systems. Here, we have developed two new methods: the accelerated-SCMC and the accelerated-SCMC with re-Gaussianization, which reduce the cost of the SCMC algorithm up to two orders of magnitude for certain systems. In many cases shown here, the new procedures are nearly as efficient as the commonly used surface hopping schemes, with little to no loss of accuracy. This implies that these modified SCMC algorithms will be of practical numerical solutions for simulating non-adiabatic dynamics in realistic molecular systems.« less

Mixed quantum-classical electrodynamics: Understanding spontaneous decay and zero-point energy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Tao E.; Nitzan, Abraham; Sukharev, Maxim

The dynamics of an electronic two-level system coupled to an electromagnetic field are simulated explicitly for one- and three-dimensional systems through semiclassical propagation of the Maxwell-Liouville equations. Here, we consider three flavors of mixed quantum-classical dynamics: (i) the classical path approximation (CPA), (ii) Ehrenfest dynamics, and (iii) symmetrical quasiclassical (SQC) dynamics. Our findings are as follows: (i) The CPA fails to recover a consistent description of spontaneous emission, (ii) a consistent “spontaneous” emission can be obtained from Ehrenfest dynamics, provided that one starts in an electronic superposition state, and (iii) spontaneous emission is always obtained using SQC dynamics. Using themore » SQC and Ehrenfest frameworks, we further calculate the dynamics following an incoming pulse, but here we find very different responses: SQC and Ehrenfest dynamics deviate sometimes strongly in the calculated rate of decay of the transient excited state. Nevertheless, our work confirms the earlier observations by Miller [J. Chem. Phys. 69, 2188 (1978)] that Ehrenfest dynamics can effectively describe some aspects of spontaneous emission and highlights interesting possibilities for studying light-matter interactions with semiclassical mechanics.« less

Mixed quantum-classical electrodynamics: Understanding spontaneous decay and zero-point energy

NASA Astrophysics Data System (ADS)

Li, Tao E.; Nitzan, Abraham; Sukharev, Maxim; Martinez, Todd; Chen, Hsing-Ta; Subotnik, Joseph E.

2018-03-01

The dynamics of an electronic two-level system coupled to an electromagnetic field are simulated explicitly for one- and three-dimensional systems through semiclassical propagation of the Maxwell-Liouville equations. We consider three flavors of mixed quantum-classical dynamics: (i) the classical path approximation (CPA), (ii) Ehrenfest dynamics, and (iii) symmetrical quasiclassical (SQC) dynamics. Our findings are as follows: (i) The CPA fails to recover a consistent description of spontaneous emission, (ii) a consistent "spontaneous" emission can be obtained from Ehrenfest dynamics, provided that one starts in an electronic superposition state, and (iii) spontaneous emission is always obtained using SQC dynamics. Using the SQC and Ehrenfest frameworks, we further calculate the dynamics following an incoming pulse, but here we find very different responses: SQC and Ehrenfest dynamics deviate sometimes strongly in the calculated rate of decay of the transient excited state. Nevertheless, our work confirms the earlier observations by Miller [J. Chem. Phys. 69, 2188 (1978), 10.1063/1.436793] that Ehrenfest dynamics can effectively describe some aspects of spontaneous emission and highlights interesting possibilities for studying light-matter interactions with semiclassical mechanics.

Mixed quantum-classical electrodynamics: Understanding spontaneous decay and zero-point energy

DOE PAGES

Li, Tao E.; Nitzan, Abraham; Sukharev, Maxim; ...

2018-03-12

The dynamics of an electronic two-level system coupled to an electromagnetic field are simulated explicitly for one- and three-dimensional systems through semiclassical propagation of the Maxwell-Liouville equations. Here, we consider three flavors of mixed quantum-classical dynamics: (i) the classical path approximation (CPA), (ii) Ehrenfest dynamics, and (iii) symmetrical quasiclassical (SQC) dynamics. Our findings are as follows: (i) The CPA fails to recover a consistent description of spontaneous emission, (ii) a consistent “spontaneous” emission can be obtained from Ehrenfest dynamics, provided that one starts in an electronic superposition state, and (iii) spontaneous emission is always obtained using SQC dynamics. Using themore » SQC and Ehrenfest frameworks, we further calculate the dynamics following an incoming pulse, but here we find very different responses: SQC and Ehrenfest dynamics deviate sometimes strongly in the calculated rate of decay of the transient excited state. Nevertheless, our work confirms the earlier observations by Miller [J. Chem. Phys. 69, 2188 (1978)] that Ehrenfest dynamics can effectively describe some aspects of spontaneous emission and highlights interesting possibilities for studying light-matter interactions with semiclassical mechanics.« less

Path Integrals for Electronic Densities, Reactivity Indices, and Localization Functions in Quantum Systems

PubMed Central

Putz, Mihai V.

2009-01-01

The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr’s quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions – all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems. PMID:20087467

Path integrals for electronic densities, reactivity indices, and localization functions in quantum systems.

PubMed

Putz, Mihai V

2009-11-10

The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr's quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions - all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems.

InGaAs tunnel diodes for the calibration of semi-classical and quantum mechanical band-to-band tunneling models

NASA Astrophysics Data System (ADS)

Smets, Quentin; Verreck, Devin; Verhulst, Anne S.; Rooyackers, Rita; Merckling, Clément; Van De Put, Maarten; Simoen, Eddy; Vandervorst, Wilfried; Collaert, Nadine; Thean, Voon Y.; Sorée, Bart; Groeseneken, Guido; Heyns, Marc M.

2014-05-01

Promising predictions are made for III-V tunnel-field-effect transistor (FET), but there is still uncertainty on the parameters used in the band-to-band tunneling models. Therefore, two simulators are calibrated in this paper; the first one uses a semi-classical tunneling model based on Kane's formalism, and the second one is a quantum mechanical simulator implemented with an envelope function formalism. The calibration is done for In0.53Ga0.47As using several p+/intrinsic/n+ diodes with different intrinsic region thicknesses. The dopant profile is determined by SIMS and capacitance-voltage measurements. Error bars are used based on statistical and systematic uncertainties in the measurement techniques. The obtained parameters are in close agreement with theoretically predicted values and validate the semi-classical and quantum mechanical models. Finally, the models are applied to predict the input characteristics of In0.53Ga0.47As n- and p-lineTFET, with the n-lineTFET showing competitive performance compared to MOSFET.

Geometric constraints in semiclassical initial value representation calculations in Cartesian coordinates: accurate reduction in zero-point energy.

PubMed

Issack, Bilkiss B; Roy, Pierre-Nicholas

2005-08-22

An approach for the inclusion of geometric constraints in semiclassical initial value representation calculations is introduced. An important aspect of the approach is that Cartesian coordinates are used throughout. We devised an algorithm for the constrained sampling of initial conditions through the use of multivariate Gaussian distribution based on a projected Hessian. We also propose an approach for the constrained evaluation of the so-called Herman-Kluk prefactor in its exact log-derivative form. Sample calculations are performed for free and constrained rare-gas trimers. The results show that the proposed approach provides an accurate evaluation of the reduction in zero-point energy. Exact basis set calculations are used to assess the accuracy of the semiclassical results. Since Cartesian coordinates are used, the approach is general and applicable to a variety of molecular and atomic systems.

Simplified approach to the mixed time-averaging semiclassical initial value representation for the calculation of dense vibrational spectra

NASA Astrophysics Data System (ADS)

Buchholz, Max; Grossmann, Frank; Ceotto, Michele

2018-03-01

We present and test an approximate method for the semiclassical calculation of vibrational spectra. The approach is based on the mixed time-averaging semiclassical initial value representation method, which is simplified to a form that contains a filter to remove contributions from approximately harmonic environmental degrees of freedom. This filter comes at no additional numerical cost, and it has no negative effect on the accuracy of peaks from the anharmonic system of interest. The method is successfully tested for a model Hamiltonian and then applied to the study of the frequency shift of iodine in a krypton matrix. Using a hierarchic model with up to 108 normal modes included in the calculation, we show how the dynamical interaction between iodine and krypton yields results for the lowest excited iodine peaks that reproduce experimental findings to a high degree of accuracy.

Theory for electron transfer from a mixed-valence dimer with paramagnetic sites to a mononuclear acceptor

NASA Astrophysics Data System (ADS)

Bominaar, E. L.; Achim, C.; Borshch, S. A.

1999-06-01

Polynuclear transition-metal complexes, such as Fe-S clusters, are the prosthetic groups in a large number of metalloproteins and serve as temporary electron storage units in a number of important redox-based biological processes. Polynuclearity distinguishes clusters from mononuclear centers and confers upon them unique properties, such as spin ordering and the presence of thermally accessible excited spin states in clusters with paramagnetic sites, and fractional valencies in clusters of the mixed-valence type. In an earlier study we presented an effective-mode (EM) analysis of electron transfer from a binuclear mixed-valence donor with paramagnetic sites to a mononuclear acceptor which revealed that the cluster-specific attributes have an important impact on the kinetics of long-range electron transfer. In the present study, the validity of these results is tested in the framework of more detailed theories which we have termed the multimode semiclassical (SC) model and the quantum-mechanical (QM) model. It is found that the qualitative trends in the rate constant are the same in all treatments and that the semiclassical models provide a good approximation of the more rigorous quantum-mechanical description of electron transfer under physiologically relevant conditions. In particular, the present results corroborate the importance of electron transfer via excited spin states in reactions with a low driving force and justify the use of semiclassical theory in cases in which the QM model is computationally too demanding. We consider cases in which either one or two donor sites of a dimer are electronically coupled to the acceptor. In the case of multiconnectivity, the rate constant for electron transfer from a valence-delocalized (class-III) donor is nonadditive with respect to transfer from individual metal sites of the donor and undergoes an order-of-magnitude change by reversing the sign of the intradimer metal-metal resonance parameter (β). In the case of single connectivity, the rate constant for electron transfer from a valence-localized (class-II) donor can readily be tuned over several orders of magnitude by introducing differences in the electronic potentials at the two metal sites of the donor. These results indicate that theories of cluster-based electron transfer, in order to be realistic, need to consider both intrinsic electronic structure and extrinsic interactions of the cluster with the protein environment.

Semi-classical analysis and pseudo-spectra

NASA Astrophysics Data System (ADS)

Davies, E. B.

We prove an approximate spectral theorem for non-self-adjoint operators and investigate its applications to second-order differential operators in the semi-classical limit. This leads to the construction of a twisted FBI transform. We also investigate the connections between pseudo-spectra and boundary conditions in the semi-classical limit.

Charge Exchange in Slow Collisions of O+ with He

NASA Astrophysics Data System (ADS)

Zhao, L. B.; Joseph, D. C.; Saha, B. C.; Lebermann, H. P.; Funke, P.; Buenker, R. J.

2009-03-01

A comparative study is reported for the charge transfer in collisions of O^+ with He using the fully quantal and semiclassical molecular-orbital close-coupling (MOCC) approaches in the adiabatic representation. The electron capture processes O^+(^4S^o, ^2D^o, ^2P^o) + He -> O(^3P) + He^+ are recalculated. The semiclassical MOCC approach was examined by a detailed comparision of cross sections and transition probabilities from both the fully quantal and semiclassical MOCC approaches. The discrepancies reported previously between the semiclassical and the quantal MOCC cross sections may be attributed due to the insufficient step-size resolution of the semiclassical calculations. Our results are also compared with the experimental cross sections and found good agreements. This work is supported by NSF, CREST program (Grant#0630370).

GENERAL: Scattering Phase Correction for Semiclassical Quantization Rules in Multi-Dimensional Quantum Systems

NASA Astrophysics Data System (ADS)

Huang, Wen-Min; Mou, Chung-Yu; Chang, Cheng-Hung

2010-02-01

While the scattering phase for several one-dimensional potentials can be exactly derived, less is known in multi-dimensional quantum systems. This work provides a method to extend the one-dimensional phase knowledge to multi-dimensional quantization rules. The extension is illustrated in the example of Bogomolny's transfer operator method applied in two quantum wells bounded by step potentials of different heights. This generalized semiclassical method accurately determines the energy spectrum of the systems, which indicates the substantial role of the proposed phase correction. Theoretically, the result can be extended to other semiclassical methods, such as Gutzwiller trace formula, dynamical zeta functions, and semiclassical Landauer-Büttiker formula. In practice, this recipe enhances the applicability of semiclassical methods to multi-dimensional quantum systems bounded by general soft potentials.

A new semiclassical decoupling scheme for electronic transitions in molecular collisions - Application to vibrational-to-electronic energy transfer

NASA Technical Reports Server (NTRS)

Lee, H.-W.; Lam, K. S.; Devries, P. L.; George, T. F.

1980-01-01

A new semiclassical decoupling scheme (the trajectory-based decoupling scheme) is introduced in a computational study of vibrational-to-electronic energy transfer for a simple model system that simulates collinear atom-diatom collisions. The probability of energy transfer (P) is calculated quasiclassically using the new scheme as well as quantum mechanically as a function of the atomic electronic-energy separation (lambda), with overall good agreement between the two sets of results. Classical mechanics with the new decoupling scheme is found to be capable of predicting resonance behavior whereas an earlier decoupling scheme (the coordinate-based decoupling scheme) failed. Interference effects are not exhibited in P vs lambda results.

New constraints for low-momentum electronic excitations in condensed matter: fundamental consequences from classical and quantum dielectric theory.

PubMed

Chantler, C T; Bourke, J D

2015-11-18

We present new constraints for the transportation behaviour of low-momentum electronic excitations in condensed matter systems, and demonstrate that these have both a fundamental physical interpretation and a significant impact on the description of low-energy inelastic electron scattering. The dispersion behaviour and characteristic lifetime properties of plasmon and single-electron excitations are investigated using popular classical, semi-classical and quantum dielectric models. We find that, irrespective of constrained agreement to the well known high-momentum and high-energy Bethe ridge limit, standard descriptions of low-momentum electron excitations are inconsistent and unphysical. These observations have direct impact on calculations of transport properties such as inelastic mean free paths, stopping powers and escape depths of charged particles in condensed matter systems.

Trace identities and their semiclassical implications

NASA Astrophysics Data System (ADS)

Smilansky, Uzy

2000-03-01

The compatibility of the semiclassical quantization of area-preserving maps with some exact identities which follow from the unitarity of the quantum evolution operator is discussed. The quantum identities involve relations between traces of powers of the evolution operator. For classically integrable maps, the semiclassical approximation is shown to be compatible with the trace identities. This is done by the identification of stationary phase manifolds which give the main contributions to the result. The compatibility of the semiclassical quantization with the trace identities demonstrates the crucial importance of non-diagonal contributions. The same technique is not applicable for chaotic maps, and the compatibility of the semiclassical theory in this case remains unsettled. However, the trace identities are applied to maps which appear naturally in the theory of quantum graphs, revealing some features of the periodic orbit theory for these paradigms of quantum chaos.

Magnon localization and Bloch oscillations in finite Heisenberg spin chains in an inhomogeneous magnetic field.

PubMed

Kosevich, Yuriy A; Gann, Vladimir V

2013-06-19

We study the localization of magnon states in finite defect-free Heisenberg spin-1/2 ferromagnetic chains placed in an inhomogeneous magnetic field with a constant spatial gradient. Continuous transformation from the extended magnon states to the localized Wannier-Zeeman states in a finite spin chain placed in an inhomogeneous field is described both analytically and numerically. We describe for the first time the non-monotonic dependence of the energy levels of magnons, both long and short wavelength, on the magnetic field gradient, which is a consequence of magnon localization in a finite spin chain. We show that, in contrast to the destruction of the magnon band and the establishment of the Wannier-Stark ladder in a vanishingly small field gradient in an infinite chain, the localization of magnon states at the chain ends preserves the memory of the magnon band. Essentially, the localization at the lower- or higher-field chain end resembles the localization of the positive- or negative-effective-mass band quasiparticles. We also show how the beat dynamics of coherent superposition of extended spin waves in a finite chain in a homogeneous or weakly inhomogeneous field transforms into magnon Bloch oscillations of the superposition of localized Wannier-Zeeman states in a strongly inhomogeneous field. We provide a semiclassical description of the magnon Bloch oscillations and show that the correspondence between the quantum and semiclassical descriptions is most accurate for Bloch oscillations of the magnon coherent states, which are built from a coherent superposition of a large number of the nearest-neighbour Wannier-Zeeman states.

Finite-size effects in surface-enhanced Raman scattering in noble-metal nanoparticles: a semiclassical approach.

PubMed

Pustovit, Vitaliy N; Shahbazyan, Tigran V

2006-06-01

We study finite-size effects in surface-enhanced Raman scattering (SERS) from molecules adsorbed on small metal particles. Within an electromagnetic description of SERS, the enhancement of the Raman signal originates from the local field of the surface plasmon resonance in a nanoparticle. With decreasing particle sizes, this enhancement is reduced due to the size-dependent Landau damping of the surface plasmon. We show that, in small noble-metal particles, the reduction of interband screening in the surface layer leads to an additional increase in the local field acting on a molecule close to the metal surface. The overall size dependence of Raman signal enhancement is determined by the interplay between Landau damping and underscreening effects. Our calculations, based on a two-region model, show that the role of the surface layer increases for smaller nanoparticle sizes due to a larger volume fraction of the underscreened region.

Some Remarks about Semiclassical Trace Invariants and Quantum Normal Forms

NASA Astrophysics Data System (ADS)

Guillemin, Victor; Paul, Thierry

2010-02-01

In this paper we explore the connection between semi-classical and quantum Birkhoff canonical forms (BCF) for Schrödinger operators. In particular we give a “non-symbolic” operator theoretic derivation of the quantum Birkhoff canonical form and provide an explicit recipe for expressing the quantum BCF in terms of the semi-classical BCF.

Average Nuclear Potentials from Selfconsistent Semiclassical Calculations

NASA Astrophysics Data System (ADS)

Bartel, J.

1999-03-01

Using the selfconsistent semiclassical Extended Thomas-Fermi (ETF) method up to 4th order in connection with Skyrme forces it is demonstrated that the neutron and proton average potentials obtained using the semiclassical functionals τ (ETF)[ρ] and vec {J}(ETF)[ρ] reproduce the corresponding Hartree-Fock fields extremely well, except for shell oscillations in the nuclear center.

Semiclassical quantization of Bohr orbits in the helium atom

NASA Astrophysics Data System (ADS)

Belov, V. V.; Maksimov, V. A.

2007-05-01

We use the complex WKB-Maslov method to construct the semiclassical spectral series corresponding to the resonance Bohr orbits in the helium atom. The semiclassical energy levels represented as the Rydberg tetra series correspond to the doubly symmetrically excited states of helium-like atoms. This level series contains the Rydberg triple series reported by Richter and Wintgen in 1991, which corresponds to the Z2+e-e- configuration of electrons observed by Eichmann and his collaborators in experiments on the laser excitation of the barium atom in 1992. The lower-level extrapolation of the formula obtained for the semiclassical spectrum gives the value of the ground state energy, which differs by 6% from the experimental value obtained by Bergeson and his collaborators in 1998. We also calculate the fine structure of the semiclassical spectrum due to the spin-orbit and spin-spin interactions of electrons.

Deterministic generation of remote entanglement with active quantum feedback

DOE PAGES

Martin, Leigh; Motzoi, Felix; Li, Hanhan; ...

2015-12-10

We develop and study protocols for deterministic remote entanglement generation using quantum feedback, without relying on an entangling Hamiltonian. In order to formulate the most effective experimentally feasible protocol, we introduce the notion of average-sense locally optimal feedback protocols, which do not require real-time quantum state estimation, a difficult component of real-time quantum feedback control. We use this notion of optimality to construct two protocols that can deterministically create maximal entanglement: a semiclassical feedback protocol for low-efficiency measurements and a quantum feedback protocol for high-efficiency measurements. The latter reduces to direct feedback in the continuous-time limit, whose dynamics can bemore » modeled by a Wiseman-Milburn feedback master equation, which yields an analytic solution in the limit of unit measurement efficiency. Our formalism can smoothly interpolate between continuous-time and discrete-time descriptions of feedback dynamics and we exploit this feature to derive a superior hybrid protocol for arbitrary nonunit measurement efficiency that switches between quantum and semiclassical protocols. Lastly, we show using simulations incorporating experimental imperfections that deterministic entanglement of remote superconducting qubits may be achieved with current technology using the continuous-time feedback protocol alone.« less

Analysis of semiclassical approximations in the framework of quantumhadrodynamics

NASA Astrophysics Data System (ADS)

Speicher, C.; Engel, E.; Dreizler, R. M.

1993-10-01

We examine the importance of gradient corrections to the Thomas-Fermi (TF) approximation for the description of semi-infinite nuclear matter and nuclei within the framework of quantumhadrodynamics. The discussion of semi-infinite nuclear matter exhibits most clearly how surface properties depend on the parametrisation of the effective interaction. In agreement with earlier studies it is found that for parametrisations with low effective mass the original extended TF (ETF) equations cannot be solved. We present a scheme to overcome this problem which is very much in the spirit of the semiclassical approach and allows for a solution in any situation. For the case of nuclei the results of the TF and ETF approximations are compared to those of Hartree calculations which serve as a standard in this context. In accordance with the sensitivity of semi-infinite nuclear matter results to the specific parametrisation, ETF does not yield a consistent improvement over TF for all parametrisations. However, by examining a larger number of parametrisations it is shown that those cases where TF results are closer to Hartree data have to be regarded as fortuitous and that on average the agreement between ETF and Hartree results is clearly better.

On Generalized Continuous D Semi-Classical Hermite and Chebychev Orthogonal Polynomials of Class One

NASA Astrophysics Data System (ADS)

Azatassou, E.; Hounkonnou, M. N.

2002-10-01

In this contribution, starting from the system of equations for recurrence coefficients generated by continuous D semi-classical Laguerre-Freud equations of class 1, we deduce the β constant recurrence relation coefficient γn leading to the generalized D semi-classical Hermite and Chebychev orthogonal polynomials of class 1. Various interesting cases are pointed out.

Few-body semiclassical approach to nucleon transfer and emission reactions

NASA Astrophysics Data System (ADS)

Sultanov, Renat A.; Guster, D.

2014-04-01

A three-body semiclassical model is proposed to describe the nucleon transfer and emission reactions in a heavy-ion collision. In this model the two heavy particles, i.e. nuclear cores A1(ZA1, MA1) and A2(ZA2, MA2), move along classical trajectories {{R}_1}( t ) and {{R}_2}( t ) respectively, while the dynamics of the lighter neutron (n) is considered from a quantum mechanical point of view. Here, Mi are the nucleon masses and Zi are the Coulomb charges of the heavy nuclei (i = 1, 2). A Faddeev-type semiclassical formulation using realistic paired nuclear-nuclear potentials is applied so that all three channels (elastic, rearrangement and break-up) are described in a unified manner. In order to solve the time-dependent equations the Faddeev components of the total three-body wave-function are expanded in terms of the input and output channel target eigenfunctions. In the special case, when the nuclear cores are identical (A1 ≡ A2) and also the two-level approximation in the expansion over the target (subsystem) functions is used, the time-dependent semiclassical Faddeev equations are resolved in an explicit way. To determine the realistic {{R}_1}( t ) and {{R}_2}( t ) trajectories of the nuclear cores, a self-consistent approach based on the Feynman path integral theory is applied.

Vacuum Decay via Lorentzian Wormholes

NASA Astrophysics Data System (ADS)

Rosales, J. L.

We speculate about the space-time description due to the presence of Lorentzian worm-holes (handles in space-time joining two distant regions or other universes) in quantum gravity. The semiclassical rate of production of these Lorentzian wormholes in Reissner-Nordström space-times is calculated as a result of the spontaneous decay of vacuum due to a real tunneling configuration. In the magnetic case it only depends on the value of the field theoretical fine structure constant. We predict that the quantum probability corresponding to the nucleation of such geodesically complete space-times should be acutally negligible in our physical Universe.

(e,2e) and (Î3,2e) Processes: Open and Closed Questions

NASA Astrophysics Data System (ADS)

An important breakthrough has been achieved recently in the description of (e,2e) and (Î3,2e) processes with the development of new ab-initio theories: the external complex scaling theory (ECS), the time dependent close coupling theory (TDCC), and the hyperspherical R-matrix theory with semiclassical outgoing waves (HRM-SOW). The principles of these various theories are summarized, their relations are considered, and their achievements are discussed with respect to the available experimental data regarding electron impact ionization of H and photo double ionization of He. Possible directions for future work are outlined.

An Experimental and Theoretical Study of Nitrogen-Broadened Acetylene Lines

NASA Technical Reports Server (NTRS)

Thibault, Franck; Martinez, Raul Z.; Bermejo, Dionisio; Ivanov, Sergey V.; Buzykin, Oleg G.; Ma, Qiancheng

2014-01-01

We present experimental nitrogen-broadening coefficients derived from Voigt profiles of isotropic Raman Q-lines measured in the 2 band of acetylene (C2H2) at 150 K and 298 K, and compare them to theoretical values obtained through calculations that were carried out specifically for this work. Namely, full classical calculations based on Gordon's approach, two kinds of semi-classical calculations based on Robert Bonamy method as well as full quantum dynamical calculations were performed. All the computations employed exactly the same ab initio potential energy surface for the C2H2N2 system which is, to our knowledge, the most realistic, accurate and up-to-date one. The resulting calculated collisional half-widths are in good agreement with the experimental ones only for the full classical and quantum dynamical methods. In addition, we have performed similar calculations for IR absorption lines and compared the results to bibliographic values. Results obtained with the full classical method are again in good agreement with the available room temperature experimental data. The quantum dynamical close-coupling calculations are too time consuming to provide a complete set of values and therefore have been performed only for the R(0) line of C2H2. The broadening coefficient obtained for this line at 173 K and 297 K also compares quite well with the available experimental data. The traditional Robert Bonamy semi-classical formalism, however, strongly overestimates the values of half-width for both Qand R-lines. The refined semi-classical Robert Bonamy method, first proposed for the calculations of pressure broadening coefficients of isotropic Raman lines, is also used for IR lines. By using this improved model that takes into account effects from line coupling, the calculated semi-classical widths are significantly reduced and closer to the measured ones.

Semiclassical fermion pair creation in de Sitter spacetime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stahl, Clément, E-mail: clement.stahl@icranet.org; Eckhard, Strobel, E-mail: eckhard.strobel@irap-phd.eu; Dipartimento di Fisica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 5, 00185 Rome

2015-12-17

We present a method to semiclassically compute the pair creation rate of bosons and fermions in de Sitter spacetime. The results in the bosonic case agree with the ones in the literature. We find that for the constant electric field the fermionic and bosonic pair creation rate are the same. This analogy of bosons and fermions in the semiclassical limit is known from several flat spacetime examples.

Comparative study of quantal and semiclassical treatments of charge transfer between O+ and He

NASA Astrophysics Data System (ADS)

Zhao, L. B.; Joseph, D. C.; Saha, B. C.; Liebermann, H. P.; Funke, P.; Buenker, R. J.

2009-03-01

A comparative study for the electron capture process O+(S40,D20,P20)+He→O(P3)+He+ is reported. The cross sections are calculated using fully quantal and semiclassical molecular-orbital close-coupling (MOCC) approaches in the adiabatic representation. Detailed comparison of transition probabilities and cross sections is made from both MOCC approaches and displays close agreement above ˜125eV/u . The remarkable discrepancies between the earlier semiclassical and quantal MOCC approaches may be attributed to the insufficient step-size resolution in their semiclassical calculation [M. Kimura , Phys. Rev. A 50, 4854 (1994)]. Our results have also been compared with experiment and found to be in good agreement.

Closed almost-periodic orbits in semiclassical quantization of generic polygons

PubMed

Biswas

2000-05-01

Periodic orbits are the central ingredients of modern semiclassical theories and corrections to these are generally nonclassical in origin. We show here that, for the class of generic polygonal billiards, the corrections are predominantly classical in origin owing to the contributions from closed almost-periodic (CAP) orbit families. Furthermore, CAP orbit families outnumber periodic families but have comparable weights. They are hence indispensable for semiclassical quantization.

Experimental Evidence for Hydrogen Tunneling when the Isotopic Arrhenius Prefactor (AH/AD) is Unity

PubMed Central

Sharma, Sudhir C.; Klinman, Judith P.

2009-01-01

The temperature dependence of the kinetic isotope effect (KIE) is one of the major tools used for the investigation of hydrogen tunneling in condensed phase. Hydrogen transfer reactions displaying isotopic Arrhenius prefactor ratios (AH/AD) of unity are generally ascribed to a semi-classical mechanism. Here, we have identified a double mutant of soybean lipoxygenase (SLO-1, an enzyme previously shown to follow quantum mechanical hydrogen tunneling), that displays an AH/AD of unity and highly elevated (non-classical) KIEs. This observation highlights the shortcoming of assigning a hydrogen transfer reaction to a semi-classical model based solely on an Arrhenius prefactor ratio. PMID:19061319

Periodic Orbits and Semiclassical Form Factor in Barrier Billiards

NASA Astrophysics Data System (ADS)

Giraud, O.

2005-11-01

Using heuristic arguments based on the trace formulas, we analytically calculate the semiclassical two-point correlation form factor for a family of rectangular billiards with a barrier of height irrational with respect to the side of the billiard and located at any rational position p/q from the side. To do this, we first obtain the asymptotic density of lengths for each family of periodic orbits by a Siegel-Veech formula. The result obtained for these pseudo-integrable, non-Veech billiards is different but not far from the value of 1/2 expected for semi-Poisson statistics and from values of obtained previously in the case of Veech billiards.

Discrete Wigner formalism for qubits and noncontextuality of Clifford gates on qubit stabilizer states

NASA Astrophysics Data System (ADS)

Kocia, Lucas; Love, Peter

2017-12-01

We show that qubit stabilizer states can be represented by non-negative quasiprobability distributions associated with a Wigner-Weyl-Moyal formalism where Clifford gates are positive state-independent maps. This is accomplished by generalizing the Wigner-Weyl-Moyal formalism to three generators instead of two—producing an exterior, or Grassmann, algebra—which results in Clifford group gates for qubits that act as a permutation on the finite Weyl phase space points naturally associated with stabilizer states. As a result, a non-negative probability distribution can be associated with each stabilizer state's three-generator Wigner function, and these distributions evolve deterministically to one another under Clifford gates. This corresponds to a hidden variable theory that is noncontextual and local for qubit Clifford gates while Clifford (Pauli) measurements have a context-dependent representation. Equivalently, we show that qubit Clifford gates can be expressed as propagators within the three-generator Wigner-Weyl-Moyal formalism whose semiclassical expansion is truncated at order ℏ0 with a finite number of terms. The T gate, which extends the Clifford gate set to one capable of universal quantum computation, requires a semiclassical expansion of the propagator to order ℏ1. We compare this approach to previous quasiprobability descriptions of qubits that relied on the two-generator Wigner-Weyl-Moyal formalism and find that the two-generator Weyl symbols of stabilizer states result in a description of evolution under Clifford gates that is state-dependent, in contrast to the three-generator formalism. We have thus extended Wigner non-negative quasiprobability distributions from the odd d -dimensional case to d =2 qubits, which describe the noncontextuality of Clifford gates and contextuality of Pauli measurements on qubit stabilizer states.

Initial-value semiclassical propagators for the Wigner phase space representation: Formulation based on the interpretation of the Moyal equation as a Schrödinger equation.

PubMed

Koda, Shin-ichi

2015-12-28

We formulate various semiclassical propagators for the Wigner phase space representation from a unified point of view. As is shown in several studies, the Moyal equation, which is an equation of motion for the Wigner distribution function, can be regarded as the Schrödinger equation of an extended Hamiltonian system where its "position" and "momentum" correspond to the middle point of two points of the original phase space and the difference between them, respectively. Then we show that various phase-space semiclassical propagators can be formulated just by applying existing semiclassical propagators to the extended system. As a result, a phase space version of the Van Vleck propagator, the initial-value Van Vleck propagator, the Herman-Kluk propagator, and the thawed Gaussian approximation are obtained. In addition, we numerically compare the initial-value phase-space Van Vleck propagator, the phase-space Herman-Kluk propagator, and the classical mechanical propagation as approximation methods for the time propagation of the Wigner distribution function in terms of both accuracy and convergence speed. As a result, we find that the convergence speed of the Van Vleck propagator is far slower than others as is the case of the Hilbert space, and the Herman-Kluk propagator keeps its accuracy for a long period compared with the classical mechanical propagation while the convergence speed of the latter is faster than the former.

Equilibration in one-dimensional quantum hydrodynamic systems

NASA Astrophysics Data System (ADS)

Sotiriadis, Spyros

2017-10-01

We study quench dynamics and equilibration in one-dimensional quantum hydrodynamics, which provides effective descriptions of the density and velocity fields in gapless quantum gases. We show that the information content of the large time steady state is inherently connected to the presence of ballistically moving localised excitations. When such excitations are present, the system retains memory of initial correlations up to infinite times, thus evading decoherence. We demonstrate this connection in the context of the Luttinger model, the simplest quantum hydrodynamic model, and in the quantum KdV equation. In the standard Luttinger model, memory of all initial correlations is preserved throughout the time evolution up to infinitely large times, as a result of the purely ballistic dynamics. However nonlinear dispersion or interactions, when separately present, lead to spreading and delocalisation that suppress the above effect by eliminating the memory of non-Gaussian correlations. We show that, for any initial state that satisfies sufficient clustering of correlations, the steady state is Gaussian in terms of the bosonised or fermionised fields in the dispersive or interacting case respectively. On the other hand, when dispersion and interaction are simultaneously present, a semiclassical approximation suggests that localisation is restored as the two effects compensate each other and solitary waves are formed. Solitary waves, or simply solitons, are experimentally observed in quantum gases and theoretically predicted based on semiclassical approaches, but the question of their stability at the quantum level remains to a large extent an open problem. We give a general overview on the subject and discuss the relevance of our findings to general out of equilibrium problems. Dedicated to John Cardy on the occasion of his 70th birthday.

Phase-Space Approach to the Tunnel Effect: A New Semiclassical Traversal Time

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xavier, A.L. Jr.; de Aguiar, M.A.

1997-11-01

We determine the semiclassical coherent-state propagator for a particle going through one-dimensional evolution in a simple barrier potential. The described semiclassical method makes use of complex trajectories which, by its turn, enables the definition of (real) traversal times in the complexified phase space. We then discuss the behavior of this time for a wave packet whose average energy is below the barrier height. {copyright} {ital 1997} {ital The American Physical Society}

Error of semiclassical eigenvalues in the semiclassical limit - an asymptotic analysis of the Sinai billiard

NASA Astrophysics Data System (ADS)

Dahlqvist, Per

1999-10-01

We estimate the error in the semiclassical trace formula for the Sinai billiard under the assumption that the largest source of error is due to penumbra diffraction: namely, diffraction effects for trajectories passing within a distance Ricons/Journals/Common/cdot" ALT="cdot" ALIGN="TOP"/>O((kR)-2/3) to the disc and trajectories being scattered in very forward directions. Here k is the momentum and R the radius of the scatterer. The semiclassical error is estimated by perturbing the Berry-Keating formula. The analysis necessitates an asymptotic analysis of very long periodic orbits. This is obtained within an approximation originally due to Baladi, Eckmann and Ruelle. We find that the average error, for sufficiently large values of kR, will exceed the mean level spacing.

Semiclassical relation between open trajectories and periodic orbits for the Wigner time delay.

PubMed

Kuipers, Jack; Sieber, Martin

2008-04-01

The Wigner time delay of a classically chaotic quantum system can be expressed semiclassically either in terms of pairs of scattering trajectories that enter and leave the system or in terms of the periodic orbits trapped inside the system. We show how these two pictures are related on the semiclassical level. We start from the semiclassical formula with the scattering trajectories and derive from it all terms in the periodic orbit formula for the time delay. The main ingredient in this calculation are correlations between scattering trajectories which are due to trajectories that approach the trapped periodic orbits closely. The equivalence between the two pictures is also demonstrated by considering correlation functions of the time delay. A corresponding calculation for the conductance gives no periodic orbit contributions in leading order.

Vibration-translation energy transfer in anharmonic diatomic molecules. 1: A critical evaluation of the semiclassical approximation

NASA Technical Reports Server (NTRS)

Mckenzie, R. L.

1974-01-01

The semiclassical approximation is applied to anharmonic diatomic oscillators in excited initial states. Multistate numerical solutions giving the vibrational transition probabilities for collinear collisions with an inert atom are compared with equivalent, exact quantum-mechanical calculations. Several symmetrization methods are shown to correlate accurately the predictions of both theories for all initial states, transitions, and molecular types tested, but only if coupling of the oscillator motion and the classical trajectory of the incident particle is considered. In anharmonic heteronuclear molecules, the customary semiclassical method of computing the classical trajectory independently leads to transition probabilities with anomalous low-energy resonances. Proper accounting of the effects of oscillator compression and recoil on the incident particle trajectory removes the anomalies and restores the applicability of the semiclassical approximation.

Numerical study of the Kadomtsev-Petviashvili equation and dispersive shock waves

NASA Astrophysics Data System (ADS)

Grava, T.; Klein, C.; Pitton, G.

2018-02-01

A detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev-Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained. It is shown that the modulation equations near the soliton line are hyperbolic for the KPII equation while they are elliptic for the KPI equation leading to a focusing effect and the formation of lumps. Such a behaviour is similar to the appearance of breathers for the focusing nonlinear Schrödinger equation in the semiclassical limit.

First experimental test of a trace formula for billiard systems showing mixed dynamics.

PubMed

Dembowski, C; Gräf, H D; Heine, A; Hesse, T; Rehfeld, H; Richter, A

2001-04-09

In general, trace formulas relate the density of states for a given quantum mechanical system to the properties of the periodic orbits of its classical counterpart. Here we report for the first time on a semiclassical description of microwave spectra taken from superconducting billiards of the Limaçon family showing mixed dynamics in terms of a generalized trace formula derived by Ullmo et al. [Phys. Rev. E 54, 136 (1996)]. This expression not only describes mixed-typed behavior but also the limiting cases of fully regular and fully chaotic systems and thus presents a continuous interpolation between the Berry-Tabor and Gutzwiller formulas.

Persistent stability of a chaotic system

NASA Astrophysics Data System (ADS)

Huber, Greg; Pradas, Marc; Pumir, Alain; Wilkinson, Michael

2018-02-01

We report that trajectories of a one-dimensional model for inertial particles in a random velocity field can remain stable for a surprisingly long time, despite the fact that the system is chaotic. We provide a detailed quantitative description of this effect by developing the large-deviation theory for fluctuations of the finite-time Lyapunov exponent of this system. Specifically, the determination of the entropy function for the distribution reduces to the analysis of a Schrödinger equation, which is tackled by semi-classical methods. The system has 'generic' instability properties, and we consider the broader implications of our observation of long-term stability in chaotic systems.

Spurious Excitations in Semiclassical Scattering Theory.

ERIC Educational Resources Information Center

Gross, D. H. E.; And Others

1980-01-01

Shows how through proper handling of the nonuniform motion of semiclassical coordinates spurious excitation terms are eliminated. An application to the problem of nuclear Coulomb excitation is presented as an example. (HM)

Semiclassical Virasoro blocks from AdS 3 gravity

DOE PAGES

Hijano, Eliot; Kraus, Per; Perlmutter, Eric; ...

2015-12-14

We present a unified framework for the holographic computation of Virasoro conformal blocks at large central charge. In particular, we provide bulk constructions that correctly reproduce all semiclassical Virasoro blocks that are known explicitly from conformal field theory computations. The results revolve around the use of geodesic Witten diagrams, recently introduced in [1], evaluated in locally AdS 3 geometries generated by backreaction of heavy operators. We also provide an alternative computation of the heavy-light semiclassical block — in which two external operators become parametrically heavy — as a certain scattering process involving higher spin gauge fields in AdS 3; thismore » approach highlights the chiral nature of Virasoro blocks. Finally, these techniques may be systematically extended to compute corrections to these blocks and to interpolate amongst the different semiclassical regimes.« less

Stochastic Gravity: Theory and Applications.

PubMed

Hu, Bei Lok; Verdaguer, Enric

2004-01-01

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operatorvalued) stress-energy bi-tensor which describes the fluctuations of quantum matter fields in curved spacetimes. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to their correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods which are convenient for computations. It also brings out the open systems concepts and the statistical and stochastic contents of the theory such as dissipation, fluctuations, noise, and decoherence. We then focus on the properties of the stress-energy bi-tensor. We obtain a general expression for the noise kernel of a quantum field defined at two distinct points in an arbitrary curved spacetime as products of covariant derivatives of the quantum field's Green function. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime. We offer an analytical solution of the Einstein-Langevin equation and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, we discuss the backreaction of Hawking radiation in the gravitational background of a quasi-static black hole (enclosed in a box). We derive a fluctuation-dissipation relation between the fluctuations in the radiation and the dissipative dynamics of metric fluctuations.

Projective limits of state spaces IV. Fractal label sets

NASA Astrophysics Data System (ADS)

Lanéry, Suzanne; Thiemann, Thomas

2018-01-01

Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski (1977) to represent quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces (see Lanéry (2016) [1] for a concise introduction to this formalism). One can thus bypass the need to select a vacuum state for the theory, and still be provided with an explicit and constructive description of the quantum state space, at least as long as the label set indexing the projective structure is countable. Because uncountable label sets are much less practical in this context, we develop in the present article a general procedure to trim an originally uncountable label set down to countable cardinality. In particular, we investigate how to perform this tightening of the label set in a way that preserves both the physical content of the algebra of observables and its symmetries. This work is notably motivated by applications to the holonomy-flux algebra underlying Loop Quantum Gravity. Building on earlier work by Okołów (2013), a projective state space was introduced for this algebra in Lanéry and Thiemann (2016). However, the non-trivial structure of the holonomy-flux algebra prevents the construction of satisfactory semi-classical states (Lanéry and Thiemann, 2017). Implementing the general procedure just mentioned in the case of a one-dimensional version of this algebra, we show how a discrete subalgebra can be extracted without destroying universality nor diffeomorphism invariance. On this subalgebra, quantum states can then be constructed which are more regular than was possible on the original algebra. In particular, this allows the design of semi-classical states whose semi-classicality is enforced step by step, starting from collective, macroscopic degrees of freedom and going down progressively toward smaller and smaller scales.

Reaching quantum limits for phase-shift detection with semiclassical states

NASA Astrophysics Data System (ADS)

Luis, Alfredo

2004-01-01

We present two measuring strategies reaching the Heisenberg limit for phase-shift measurements using semiclassical coherent states exclusively. We examine their performance by assuming practical experimental conditions such as losses and nonideal detectors.

Semiclassical approximations in the coherent-state representation

NASA Technical Reports Server (NTRS)

Kurchan, J.; Leboeuf, P.; Saraceno, M.

1989-01-01

The semiclassical limit of the stationary Schroedinger equation in the coherent-state representation is analyzed simultaneously for the groups W1, SU(2), and SU(1,1). A simple expression for the first two orders for the wave function and the associated semiclassical quantization rule is obtained if a definite choice for the classical Hamiltonian and expansion parameter is made. The behavior of the modulus of the wave function, which is a distribution function in a curved phase space, is studied for the three groups. The results are applied to the quantum triaxial rotor.

The extreme wings of atomic emission and absorption lines. [in low pressure gases

NASA Technical Reports Server (NTRS)

Dalgarno, A.; Sando, K. M.

1973-01-01

Consideration of the extreme wings of atomic and molecular emission and absorption lines in low pressure gases. Classical and semiclassical results are compared with accurate quantal calculations of the self-broadening of Lyman-alpha in the hydrogen absorption spectrum that arises from quasimolecular transition. The results of classical, quantal, and semiclassical calculations of the absorption coefficient in the red wing are shown for temperatures of 500, 200, and 100 K. The semiclassical and quantal spectra agree well in shape at 500 K. Various other findings are discused.

Is the Filinov integral conditioning technique useful in semiclassical initial value representation methods?

DOE Office of Scientific and Technical Information (OSTI.GOV)

Spanner, Michael; Batista, Victor S.; Brumer, Paul

2005-02-22

The utility of the Filinov integral conditioning technique, as implemented in semiclassical initial value representation (SC-IVR) methods, is analyzed for a number of regular and chaotic systems. For nonchaotic systems of low dimensionality, the Filinov technique is found to be quite ineffective at accelerating convergence of semiclassical calculations since, contrary to the conventional wisdom, the semiclassical integrands usually do not exhibit significant phase oscillations in regions of large integrand amplitude. In the case of chaotic dynamics, it is found that the regular component is accurately represented by the SC-IVR, even when using the Filinov integral conditioning technique, but that quantummore » manifestations of chaotic behavior was easily overdamped by the filtering technique. Finally, it is shown that the level of approximation introduced by the Filinov filter is, in general, comparable to the simpler ad hoc truncation procedure introduced by Kay [J. Chem. Phys. 101, 2250 (1994)].« less

Wavepacket propagation using time-sliced semiclassical initial value methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wallace, Brett B.; Reimers, Jeffrey R.; School of Chemistry, University of Sydney, Sydney NSW 2006

2004-12-22

A new semiclassical initial value representation (SC-IVR) propagator and a SC-IVR propagator originally introduced by Kay [J. Chem. Phys. 100, 4432 (1994)], are investigated for use in the split-operator method for solving the time-dependent Schroedinger equation. It is shown that the SC-IVR propagators can be derived from a procedure involving modified Filinov filtering of the Van Vleck expression for the semiclassical propagator. The two SC-IVR propagators have been selected for investigation because they avoid the need to perform a coherent state basis set expansion that is necessary in other time-slicing propagation schemes. An efficient scheme for solving the propagators ismore » introduced and can be considered to be a semiclassical form of the effective propagators of Makri [Chem. Phys. Lett. 159, 489 (1989)]. Results from applications to a one-dimensional, two-dimensional, and three-dimensional Hamiltonian for a double-well potential are presented.« less

Why firewalls need not exist

DOE PAGES

Nomura, Yasunori; Salzetta, Nico

2016-08-04

The firewall paradox for black holes is often viewed as indicating a conflict between unitarity and the equivalence principle. We elucidate how the paradox manifests as a limitation of semiclassical theory, rather than presents a conflict between fundamental principles. Two principal features of the fundamental and semiclassical theories address two versions of the paradox: the entanglement and typicality arguments. First, the physical Hilbert space describing excitations on a fixed black hole background in the semiclassical theory is exponentially smaller than the number of physical states in the fundamental theory of quantum gravity. Second, in addition to the Hilbert space formore » physical excitations, the semiclassical theory possesses an unphysically large Fock space built by creation and annihilation operators on the fixed black hole background. Understanding these features not only eliminates the necessity of firewalls but also leads to a new picture of Hawking emission contrasting pair creation at the horizon.« less

Tunable axial gauge fields in engineered Weyl semimetals: semiclassical analysis and optical lattice implementations

NASA Astrophysics Data System (ADS)

Roy, Sthitadhi; Kolodrubetz, Michael; Goldman, Nathan; Grushin, Adolfo G.

2018-04-01

In this work, we describe a toolbox to realize and probe synthetic axial gauge fields in engineered Weyl semimetals. These synthetic electromagnetic fields, which are sensitive to the chirality associated with Weyl nodes, emerge due to spatially and temporally dependent shifts of the corresponding Weyl momenta. First, we introduce two realistic models, inspired by recent cold-atom developments, which are particularly suitable for the exploration of these synthetic axial gauge fields. Second, we describe how to realize and measure the effects of such axial fields through center-of-mass observables, based on semiclassical equations of motion and exact numerical simulations. In particular, we suggest realistic protocols to reveal an axial Hall response due to the axial electric field \

Time-dependent importance sampling in semiclassical initial value representation calculations for time correlation functions.

PubMed

Tao, Guohua; Miller, William H

2011-07-14

An efficient time-dependent importance sampling method is developed for the Monte Carlo calculation of time correlation functions via the initial value representation (IVR) of semiclassical (SC) theory. A prefactor-free time-dependent sampling function weights the importance of a trajectory based on the magnitude of its contribution to the time correlation function, and global trial moves are used to facilitate the efficient sampling the phase space of initial conditions. The method can be generally applied to sampling rare events efficiently while avoiding being trapped in a local region of the phase space. Results presented in the paper for two system-bath models demonstrate the efficiency of this new importance sampling method for full SC-IVR calculations.

Nonclassical and semiclassical para-Bose states

NASA Astrophysics Data System (ADS)

Huerta Alderete, C.; Villanueva Vergara, Liliana; Rodríguez-Lara, B. M.

2017-04-01

Motivated by the proposal to simulate para-Bose oscillators in a trapped-ion setup [C. Huerta Alderete and B. M. Rodríguez-Lara, Phys. Rev. A 95, 013820 (2017), 10.1103/PhysRevA.95.013820], we introduce an overcomplete, nonorthogonal basis for para-Bose Hilbert spaces. The states spanning these bases can be experimentally realized in the trapped-ion simulation via time evolution. The para-Bose states show both nonclassical and semiclassical statistics on their Fock state distribution, asymmetric field quadrature variances, and do not minimize the uncertainty relation for the field quadratures. These properties are analytically controlled by the para-Bose order and the evolution time; both parameters might be feasible for fine tuning in the trapped-ion quantum simulation.

Semiclassical Planetology: a progress report

NASA Astrophysics Data System (ADS)

Celebonovic, V.

1999-12-01

Work on planetary internal structure has started in Yugoslavia in the early sixties.It was initiated by P.Savic and R.Kasanin,who have jointly developed a theory of the behaviour of materials under high pressure.By its physical basis,this theory is semiclassical,because it is based on classical physics combined with some quantum mechanical results.The calculations in the theory ( both laboratory and planetological) are baed on ths idea that high pressure leads to excitation and ionisation of atoms and/or molecules which make up the specimen. In this paper we shall briefly present the main ideas of this theory,and then discuss its planetological applications. References P.Savic and V.Celebonovic: 1994,AIP Conf.Proc.,vol.309,p.53. V.Celebonovic: 1999,preprint cond-mat/9906027

Highlights from the previous volumes

NASA Astrophysics Data System (ADS)

Vergini Eduardo, G.; Pan, Y.; al., Vardi R. et; al., Akkermans Eric et; et al.

2014-01-01

Semiclassical propagation up to the Heisenberg time Superconductivity and magnetic order in the half-Heusler compound ErPdBi An experimental evidence-based computational paradigm for new logic-gates in neuronal activity Universality in the symmetric exclusion process and diffusive systems

Reliable semiclassical computations in QCD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dine, Michael; Department of Physics, Stanford University Stanford, California 94305-4060; Festuccia, Guido

We revisit the question of whether or not one can perform reliable semiclassical QCD computations at zero temperature. We study correlation functions with no perturbative contributions, and organize the problem by means of the operator product expansion, establishing a precise criterion for the validity of a semiclassical calculation. For N{sub f}>N, a systematic computation is possible; for N{sub f}

Semiclassical limit of the focusing NLS: Whitham equations and the Riemann-Hilbert Problem approach

NASA Astrophysics Data System (ADS)

Tovbis, Alexander; El, Gennady A.

2016-10-01

The main goal of this paper is to put together: a) the Whitham theory applicable to slowly modulated N-phase nonlinear wave solutions to the focusing nonlinear Schrödinger (fNLS) equation, and b) the Riemann-Hilbert Problem approach to particular solutions of the fNLS in the semiclassical (small dispersion) limit that develop slowly modulated N-phase nonlinear wave in the process of evolution. Both approaches have their own merits and limitations. Understanding of the interrelations between them could prove beneficial for a broad range of problems involving the semiclassical fNLS.

Do semiclassical zero temperature black holes exist?

PubMed

Anderson, P R; Hiscock, W A; Taylor, B E

2000-09-18

The semiclassical Einstein equations are solved to first order in epsilon = Planck's over 2pi/M2 for the case of a Reissner-Nordström black hole perturbed by the vacuum stress energy of quantized free fields. Massless and massive fields of spin 0, 1/2, and 1 are considered. We show that in all physically realistic cases, macroscopic zero temperature black hole solutions do not exist. Any static zero temperature semiclassical black hole solutions must then be microscopic and isolated in the space of solutions; they do not join smoothly onto the classical extreme Reissner-Nordström solution as epsilon-->0.

Wentzel-Kramers-Brillouin method in the Bargmann representation. [of quantum mechanics

NASA Technical Reports Server (NTRS)

Voros, A.

1989-01-01

It is demonstrated that the Bargmann representation of quantum mechanics is ideally suited for semiclassical analysis, using as an example the WKB method applied to the bound-state problem in a single well of one degree of freedom. For the harmonic oscillator, this WKB method trivially gives the exact eigenfunctions in addition to the exact eigenvalues. For an anharmonic well, a self-consistent variational choice of the representation greatly improves the accuracy of the semiclassical ground state. Also, a simple change of scale illuminates the relationship of semiclassical versus linear perturbative expansions, allowing a variety of multidimensional extensions.

Semiclassical dynamics, Berry curvature, and spiral holonomy in optical quasicrystals

NASA Astrophysics Data System (ADS)

Spurrier, Stephen; Cooper, Nigel R.

2018-04-01

We describe the theory of the dynamics of atoms in two-dimensional quasicrystalline optical lattices. We focus on a regime of shallow lattice depths under which the applied force can cause Landau-Zener tunneling past a dense hierarchy of gaps in the quasiperiodic energy spectrum. We derive conditions on the external force that allow for a "semiadiabatic" regime in which semiclassical equations of motion can apply, leading to Bloch oscillations between the edges of a pseudo-Brillouin-zone. We verify this semiclassical theory by comparing to the results of an exact numerical solution. Interesting features appear in the semiclassical dynamics for the quasicrystal for a particle driven in a cyclic trajectory around the corner of the pseudo-Brillouin-zone: The particle fails to return to its initial state, providing a realization of a "spiral holonomy" in the dynamics. We show that there can appear anomalous velocity contributions, associated with nonzero Berry curvature. We relate these to the Berry phase associated with the spiral holonomy, and show how the Berry curvature can be accessed from the semiclassical dynamics. Finally, by identifying the pseudo-Brillouin-zone as a higher genus surface, we show that the Chern number classification for periodic systems can be extended to a quasicrystal, thereby determining a topological index for the system.

The gravity duals of modular Hamiltonians

DOE PAGES

Jafferis, Daniel L.; Suh, S. Josephine

2016-09-12

In this study, we investigate modular Hamiltonians defined with respect to arbitrary spatial regions in quantum field theory states which have semi-classical gravity duals. We find prescriptions in the gravity dual for calculating the action of the modular Hamiltonian on its defining state, including its dual metric, and also on small excitations around the state. Curiously, use of the covariant holographic entanglement entropy formula leads us to the conclusion that the modular Hamiltonian, which in the quantum field theory acts only in the causal completion of the region, does not commute with bulk operators whose entire gauge-invariant description is space-likemore » to the causal completion of the region.« less

The gravity duals of modular Hamiltonians

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jafferis, Daniel L.; Suh, S. Josephine

In this study, we investigate modular Hamiltonians defined with respect to arbitrary spatial regions in quantum field theory states which have semi-classical gravity duals. We find prescriptions in the gravity dual for calculating the action of the modular Hamiltonian on its defining state, including its dual metric, and also on small excitations around the state. Curiously, use of the covariant holographic entanglement entropy formula leads us to the conclusion that the modular Hamiltonian, which in the quantum field theory acts only in the causal completion of the region, does not commute with bulk operators whose entire gauge-invariant description is space-likemore » to the causal completion of the region.« less

Microscopic description of fission properties for r-process nuclei

NASA Astrophysics Data System (ADS)

Giuliani, S. A.; Martínez-Pinedo, G.; Robledo, L. M.

2018-01-01

Fission properties of 886 even-even nuclei in the region 84 ≤ Z ≤ 120 and 118 ≤ Z ≤ 250 were computed using the Barcelona-Catania-Paris-Madrid energy density functional. An extensive study of both the potential energy surfaces and collectives inertias was performed. Spontaneous fission half-lives are computed using the semiclassical Wentzel-Kramers-Brillouin formalism. By comparing these three quantities we found that the stability of the nucleus against the fission process is driven by the interplay between both the potential energy and the collective inertias. In our calculations, nuclei with relative long half-lives were found in two regions around Z = 120, N = 182 and Z = 104, N = 222.

Study of optimum methods of optical communication

NASA Technical Reports Server (NTRS)

Harger, R. O.

1972-01-01

Optimum methods of optical communication accounting for the effects of the turbulent atmosphere and quantum mechanics, both by the semi-classical method and the full-fledged quantum theoretical model are described. A concerted effort to apply the techniques of communication theory to the novel problems of optical communication by a careful study of realistic models and their statistical descriptions, the finding of appropriate optimum structures and the calculation of their performance and, insofar as possible, comparing them to conventional and other suboptimal systems are discussed. In this unified way the bounds on performance and the structure of optimum communication systems for transmission of information, imaging, tracking, and estimation can be determined for optical channels.

Non-Condon nonequilibrium Fermi’s golden rule rates from the linearized semiclassical method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sun, Xiang; Geva, Eitan

2016-08-14

The nonequilibrium Fermi’s golden rule describes the transition between a photoexcited bright donor electronic state and a dark acceptor electronic state, when the nuclear degrees of freedom start out in a nonequilibrium state. In a previous paper [X. Sun and E. Geva, J. Chem. Theory Comput. 12, 2926 (2016)], we proposed a new expression for the nonequilibrium Fermi’s golden rule within the framework of the linearized semiclassical approximation and based on the Condon approximation, according to which the electronic coupling between donor and acceptor is assumed constant. In this paper we propose a more general expression, which is applicable tomore » the case of non-Condon electronic coupling. We test the accuracy of the new non-Condon nonequilibrium Fermi’s golden rule linearized semiclassical expression on a model where the donor and acceptor potential energy surfaces are parabolic and identical except for shifts in the equilibrium energy and geometry, and the coupling between them is linear in the nuclear coordinates. Since non-Condon effects may or may not give rise to conical intersections, both possibilities are examined by considering the following: (1) A modified Garg-Onuchic-Ambegaokar model for charge transfer in the condensed phase, where the donor-acceptor coupling is linear in the primary-mode coordinate, and for which non-Condon effects do not give rise to a conical intersection; (2) the linear vibronic coupling model for electronic transitions in gas phase molecules, where non-Condon effects give rise to conical intersections. We also present a comprehensive comparison between the linearized semiclassical expression and a progression of more approximate expressions, in both normal and inverted regions, and over a wide range of initial nonequilibrium states, temperatures, and frictions.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Donangelo, R.J.

An integral representation for the classical limit of the quantum mechanical S-matrix is developed and applied to heavy-ion Coulomb excitation and Coulomb-nuclear interference. The method combines the quantum principle of superposition with exact classical dynamics to describe the projectile-target system. A detailed consideration of the classical trajectories and of the dimensionless parameters that characterize the system is carried out. The results are compared, where possible, to exact quantum mechanical calculations and to conventional semiclassical calculations. It is found that in the case of backscattering the classical limit S-matrix method is able to almost exactly reproduce the quantum-mechanical S-matrix elements, andmore » therefore the transition probabilities, even for projectiles as light as protons. The results also suggest that this approach should be a better approximation for heavy-ion multiple Coulomb excitation than earlier semiclassical methods, due to a more accurate description of the classical orbits in the electromagnetic field of the target nucleus. Calculations using this method indicate that the rotational excitation probabilities in the Coulomb-nuclear interference region should be very sensitive to the details of the potential at the surface of the nucleus, suggesting that heavy-ion rotational excitation could constitute a sensitive probe of the nuclear potential in this region. The application to other problems as well as the present limits of applicability of the formalism are also discussed.« less

Statistical effects in large N supersymmetric gauge theories

NASA Astrophysics Data System (ADS)

Czech, Bartlomiej Stanislaw

This thesis discusses statistical simplifications arising in supersymmetric gauge theories in the limit of large rank. Applications involve the physics of black holes and the problem of predicting the low energy effective theory from a landscape of string vacua. The first part of this work uses the AdS/CFT correspondence to explain properties of black holes. We establish that in the large charge sector of toric quiver gauge theories there exists a typical state whose structure is closely mimicked by almost all other states. Then, working in the settings of the half-BPS sector of N = 4 super-Yang-Mills theory, we show that in the dual gravity theory semiclassical observations cannot distinguish a pair of geometries corresponding to two generic heavy states. Finally, we argue on general grounds that these conclusions are exponentially enhanced in quantum cosmological settings. The results establish that one may consistently account for the entropy of a black hole with heavy states in the dual field theory and suggest that the usual properties of black holes arise as artifacts of imposing a semiclassical description on a quantum system. In the second half we develop new tools to determine the infrared behavior of quiver gauge theories in a certain class. We apply the dynamical results to a toy model of the landscape of effective field theories defined at some high energy scale, and derive firm statistical predictions for the low energy effective theory.

Semiclassical unified description of wobbling motion in even-even and even-odd nuclei

NASA Astrophysics Data System (ADS)

Raduta, A. A.; Poenaru, R.; Ixaru, L. Gr.

2017-11-01

A unitary description for wobbling motion in even-even and even-odd nuclei is presented. In both cases compact formulas for wobbling frequencies are derived. The accuracy of the harmonic approximation is studied for the yrast as well as for the excited bands in the even-even case. Important results for the structure of the wave function and its behavior inside the two wells of the potential energy function corresponding to the Bargmann representation are pointed out. Applications to 158Er and 163Lu reveal a very good agreement with available data. Indeed, the yrast energy levels in the even-even case and the first four triaxial superdeformed bands, TSD1, TSD2, TSD3, and TSD4, are realistically described. Also, the results agree with the data for the E 2 and M 1 intra- as well as interband transitions. Perspectives for the formalism development and an extensive application to several nuclei from various regions of the nuclides chart are presented.

On the late-time behavior of Virasoro blocks and a classification of semiclassical saddles

DOE PAGES

Fitzpatrick, A. Liam; Kaplan, Jared

2017-04-12

Recent work has demonstrated that black hole thermodynamics and information loss/restoration in AdS 3/CFT 2 can be derived almost entirely from the behavior of the Virasoro conformal blocks at large central charge, with relatively little dependence on the precise details of the CFT spectrum or OPE coefficients. Here, we elaborate on the non-perturbative behavior of Virasoro blocks by classifying all ‘saddles’ that can contribute for arbitrary values of external and internal operator dimensions in the semiclassical large central charge limit. The leading saddles, which determine the naive semiclassical behavior of the Virasoro blocks, all decay exponentially at late times, andmore » at a rate that is independent of internal operator dimensions. Consequently, the semiclassical contribution of a finite number of high-energy states cannot resolve a well-known version of the information loss problem in AdS 3. Furthermore, we identify two infinite classes of sub-leading saddles, and one of these classes does not decay at late times.« less

On the late-time behavior of Virasoro blocks and a classification of semiclassical saddles

NASA Astrophysics Data System (ADS)

Fitzpatrick, A. Liam; Kaplan, Jared

2017-04-01

Recent work has demonstrated that black hole thermodynamics and information loss/restoration in AdS3/CFT2 can be derived almost entirely from the behavior of the Virasoro conformal blocks at large central charge, with relatively little dependence on the precise details of the CFT spectrum or OPE coefficients. Here, we elaborate on the non-perturbative behavior of Virasoro blocks by classifying all `saddles' that can contribute for arbitrary values of external and internal operator dimensions in the semiclassical large central charge limit. The leading saddles, which determine the naive semiclassical behavior of the Virasoro blocks, all decay exponentially at late times, and at a rate that is independent of internal operator dimensions. Consequently, the semiclassical contribution of a finite number of high-energy states cannot resolve a well-known version of the information loss problem in AdS3. However, we identify two infinite classes of sub-leading saddles, and one of these classes does not decay at late times.

Remnants of semiclassical bistability in the few-photon regime of cavity QED.

PubMed

Kerckhoff, Joseph; Armen, Michael A; Mabuchi, Hideo

2011-11-21

Broadband homodyne detection of the light transmitted by a Fabry-Perot cavity containing a strongly-coupled (133)Cs atom is used to probe the dynamic optical response in a regime where semiclassical theory predicts bistability but strong quantum corrections should apply. While quantum fluctuations destabilize true equilibrium bistability, our observations confirm the existence of metastable states with finite lifetimes and a hysteretic response is apparent when the optical drive is modulated on comparable timescales. Our experiment elucidates remnant semiclassical behavior in the attojoule (~10 photon) regime of single-atom cavity QED, of potential significance for ultra-low power photonic signal processing. © 2011 Optical Society of America

The symmetric = ω -semi-classical orthogonal polynomials of class one

NASA Astrophysics Data System (ADS)

Maroni, P.; Mejri, M.

2008-12-01

We give the system of Laguerre-Freud equations associated with the = ω -semi-classical functionals of class one, where = ω is the divided difference operator. This system is solved in the symmetric case. There are essentially two canonical cases. The corresponding integral representations are given.

Semiclassical geometry of integrable systems

NASA Astrophysics Data System (ADS)

Reshetikhin, Nicolai

2018-04-01

The main result of this paper is a formula for the scalar product of semiclassical eigenvectors of two integrable systems on the same symplectic manifold. An important application of this formula is the Ponzano–Regge type of asymptotic of Racah–Wigner coefficients. Dedicated to the memory of P P Kulish.

Linearized semiclassical initial value time correlation functions with maximum entropy analytic continuation.

PubMed

Liu, Jian; Miller, William H

2008-09-28

The maximum entropy analytic continuation (MEAC) method is used to extend the range of accuracy of the linearized semiclassical initial value representation (LSC-IVR)/classical Wigner approximation for real time correlation functions. LSC-IVR provides a very effective "prior" for the MEAC procedure since it is very good for short times, exact for all time and temperature for harmonic potentials (even for correlation functions of nonlinear operators), and becomes exact in the classical high temperature limit. This combined MEAC+LSC/IVR approach is applied here to two highly nonlinear dynamical systems, a pure quartic potential in one dimensional and liquid para-hydrogen at two thermal state points (25 and 14 K under nearly zero external pressure). The former example shows the MEAC procedure to be a very significant enhancement of the LSC-IVR for correlation functions of both linear and nonlinear operators, and especially at low temperature where semiclassical approximations are least accurate. For liquid para-hydrogen, the LSC-IVR is seen already to be excellent at T=25 K, but the MEAC procedure produces a significant correction at the lower temperature (T=14 K). Comparisons are also made as to how the MEAC procedure is able to provide corrections for other trajectory-based dynamical approximations when used as priors.

Instanton and noninstanton tunneling in periodically perturbed barriers: semiclassical and quantum interpretations.

PubMed

Takahashi, Kin'ya; Ikeda, Kensuke S

2012-11-01

In multidimensional barrier tunneling, there exist two different types of tunneling mechanisms, instanton-type tunneling and noninstanton tunneling. In this paper we investigate transitions between the two tunneling mechanisms from the semiclassical and quantum viewpoints taking two simple models: a periodically perturbed Eckart barrier for the semiclassical analysis and a periodically perturbed rectangular barrier for the quantum analysis. As a result, similar transitions are observed with change of the perturbation frequency ω for both systems, and we obtain a comprehensive scenario from both semiclassical and quantum viewpoints for them. In the middle range of ω, in which the plateau spectrum is observed, noninstanton tunneling dominates the tunneling process, and the tunneling amplitude takes the maximum value. Noninstanton tunneling explained by stable-unstable manifold guided tunneling (SUMGT) from the semiclassical viewpoint is interpreted as multiphoton-assisted tunneling from the quantum viewpoint. However, in the limit ω→0, instanton-type tunneling takes the place of noninstanton tunneling, and the tunneling amplitude converges on a constant value depending on the perturbation strength. The spectrum localized around the input energy is observed, and there is a scaling law with respect to the width of the spectrum envelope, i.e., the width ∝ℏω. In the limit ω→∞, the tunneling amplitude converges on that of the unperturbed system, i.e., the instanton of the unperturbed system.

Laguerre-Freud Equations for the Recurrence Coefficients of Some Discrete Semi-Classical Orthogonal Polynomials of Class Two

NASA Astrophysics Data System (ADS)

Hounga, C.; Hounkonnou, M. N.; Ronveaux, A.

2006-10-01

In this paper, we give Laguerre-Freud equations for the recurrence coefficients of discrete semi-classical orthogonal polynomials of class two, when the polynomials in the Pearson equation are of the same degree. The case of generalized Charlier polynomials is also presented.

Double-wells and double-layers in dusty Fermi-Dirac plasmas: Comparison with the semiclassical Thomas-Fermi counterpart

DOE Office of Scientific and Technical Information (OSTI.GOV)

Akbari-Moghanjoughi, M.

Based on the quantum hydrodynamics (QHD) model, a new relationship between the electrostatic-potential and the electron-density in the ultradense plasma is derived. Propagation of arbitrary amplitude nonlinear ion waves is, then, investigated in a completely degenerate dense dusty electron-ion plasma, using this new energy relation for the relativistic electrons, in the ground of quantum hydrodynamics model and the results are compared to the case of semiclassical Thomas-Fermi dusty plasma. Based on the standard pseudopotential approach, it is remarked that the Fermi-Dirac plasma, in contrast to the Thomas-Fermi counterpart, accommodates a wide variety of nonlinear excitations such as positive/negative-potential ion solitarymore » and periodic waves, double-layers, and double-wells. It is also remarked that the relativistic degeneracy parameter which relates to the mass-density of plasma has significant effects on the allowed matching-speed range in Fermi-Dirac dusty plasmas.« less

Semiclassical Path Integral Calculation of Nonlinear Optical Spectroscopy.

PubMed

Provazza, Justin; Segatta, Francesco; Garavelli, Marco; Coker, David F

2018-02-13

Computation of nonlinear optical response functions allows for an in-depth connection between theory and experiment. Experimentally recorded spectra provide a high density of information, but to objectively disentangle overlapping signals and to reach a detailed and reliable understanding of the system dynamics, measurements must be integrated with theoretical approaches. Here, we present a new, highly accurate and efficient trajectory-based semiclassical path integral method for computing higher order nonlinear optical response functions for non-Markovian open quantum systems. The approach is, in principle, applicable to general Hamiltonians and does not require any restrictions on the form of the intrasystem or system-bath couplings. This method is systematically improvable and is shown to be valid in parameter regimes where perturbation theory-based methods qualitatively breakdown. As a test of the methodology presented here, we study a system-bath model for a coupled dimer for which we compare against numerically exact results and standard approximate perturbation theory-based calculations. Additionally, we study a monomer with discrete vibronic states that serves as the starting point for future investigation of vibronic signatures in nonlinear electronic spectroscopy.

The recurrence coefficients of semi-classical Laguerre polynomials and the fourth Painlevé equation

NASA Astrophysics Data System (ADS)

Filipuk, Galina; Van Assche, Walter; Zhang, Lun

2012-05-01

We show that the coefficients of the three-term recurrence relation for orthogonal polynomials with respect to a semi-classical extension of the Laguerre weight satisfy the fourth Painlevé equation when viewed as functions of one of the parameters in the weight. We compare different approaches to derive this result, namely, the ladder operators approach, the isomonodromy deformations approach and combining the Toda system for the recurrence coefficients with a discrete equation. We also discuss a relation between the recurrence coefficients for the Freud weight and the semi-classical Laguerre weight and show how it arises from the Bäcklund transformation of the fourth Painlevé equation.

Influence of semiclassical plasma on the energy levels and radiative transitions in highly charged ions★

NASA Astrophysics Data System (ADS)

Hu, Hong-Wei; Chen, Zhan-Bin; Chen, Wen-Cong; Liu, Xiao-Bin; Fu, Nian; Wang, Kai

2017-11-01

Considering the quantum effects of diffraction and the collective screening effects, the potential of test charge in semiclassical plasmas is derived. It is generalized exponential screened Coulomb potential. Using the Ritz variational method incorporating this potential, the effects of semiclassical plasma on the energy levels and radiative transitions are investigated systematically, taking highly charged H-like ion as an example. The Debye plasma model is also employed for comparison purposes. Comparisons and analysis are made between these two sets of results and the differences are discussed. Contribution to the Topical Issue "Atomic and Molecular Data and their Applications", edited by Gordon W.F. Drake, Jung-Sik Yoon, Daiji Kato, Grzegorz Karwasz.

Time-dependent variational approach in terms of squeezed coherent states: Implication to semi-classical approximation

NASA Technical Reports Server (NTRS)

Tsue, Yasuhiko

1994-01-01

A general framework for time-dependent variational approach in terms of squeezed coherent states is constructed with the aim of describing quantal systems by means of classical mechanics including higher order quantal effects with the aid of canonicity conditions developed in the time-dependent Hartree-Fock theory. The Maslov phase occurring in a semi-classical quantization rule is investigated in this framework. In the limit of a semi-classical approximation in this approach, it is definitely shown that the Maslov phase has a geometric nature analogous to the Berry phase. It is also indicated that this squeezed coherent state approach is a possible way to go beyond the usual WKB approximation.

Quantum mean-field approximation for lattice quantum models: Truncating quantum correlations and retaining classical ones

NASA Astrophysics Data System (ADS)

Malpetti, Daniele; Roscilde, Tommaso

2017-02-01

The mean-field approximation is at the heart of our understanding of complex systems, despite its fundamental limitation of completely neglecting correlations between the elementary constituents. In a recent work [Phys. Rev. Lett. 117, 130401 (2016), 10.1103/PhysRevLett.117.130401], we have shown that in quantum many-body systems at finite temperature, two-point correlations can be formally separated into a thermal part and a quantum part and that quantum correlations are generically found to decay exponentially at finite temperature, with a characteristic, temperature-dependent quantum coherence length. The existence of these two different forms of correlation in quantum many-body systems suggests the possibility of formulating an approximation, which affects quantum correlations only, without preventing the correct description of classical fluctuations at all length scales. Focusing on lattice boson and quantum Ising models, we make use of the path-integral formulation of quantum statistical mechanics to introduce such an approximation, which we dub quantum mean-field (QMF) approach, and which can be readily generalized to a cluster form (cluster QMF or cQMF). The cQMF approximation reduces to cluster mean-field theory at T =0 , while at any finite temperature it produces a family of systematically improved, semi-classical approximations to the quantum statistical mechanics of the lattice theory at hand. Contrary to standard MF approximations, the correct nature of thermal critical phenomena is captured by any cluster size. In the two exemplary cases of the two-dimensional quantum Ising model and of two-dimensional quantum rotors, we study systematically the convergence of the cQMF approximation towards the exact result, and show that the convergence is typically linear or sublinear in the boundary-to-bulk ratio of the clusters as T →0 , while it becomes faster than linear as T grows. These results pave the way towards the development of semiclassical numerical approaches based on an approximate, yet systematically improved account of quantum correlations.

Interference effect in the resonant emission of a semiconductor microcavity

NASA Astrophysics Data System (ADS)

Cassabois, G.; Bogani, F.; Triques, A. L.; Delalande, C.; Roussignol, Ph.

2001-07-01

We present a phenomenological description of the coherent emission from a semiconductor microcavity in the strong-coupling regime. We consider two main contributions which are calculated in the framework of the semiclassical approach of the linear dispersion theory: reflectivity corresponds to the response of a uniform microcavity while resonant Rayleigh scattering (RRS) arises from disorder. Our simulations are compared to experimental results obtained at normal incidence in a backscattering geometry by means of cw spectroscopy and interferometric correlation with subpicosecond resolution. In this geometry, a fair agreement is reached assuming interferences between the two aforementioned contributions. This interference effect gives evidence of the drastic modification of the RRS emission pattern of the embedded quantum well induced by the Fabry-Pérot cavity.

Electronic wave function and binding effects in M-shell ionization of gold by protons

NASA Astrophysics Data System (ADS)

Pajek, M.; Banaś, D.; Jabłoński, Ł.; Mukoyama, T.

2018-02-01

The measured M-X-ray production cross sections for protons, which are used in the particle induced X-ray emission (PIXE) technique, are systematically underestimated for low impact energies by the ECPSSR and ECUSAR theories. These theories, which are based on the plane wave Born approximation (PWBA) and use the screened hydrogenic wave functions, include corrections for the projectile Coulomb deflection and electron relativistic and binding effects. In the present paper, in order to interpret the observed disagreement at low impact energies, the systematic calculations of the M-shell ionization cross sections for gold were performed using the semiclassical (SCA) and the binary encounter (BEA) approximations in order to identify a role of the electronic wave function and electron binding effects. In these calculations the different wave functions, from nonrelativistic hydrogenic to selfconsistent Dirac-Hartree-Fock, were considered and the binding effect was treated within extreme separated- (SA) and united-atoms (UA) limits. The results are discussed in details and the observed discrepancies are attributed to inadequate description of the electron binding effect at the lowest impact energies for which the molecular approach is required.

Hybrid quantum-classical modeling of quantum dot devices

NASA Astrophysics Data System (ADS)

Kantner, Markus; Mittnenzweig, Markus; Koprucki, Thomas

2017-11-01

The design of electrically driven quantum dot devices for quantum optical applications asks for modeling approaches combining classical device physics with quantum mechanics. We connect the well-established fields of semiclassical semiconductor transport theory and the theory of open quantum systems to meet this requirement. By coupling the van Roosbroeck system with a quantum master equation in Lindblad form, we introduce a new hybrid quantum-classical modeling approach, which provides a comprehensive description of quantum dot devices on multiple scales: it enables the calculation of quantum optical figures of merit and the spatially resolved simulation of the current flow in realistic semiconductor device geometries in a unified way. We construct the interface between both theories in such a way, that the resulting hybrid system obeys the fundamental axioms of (non)equilibrium thermodynamics. We show that our approach guarantees the conservation of charge, consistency with the thermodynamic equilibrium and the second law of thermodynamics. The feasibility of the approach is demonstrated by numerical simulations of an electrically driven single-photon source based on a single quantum dot in the stationary and transient operation regime.

On the accuracy of the LSC-IVR approach for excitation energy transfer in molecular aggregates

NASA Astrophysics Data System (ADS)

Teh, Hung-Hsuan; Cheng, Yuan-Chung

2017-04-01

We investigate the applicability of the linearized semiclassical initial value representation (LSC-IVR) method to excitation energy transfer (EET) problems in molecular aggregates by simulating the EET dynamics of a dimer model in a wide range of parameter regime and comparing the results to those obtained from a numerically exact method. It is found that the LSC-IVR approach yields accurate population relaxation rates and decoherence rates in a broad parameter regime. However, the classical approximation imposed by the LSC-IVR method does not satisfy the detailed balance condition, generally leading to incorrect equilibrium populations. Based on this observation, we propose a post-processing algorithm to solve the long time equilibrium problem and demonstrate that this long-time correction method successfully removed the deviations from exact results for the LSC-IVR method in all of the regimes studied in this work. Finally, we apply the LSC-IVR method to simulate EET dynamics in the photosynthetic Fenna-Matthews-Olson complex system, demonstrating that the LSC-IVR method with long-time correction provides excellent description of coherent EET dynamics in this typical photosynthetic pigment-protein complex.

Global thermodynamics of confined inhomogeneous dilute gases: A semi-classical approach

NASA Astrophysics Data System (ADS)

Poveda-Cuevas, F. J.; Reyes-Ayala, I.; Seman, J. A.; Romero-Rochín, V.

2018-04-01

In this work we present our contribution to the Latin American School of Physics "Marcos Moshinsky" 2017 on Quantum Correlations which was held in Mexico City during the summer of 2017. We review the efforts that have been done to construct a global thermodynamic description of ultracold dilute gases confined in inhomogeneous potentials. This is difficult because the presence of this non-uniform trap makes the pressure of the gas to be a spatially dependent variable and its volume an ambiguously defined quantity. In this paper we introduce new global thermodynamic variables, equivalent to pressure and volume, and propose a realistic model of the equation of state of the system. This model is based on a mean-field approach which asymptotically reaches the Thomas-Fermi limit for a weakly interacting Bose gas. We put special emphasis to the transition between the normal and superfluid phases by studying the behavior of the isothermal compressibility across the transition. We reveal how the potential modifies the critical properties of the transition by determining the critical exponents associated to the divergences not of the susceptibilities but of their derivatives.

Diffraction catastrophes and semiclassical quantum mechanics for Veselago lensing in graphene

NASA Astrophysics Data System (ADS)

Reijnders, K. J. A.; Katsnelson, M. I.

2017-07-01

We study the effect of trigonal warping on the focusing of electrons by n-p junctions in graphene. We find that perfect focusing, which was predicted for massless Dirac fermions, is only preserved for one specific lattice orientation. In the general case, trigonal warping leads to the formation of cusp caustics, with a different position of the focus for graphene's two valleys. We develop a semiclassical theory to compute these positions and find very good agreement with tight-binding simulations. Considering the transmission as a function of potential strength, we find that trigonal warping splits the single Dirac peak into two distinct peaks, leading to valley polarization. We obtain the transmission curves from tight-binding simulations and find that they are in very good agreement with the results of a billiard model that incorporates trigonal warping. Furthermore, the positions of the transmission maxima and the scaling of the peak width are accurately predicted by our semiclassical theory. Our semiclassical analysis can easily be carried over to other Dirac materials, which generally have different Fermi surface distortions.

Symmetry-Based Techniques for Qualitative Understanding of Rovibrational Effects in Spherical-Top Molecular Spectra and Dynamics

NASA Astrophysics Data System (ADS)

Mitchell, Justin Chadwick

2011-12-01

Using light to probe the structure of matter is as natural as opening our eyes. Modern physics and chemistry have turned this art into a rich science, measuring the delicate interactions possible at the molecular level. Perhaps the most commonly used tool in computational spectroscopy is that of matrix diagonalization. While this is invaluable for calculating everything from molecular structure and energy levels to dipole moments and dynamics, the process of numerical diagonalization is an opaque one. This work applies symmetry and semi-classical techniques to elucidate numerical spectral analysis for high-symmetry molecules. Semi-classical techniques, such as the Potential Energy Surfaces, have long been used to help understand molecular vibronic and rovibronic spectra and dynamics. This investigation focuses on newer semi-classical techniques that apply Rotational Energy Surfaces (RES) to rotational energy level clustering effects in high-symmetry molecules. Such clusters exist in rigid rotor molecules as well as deformable spherical tops. This study begins by using the simplicity of rigid symmetric top molecules to clarify the classical-quantum correspondence of RES semi-classical analysis and then extends it to a more precise and complete theory of modern high-resolution spectra. RES analysis is extended to molecules having more complex and higher rank tensorial rotational and rovibrational Hamiltonians than were possible to understand before. Such molecules are shown to produce an extraordinary range of rotational level clusters, corresponding to a panoply of symmetries ranging from C4v to C2 and C1 (no symmetry) with a corresponding range of new angular momentum localization and J-tunneling effects. Using RES topography analysis and the commutation duality relations between symmetry group operators in the lab-frame to those in the body-frame, it is shown how to better describe and catalog complex splittings found in rotational level clusters. Symmetry character analysis is generalized to give analytic eigensolutions. An appendix provides vibrational analogies. For the first time, interactions between molecular vibrations (polyads) are described semi-classically by multiple RES. This is done for the nu 3/2nu4 dyad of CF4. The nine-surface RES topology of the U(9)-dyad agrees with both computational and experimental work. A connection between this and a simpler U(2) example is detailed in an Appendix.

Quantum Stark broadening of Ar XV lines. Strong collision and quadrupolar potential contributions

NASA Astrophysics Data System (ADS)

Elabidi, H.; Sahal-Bréchot, S.; Dimitrijević, M. S.

2014-10-01

We present in this paper electron impact broadening for six Ar XV lines using our quantum mechanical formalism and the semiclassical perturbation one. Additionally, our calculations of the corresponding atomic structure data (energy levels and oscillator strengths) and collision strengths are given as well. The lines considered here are divided into two sets: a first set of four lines involving the ground level: 1s22s21S0- 1s22snp 1P1o where 2⩽n⩽5 and a second set of two lines involving excited levels: 1s22s2p 1P1o-1s22s3s 1S0 and 1s22s2p 3P0o-1s22s3s 3S1. An extensive comparison between the quantum and the semiclassical results was performed in order to analyze the reason for differences between quantum and semiclassical results up to the factor of two. It has been shown that the difference between the two results may be due to the evaluation of strong collision contributions by the semiclassical formalism. Except few semiclassical results, the present results are the first to be published. After the recent discovery of the far UV lines of Ar VII in the spectra of very hot central stars of planetary nebulae and white dwarfs, the present -and may be further- results can be used also for the corresponding future spectral analysis.

What Is Light?. Students' Reflections on the Wave-Particle Duality of Light and the Nature of Physics

NASA Astrophysics Data System (ADS)

Henriksen, Ellen Karoline; Angell, Carl; Vistnes, Arnt Inge; Bungum, Berit

2018-03-01

Quantum physics describes light as having both particle and wave properties; however, there is no consensus about how to interpret this duality on an ontological level. This article explores how pre-university physics students, while working with learning material focusing on historical-philosophical aspects of quantum physics, interpreted the wave-particle duality of light and which views they expressed on the nature of physics. A thematic analysis was performed on 133 written responses about the nature of light, given in the beginning of the teaching sequence, and 55 audio-recorded small-group discussions addressing the wave-particle duality, given later in the sequence. Most students initially expressed a wave and particle view of light, but some of these gave an "uncritical duality description", accepting without question the two ontologically different descriptions of light. In the small-group discussions, students expressed more nuanced views. Many tried to reconcile the two descriptions using semi-classical reasoning; others entered into philosophical discussions about the status of the current scientific description of light and expected science to come up with a better model. Some found the wave description of light particularly challenging and lacked a conception of "what is waving". Many seemed to implicitly take a realist view on the description of physical phenomena, contrary with the Copenhagen interpretation which is prevalent in textbooks. Results are discussed in light of different interpretations of quantum physics, and we conclude by arguing for a historical-philosophical perspective as an entry point for upper secondary physics students to explore the development and interpretation of quantum physical concepts.

Semiclassical spectrum for BMN string in Sch 5 × S 5

NASA Astrophysics Data System (ADS)

Ouyang, Hao

2017-12-01

We investigate the algebraic curve for string in Sch 5 × S 5. We compute the semiclassical spectrum for BMN string in Sch 5 × S 5 from the algebraic curve. We compare our results with the anomalous dimensions in sl(2) sector of the null dipole deformation of N=4 superYang-Millstheory.

Semiclassical Models for Virtual Antiparticle Pairs, the Unit of Charge e, and the QCD Coupling alpha(sub s)

NASA Technical Reports Server (NTRS)

Batchelor, David; Zukor, Dorothy (Technical Monitor)

2001-01-01

New semiclassical models of virtual antiparticle pairs are used to compute the pair lifetimes, and good agreement with the Heisenberg lifetimes from quantum field theory (QFT) is found. The modeling method applies to both the electromagnetic and color forces. Evaluation of the action integral of potential field fluctuation for each interaction potential yields approximately Planck's constant/2 for both electromagnetic and color fluctuations, in agreement with QFT. Thus each model is a quantized semiclassical representation for such virtual antiparticle pairs, to good approximation. When the results of the new models and QFT are combined, formulae for e and alpha(sub s)(q) are derived in terms of only Planck's constant and c.

Cascading and local-field effects in non-linear optics revisited: a quantum-field picture based on exchange of photons.

PubMed

Bennett, Kochise; Mukamel, Shaul

2014-01-28

The semi-classical theory of radiation-matter coupling misses local-field effects that may alter the pulse time-ordering and cascading that leads to the generation of new signals. These are then introduced macroscopically by solving Maxwell's equations. This procedure is convenient and intuitive but ad hoc. We show that both effects emerge naturally by including coupling to quantum modes of the radiation field that are initially in the vacuum state to second order. This approach is systematic and suggests a more general class of corrections that only arise in a QED framework. In the semi-classical theory, which only includes classical field modes, the susceptibility of a collection of N non-interacting molecules is additive and scales as N. Second-order coupling to a vacuum mode generates an effective retarded interaction that leads to cascading and local field effects both of which scale as N(2).

Theory of the stopping power of fast multicharged ions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yudin, G.L.

1991-12-01

The processes of Coulomb excitation and ionization of atoms by a fast charged particle moving along a classical trajectory are studied. The target electrons are described by the Dirac equation, while the field of the incident particle is described by the Lienard-Wiechert potential. The theory is formulated in the form most convenient for investigation of various characteristics of semiclassical atomic collisions. The theory of sudden perturbations, which is valid at high enough velocities for a high projectile charge, is employed to obtain probabilities and cross sections of the Coulomb excitation and ionization of atomic hydrogen by fast multiply charged ions.more » Based on the semiclassical sudden Born approximation, the ionization cross section and the average electronic energy loss of a fast ion in a single collision with an atom are investigated over a wide specific energy range from 500 keV/amu to 50 MeV/amu.« less

A semiclassical study of laser-induced atomic fluorescence from Na2, K2 and NaK

NASA Technical Reports Server (NTRS)

Yuan, J.-M.; Bhattacharyya, D. K.; George, T. F.

1982-01-01

A semiclassical treatment of laser-induced atomic fluorescence for the alkali-dimer systems Na2, K2 and NaK is presented. The variation of the fluorescence intensity with the frequency of the exciting laser photon is studied and a comparison of theoretical results with a set of experimental data is presented.

Quantum dynamics of the Einstein-Rosen wormhole throat

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kunstatter, Gabor; Peltola, Ari; Louko, Jorma

2011-02-15

We consider the polymer quantization of the Einstein wormhole throat theory for an eternal Schwarzschild black hole. We numerically solve the difference equation describing the quantum evolution of an initially Gaussian, semiclassical wave packet. As expected from previous work on loop quantum cosmology, the wave packet remains semiclassical until it nears the classical singularity at which point it enters a quantum regime in which the fluctuations become large. The expectation value of the radius reaches a minimum as the wave packet is reflected from the origin and emerges to form a near-Gaussian but asymmetrical semiclassical state at late times. Themore » value of the minimum depends in a nontrivial way on the initial mass/energy of the pulse, its width, and the polymerization scale. For wave packets that are sufficiently narrow near the bounce, the semiclassical bounce radius is obtained. Although the numerics become difficult to control in this limit, we argue that for pulses of finite width the bounce persists as the polymerization scale goes to zero, suggesting that in this model the loop quantum gravity effects mimicked by polymer quantization do not play a crucial role in the quantum bounce.« less

Short distance modification of the quantum virial theorem

NASA Astrophysics Data System (ADS)

Zhao, Qin; Faizal, Mir; Zaz, Zaid

2017-07-01

In this letter, we will analyse the deformation of a semi-classical gravitational system from minimal measurable length scale. In the semi-classical approximation, the gravitational field will be analysed as a classical field, and the matter fields will be treated quantum mechanically. Thus, using this approximation, this system will be represented by a deformation of Schrödinger-Newton equation by the generalised uncertainty principle (GUP). We will analyse the effects of this GUP deformed Schrödinger-Newton equation on the behaviour of such a semi-classical gravitational system. As the quantum mechanical virial theorem can be obtained using the Schrödinger-Newton equation, a short distance modification of the Schrödinger-Newton equation will also result in a short distance modification of the quantum mechanical virial theorem.

Relativistic space-charge-limited transport in Dirac semiconductor

NASA Astrophysics Data System (ADS)

Ang, Yee Sin; Zubair, M.; Ang, L. K.; Lavoie, Philippe

The theory of space-charge-limited (SCL) current was first formulated by Mott and Gurney more than 70 years ago based on the semiclassical transport of quasi-free electron in dielectric solids. Its validity for recently fabricated 2D materials, which can host different classes of exotic quasiparticles, remains questionable. Recently, SCL transport measurements in 2D Dirac semiconductor, such as MoS2 and hBN monolayers, revealed anomalous current-voltage scaling of J V 1 . 7 which cannot be satisfactorily explained by conventional theories. In this work, we propose a theory of space-charge-limited transport that takes into account the relativistic quasiparticle dynamics in 2D Dirac semiconductor based on semiclassical Boltzmann transport equation. Our relativistic SCL model reveals an unconventional scaling relation of J Vα with 3 / 2 < α < 2 in the trap-free (or trap-filled) regime, which is in stark contrast to the Mott-Gurney relation of α = 2 and the Mark-Helfrich relation of α > 2 . The α < 2 scaling is a unique manifestation of the massive Dirac quasiparticles and is supported by the experimental data of MoS2. The relativistic SCL model proposed here shall provide a physical basis for the modelling of Dirac-material-based devices

Systematic study of 16O-induced fusion with the improved quantum molecular dynamics model

NASA Astrophysics Data System (ADS)

Wang, Ning; Zhao, Kai; Li, Zhuxia

2014-11-01

The heavy-ion fusion reactions with 16O bombarding on 62Ni,65Cu,74Ge,148Nd,180Hf,186W,208Pb,238U are systematically investigated with the improved quantum molecular dynamics model. The fusion cross sections at energies near and above the Coulomb barriers can be reasonably well reproduced by using this semiclassical microscopic transport model with the parameter sets SkP* and IQ3a. The dynamical nucleus-nucleus potentials and the influence of Fermi constraint on the fusion process are also studied simultaneously. In addition to the mean field, the Fermi constraint also plays a key role for the reliable description of the fusion process and for improving the stability of fragments in heavy-ion collisions.

Electron transport in ultra-thin films and ballistic electron emission microscopy

NASA Astrophysics Data System (ADS)

Claveau, Y.; Di Matteo, S.; de Andres, P. L.; Flores, F.

2017-03-01

We have developed a calculation scheme for the elastic electron current in ultra-thin epitaxial heterostructures. Our model uses a Keldysh’s non-equilibrium Green’s function formalism and a layer-by-layer construction of the epitaxial film. Such an approach is appropriate to describe the current in a ballistic electron emission microscope (BEEM) where the metal base layer is ultra-thin and generalizes a previous one based on a decimation technique appropriated for thick slabs. This formalism allows a full quantum mechanical description of the transmission across the epitaxial heterostructure interface, including multiple scattering via the Dyson equation, which is deemed a crucial ingredient to describe interfaces of ultra-thin layers properly in the future. We introduce a theoretical formulation needed for ultra-thin layers and we compare with results obtained for thick Au(1 1 1) metal layers. An interesting effect takes place for a width of about ten layers: a BEEM current can propagate via the center of the reciprocal space (\\overlineΓ ) along the Au(1 1 1) direction. We associate this current to a coherent interference finite-width effect that cannot be found using a decimation technique. Finally, we have tested the validity of the handy semiclassical formalism to describe the BEEM current.

2D Quantum Simulation of MOSFET Using the Non Equilibrium Green's Function Method

NASA Technical Reports Server (NTRS)

Svizhenko, Alexel; Anantram, M. P.; Govindan, T. R.; Yan, Jerry (Technical Monitor)

2000-01-01

The objectives this viewgraph presentation summarizes include: (1) the development of a quantum mechanical simulator for ultra short channel MOSFET simulation, including theory, physical approximations, and computer code; (2) explore physics that is not accessible by semiclassical methods; (3) benchmarking of semiclassical and classical methods; and (4) study other two-dimensional devices and molecular structure, from discretized Hamiltonian to tight-binding Hamiltonian.

Semiclassical treatment of fusion and breakup processes of ^{6,8}He halo nuclei

NASA Astrophysics Data System (ADS)

Majeed, Fouad A.; Abdul-Hussien, Yousif A.

2016-06-01

A semiclassical approach has been used to study the effect of channel coupling on the calculations of the total fusion reaction cross section σ _{fus}, and the fusion barrier distribution D_{fus} for the systems 6He +^{238}U and 8He +^{197}Au. Since these systems invloves light exotic nuclei, breakup states channel play an important role that should be considered in the calculations. In semiclassical treatment, the relative motion between the projectile and target nuclei is approximated by a classical trajectory while the intrinsic dynamics is handled by time-dependent quantum mechanics. The calculations of the total fusion cross section σ _{fus}, and the fusion barrier distribution D_{fus} are compared with the full quantum mechanical calculations using the coupled-channels calculations with all order coupling using the computer code and with the available experimental data.

Stellar Equilibrium in Semiclassical Gravity.

PubMed

Carballo-Rubio, Raúl

2018-02-09

The phenomenon of quantum vacuum polarization in the presence of a gravitational field is well understood and is expected to have a physical reality, but studies of its backreaction on the dynamics of spacetime are practically nonexistent outside of the specific context of homogeneous cosmologies. Building on previous results of quantum field theory in curved spacetimes, in this Letter we first derive the semiclassical equations of stellar equilibrium in the s-wave Polyakov approximation. It is highlighted that incorporating the polarization of the quantum vacuum leads to a generalization of the classical Tolman-Oppenheimer-Volkoff equation. Despite the complexity of the resulting field equations, it is possible to find exact solutions. Aside from being the first known exact solutions that describe relativistic stars including the nonperturbative backreaction of semiclassical effects, these are identified as a nontrivial combination of the black star and gravastar proposals.

Firewall or smooth horizon?

NASA Astrophysics Data System (ADS)

Ori, Amos

2016-01-01

Almheiri, Marolf, Polchinski, and Sully pointed out that for a sufficiently old black hole (BH), the set of assumptions known as the complementarity postulates appears to be inconsistent with the assumption of local regularity at the horizon. They concluded that the horizon of an old BH is likely to be the locus of local irregularity, a "firewall". Here I point out that if one adopts a different assumption, namely that semiclassical physics holds throughout its anticipated domain of validity, then the inconsistency is avoided, and the horizon retains its regularity. In this alternative view-point, the vast portion of the original BH information remains trapped inside the BH throughout the semiclassical domain of evaporation, and possibly leaks out later on. This appears to be an inevitable outcome of semiclassical gravity (if assumed to apply throughout its anticipated domain of validity).

Vibration-translation energy transfer in vibrationally excited diatomic molecules. Ph.D. Thesis - York Univ., Toronto

NASA Technical Reports Server (NTRS)

Mckenzie, R. L.

1976-01-01

A semiclassical collision model is applied to the study of energy transfer rates between a vibrationally excited diatomic molecule and a structureless atom. The molecule is modeled as an anharmonic oscillator with a multitude of dynamically coupled vibrational states. Three main aspects in the prediction of vibrational energy transfer rates are considered. The applicability of the semiclassical model to an anharmonic oscillator is first evaluated for collinear encounters. Second, the collinear semiclassical model is applied to obtain numerical predictions of the vibrational energy transfer rate dependence on the initial vibrational state quantum number. Thermally averaged vibration-translation rate coefficients are predicted and compared with CO-He experimental values for both ground and excited initial states. The numerical model is also used as a basis for evaluating several less complete but analytic models. Third, the role of rational motion in the dynamics of vibrational energy transfer is examined. A three-dimensional semiclassical collision model is constructed with coupled rotational motion included. Energy transfer within the molecule is shown to be dominated by vibration-rotation transitions with small changes in angular momentum. The rates of vibrational energy transfer in molecules with rational frequencies that are very small in comparison to their vibrational frequency are shown to be adequately treated by the preceding collinear models.

Increasing the efficiency and accuracy of time-resolved electronic spectra calculations with on-the-fly ab initio quantum dynamics methods

NASA Astrophysics Data System (ADS)

Vanicek, Jiri

2014-03-01

Rigorous quantum-mechanical calculations of coherent ultrafast electronic spectra remain difficult. I will present several approaches developed in our group that increase the efficiency and accuracy of such calculations: First, we justified the feasibility of evaluating time-resolved spectra of large systems by proving that the number of trajectories needed for convergence of the semiclassical dephasing representation/phase averaging is independent of dimensionality. Recently, we further accelerated this approximation with a cellular scheme employing inverse Weierstrass transform and optimal scaling of the cell size. The accuracy of potential energy surfaces was increased by combining the dephasing representation with accurate on-the-fly ab initio electronic structure calculations, including nonadiabatic and spin-orbit couplings. Finally, the inherent semiclassical approximation was removed in the exact quantum Gaussian dephasing representation, in which semiclassical trajectories are replaced by communicating frozen Gaussian basis functions evolving classically with an average Hamiltonian. Among other examples I will present an on-the-fly ab initio semiclassical dynamics calculation of the dispersed time-resolved stimulated emission spectrum of the 54-dimensional azulene. This research was supported by EPFL and by the Swiss National Science Foundation NCCR MUST (Molecular Ultrafast Science and Technology) and Grant No. 200021124936/1.

"Divide-and-conquer" semiclassical molecular dynamics: An application to water clusters

NASA Astrophysics Data System (ADS)

Di Liberto, Giovanni; Conte, Riccardo; Ceotto, Michele

2018-03-01

We present an investigation of vibrational features in water clusters performed by means of our recently established divide-and-conquer semiclassical approach [M. Ceotto, G. Di Liberto, and R. Conte, Phys. Rev. Lett. 119, 010401 (2017)]. This technique allows us to simulate quantum vibrational spectra of high-dimensional systems starting from full-dimensional classical trajectories and projection of the semiclassical propagator onto a set of lower dimensional subspaces. The potential energy surface employed is a many-body representation up to three-body terms, in which monomers and two-body interactions are described by the high level Wang-Huang-Braams-Bowman (WHBB) water potential, while, for three-body interactions, calculations adopt a fast permutationally invariant ab initio surface at the same level of theory of the WHBB 3-body potential. Applications range from the water dimer up to the water decamer, a system made of 84 vibrational degrees of freedom. Results are generally in agreement with previous variational estimates in the literature. This is particularly true for the bending and the high-frequency stretching motions, while estimates of modes strongly influenced by hydrogen bonding are red shifted, in a few instances even substantially, as a consequence of the dynamical and global picture provided by the semiclassical approach.

Regular-to-Chaotic Tunneling Rates: From the Quantum to the Semiclassical Regime

NASA Astrophysics Data System (ADS)

Löck, Steffen; Bäcker, Arnd; Ketzmerick, Roland; Schlagheck, Peter

2010-03-01

We derive a prediction of dynamical tunneling rates from regular to chaotic phase-space regions combining the direct regular-to-chaotic tunneling mechanism in the quantum regime with an improved resonance-assisted tunneling theory in the semiclassical regime. We give a qualitative recipe for identifying the relevance of nonlinear resonances in a given ℏ regime. For systems with one or multiple dominant resonances we find excellent agreement to numerics.

Quantum Bound to Chaos and the Semiclassical Limit

NASA Astrophysics Data System (ADS)

Kurchan, Jorge

2018-06-01

We discuss the quantum bound on chaos in the context of the free propagation of a particle in an arbitrarily curved surface at low temperatures. The semiclassical calculation of the Lyapunov exponent can be performed in much the same way as the corresponding one for the `Loschmidt echo'. The bound appears here as the impossibility to scatter a wave, by effect of the curvature, over characteristic lengths smaller than the deBroglie wavelength.

Magnon edge states in the hardcore- Bose-Hubbard model.

PubMed

Owerre, S A

2016-11-02

Quantum Monte Carlo (QMC) simulation has uncovered nonzero Berry curvature and bosonic edge states in the hardcore-Bose-Hubbard model on the gapped honeycomb lattice. The competition between the chemical potential and staggered onsite potential leads to an interesting quantum phase diagram comprising the superfluid phase, Mott insulator, and charge density wave insulator. In this paper, we present a semiclassical perspective of this system by mapping to a spin-1/2 quantum XY model. We give an explicit analytical origin of the quantum phase diagram, the Berry curvatures, and the edge states using semiclassical approximations. We find very good agreement between the semiclassical analyses and the QMC results. Our results show that the topological properties of the hardcore-Bose-Hubbard model are the same as those of magnon in the corresponding quantum spin system. Our results are applicable to systems of ultracold bosonic atoms trapped in honeycomb optical lattices.

Hadronic density of states from string theory.

PubMed

Pando Zayas, Leopoldo A; Vaman, Diana

2003-09-12

We present an exact calculation of the finite temperature partition function for the hadronic states corresponding to a Penrose-Güven limit of the Maldacena-Nùñez embedding of the N=1 super Yang-Mills (SYM) into string theory. It is established that the theory exhibits a Hagedorn density of states. We propose a semiclassical string approximation to the finite temperature partition function for confining gauge theories admitting a supergravity dual, by performing an expansion around classical solutions characterized by temporal windings. This semiclassical approximation reveals a hadronic energy density of states of a Hagedorn type, with the coefficient determined by the gauge theory string tension as expected for confining theories. We argue that our proposal captures primarily information about states of pure N=1 SYM theory, given that this semiclassical approximation does not entail a projection onto states of large U(1) charge.

Hawking radiation due to photon and gravitino tunneling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Majhi, Bibhas Ranjan, E-mail: bibhas@bose.res.i; Samanta, Saurav, E-mail: srvsmnt@gmail.co

2010-11-15

Applying the Hamilton-Jacobi method we investigate the tunneling of photon across the event horizon of a static spherically symmetric black hole. The necessity of the gauge condition on the photon field, to derive the semiclassical Hawking temperature, is explicitly shown. Also, the tunneling of photon and gravitino beyond this semiclassical approximation are presented separately. Quantum corrections of the action for both cases are found to be proportional to the semiclassical contribution. Modifications to the Hawking temperature and Bekenstein-Hawking area law are thereby obtained. Using this corrected temperature and Hawking's periodicity argument, the modified metric for the Schwarzschild black hole ismore » given. This corrected version of the metric, up to h order is equivalent to the metric obtained by including one loop back reaction effect. Finally, the coefficient of the leading order correction of entropy is shown to be related to the trace anomaly.« less

Implementation of the semiclassical quantum Fourier transform in a scalable system.

PubMed

Chiaverini, J; Britton, J; Leibfried, D; Knill, E; Barrett, M D; Blakestad, R B; Itano, W M; Jost, J D; Langer, C; Ozeri, R; Schaetz, T; Wineland, D J

2005-05-13

We report the implementation of the semiclassical quantum Fourier transform in a system of three beryllium ion qubits (two-level quantum systems) confined in a segmented multizone trap. The quantum Fourier transform is the crucial final step in Shor's algorithm, and it acts on a register of qubits to determine the periodicity of the quantum state's amplitudes. Because only probability amplitudes are required for this task, a more efficient semiclassical version can be used, for which only single-qubit operations conditioned on measurement outcomes are required. We apply the transform to several input states of different periodicities; the results enable the location of peaks corresponding to the original periods. This demonstration incorporates the key elements of a scalable ion-trap architecture, suggesting the future capability of applying the quantum Fourier transform to a large number of qubits as required for a useful quantum factoring algorithm.

The quantum holonomy-diffeomorphism algebra and quantum gravity

NASA Astrophysics Data System (ADS)

Aastrup, Johannes; Grimstrup, Jesper Møller

2016-03-01

We introduce the quantum holonomy-diffeomorphism ∗-algebra, which is generated by holonomy-diffeomorphisms on a three-dimensional manifold and translations on a space of SU(2)-connections. We show that this algebra encodes the canonical commutation relations of canonical quantum gravity formulated in terms of Ashtekar variables. Furthermore, we show that semiclassical states exist on the holonomy-diffeomorphism part of the algebra but that these states cannot be extended to the full algebra. Via a Dirac-type operator we derive a certain class of unbounded operators that act in the GNS construction of the semiclassical states. These unbounded operators are the type of operators, which we have previously shown to entail the spatial three-dimensional Dirac operator and Dirac-Hamiltonian in a semiclassical limit. Finally, we show that the structure of the Hamilton constraint emerges from a Yang-Mills-type operator over the space of SU(2)-connections.

Semiclassical magnetotransport in strongly spin-orbit coupled Rashba two-dimensional electron systems.

PubMed

Xiao, Cong; Li, Dingping

2016-06-15

Semiclassical magnetoelectric and magnetothermoelectric transport in strongly spin-orbit coupled Rashba two-dimensional electron systems is investigated. In the presence of a perpendicular classically weak magnetic field and short-range impurity scattering, we solve the linearized Boltzmann equation self-consistently. Using the solution, it is found that when Fermi energy E F locates below the band crossing point (BCP), the Hall coefficient is a nonmonotonic function of electron density n e and not inversely proportional to n e. While the magnetoresistance (MR) and Nernst coefficient vanish when E F locates above the BCP, non-zero MR and enhanced Nernst coefficient emerge when E F decreases below the BCP. Both of them are nonmonotonic functions of E F below the BCP. The different semiclassical magnetotransport behaviors between the two sides of the BCP can be helpful to experimental identifications of the band valley regime and topological change of Fermi surface in considered systems.

Semiclassical magnetotransport in strongly spin-orbit coupled Rashba two-dimensional electron systems

NASA Astrophysics Data System (ADS)

Xiao, Cong; Li, Dingping

2016-06-01

Semiclassical magnetoelectric and magnetothermoelectric transport in strongly spin-orbit coupled Rashba two-dimensional electron systems is investigated. In the presence of a perpendicular classically weak magnetic field and short-range impurity scattering, we solve the linearized Boltzmann equation self-consistently. Using the solution, it is found that when Fermi energy E F locates below the band crossing point (BCP), the Hall coefficient is a nonmonotonic function of electron density n e and not inversely proportional to n e. While the magnetoresistance (MR) and Nernst coefficient vanish when E F locates above the BCP, non-zero MR and enhanced Nernst coefficient emerge when E F decreases below the BCP. Both of them are nonmonotonic functions of E F below the BCP. The different semiclassical magnetotransport behaviors between the two sides of the BCP can be helpful to experimental identifications of the band valley regime and topological change of Fermi surface in considered systems.

Semiclassical evaluation of quantum fidelity

NASA Astrophysics Data System (ADS)

Vaníček, Jiří; Heller, Eric J.

2003-11-01

We present a numerically feasible semiclassical (SC) method to evaluate quantum fidelity decay (Loschmidt echo) in a classically chaotic system. It was thought that such evaluation would be intractable, but instead we show that a uniform SC expression not only is tractable but it also gives remarkably accurate numerical results for the standard map in both the Fermi-golden-rule and Lyapunov regimes. Because it allows Monte Carlo evaluation, the uniform expression is accurate at times when there are 1070 semiclassical contributions. Remarkably, it also explicitly contains the “building blocks” of analytical theories of recent literature, and thus permits a direct test of the approximations made by other authors in these regimes, rather than an a posteriori comparison with numerical results. We explain in more detail the extended validity of the classical perturbation approximation and show that within this approximation, the so-called “diagonal approximation” is automatic and does not require ensemble averaging.

Black hole radiation and S-matrix.

NASA Astrophysics Data System (ADS)

Russo, J. G.

1999-04-01

The existence of an S-matrix below the threshold of black hole formation would be enough to exhibit, through its analytic structure, eventual thresholds for the creation of new objects and to describe, through analytic continuation, the physics above them in a unitary framework. In the context of a two-dimensional exactly soluble model, the semiclassical dynamics of quantum black holes is obtained by analytically continuing the description of the regime where no black hole is formed. The resulting spectrum of outgoing radiation departs from the one predicted by the Hawking model by the time the outgoing modes arise from the horizon with Planck-order frequencies. The theory predicts an unconventional scenario for the evolution: black holes only radiate out an energy of Planck mass order, stabilizing after a transitory period. A similar picture is obtained in 3+1 dimensions with spherical symmetry.

Scale covariance and G-varying cosmology. II - Thermodynamics, radiation, and the 3 K background

NASA Technical Reports Server (NTRS)

Canuto, V. M.; Hsieh, S.-H.

1979-01-01

Within the framework of a scale-covariant theory of gravitation, a semiclassical description of particles and photons is given. Thermodynamic relations consistent with the modified conservation equations are derived. Application to a system of radiation shows that the observed 3-K background radiation can be interpreted, within the present framework, as a remnant of equilibrium radiation in the past. As the theory postulates a nonstandard coupling between gravitation and electrodynamics, the assumption that Einstein's theory of gravitation is unchanged forces modifications at the atomic level. The use of Minkowskian spacetime in atomic physics is found to be adequate only over small, but not large, time scales compared with the age of the universe. As a result, a relation between energy and the frequency of a free photon is demonstrated. Possible observational consequences of this relation are discussed.

Semiclassical spatial correlations in chaotic wave functions.

PubMed

Toscano, Fabricio; Lewenkopf, Caio H

2002-03-01

We study the spatial autocorrelation of energy eigenfunctions psi(n)(q) corresponding to classically chaotic systems in the semiclassical regime. Our analysis is based on the Weyl-Wigner formalism for the spectral average C(epsilon)(q(+),q(-),E) of psi(n)(q(+))psi(*)(n)(q(-)), defined as the average over eigenstates within an energy window epsilon centered at E. In this framework C(epsilon) is the Fourier transform in the momentum space of the spectral Wigner function W(x,E;epsilon). Our study reveals the chord structure that C(epsilon) inherits from the spectral Wigner function showing the interplay between the size of the spectral average window, and the spatial separation scale. We discuss under which conditions is it possible to define a local system independent regime for C(epsilon). In doing so, we derive an expression that bridges the existing formulas in the literature and find expressions for C(epsilon)(q(+),q(-),E) valid for any separation size /q(+)-q(-)/.

Noncommutative gauge theory for Poisson manifolds

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Schupp, Peter; Wess, Julius

2000-09-01

A noncommutative gauge theory is associated to every Abelian gauge theory on a Poisson manifold. The semi-classical and full quantum version of the map from the ordinary gauge theory to the noncommutative gauge theory (Seiberg-Witten map) is given explicitly to all orders for any Poisson manifold in the Abelian case. In the quantum case the construction is based on Kontsevich's formality theorem.

Magnetothermoelectric properties of layered structures for ion impurity scattering

NASA Astrophysics Data System (ADS)

Figarova, S. R.; Huseynov, H. I.; Figarov, V. R.

2018-05-01

In the paper, longitudinal and transverse thermoelectric powers are considered in a magnetic field parallel to the layer plane for scattering of charge carriers by weakly screened impurity ions. Based on the semiclassical approximation, it is obtained that, depending on the position of the Fermi level relative to the miniband top and superlattice period, the thermoelectric power can change sign and amplify.

Counting statistics of chaotic resonances at optical frequencies: Theory and experiments

NASA Astrophysics Data System (ADS)

Lippolis, Domenico; Wang, Li; Xiao, Yun-Feng

2017-07-01

A deformed dielectric microcavity is used as an experimental platform for the analysis of the statistics of chaotic resonances, in the perspective of testing fractal Weyl laws at optical frequencies. In order to surmount the difficulties that arise from reading strongly overlapping spectra, we exploit the mixed nature of the phase space at hand, and only count the high-Q whispering-gallery modes (WGMs) directly. That enables us to draw statistical information on the more lossy chaotic resonances, coupled to the high-Q regular modes via dynamical tunneling. Three different models [classical, Random-Matrix-Theory (RMT) based, semiclassical] to interpret the experimental data are discussed. On the basis of least-squares analysis, theoretical estimates of Ehrenfest time, and independent measurements, we find that a semiclassically modified RMT-based expression best describes the experiment in all its realizations, particularly when the resonator is coupled to visible light, while RMT alone still works quite well in the infrared. In this work we reexamine and substantially extend the results of a short paper published earlier [L. Wang et al., Phys. Rev. E 93, 040201(R) (2016), 10.1103/PhysRevE.93.040201].

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nomura, Yasunori; Salzetta, Nico; Sanches, Fabio

We study the Hilbert space structure of classical spacetimes under the assumption that entanglement in holographic theories determines semiclassical geometry. We show that this simple assumption has profound implications; for example, a superposition of classical spacetimes may lead to another classical spacetime. Despite its unconventional nature, this picture admits the standard interpretation of superpositions of well-defined semiclassical spacetimes in the limit that the number of holographic degrees of freedom becomes large. We illustrate these ideas using a model for the holographic theory of cosmological spacetimes.

Application of semiclassical and geometrical optics theories to resonant modes of a coated sphere.

PubMed

Bambino, Túlio M; Breitschaft, Ana Maria S; Barbosa, Valmar C; Guimarães, Luiz G

2003-03-01

This work deals with some aspects of the resonant scattering of electromagnetic waves by a metallic sphere covered by a dielectric layer, in the weak-absorption approximation. We carry out a geometrical optics treatment of the scattering and develop semiclassical formulas to determine the positions and widths of the system resonances. In addition, we show that the mean lifetime of broad resonances is strongly dependent on the polarization of the incident light.

Coherent and Semiclassical States of a Charged Particle in a Constant Electric Field

NASA Astrophysics Data System (ADS)

Adorno, T. C.; Pereira, A. S.

2018-05-01

The method of integrals of motion is used to construct families of generalized coherent states of a nonrelativistic spinless charged particle in a constant electric field. Families of states, differing in the values of their standard deviations at the initial time, are obtained. Depending on the initial values of the standard deviations, and also on the electric field, it turns out to be possible to identify some families with semiclassical states.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chęcińska, Agata; Heaney, Libby; Pollock, Felix A.

Motivated by a proposed olfactory mechanism based on a vibrationally activated molecular switch, we study electron transport within a donor-acceptor pair that is coupled to a vibrational mode and embedded in a surrounding environment. We derive a polaron master equation with which we study the dynamics of both the electronic and vibrational degrees of freedom beyond previously employed semiclassical (Marcus-Jortner) rate analyses. We show (i) that in the absence of explicit dissipation of the vibrational mode, the semiclassical approach is generally unable to capture the dynamics predicted by our master equation due to both its assumption of one-way (exponential) electronmore » transfer from donor to acceptor and its neglect of the spectral details of the environment; (ii) that by additionally allowing strong dissipation to act on the odorant vibrational mode, we can recover exponential electron transfer, though typically at a rate that differs from that given by the Marcus-Jortner expression; (iii) that the ability of the molecular switch to discriminate between the presence and absence of the odorant, and its sensitivity to the odorant vibrational frequency, is enhanced significantly in this strong dissipation regime, when compared to the case without mode dissipation; and (iv) that details of the environment absent from previous Marcus-Jortner analyses can also dramatically alter the sensitivity of the molecular switch, in particular, allowing its frequency resolution to be improved. Our results thus demonstrate the constructive role dissipation can play in facilitating sensitive and selective operation in molecular switch devices, as well as the inadequacy of semiclassical rate equations in analysing such behaviour over a wide range of parameters.« less

Semiclassical stochastic mechanics for the Coulomb potential with applications to modelling dark matter

NASA Astrophysics Data System (ADS)

Neate, Andrew; Truman, Aubrey

2016-05-01

Little is known about dark matter particles save that their most important interactions with ordinary matter are gravitational and that, if they exist, they are stable, slow moving and relatively massive. Based on these assumptions, a semiclassical approximation to the Schrödinger equation under the action of a Coulomb potential should be relevant for modelling their behaviour. We investigate the semiclassical limit of the Schrödinger equation for a particle of mass M under a Coulomb potential in the context of Nelson's stochastic mechanics. This is done using a Freidlin-Wentzell asymptotic series expansion in the parameter ɛ = √{ ħ / M } for the Nelson diffusion. It is shown that for wave functions ψ ˜ exp((R + iS)/ɛ2) where R and S are real valued, the ɛ = 0 behaviour is governed by a constrained Hamiltonian system with Hamiltonian Hr and constraint Hi = 0 where the superscripts r and i denote the real and imaginary parts of the Bohr correspondence limit of the quantum mechanical Hamiltonian, independent of Nelson's ideas. Nelson's stochastic mechanics is restored in dealing with the nodal surface singularities and by computing (correct to first order in ɛ) the relevant diffusion process in terms of Jacobi fields thereby revealing Kepler's laws in a new light. The key here is that the constrained Hamiltonian system has just two solutions corresponding to the forward and backward drifts in Nelson's stochastic mechanics. We discuss the application of this theory to modelling dark matter particles under the influence of a large gravitating point mass.

Toward a holographic theory for general spacetimes

NASA Astrophysics Data System (ADS)

Nomura, Yasunori; Salzetta, Nico; Sanches, Fabio; Weinberg, Sean J.

2017-04-01

We study a holographic theory of general spacetimes that does not rely on the existence of asymptotic regions. This theory is to be formulated in a holographic space. When a semiclassical description is applicable, the holographic space is assumed to be a holographic screen: a codimension-1 surface that is capable of encoding states of the gravitational spacetime. Our analysis is guided by conjectured relationships between gravitational spacetime and quantum entanglement in the holographic description. To understand basic features of this picture, we catalog predictions for the holographic entanglement structure of cosmological spacetimes. We find that qualitative features of holographic entanglement entropies for such spacetimes differ from those in AdS/CFT but that the former reduce to the latter in the appropriate limit. The Hilbert space of the theory is analyzed, and two plausible structures are found: a direct-sum and "spacetime-equals-entanglement" structure. The former preserves a naive relationship between linear operators and observable quantities, while the latter respects a more direct connection between holographic entanglement and spacetime. We also discuss the issue of selecting a state in quantum gravity, in particular how the state of the multiverse may be selected in the landscape.

Dirac equation in 2-dimensional curved spacetime, particle creation, and coupled waveguide arrays

DOE Office of Scientific and Technical Information (OSTI.GOV)

Koke, Christian, E-mail: christian.koke@stud.uni-heidelberg.de; Noh, Changsuk, E-mail: changsuk@kias.re.kr; Angelakis, Dimitris G., E-mail: dimitris.angelakis@gmail.com

When quantum fields are coupled to gravitational fields, spontaneous particle creation may occur similarly to when they are coupled to external electromagnetic fields. A gravitational field can be incorporated as a background spacetime if the back-action of matter on the field can be neglected, resulting in modifications of the Dirac or Klein–Gordon equations for elementary fermions and bosons respectively. The semi-classical description predicts particle creation in many situations, including the expanding-universe scenario, near the event horizon of a black hole (the Hawking effect), and an accelerating observer in flat spacetime (the Unruh effect). In this work, we give a pedagogicalmore » introduction to the Dirac equation in a general 2D spacetime and show examples of spinor wave packet dynamics in flat and curved background spacetimes. In particular, we cover the phenomenon of particle creation in a time-dependent metric. Photonic analogs of these effects are then proposed, where classical light propagating in an array of coupled waveguides provides a visualisation of the Dirac spinor propagating in a curved 2D spacetime background. The extent to which such a single-particle description can be said to mimic particle creation is discussed.« less

Boundary conditions for the Swain-Schaad relationship as a criterion for hydrogen tunneling.

PubMed

Kohen, Amnon; Jensen, Jan H

2002-04-17

Hydrogen quantum mechanical tunneling has been suggested to play a role in a wide variety of hydrogen-transfer reactions in chemistry and enzymology. An important experimental criterion for tunneling is based on the breakdown of the semiclassical prediction for the relationship among the rates of the three isotopes of hydrogen (hydrogen -H, deuterium -D, and tritium -T). This is denoted the Swain-Schaad relationship. This study examines the breakdown of the Swain-Schaad relationship as criterion for tunneling. The semiclassical (no tunneling) limit used hereto (e.g., 3.34, for H/T to D/T kinetic isotope effects), was based on simple theoretical considerations of a diatomic cleavage of a stable covalent bond, for example, a C-H bond. Yet, most experimental evidence for a tunneling contribution has come from breakdown of those relationship for a secondary hydrogen, that is, not the hydrogen whose bond is being cleaved but its geminal neighbor. Furthermore, many of the reported experiments have been mixed-labeling experiments, in which a secondary H/T kinetic isotope effect was measured for C-H cleavage, while the D/T secondary effect accompanied C-D cleavage. In experiments of this type, the breakdown of the Swain-Schaad relationship indicates both tunneling and the degree of coupled motion between the primary and secondary hydrogens. We found a new semiclassical limit (e.g., 4.8 for H/T to D/T kinetic isotope effects), whose breakdown can serve as a more reliable experimental evidence for tunneling in this common mixed-labeling experiment. We study the tunneling contribution to C-H bond activation, for which many relevant experimental and theoretical data are available. However, these studies can be applied to any hydrogen-transfer reaction. First, an extension of the original approach was applied, and then vibrational analysis studies were carried out for a model system (the enzyme alcohol dehydrogenase). Finally, the effect of complex kinetics on the observed Swain-Schaad relationship was examined. All three methods yield a new semiclassical limit (4.8), above which tunneling must be considered. Yet, it was found that for many cases the original, localized limit (3.34), holds fairly well. For experimental results that are between the original and new limits (within statistical errors), several methods are suggested that can support or exclude tunneling. These new and clearer criteria provide a basis for future applications of the Swain-Schaad relationship to demonstrate tunneling in complex systems.

Sequential Double lonization: The Timing of Release

NASA Astrophysics Data System (ADS)

Pfeiffer, A.

2011-05-01

The timing of electron release in strong field double ionization poses great challenges both for conceptual definition and for conducting experimental measurement. Here we present coincidence momentum measurements of the doubly charged ion and of the two electrons arising from double ionization of Argon using elliptically (close to circularly) polarized laser pulses. Based on a semi-classical model, the ionization times are calculated from the measured electron momenta across a large intensity range. Exploiting the attoclock technique we have direct access to timings on a coarse and on a fine scale, similar to the hour and the minute hand of a clock. In our attoclock, the magnitude of the electron momenta follows the envelope of the laser pulse and gives a coarse timing for the electron releases (the hour hand), while the fine timing (the minute hand) is provided by the emission angle of the electrons. The first of our findings is that due to depletion the averaged ionization time moves towards the beginning of the pulse with increasing intensity, confirming the results of Maharjan et al., and that the ion momentum distribution projected onto the minor polarization axis shows a bifurcation from a 3-peak to a 4-peak structure. This effect can be fully understood by modeling the process semi-classically in the independent electron approximation following the simple man's model. The ionization time measurement performed with the attoclock shows that the release time of the first electron is in good agreement with the semi-classical simulation performed on the basis of Sequential Double lonization (SDI), whereas the ionization of the second electron occurs significantly earlier than predicted. This observation suggests that electron correlation and other Non-Sequential Double lonization (NSDI) mechanisms may play an important role also in the case of strong field double ionization by close-to-circularly polarized laser pulses. The timing of electron release in strong field double ionization poses great challenges both for conceptual definition and for conducting experimental measurement. Here we present coincidence momentum measurements of the doubly charged ion and of the two electrons arising from double ionization of Argon using elliptically (close to circularly) polarized laser pulses. Based on a semi-classical model, the ionization times are calculated from the measured electron momenta across a large intensity range. Exploiting the attoclock technique we have direct access to timings on a coarse and on a fine scale, similar to the hour and the minute hand of a clock. In our attoclock, the magnitude of the electron momenta follows the envelope of the laser pulse and gives a coarse timing for the electron releases (the hour hand), while the fine timing (the minute hand) is provided by the emission angle of the electrons. The first of our findings is that due to depletion the averaged ionization time moves towards the beginning of the pulse with increasing intensity, confirming the results of Maharjan et al., and that the ion momentum distribution projected onto the minor polarization axis shows a bifurcation from a 3-peak to a 4-peak structure. This effect can be fully understood by modeling the process semi-classically in the independent electron approximation following the simple man's model. The ionization time measurement performed with the attoclock shows that the release time of the first electron is in good agreement with the semi-classical simulation performed on the basis of Sequential Double lonization (SDI), whereas the ionization of the second electron occurs significantly earlier than predicted. This observation suggests that electron correlation and other Non-Sequential Double lonization (NSDI) mechanisms may play an important role also in the case of strong field double ionization by close-to-circularly polarized laser pulses. In collaboration with C. Cirelli and M. Smolarski, Physics Department, ETH Zurich, 8093 Zurich, Switzerland; R. Doerner, Institut fiir Kernphysik, Johann Wolfgang Goethe Universitat, 60438 Frankfurt am Main, Germany; and U. Keller, ETH Zurich.

Semiclassical neutral atom as a reference system in density functional theory.

PubMed

Constantin, Lucian A; Fabiano, E; Laricchia, S; Della Sala, F

2011-05-06

We use the asymptotic expansions of the semiclassical neutral atom as a reference system in density functional theory to construct accurate generalized gradient approximations (GGAs) for the exchange-correlation and kinetic energies without any empiricism. These asymptotic functionals are among the most accurate GGAs for molecular systems, perform well for solid state, and overcome current GGA state of the art in frozen density embedding calculations. Our results also provide evidence for the conjointness conjecture between exchange and kinetic energies of atomic systems.

Some semiclassical structure constants for AdS 4 × CP 3

NASA Astrophysics Data System (ADS)

Ahn, Changrim; Bozhilov, Plamen

2018-02-01

We compute structure constants in three-point functions of three string states in AdS 4× CP 3 in the framework of the semiclassical approach. We consider HHL correlation functions where two of the states are "heavy" string states of finite-size giant magnons carrying one or two angular momenta and the other one corresponds to such "light" states as dilaton operators with non-zero momentum, primary scalar operators, and singlet scalar operators with higher string levels.

Relativistic extended Thomas-Fermi calculations with exchange term contributions

NASA Astrophysics Data System (ADS)

Haddad, S.; Weigel, M. K.

1994-10-01

In this investigation we present self-consistent relativistic extended Thomas-Fermi (ETF) and extended Thomas-Fermi-Fock (ETFF) approaches, derived from the semiclassical treatment of the relativistic nuclear Hartree-Fock problem. The approximations are used to describe the ground-state properties of finite nuclei. The resulting equations are solved numerically for several one-boson-exchange (OBE) lagrangians. The results are discussed and compared with the outcome of full quantal Hartree and Hartree-Fock calculations, other semiclassical treatments and experimental data.

Suppression of Bekenstein-Hawking radiation in f(T)-gravity

NASA Astrophysics Data System (ADS)

Addazi, Andrea

2018-01-01

We discuss semiclassical Nariai black holes in the framework of f(T)-gravity. For a diagonal choice of tetrads, stable Nariai metrics can be found, emitting Bekenstein-Hawking radiation in semiclassical limit. However, for a nondiagonal choice of tetrads, evaporation and anti-evaporation instabilities are turned on. In turn, this causes a backreaction effect suppressing the Bekenstein-Hawking radiation. In particular, evaporation instabilities produce a new radiation — different by Bekenstein-Hawking emission — nonviolating unitarity in particle physics sector.

Semiclassical perturbation Stark widths of singly charged argon spectral lines

NASA Astrophysics Data System (ADS)

Hamdi, Rafik; Ben Nessib, Nabil; Sahal-Bréchot, Sylvie; Dimitrijević, Milan S.

2018-03-01

Using a semiclassical perturbation approach with the impact approximation, Stark widths for singly charged argon (Ar II) spectral lines have been calculated. Energy levels and oscillator strengths needed for this calculation have been determined using the Hartree-Fock method with relativistic corrections. Our Stark widths are compared with experimental results for 178 spectral lines. Our results may be of interest not only for laboratory plasma, lasers and technological plasmas but also for white dwarfs and A- and B-type stars.

Quantum Optics in Phase Space

NASA Astrophysics Data System (ADS)

Schleich, Wolfgang P.

2001-04-01

Quantum Optics in Phase Space provides a concise introduction to the rapidly moving field of quantum optics from the point of view of phase space. Modern in style and didactically skillful, Quantum Optics in Phase Space prepares students for their own research by presenting detailed derivations, many illustrations and a large set of workable problems at the end of each chapter. Often, the theoretical treatments are accompanied by the corresponding experiments. An exhaustive list of references provides a guide to the literature. Quantum Optics in Phase Space also serves advanced researchers as a comprehensive reference book. Starting with an extensive review of the experiments that define quantum optics and a brief summary of the foundations of quantum mechanics the author Wolfgang P. Schleich illustrates the properties of quantum states with the help of the Wigner phase space distribution function. His description of waves ala WKB connects semi-classical phase space with the Berry phase. These semi-classical techniques provide deeper insight into the timely topics of wave packet dynamics, fractional revivals and the Talbot effect. Whereas the first half of the book deals with mechanical oscillators such as ions in a trap or atoms in a standing wave the second half addresses problems where the quantization of the radiation field is of importance. Such topics extensively discussed include optical interferometry, the atom-field interaction, quantum state preparation and measurement, entanglement, decoherence, the one-atom maser and atom optics in quantized light fields. Quantum Optics in Phase Space presents the subject of quantum optics as transparently as possible. Giving wide-ranging references, it enables students to study and solve problems with modern scientific literature. The result is a remarkably concise yet comprehensive and accessible text- and reference book - an inspiring source of information and insight for students, teachers and researchers alike.

Quantum diffraction and shielding effects on the low-energy electron-ion bremsstrahlung in two-component semiclassical plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lee, Myoung-Jae; Jung, Young-Dae, E-mail: ydjung@hanyang.ac.kr; Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590

2015-10-15

The quantum diffraction and shielding effects on the low-energy bremsstrahlung process are investigated in two-component semiclassical plasmas. The impact-parameter analysis with the micropotential taking into account the quantum diffraction and shielding effects is employed to obtain the electron-ion bremsstrahlung radiation cross section as a function of the de Broglie wavelength, density parameter, impact parameter, photon energy, and projectile energy. The result shows that the influence of quantum diffraction and shielding strongly suppresses the bremsstrahlung radiation spectrum in semiclassical plasmas. It is found that the quantum diffraction and shielding effects have broaden the photon emission domain. It is also found thatmore » the photon emission domain is almost independent of the radiation photon energy. In addition, it is found that the influence of quantum diffraction and shielding on the bremsstrahlung spectrum decreases with an increase of the projectile energy. The density effect on the electron-ion bremsstrahlung cross section is also discussed.« less

Signature of charge migration in modulations of double ionization

NASA Astrophysics Data System (ADS)

Mauger, François; Abanador, Paul M.; Bruner, Adam; Sissay, Adonay; Gaarde, Mette B.; Lopata, Kenneth; Schafer, Kenneth J.

2018-04-01

We present a theoretical investigation of charge migration following strong-field ionization in a multielectron system. We study a model homonuclear molecule with two electrons, each restricted to one dimension (1 +1 D ), interacting with a strong, static electric field. We show that in this system charge migration results from the interplay between multiple ionization channels that overlap in space, creating a coherent electron-hole wave packet in the cation. We also find that, in our case, charge migration following the first ionization manifests as a modulation of the subsequent double-ionization signal. We derive a parametrized semiclassical model from the full multielectron system and we discuss the importance of the choice of cation electronic-structure basis for the efficacy of the semiclassical representation. We use the ab initio solution of the full 1 +1 D system as a reference for the qualitative and quantitative results of the parametrized semiclassical model. We discuss the extension of our model to long-wavelength time-dependent fields with full-dimension, many-electron targets.

Semi-Classical Models for Virtual Antiparticle Pairs

NASA Technical Reports Server (NTRS)

Batchelor, David; Zukor, Dorothy (Technical Monitor)

2001-01-01

Virtual particle-antiparticle pairs of massive elementary particle& are predicted in Quantum Field Theory (QFT) to appear from the vacuum and annihilate each other again within their Heisenberg lifetimes h/4mc(exp 2). In this work, semiclassical models of this process - for the cases of massive leptons, quarks, and the massive weak bosons W and Z - are constructed. It is shown that the dynamical lifetime of the particle- antiparticle system in each case equals the Heisenberg lifetime to good approximation, and obeys appropriate quantization conditions on the field fluctuation action. In other words, the dynamical lifetime of the semiclassical model agrees with QED and QCD to good approximation. But the formula for the dynamical lifetime in each model includes the force strength coupling constant (e in the lepton case, alpha(sup s) (q(exp 2)) in the quark cases), while the Heisenberg lifetime formula does not. Observing the agreement of the Heisenberg and dynamical lifetimes, we may derive the QED and QCD coupling constants in terms of h, c, and numerical factors only.

Thermal helium clusters at 3.2 Kelvin in classical and semiclassical simulations

NASA Astrophysics Data System (ADS)

Schulte, J.

1993-03-01

The thermodynamic stability of4He4-13 at 3.2 K is investigated with the classical Monte Carlo method, with the semiclassical path-integral Monte Carlo (PIMC) method, and with the semiclassical all-order many-body method. In the all-order many-body simulation the dipole-dipole approximation including short-range correction is used. The resulting stability plots are discussed and related to recent TOF experiments by Stephens and King. It is found that with classical Monte Carlo of course the characteristics of the measured mass spectrum cannot be resolved. With PIMC, switching on more and more quantum mechanics. by raising the number of virtual time steps results in more structure in the stability plot, but this did not lead to sufficient agreement with the TOF experiment. Only the all-order many-body method resolved the characteristic structures of the measured mass spectrum, including magic numbers. The result shows the influence of quantum statistics and quantum mechanics on the stability of small neutral helium clusters.

Communication: Overcoming the root search problem in complex quantum trajectory calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zamstein, Noa; Tannor, David J.

2014-01-28

Three new developments are presented regarding the semiclassical coherent state propagator. First, we present a conceptually different derivation of Huber and Heller's method for identifying complex root trajectories and their equations of motion [D. Huber and E. J. Heller, J. Chem. Phys. 87, 5302 (1987)]. Our method proceeds directly from the time-dependent Schrödinger equation and therefore allows various generalizations of the formalism. Second, we obtain an analytic expression for the semiclassical coherent state propagator. We show that the prefactor can be expressed in a form that requires solving significantly fewer equations of motion than in alternative expressions. Third, the semiclassicalmore » coherent state propagator is used to formulate a final value representation of the time-dependent wavefunction that avoids the root search, eliminates problems with caustics and automatically includes interference. We present numerical results for the 1D Morse oscillator showing that the method may become an attractive alternative to existing semiclassical approaches.« less

Using the thermal Gaussian approximation for the Boltzmann operator in semiclassical initial value time correlation functions.

PubMed

Liu, Jian; Miller, William H

2006-12-14

The thermal Gaussian approximation (TGA) recently developed by Frantsuzov et al. [Chem. Phys. Lett. 381, 117 (2003)] has been demonstrated to be a practical way for approximating the Boltzmann operator exp(-betaH) for multidimensional systems. In this paper the TGA is combined with semiclassical (SC) initial value representations (IVRs) for thermal time correlation functions. Specifically, it is used with the linearized SC-IVR (LSC-IVR, equivalent to the classical Wigner model), and the "forward-backward semiclassical dynamics" approximation developed by Shao and Makri [J. Phys. Chem. A 103, 7753 (1999); 103, 9749 (1999)]. Use of the TGA with both of these approximate SC-IVRs allows the oscillatory part of the IVR to be integrated out explicitly, providing an extremely simple result that is readily applicable to large molecular systems. Calculation of the force-force autocorrelation for a strongly anharmonic oscillator demonstrates its accuracy, and calculation of the velocity autocorrelation function (and thus the diffusion coefficient) of liquid neon demonstrates its applicability.

Semiclassical transport properties of IrGa₃: a promising thermoelectric material.

PubMed

Alvarez Quiceno, Juan Camilo; Dalpian, Gustavo; Fazzio, Adalberto; Osorio-Guillén, Jorge M

2018-01-09

IrGa3 is an intermetallic compound which is expected to be a metal, but a study on the electronic properties of this material to confirm its metallic character is not available in the literature. In this work, we report for the first time a first-principles Density Functional Theory and semiclassical Boltzmann theory study of the structural, electronic and transport properties of this material. The inclusion of the spin-orbit coupling term is crucial to calculate accurately the electronic properties of this compound. We have established that IrGa3 is an indirect semiconductor with a narrow gap of 0.07 eV. From semiclassical Boltzmann transport theory, it is inferred that this material, with the appropriate hole concentration, could have a thermoelectric figure of merit at room temperature comparable to other intermetallic compounds such as FeGa3, though the transport properties of IrGa3 are highly anisotropic. . © 2018 IOP Publishing Ltd.

Semiclassical S-matrix for black holes

DOE PAGES

Bezrukov, Fedor; Levkov, Dmitry; Sibiryakov, Sergey

2015-12-01

In this study, we propose a semiclassical method to calculate S-matrix elements for two-stage gravitational transitions involving matter collapse into a black hole and evaporation of the latter. The method consistently incorporates back-reaction of the collapsing and emitted quanta on the metric. We illustrate the method in several toy models describing spherical self-gravitating shells in asymptotically flat and AdS space-times. We find that electrically neutral shells reflect via the above collapse-evaporation process with probability exp(–B), where B is the Bekenstein-Hawking entropy of the intermediate black hole. This is consistent with interpretation of exp(B) as the number of black hole states.more » The same expression for the probability is obtained in the case of charged shells if one takes into account instability of the Cauchy horizon of the intermediate Reissner-Nordström black hole. As a result, our semiclassical method opens a new systematic approach to the gravitational S-matrix in the non-perturbative regime.« less

Gravitational-Like Lens Based on Graphene Ripple.

PubMed

Liu, Daqing; Chen, Shuyue; Ma, Ning; Zhao, Xiang; Xu, Zhuo

2015-10-01

We conducted a semiclassical study on carrier movement in curved graphene. A previous attempt was made to show that curved graphene is a readily available and cheap laboratory material used to study general relativity effects, especially if the electron energies satisfy 4μeV ≪ |E| ≪ 3eV. Furthermore, a gravitational-like lens can be constructed based on a special graphene ripple; this lens has neither chromatic nor cometic aberration. One can design an ideal electron lens using a graphene ripple.

Event-by-Event Study of Space-Time Dynamics in Flux-Tube Fragmentation

DOE PAGES

Wong, Cheuk-Yin

2017-05-25

In the semi-classical description of the flux-tube fragmentation process for hadron production and hadronization in high-energymore » $e^+e^-$ annihilations and $pp$ collisions, the rapidity-space-time ordering and the local conservation laws of charge, flavor, and momentum provide a set of powerful tools that may allow the reconstruction of the space-time dynamics of quarks and mesons in exclusive measurements of produced hadrons, on an event-by-event basis. We propose procedures to reconstruct the space-time dynamics from event-by-event exclusive hadron data to exhibit explicitly the ordered chain of hadrons produced in a flux tube fragmentation. As a supplementary tool, we infer the average space-time coordinates of the $q$-$$\\bar q$$ pair production vertices from the $$\\pi^-$$ rapidity distribution data obtained by the NA61/SHINE Collaboration in $pp$ collisions at $$\\sqrt{s}$$ = 6.3 to 17.3 GeV.« less

From Computational Photobiology to the Design of Vibrationally Coherent Molecular Devices and Motors

NASA Astrophysics Data System (ADS)

Olivucci, Massimo

2014-03-01

In the past multi-configurational quantum chemical computations coupled with molecular mechanics force fields have been employed to investigate spectroscopic, thermal and photochemical properties of visual pigments. Here we show how the same computational technology can nowadays be used to design, characterize and ultimately, prepare light-driven molecular switches which mimics the photophysics of the visual pigment bovine rhodopsin (Rh). When embedded in the protein cavity the chromophore of Rh undergoes an ultrafast and coherent photoisomerization. In order to design a synthetic chromophore displaying similar properties in common solvents, we recently focused on indanylidene-pyrroline (NAIP) systems. We found that these systems display light-induced ground state coherent vibrational motion similar to the one detected in Rh. Semi-classical trajectories provide a mechanistic description of the structural changes associated to the observed coherent motion which is shown to be ultimately due to periodic changes in the π-conjugation.

Atom transistor from the point of view of nonequilibrium dynamics

NASA Astrophysics Data System (ADS)

Zhang, Z.; Dunjko, V.; Olshanii, M.

2015-12-01

We analyze the atom field-effect transistor scheme (Stickney et al 2007 Phys. Rev. A 75 013608) using the standard tools of quantum and classical nonequlilibrium dynamics. We first study the correspondence between the quantum and the mean-field descriptions of this system by computing, both ab initio and by using their mean-field analogs, the deviations from the Eigenstate Thermalization Hypothesis, quantum fluctuations, and the density of states. We find that, as far as the quantities that interest us, the mean-field model can serve as a semi-classical emulator of the quantum system. Then, using the mean-field model, we interpret the point of maximal output signal in our transistor as the onset of ergodicity—the point where the system becomes, in principle, able to attain the thermal values of the former integrals of motion, albeit not being fully thermalized yet.

Electron transfer from a carbon nanotube into vacuum under high electric fields

NASA Astrophysics Data System (ADS)

Filip, L. D.; Smith, R. C.; Carey, J. D.; Silva, S. R. P.

2009-05-01

The transfer of an electron from a carbon nanotube (CNT) tip into vacuum under a high electric field is considered beyond the usual one-dimensional semi-classical approach. A model of the potential energy outside the CNT cap is proposed in order to show the importance of the intrinsic CNT parameters such as radius, length and vacuum barrier height. This model also takes into account set-up parameters such as the shape of the anode and the anode-to-cathode distance, which are generically portable to any modelling study of electron emission from a tip emitter. Results obtained within our model compare well to experimental data. Moreover, in contrast to the usual one-dimensional Wentzel-Kramers-Brillouin description, our model retains the ability to explain non-standard features of the process of electron field emission from CNTs that arise as a result of the quantum behaviour of electrons on the surface of the CNT.

Angular dependence of novel magnetic quantum oscillations in a quasi-two-dimensional multiband Fermi liquid with impurities

NASA Astrophysics Data System (ADS)

Bratkovsky, A. M.; Alexandrov, A. S.

2002-03-01

The semiclassical Lifshitz-Kosevich-type description is given for the angular dependence of quantum oscillations with combination frequencies in a multiband quasi-two-dimensional Fermi liquid with a constant number of electrons. The analytical expressions are found for the Dingle, thermal, spin, and amplitude (Yamaji) reduction factors of the novel combination harmonics, where the latter two strongly oscillate with the direction of the field [1]. At the magic angles those factors reduce to the purely two-dimensional expressions given earlier. The combination harmonics are suppressed in the presence of the nonquantized background states, and they decay exponentially faster with temperature and/or disorder compared to the standard harmonics, providing an additional tool for electronic structure determination. The theory is applied to Sr2RuO4. [1] A.M. Bratkovsky and A.S. Alexandrov, Phys. Rev. B 65, xxxx (2002); cond-mat/0104520.

Event-by-Event Study of Space-Time Dynamics in Flux-Tube Fragmentation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wong, Cheuk-Yin

In the semi-classical description of the flux-tube fragmentation process for hadron production and hadronization in high-energymore » $e^+e^-$ annihilations and $pp$ collisions, the rapidity-space-time ordering and the local conservation laws of charge, flavor, and momentum provide a set of powerful tools that may allow the reconstruction of the space-time dynamics of quarks and mesons in exclusive measurements of produced hadrons, on an event-by-event basis. We propose procedures to reconstruct the space-time dynamics from event-by-event exclusive hadron data to exhibit explicitly the ordered chain of hadrons produced in a flux tube fragmentation. As a supplementary tool, we infer the average space-time coordinates of the $q$-$$\\bar q$$ pair production vertices from the $$\\pi^-$$ rapidity distribution data obtained by the NA61/SHINE Collaboration in $pp$ collisions at $$\\sqrt{s}$$ = 6.3 to 17.3 GeV.« less

Nonadiabatic Molecular Dynamics and Orthogonality Constrained Density Functional Theory

NASA Astrophysics Data System (ADS)

Shushkov, Philip Georgiev

The exact quantum dynamics of realistic, multidimensional systems remains a formidable computational challenge. In many chemical processes, however, quantum effects such as tunneling, zero-point energy quantization, and nonadiabatic transitions play an important role. Therefore, approximate approaches that improve on the classical mechanical framework are of special practical interest. We propose a novel ring polymer surface hopping method for the calculation of chemical rate constants. The method blends two approaches, namely ring polymer molecular dynamics that accounts for tunneling and zero-point energy quantization, and surface hopping that incorporates nonadiabatic transitions. We test the method against exact quantum mechanical calculations for a one-dimensional, two-state model system. The method reproduces quite accurately the tunneling contribution to the rate and the distribution of reactants between the electronic states for this model system. Semiclassical instanton theory, an approach related to ring polymer molecular dynamics, accounts for tunneling by the use of periodic classical trajectories on the inverted potential energy surface. We study a model of electron transfer in solution, a chemical process where nonadiabatic events are prominent. By representing the tunneling electron with a ring polymer, we derive Marcus theory of electron transfer from semiclassical instanton theory after a careful analysis of the tunneling mode. We demonstrate that semiclassical instanton theory can recover the limit of Fermi's Golden Rule rate in a low-temperature, deep-tunneling regime. Mixed quantum-classical dynamics treats a few important degrees of freedom quantum mechanically, while classical mechanics describes affordably the rest of the system. But the interface of quantum and classical description is a challenging theoretical problem, especially for low-energy chemical processes. We therefore focus on the semiclassical limit of the coupled nuclear-electronic dynamics. We show that the time-dependent Schrodinger equation for the electrons employed in the widely used fewest switches surface hopping method is applicable only in the limit of nearly identical classical trajectories on the different potential energy surfaces. We propose a short-time decoupling algorithm that restricts the use of the Schrodinger equation only to the interaction regions. We test the short-time approximation on three model systems against exact quantum-mechanical calculations. The approximation improves the performance of the surface hopping approach. Nonadiabatic molecular dynamics simulations require the efficient and accurate computation of ground and excited state potential energy surfaces. Unlike the ground state calculations where standard methods exist, the computation of excited state properties is a challenging task. We employ time-independent density functional theory, in which the excited state energy is represented as a functional of the total density. We suggest an adiabatic-like approximation that simplifies the excited state exchange-correlation functional. We also derive a set of minimal conditions to impose exactly the orthogonality of the excited state Kohn-Sham determinant to the ground state determinant. This leads to an efficient, variational algorithm for the self-consistent optimization of the excited state energy. Finally, we assess the quality of the excitation energies obtained by the new method on a set of 28 organic molecules. The new approach provides results of similar accuracy to time-dependent density functional theory.

An open-chain imaginary-time path-integral sampling approach to the calculation of approximate symmetrized quantum time correlation functions.

PubMed

Cendagorta, Joseph R; Bačić, Zlatko; Tuckerman, Mark E

2018-03-14

We introduce a scheme for approximating quantum time correlation functions numerically within the Feynman path integral formulation. Starting with the symmetrized version of the correlation function expressed as a discretized path integral, we introduce a change of integration variables often used in the derivation of trajectory-based semiclassical methods. In particular, we transform to sum and difference variables between forward and backward complex-time propagation paths. Once the transformation is performed, the potential energy is expanded in powers of the difference variables, which allows us to perform the integrals over these variables analytically. The manner in which this procedure is carried out results in an open-chain path integral (in the remaining sum variables) with a modified potential that is evaluated using imaginary-time path-integral sampling rather than requiring the generation of a large ensemble of trajectories. Consequently, any number of path integral sampling schemes can be employed to compute the remaining path integral, including Monte Carlo, path-integral molecular dynamics, or enhanced path-integral molecular dynamics. We believe that this approach constitutes a different perspective in semiclassical-type approximations to quantum time correlation functions. Importantly, we argue that our approximation can be systematically improved within a cumulant expansion formalism. We test this approximation on a set of one-dimensional problems that are commonly used to benchmark approximate quantum dynamical schemes. We show that the method is at least as accurate as the popular ring-polymer molecular dynamics technique and linearized semiclassical initial value representation for correlation functions of linear operators in most of these examples and improves the accuracy of correlation functions of nonlinear operators.

An open-chain imaginary-time path-integral sampling approach to the calculation of approximate symmetrized quantum time correlation functions

NASA Astrophysics Data System (ADS)

Cendagorta, Joseph R.; Bačić, Zlatko; Tuckerman, Mark E.

2018-03-01

We introduce a scheme for approximating quantum time correlation functions numerically within the Feynman path integral formulation. Starting with the symmetrized version of the correlation function expressed as a discretized path integral, we introduce a change of integration variables often used in the derivation of trajectory-based semiclassical methods. In particular, we transform to sum and difference variables between forward and backward complex-time propagation paths. Once the transformation is performed, the potential energy is expanded in powers of the difference variables, which allows us to perform the integrals over these variables analytically. The manner in which this procedure is carried out results in an open-chain path integral (in the remaining sum variables) with a modified potential that is evaluated using imaginary-time path-integral sampling rather than requiring the generation of a large ensemble of trajectories. Consequently, any number of path integral sampling schemes can be employed to compute the remaining path integral, including Monte Carlo, path-integral molecular dynamics, or enhanced path-integral molecular dynamics. We believe that this approach constitutes a different perspective in semiclassical-type approximations to quantum time correlation functions. Importantly, we argue that our approximation can be systematically improved within a cumulant expansion formalism. We test this approximation on a set of one-dimensional problems that are commonly used to benchmark approximate quantum dynamical schemes. We show that the method is at least as accurate as the popular ring-polymer molecular dynamics technique and linearized semiclassical initial value representation for correlation functions of linear operators in most of these examples and improves the accuracy of correlation functions of nonlinear operators.

Quantum Tunneling from Apparent Horizon of Rainbow-FRW Universe

NASA Astrophysics Data System (ADS)

Lin, Kai; Yang, Shuzheng

2009-07-01

The quantum tunneling from the apparent horizon of rainbow-FRW universe is studied in this paper. We apply the semi-classical approximation, which is put forward by Parikh and Wilczek et al., to research on the scalar field particles tunneling from the apparent horizon of the rainbow-FRW universe, and then use the spin 1/2 Fermions tunneling theory, which brought forward by Kerner and Mann firstly, to research on the Fermions Hawking radiation via semi-classical approximation. Finally, we discuss the meanings of the quantum effect via Finsler geometry.

Semi-classical Reissner-Nordstrom model for the structure of charged leptons

NASA Technical Reports Server (NTRS)

Rosen, G.

1980-01-01

The lepton self-mass problem is examined within the framework of the quantum theory of electromagnetism and gravity. Consideration is given to the Reissner-Nordstrom solution to the Einstein-Maxwell classical field equations for an electrically charged mass point, and the WKB theory for a semiclassical system with total energy zero is used to obtain an expression for the Einstein-Maxwell action factor. The condition obtained is found to account for the observed mass values of the three charged leptons, and to be in agreement with the correspondence principle.

Semiclassical gravitoelectromagnetic inflation in a Lorentz gauge: Seminal inflaton fluctuations and electromagnetic fields from a 5D vacuum state

NASA Astrophysics Data System (ADS)

Membiela, Federico Agustín; Bellini, Mauricio

2010-02-01

Using a semiclassical approach to Gravitoelectromagnetic Inflation (GEMI), we study the origin and evolution of seminal inflaton and electromagnetic fields in the early inflationary universe from a 5D vacuum state. The difference with other previous works is that in this one we use a Lorentz gauge. Our formalism is naturally not conformal invariant on the effective 4D de Sitter metric, which make possible the super adiabatic amplification of magnetic field modes during the early inflationary epoch of the universe on cosmological scales.

Semi-classical Electrodynamics

NASA Astrophysics Data System (ADS)

Lestone, John

2016-03-01

Quantum electrodynamics is complex and its associated mathematics can appear overwhelming for those not trained in this field. We describe semi-classical approaches that can be used to obtain a more intuitive physical feel for several QED processes including electro-statics, Compton scattering, pair annihilation, the anomalous magnetic moment, and the Lamb shift, that could be taught easily to undergraduate students. Any physicist who brings their laptop to the talk will be able to build spread sheets in less than 10 minutes to calculate g/2 =1.001160 and a Lamb shift of 1057 MHz.

On the semiclassical treatment of hot nuclear systems

NASA Astrophysics Data System (ADS)

Bartel, J.; Brack, M.; Guet, C.; Håkansson, H.-B.

1984-05-01

We discuss two different semiclassical approaches for calculating properties of hot nuclei and compare them to Hartree-Fock calculations using the same effective interaction. Good agreement is found for the entropy and the root-mean square radii as functions of the excitation energy. For a realistic Skyrme force we evaluate the temperature dependence of the free surface, curvature and constant energy coefficients of the liquid drop model, considering a plane interface of condensed symmetric nuclear matter in thermodynamical equilibrium with a nucleon gas. Present address: ASEA-PFBC AB, S-61220 Finspong, Sweden.

Simulation of vibrational dephasing of I(2) in solid Kr using the semiclassical Liouville method.

PubMed

Riga, Jeanne M; Fredj, Erick; Martens, Craig C

2006-02-14

In this paper, we present simulations of the decay of quantum coherence between vibrational states of I(2) in its ground (X) electronic state embedded in a cryogenic Kr matrix. We employ a numerical method based on the semiclassical limit of the quantum Liouville equation, which allows the simulation of the evolution and decay of quantum vibrational coherence using classical trajectories and ensemble averaging. The vibrational level-dependent interaction of the I(2)(X) oscillator with the rare-gas environment is modeled using a recently developed method for constructing state-dependent many-body potentials for quantum vibrations in a many-body classical environment [J. M. Riga, E. Fredj, and C. C. Martens, J. Chem. Phys. 122, 174107 (2005)]. The vibrational dephasing rates gamma(0n) for coherences prepared between the ground vibrational state mid R:0 and excited vibrational state mid R:n are calculated as a function of n and lattice temperature T. Excellent agreement with recent experiments performed by Karavitis et al. [Phys. Chem. Chem. Phys. 7, 791 (2005)] is obtained.

Thermoelectric properties of fully hydrogenated graphene: Semi-classical Boltzmann theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Reshak, A. H., E-mail: maalidph@yahoo.co.uk; Center of Excellence Geopolymer and Green Technology, School of Material Engineering, University Malaysia Perlis, 01007 Kangar, Perlis

2015-06-14

Based on the calculated band structure, the electronic transport coefficients of chair-/boat-like graphane were evaluated by using the semi-classical Boltzmann theory and rigid band model. The maximum value of electrical conductivity for chair (boat)-like graphane of about 1.4 (0.6) × 10{sup 19} (Ωms){sup −1} is achieved at 600 K. The charge carrier concentration and the electrical conductivity linearly increase with increasing the temperature in agreement with the experimental work for graphene. The investigated materials exhibit the highest value of Seebeck coefficient at 300 K. We should emphasize that in the chemical potential between ∓0.125 μ(eV) the investigated materials exhibit minimum value of electronic thermalmore » conductivity, therefore, maximum efficiency. As the temperature increases, the electronic thermal conductivity increases exponentially, in agreement with the experimental data of graphene. We also calculated the power factor of chair-/boat-like graphane at 300 and 600 K as a function of chemical potential between ∓0.25 μ(eV)« less

A modification of \\mathsf {WKB} method for fractional differential operators of Schrödinger's type

NASA Astrophysics Data System (ADS)

Sayevand, K.; Pichaghchi, K.

2017-09-01

In this paper, we were concerned with the description of the singularly perturbed differential equations within the scope of fractional calculus. However, we shall note that one of the main methods used to solve these problems is the so-called WKB method. We should mention that this was not achievable via the existing fractional derivative definitions, because they do not obey the chain rule. In order to accommodate the WKB to the scope of fractional derivative, we proposed a relatively new derivative called the local fractional derivative. By use of properties of local fractional derivative, we extend the WKB method in the scope of the fractional differential equation. By means of this extension, the WKB analysis based on the Borel resummation, for fractional differential operators of WKB type are investigated. The convergence and the Mittag-Leffler stability of the proposed approach is proven. The obtained results are in excellent agreement with the existing ones in open literature and it is shown that the present approach is very effective and accurate. Furthermore, we are mainly interested to construct the solution of fractional Schrödinger equation in the Mittag-Leffler form and how it leads naturally to this semi-classical approximation namely modified WKB.

On the initial singularity problem in rainbow cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Santos, Grasiele; Gubitosi, Giulia; Amelino-Camelia, Giovanni, E-mail: grasiele.dossantos@icranet.org, E-mail: g.gubitosi@imperial.ac.uk, E-mail: giovanni.amelino-camelia@roma1.infn.it

2015-08-01

It has been recently claimed that the initial singularity might be avoided in the context of rainbow cosmology, where one attempts to account for quantum-gravitational corrections through an effective-theory description based on an energy-dependent ('rainbow') spacetime metric. We here scrutinize this exciting hypothesis much more in depth than previous analyses. In particular, we take into account all requirements for singularity avoidance, while previously only a subset of these requirements had been considered. Moreover, we show that the implications of a rainbow metric for thermodynamics are more significant than previously appreciated. Through the analysis of two particularly meaningful examples of rainbowmore » metrics we find that our concerns are not merely important conceptually, but actually change in quantitatively significant manner the outcome of the analysis. Notably we only find examples where the singularity is not avoided, though one can have that in the regime where our semi-classical picture is still reliable the approach to the singularity is slowed down when compared to the standard classical scenario. We conclude that the study of rainbow metrics provides tantalizing hints of singularity avoidance but is inconclusive, since some key questions remain to be addressed just when the scale factor is very small, a regime which, as here argued, cannot be reliably described by an effective rainbow-metric picture.« less

Generalization of the coherent-state path integrals and systematic derivation of semiclassical propagators

DOE Office of Scientific and Technical Information (OSTI.GOV)

Koda, Shin-ichi; Takatsuka, Kazuo

The coherent path integral is generalized such that the identity operator represented in a complete (actually overcomplete) set of the coherent states with the ''time-variable'' exponents are inserted between two consecutive short-time propagators. Since such a complete set of any given exponent can constitute the identity operator, the exponent may be varied from time to time without loss of generality as long as it is set common to all the Gaussians. However, a finite truncation of the coherent state expansion should result in different values of the propagator depending on the choice of the exponents. Furthermore, approximation methodology to treatmore » with the exact propagator can also depend on this choice, and thereby many different semiclassical propagators may emerge from these combinations. Indeed, we show that the well-known semiclassical propagators such as those of Van Vleck, Herman-Kluk, Heller's thawed Gaussian, and many others can be derived in a systematic manner, which enables one to comprehend these semiclassical propagators from a unified point of view. We are particularly interested in our generalized form of the Herman-Kluk propagator, since the relative accuracy of this propagator has been well established by Kay, and since, nevertheless, its derivation was not necessarily clear. Thus our generalized Herman-Kluk propagator replaces the classical Hamiltonian with a Gaussian averaged quantum Hamiltonian, generating non-Newtonian trajectories. We perform a numerical test to assess the quality of such a family of generalized Herman-Kluk propagators and find that the original Herman-Kluk gives an accurate result. The reason why this has come about is also discussed.« less

Non-Condon equilibrium Fermi’s golden rule electronic transition rate constants via the linearized semiclassical method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sun, Xiang; Geva, Eitan

2016-06-28

In this paper, we test the accuracy of the linearized semiclassical (LSC) expression for the equilibrium Fermi’s golden rule rate constant for electronic transitions in the presence of non-Condon effects. We do so by performing a comparison with the exact quantum-mechanical result for a model where the donor and acceptor potential energy surfaces are parabolic and identical except for shifts in the equilibrium energy and geometry, and the coupling between them is linear in the nuclear coordinates. Since non-Condon effects may or may not give rise to conical intersections, both possibilities are examined by considering: (1) A modified Garg-Onuchic-Ambegaokar modelmore » for charge transfer in the condensed phase, where the donor-acceptor coupling is linear in the primary mode coordinate, and for which non-Condon effects do not give rise to a conical intersection; (2) the linear vibronic coupling model for electronic transitions in gas phase molecules, where non-Condon effects give rise to conical intersections. We also present a comprehensive comparison between the linearized semiclassical expression and a progression of more approximate expressions. The comparison is performed over a wide range of frictions and temperatures for model (1) and over a wide range of temperatures for model (2). The linearized semiclassical method is found to reproduce the exact quantum-mechanical result remarkably well for both models over the entire range of parameters under consideration. In contrast, more approximate expressions are observed to deviate considerably from the exact result in some regions of parameter space.« less

Semiclassical Wigner theory of photodissociation in three dimensions: Shedding light on its basis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arbelo-González, W.; CNRS, Institut des Sciences Moléculaires, UMR 5255, 33405 Talence; Université Bordeaux, Institut des Sciences Moléculaires, UMR 5255, 33405 Talence

2015-04-07

The semiclassical Wigner theory (SCWT) of photodissociation dynamics, initially proposed by Brown and Heller [J. Chem. Phys. 75, 186 (1981)] in order to describe state distributions in the products of direct collinear photodissociations, was recently extended to realistic three-dimensional triatomic processes of the same type [Arbelo-González et al., Phys. Chem. Chem. Phys. 15, 9994 (2013)]. The resulting approach, which takes into account rotational motions in addition to vibrational and translational ones, was applied to a triatomic-like model of methyl iodide photodissociation and its predictions were found to be in nearly quantitative agreement with rigorous quantum results, but at a muchmore » lower computational cost, making thereby SCWT a potential tool for the study of polyatomic reaction dynamics. Here, we analyse the main reasons for this agreement by means of an elementary model of fragmentation explicitly dealing with the rotational motion only. We show that our formulation of SCWT makes it a semiclassical approximation to an approximate planar quantum treatment of the dynamics, both of sufficient quality for the whole treatment to be satisfying.« less

The state of Hawking radiation is non-classical

NASA Astrophysics Data System (ADS)

Brustein, Ram; Medved, A. J. M.; Zigdon, Yoav

2018-01-01

We show that the state of the Hawking radiation emitted from a large Schwarzschild black hole (BH) deviates significantly from a classical state, in spite of its apparent thermal nature. For this state, the occupation numbers of single modes of massless asymptotic fields, such as photons, gravitons and possibly neutrinos, are small and, as a result, their relative fluctuations are large. The occupation numbers of massive fields are much smaller and suppressed beyond even the expected Boltzmann suppression. It follows that this type of thermal state cannot be viewed as classical or even semiclassical. We substantiate this claim by showing that, in a state with low occupation numbers, physical observables have large quantum fluctuations and, as such, cannot be faithfully described by a mean-field or by a WKB-like semiclassical state. Since the evolution of the BH is unitary, our results imply that the state of the BH interior must also be non-classical when described in terms of the asymptotic fields. We show that such a non-classical interior cannot be described in terms of a semiclassical geometry, even though the average curvature is sub-Planckian.

Barrier modification in sub-barrier fusion reaction 64Ni+100Mo using Wong formula with Skyrme forces in semiclassical formalism

NASA Astrophysics Data System (ADS)

Kumar, Raj; Gupta, Raj K.

2011-09-01

We obtain the nuclear proximity potential by using semiclassical extended Thomas Fermi (ETF) approach in Skyrme energy density formalism (SEDF), and use it in the extended l-summed Wong formula under frozen density approximation. This method has the advantage of allowing the use of different Skyrme forces, giving different barriers. Thus, for a given reaction, we could choose a Skyrme force with proper barrier characteristics, not-requiring extra "barrier lowering" or "barrier narrowing" for a best fit to data. For the 64Ni+100Mo reaction, the l-summed Wong formula, with effects of deformations and orientations of nuclei included, fits the fusion-evaporation cross section data exactly for the force GSkI, requiring additional barrier modifications for forces SIII and SV. However, the same for other similar reactions, like 58,64Ni+58,64Ni, fit the data best for SIII force. Hence, the barrier modification effects in l-summed Wong expression depend on the choice of Skyrme force in semiclassical ETF method.

Semiclassical regularization of Vlasov equations and wavepackets for nonlinear Schrödinger equations

NASA Astrophysics Data System (ADS)

Athanassoulis, Agissilaos

2018-03-01

We consider the semiclassical limit of nonlinear Schrödinger equations with initial data that are well localized in both position and momentum (non-parametric wavepackets). We recover the Wigner measure (WM) of the problem, a macroscopic phase-space density which controls the propagation of the physical observables such as mass, energy and momentum. WMs have been used to create effective models for wave propagation in: random media, quantum molecular dynamics, mean field limits, and the propagation of electrons in graphene. In nonlinear settings, the Vlasov-type equations obtained for the WM are often ill-posed on the physically interesting spaces of initial data. In this paper we are able to select the measure-valued solution of the 1  +  1 dimensional Vlasov-Poisson equation which correctly captures the semiclassical limit, thus finally resolving the non-uniqueness in the seminal result of Zhang et al (2012 Comm. Pure Appl. Math. 55 582-632). The same approach is also applied to the Vlasov-Dirac-Benney equation with small wavepacket initial data, extending several known results.

Numerical solutions of the semiclassical Boltzmann ellipsoidal-statistical kinetic model equation

PubMed Central

Yang, Jaw-Yen; Yan, Chin-Yuan; Huang, Juan-Chen; Li, Zhihui

2014-01-01

Computations of rarefied gas dynamical flows governed by the semiclassical Boltzmann ellipsoidal-statistical (ES) kinetic model equation using an accurate numerical method are presented. The semiclassical ES model was derived through the maximum entropy principle and conserves not only the mass, momentum and energy, but also contains additional higher order moments that differ from the standard quantum distributions. A different decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. The numerical method in phase space combines the discrete-ordinate method in momentum space and the high-resolution shock capturing method in physical space. Numerical solutions of two-dimensional Riemann problems for two configurations covering various degrees of rarefaction are presented and various contours of the quantities unique to this new model are illustrated. When the relaxation time becomes very small, the main flow features a display similar to that of ideal quantum gas dynamics, and the present solutions are found to be consistent with existing calculations for classical gas. The effect of a parameter that permits an adjustable Prandtl number in the flow is also studied. PMID:25104904

Distribution of eigenfrequencies for oscillations of the ground state in the Thomas-Fermi limit

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kevrekidis, P. G.; Pelinovsky, D. E.

In this work, we present a systematic derivation of the distribution of eigenfrequencies for oscillations of the ground state of a repulsive Bose-Einstein condensate in the semi-classical (Thomas-Fermi) limit. Our calculations are performed in one, two, and three-dimensional settings. Connections with the earlier work of Stringari, with numerical computations, and with theoretical expectations for invariant frequencies based on symmetry principles are also given.

Approximate solution to the Callan-Giddings-Harvey-Strominger field equations for two-dimensional evaporating black holes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ori, Amos

2010-11-15

Callan, Giddings, Harvey, and Strominger (CGHS) previously introduced a two-dimensional semiclassical model of gravity coupled to a dilaton and to matter fields. Their model yields a system of field equations which may describe the formation of a black hole in gravitational collapse as well as its subsequent evaporation. Here we present an approximate analytical solution to the semiclassical CGHS field equations. This solution is constructed using the recently introduced formalism of flux-conserving hyperbolic systems. We also explore the asymptotic behavior at the horizon of the evaporating black hole.

Mean-trajectory approximation for electronic and vibrational-electronic nonlinear spectroscopy

NASA Astrophysics Data System (ADS)

Loring, Roger F.

2017-04-01

Mean-trajectory approximations permit the calculation of nonlinear vibrational spectra from semiclassically quantized trajectories on a single electronically adiabatic potential surface. By describing electronic degrees of freedom with classical phase-space variables and subjecting these to semiclassical quantization, mean-trajectory approximations may be extended to compute both nonlinear electronic spectra and vibrational-electronic spectra. A general mean-trajectory approximation for both electronic and nuclear degrees of freedom is presented, and the results for purely electronic and for vibrational-electronic four-wave mixing experiments are quantitatively assessed for harmonic surfaces with linear electronic-nuclear coupling.

Scale-invariant curvature fluctuations from an extended semiclassical gravity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pinamonti, Nicola, E-mail: pinamont@dima.unige.it, E-mail: siemssen@dima.unige.it; INFN Sezione di Genova, Via Dodecaneso 33, 16146 Genova; Siemssen, Daniel, E-mail: pinamont@dima.unige.it, E-mail: siemssen@dima.unige.it

2015-02-15

We present an extension of the semiclassical Einstein equations which couple n-point correlation functions of a stochastic Einstein tensor to the n-point functions of the quantum stress-energy tensor. We apply this extension to calculate the quantum fluctuations during an inflationary period, where we take as a model a massive conformally coupled scalar field on a perturbed de Sitter space and describe how a renormalization independent, almost-scale-invariant power spectrum of the scalar metric perturbation is produced. Furthermore, we discuss how this model yields a natural basis for the calculation of non-Gaussianities of the considered metric fluctuations.

Subdiffraction incoherent optical imaging via spatial-mode demultiplexing: Semiclassical treatment

NASA Astrophysics Data System (ADS)

Tsang, Mankei

2018-02-01

I present a semiclassical analysis of a spatial-mode demultiplexing (SPADE) measurement scheme for far-field incoherent optical imaging under the effects of diffraction and photon shot noise. Building on previous results that assume two point sources or the Gaussian point-spread function, I generalize SPADE for a larger class of point-spread functions and evaluate its errors in estimating the moments of an arbitrary subdiffraction object. Compared with the limits to direct imaging set by the Cramér-Rao bounds, the results show that SPADE can offer far superior accuracy in estimating second- and higher-order moments.

Swings and roundabouts: optical Poincaré spheres for polarization and Gaussian beams

NASA Astrophysics Data System (ADS)

Dennis, M. R.; Alonso, M. A.

2017-02-01

The connection between Poincaré spheres for polarization and Gaussian beams is explored, focusing on the interpretation of elliptic polarization in terms of the isotropic two-dimensional harmonic oscillator in Hamiltonian mechanics, its canonical quantization and semiclassical interpretation. This leads to the interpretation of structured Gaussian modes, the Hermite-Gaussian, Laguerre-Gaussian and generalized Hermite-Laguerre-Gaussian modes as eigenfunctions of operators corresponding to the classical constants of motion of the two-dimensional oscillator, which acquire an extra significance as families of classical ellipses upon semiclassical quantization. This article is part of the themed issue 'Optical orbital angular momentum'.

Can Black Hole Relax Unitarily?

NASA Astrophysics Data System (ADS)

Solodukhin, S. N.

2005-03-01

We review the way the BTZ black hole relaxes back to thermal equilibrium after a small perturbation and how it is seen in the boundary (finite volume) CFT. The unitarity requires the relaxation to be quasi-periodic. It is preserved in the CFT but is not obvious in the case of the semiclassical black hole the relaxation of which is driven by complex quasi-normal modes. We discuss two ways of modifying the semiclassical black hole geometry to maintain unitarity: the (fractal) brick wall and the worm-hole modification. In the latter case the entropy comes out correctly as well.

Elastic scattering of low energy electrons in partially ionized dense semiclassical plasma

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dzhumagulova, K. N., E-mail: dzhumagulova.karlygash@gmail.com; Shalenov, E. O.; Ramazanov, T. S.

2015-08-15

Elastic scattering of electrons by hydrogen atoms in a dense semiclassical hydrogen plasma for low impact energies has been studied. Differential scattering cross sections were calculated within the effective model of electron-atom interaction taking into account the effect of screening as well as the quantum mechanical effect of diffraction. The calculations were carried out on the basis of the phase-function method. The influence of the diffraction effect on the Ramsauer–Townsend effect was studied on the basis of a comparison with results made within the effective polarization model of the Buckingham type.

On the semi-classical limit of scalar products of the XXZ spin chain

NASA Astrophysics Data System (ADS)

Jiang, Yunfeng; Brunekreef, Joren

2017-03-01

We study the scalar products between Bethe states in the XXZ spin chain with anisotropy |Δ| > 1 in the semi-classical limit where the length of the spin chain and the number of magnons tend to infinity with their ratio kept finite and fixed. Our method is a natural yet non-trivial generalization of similar methods developed for the XXX spin chain. The final result can be written in a compact form as a contour integral in terms of Faddeev's quantum dilogarithm function, which in the isotropic limit reduces to the classical dilogarithm function.

Semiclassical analysis for pseudo-relativistic Hartree equations

NASA Astrophysics Data System (ADS)

Cingolani, Silvia; Secchi, Simone

2015-06-01

In this paper we study the semiclassical limit for the pseudo-relativistic Hartree equation $\\sqrt{-\\varepsilon^2 \\Delta + m^2}u + V u = (I_\\alpha * |u|^{p}) |u|^{p-2}u$ in $\\mathbb{R}^N$ where $m>0$, $2 \\leq p < \\frac{2N}{N-1}$, $V \\colon \\mathbb{R}^N \\to \\mathbb{R}$ is an external scalar potential, $I_\\alpha (x) = \\frac{c_{N,\\alpha}}{|x|^{N-\\alpha}}$ is a convolution kernel, $c_{N,\\alpha}$ is a positive constant and $(N-1)p-N<\\alpha

The quantum N-body problem in the mean-field and semiclassical regime

NASA Astrophysics Data System (ADS)

Golse, François

2018-04-01

The present work discusses the mean-field limit for the quantum N-body problem in the semiclassical regime. More precisely, we establish a convergence rate for the mean-field limit which is uniform as the ratio of Planck constant to the action of the typical single particle tends to zero. This convergence rate is formulated in terms of a quantum analogue of the quadratic Monge-Kantorovich or Wasserstein distance. This paper is an account of some recent collaboration with C. Mouhot, T. Paul and M. Pulvirenti. This article is part of the themed issue `Hilbert's sixth problem'.

Mixed semiclassical-classical propagators for the Wigner phase space representation

NASA Astrophysics Data System (ADS)

Koda, Shin-ichi

2016-04-01

We formulate mixed semiclassical-classical (SC-Cl) propagators by adding a further approximation to the phase-space SC propagators, which have been formulated in our previous paper [S. Koda, J. Chem. Phys. 143, 244110 (2015)]. We first show that the stationary phase approximation over the operation of the phase-space van Vleck propagator on initial distribution functions results in the classical mechanical time propagation. Then, after dividing the degrees of freedom (DOFs) of the total system into the semiclassical DOFs and the classical DOFs, the SC-Cl van Vleck propagator and the SC-Cl Herman-Kluk (HK) propagator are derived by performing the stationary phase approximation only with respect to the classical DOFs. These SC-Cl propagators are naturally decomposed to products of the phase-space SC propagators and the classical mechanical propagators when the system does not have any interaction between the semiclassical and the classical DOFs. In addition, we also numerically compare the original phase-space HK (full HK) propagator and the SC-Cl HK propagator in terms of accuracy and efficiency to find that the accuracy of the SC-Cl HK propagator can be comparable to that of the full HK propagator although the latter is more accurate than the former in general. On the other hand, we confirm that the convergence speed of the SC-Cl HK propagator is faster than that of the full HK propagator. The present numerical tests indicate that the SC-Cl HK propagator can be more accurate than the full HK propagator when they use a same and finite number of classical trajectories due to the balance of the accuracy and the efficiency.

Mixed semiclassical-classical propagators for the Wigner phase space representation.

PubMed

Koda, Shin-Ichi

2016-04-21

We formulate mixed semiclassical-classical (SC-Cl) propagators by adding a further approximation to the phase-space SC propagators, which have been formulated in our previous paper [S. Koda, J. Chem. Phys. 143, 244110 (2015)]. We first show that the stationary phase approximation over the operation of the phase-space van Vleck propagator on initial distribution functions results in the classical mechanical time propagation. Then, after dividing the degrees of freedom (DOFs) of the total system into the semiclassical DOFs and the classical DOFs, the SC-Cl van Vleck propagator and the SC-Cl Herman-Kluk (HK) propagator are derived by performing the stationary phase approximation only with respect to the classical DOFs. These SC-Cl propagators are naturally decomposed to products of the phase-space SC propagators and the classical mechanical propagators when the system does not have any interaction between the semiclassical and the classical DOFs. In addition, we also numerically compare the original phase-space HK (full HK) propagator and the SC-Cl HK propagator in terms of accuracy and efficiency to find that the accuracy of the SC-Cl HK propagator can be comparable to that of the full HK propagator although the latter is more accurate than the former in general. On the other hand, we confirm that the convergence speed of the SC-Cl HK propagator is faster than that of the full HK propagator. The present numerical tests indicate that the SC-Cl HK propagator can be more accurate than the full HK propagator when they use a same and finite number of classical trajectories due to the balance of the accuracy and the efficiency.

Phenomenological implications of an alternative Hamiltonian constraint for quantum cosmology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kagan, Mikhail

2005-11-15

In this paper we review a model based on loop quantum cosmology that arises from a symmetry reduction of the self-dual Plebanski action. In this formulation the symmetry reduction leads to a very simple Hamiltonian constraint that can be quantized explicitly in the framework of loop quantum cosmology. We investigate the phenomenological implications of this model in the semiclassical regime and compare those with the known results of the standard Loop Quantum Cosmology.

A remark on the energy conditions for Hawking's area theorem

NASA Astrophysics Data System (ADS)

Lesourd, Martin

2018-06-01

Hawking's area theorem is a fundamental result in black hole theory that is universally associated with the null energy condition. That this condition can be weakened is illustrated by the formulation of a strengthened version of the theorem based on an energy condition that allows for violations of the null energy condition. With the semi-classical context in mind, some brief remarks pertaining to the suitability of the area theorem and its energy condition are made.

Semiclassical theory of the tunneling anomaly in partially spin-polarized compressible quantum Hall states

NASA Astrophysics Data System (ADS)

Chowdhury, Debanjan; Skinner, Brian; Lee, Patrick A.

2018-05-01

Electron tunneling into a system with strong interactions is known to exhibit an anomaly, in which the tunneling conductance vanishes continuously at low energy due to many-body interactions. Recent measurements have probed this anomaly in a quantum Hall bilayer of the half-filled Landau level, and shown that the anomaly apparently gets stronger as the half-filled Landau level is increasingly spin polarized. Motivated by this result, we construct a semiclassical hydrodynamic theory of the tunneling anomaly in terms of the charge-spreading action associated with tunneling between two copies of the Halperin-Lee-Read state with partial spin polarization. This theory is complementary to our recent work (D. Chowdhury, B. Skinner, and P. A. Lee, arXiv:1709.06091) where the electron spectral function was computed directly using an instanton-based approach. Our results show that the experimental observation cannot be understood within conventional theories of the tunneling anomaly, in which the spreading of the injected charge is driven by the mean-field Coulomb energy. However, we identify a qualitatively new regime, in which the mean-field Coulomb energy is effectively quenched and the tunneling anomaly is dominated by the finite compressibility of the composite Fermion liquid.

Theory of molecular rate processes in the presence of intense laser radiation

NASA Technical Reports Server (NTRS)

George, T. F.; Zimmerman, I. H.; Devries, P. L.; Yuan, J.-M.; Lam, K.-S.; Bellum, J. C.; Lee, H.-W.; Slutsky, M. S.; Lin, J.-T.

1979-01-01

The present paper deals with the influence of intense laser radiation on gas-phase molecular rate processes. Representations of the radiation field, the particle system, and the interaction involving these two entities are discussed from a general rather than abstract point of view. The theoretical methods applied are outlined, and the formalism employed is illustrated by application to a variety of specific processes. Quantum mechanical and semiclassical treatments of representative atom-atom and atom-diatom collision processes in the presence of a field are examined, and examples of bound-continuum processes and heterogeneous catalysis are discussed within the framework of both quantum-mechanical and semiclassical theories.

Gravitational decoherence, alternative quantum theories and semiclassical gravity

NASA Astrophysics Data System (ADS)

Hu, B. L.

2014-04-01

In this report we discuss three aspects: 1) Semiclassical gravity theory (SCG): 4 levels of theories describing the interaction of quantum matter with classical gravity. 2) Alternative Quantum Theories: Discerning those which are derivable from general relativity (GR) plus quantum field theory (QFT) from those which are not 3) Gravitational Decoherence: derivation of a master equation and examination of the assumptions which led to the claims of observational possibilities. We list three sets of corresponding problems worthy of pursuit: a) Newton-Schrödinger Equations in relation to SCG; b) Master equation of gravity-induced effects serving as discriminator of 2); and c) Role of gravity in macroscopic quantum phenomena.

Quadratic Forms and Semiclassical Eigenfunction Hypothesis for Flat Tori

NASA Astrophysics Data System (ADS)

T. Sardari, Naser

2018-03-01

Let Q( X) be any integral primitive positive definite quadratic form in k variables, where {k≥4}, and discriminant D. For any integer n, we give an upper bound on the number of integral solutions of Q( X) = n in terms of n, k, and D. As a corollary, we prove a conjecture of Lester and Rudnick on the small scale equidistribution of almost all functions belonging to any orthonormal basis of a given eigenspace of the Laplacian on the flat torus {T^d} for {d≥ 5}. This conjecture is motivated by the work of Berry [2,3] on the semiclassical eigenfunction hypothesis.

Semiclassical Wheeler-DeWitt equation: Solutions for long-wavelength fields

NASA Astrophysics Data System (ADS)

Salopek, D. S.; Stewart, J. M.; Parry, J.

1993-07-01

In the long-wavelength approximation, a general set of semiclassical wave functionals is given for gravity and matter interacting in 3+1 dimensions. In the long-wavelength theory, one neglects second-order spatial gradients in the energy constraint. These solutions satisfy the Hamilton-Jacobi equation, the momentum constraint, and the equation of continuity. It is essential to introduce inhomogeneities to discuss the role of time. The time hypersurface is chosen to be a homogeneous field in the wave functional. It is shown how to introduce tracer particles through a dust field χ into the dynamical system. The formalism can be used to describe stochastic inflation.

Analysis of a semiclassical model for rotational transition probabilities. [in highly nonequilibrium flow of diatomic molecules

NASA Technical Reports Server (NTRS)

Deiwert, G. S.; Yoshikawa, K. K.

1975-01-01

A semiclassical model proposed by Pearson and Hansen (1974) for computing collision-induced transition probabilities in diatomic molecules is tested by the direct-simulation Monte Carlo method. Specifically, this model is described by point centers of repulsion for collision dynamics, and the resulting classical trajectories are used in conjunction with the Schroedinger equation for a rigid-rotator harmonic oscillator to compute the rotational energy transition probabilities necessary to evaluate the rotation-translation exchange phenomena. It is assumed that a single, average energy spacing exists between the initial state and possible final states for a given collision.

Estimates of the thermal conductivity and the thermoelectric properties of PbTiO3 from first principles

NASA Astrophysics Data System (ADS)

Roy, Anindya

2016-03-01

The lattice thermal conductivity (κL) of PbTiO3 is estimated using a combination of ab initio calculations and the semiclassical Boltzmann transport equation. The computed κL is remarkably low, nearly comparable with the κL of good thermoelectric materials such as PbTe. In addition, a semiclassical analysis of the electronic transport quantities is presented, which suggests excellent thermoelectric properties, with a figure of merit z T well over 1 for a wide range of temperatures. For thermoelectric applications, the κL could be further reduced by utilizing different morphologies and compositions.

The resonant state at filling factor ν = 1/2 in chiral fermionic ladders

NASA Astrophysics Data System (ADS)

Haller, Andreas; Rizzi, Matteo; Burrello, Michele

2018-05-01

Helical liquids have been experimentally realized in both nanowires and ultracold atomic chains as the result of strong spin–orbit interactions. In both cases the inner degrees of freedom can be considered as an additional space dimension, providing an interpretation of these systems as chiral synthetic ladders, with artificial magnetic fluxes determined by the spin–orbit terms. In this work, we characterize the helical state which appears at filling ν = 1/2: this state is generated by a gap arising in the spin sector of the corresponding Luttinger liquid and it can be interpreted as the one-dimensional (1D) limit of a fractional quantum Hall state of bosonic pairs of fermions. We study its main features, focusing on entanglement properties and correlation functions. The techniques developed here provide a key example for the study of similar quasi-1D systems beyond the semiclassical approximation commonly adopted in the description of the Laughlin-like states.

Black holes as bubble nucleation sites

NASA Astrophysics Data System (ADS)

Gregory, Ruth; Moss, Ian G.; Withers, Benjamin

2014-03-01

We consider the effect of inhomogeneities on the rate of false vacuum decay. Modelling the inhomogeneity by a black hole, we construct explicit Euclidean instantons which describe the nucleation of a bubble of true vacuum centred on the inhomogeneity. We find that inhomogeneity significantly enhances the nucleation rate over that of the Coleman-de Luccia instanton — the black hole acts as a nucleation site for the bubble. The effect is larger than previously believed due to the contributions to the action from conical singularities. For a sufficiently low initial mass, the original black hole is replaced by flat space during this process, as viewed by a single causal patch observer. Increasing the initial mass, we find a critical value above which a black hole remnant survives the process. This resulting black hole can have a higher mass than the original black hole, but always has a lower entropy. We compare the process to bubble-to-bubble transitions, where there is a semi-classical Lorentzian description in the WKB approximation.

Gyrotropic Magnetic Effect and the Magnetic Moment on the Fermi Surface.

PubMed

Zhong, Shudan; Moore, Joel E; Souza, Ivo

2016-02-19

The current density j^{B} induced in a clean metal by a slowly-varying magnetic field B is formulated as the low-frequency limit of natural optical activity, or natural gyrotropy. Working with a multiband Pauli Hamiltonian, we obtain from the Kubo formula a simple expression for α_{ij}^{GME}=j_{i}^{B}/B_{j} in terms of the intrinsic magnetic moment (orbital plus spin) of the Bloch electrons on the Fermi surface. An alternate semiclassical derivation provides an intuitive picture of the effect, and takes into account the influence of scattering processes in dirty metals. This "gyrotropic magnetic effect" is fundamentally different from the chiral magnetic effect driven by the chiral anomaly and governed by the Berry curvature on the Fermi surface, and the two effects are compared for a minimal model of a Weyl semimetal. Like the Berry curvature, the intrinsic magnetic moment should be regarded as a basic ingredient in the Fermi-liquid description of transport in broken-symmetry metals.

Gyrotropic Magnetic Effect and the Magnetic Moment on the Fermi Surface

NASA Astrophysics Data System (ADS)

Zhong, Shudan; Moore, Joel E.; Souza, Ivo

2016-02-01

The current density jB induced in a clean metal by a slowly-varying magnetic field B is formulated as the low-frequency limit of natural optical activity, or natural gyrotropy. Working with a multiband Pauli Hamiltonian, we obtain from the Kubo formula a simple expression for αij GME=jiB/Bj in terms of the intrinsic magnetic moment (orbital plus spin) of the Bloch electrons on the Fermi surface. An alternate semiclassical derivation provides an intuitive picture of the effect, and takes into account the influence of scattering processes in dirty metals. This "gyrotropic magnetic effect" is fundamentally different from the chiral magnetic effect driven by the chiral anomaly and governed by the Berry curvature on the Fermi surface, and the two effects are compared for a minimal model of a Weyl semimetal. Like the Berry curvature, the intrinsic magnetic moment should be regarded as a basic ingredient in the Fermi-liquid description of transport in broken-symmetry metals.

Quantum-mechanical predictions of electron-induced ionization cross sections of DNA components

NASA Astrophysics Data System (ADS)

Champion, Christophe

2013-05-01

Ionization of biomolecules remains still today rarely investigated on both the experimental and the theoretical sides. In this context, the present work appears as one of the first quantum mechanical approaches providing a multi-differential description of the electron-induced ionization process of the main DNA components for impact energies ranging from the target ionization threshold up to about 10 keV. The cross section calculations are here performed within the 1st Born approximation framework in which the ejected electron is described by a Coulomb wave whereas the incident and the scattered electrons are both described by a plane wave. The biological targets of interest, namely, the DNA nucleobases and the sugar-phosphate backbone, are here described by means of the GAUSSIAN 09 system using the restricted Hartree-Fock method with geometry optimization. The theoretical predictions also obtained have shown a reasonable agreement with the experimental total ionization cross sections while huge discrepancies have been pointed out with existing theoretical models, mainly developed within a semi-classical framework.

On the Charge transport regime of crystalline organic semiconductors: diffusion limited by thermal off-diagonal electronic disorder

NASA Astrophysics Data System (ADS)

Troisi, Alessandro

2006-03-01

In organic crystalline semiconductor molecular components are held together by very weak interactions and the transfer integrals between neighboring molecular orbitals are extremely sensitive to small nuclear displacements. We used a mixed quantum chemical and molecular dynamic methodology to assess the effect of thermal structural fluctuations on the modulation of the transfer integrals between close molecules. We have found that the fluctuations of the transfer integrals are of the same order of magnitude of their average value for pentacene and anthracene. This condition makes the band description inadequate because a dynamic localization takes place and the translational symmetry is completely broken for the electronic states. We also present a simple one-dimensional semiclassical model that incorporates the effects of dynamical localization and allows the numerical computation of the charge mobility for ordered organic semiconductors. These results explain several contrasting experimental observations pointing sometimes to a delocalized ``band-like'' transport and sometimes to the existence of strongly localized charge carriers.

High order harmonic generation in rare gases

DOE Office of Scientific and Technical Information (OSTI.GOV)

Budil, Kimberly Susan

1994-05-01

The process of high order harmonic generation in atomic gases has shown great promise as a method of generating extremely short wavelength radiation, extending far into the extreme ultraviolet (XUV). The process is conceptually simple. A very intense laser pulse (I ~10 13-10 14 W/cm 2) is focused into a dense (~10 17 particles/cm 3) atomic medium, causing the atoms to become polarized. These atomic dipoles are then coherently driven by the laser field and begin to radiate at odd harmonics of the laser field. This dissertation is a study of both the physical mechanism of harmonic generation as wellmore » as its development as a source of coherent XUV radiation. Recently, a semiclassical theory has been proposed which provides a simple, intuitive description of harmonic generation. In this picture the process is treated in two steps. The atom ionizes via tunneling after which its classical motion in the laser field is studied. Electron trajectories which return to the vicinity of the nucleus may recombine and emit a harmonic photon, while those which do not return will ionize. An experiment was performed to test the validity of this model wherein the trajectory of the electron as it orbits the nucleus or ion core is perturbed by driving the process with elliptically, rather than linearly, polarized laser radiation. The semiclassical theory predicts a rapid turn-off of harmonic production as the ellipticity of the driving field is increased. This decrease in harmonic production is observed experimentally and a simple quantum mechanical theory is used to model the data. The second major focus of this work was on development of the harmonic "source". A series of experiments were performed examining the spatial profiles of the harmonics. The quality of the spatial profile is crucial if the harmonics are to be used as the source for experiments, particularly if they must be refocused.« less

Vacuum polarization and Hawking radiation

NASA Astrophysics Data System (ADS)

Rahmati, Shohreh

Quantum gravity is one of the interesting fields in contemporary physics which is still in progress. The purpose of quantum gravity is to present a quantum description for spacetime at 10-33cm or find the 'quanta' of gravitational interaction.. At present, the most viable theory to describe gravitational interaction is general relativity which is a classical theory. Semi-classical quantum gravity or quantum field theory in curved spacetime is an approximation to a full quantum theory of gravity. This approximation considers gravity as a classical field and matter fields are quantized. One interesting phenomena in semi-classical quantum gravity is Hawking radiation. Hawking radiation was derived by Stephen Hawking as a thermal emission of particles from the black hole horizon. In this thesis we obtain the spectrum of Hawking radiation using a new method. Vacuum is defined as the possible lowest energy state which is filled with pairs of virtual particle-antiparticle. Vacuum polarization is a consequence of pair creation in the presence of an external field such as an electromagnetic or gravitational field. Vacuum polarization in the vicinity of a black hole horizon can be interpreted as the cause of the emission from black holes known as Hawking radiation. In this thesis we try to obtain the Hawking spectrum using this approach. We re-examine vacuum polarization of a scalar field in a quasi-local volume that includes the horizon. We study the interaction of a scalar field with the background gravitational field of the black hole in the desired quasi-local region. The quasi-local volume is a hollow cylinder enclosed by two membranes, one inside the horizon and one outside the horizon. The net rate of particle emission can be obtained as the difference of the vacuum polarization from the outer boundary and inner boundary of the cylinder. Thus we found a new method to derive Hawking emission which is unitary and well defined in quantum field theory.

A review of recent advances in the spherical harmonics expansion method for semiconductor device simulation.

PubMed

Rupp, K; Jungemann, C; Hong, S-M; Bina, M; Grasser, T; Jüngel, A

The Boltzmann transport equation is commonly considered to be the best semi-classical description of carrier transport in semiconductors, providing precise information about the distribution of carriers with respect to time (one dimension), location (three dimensions), and momentum (three dimensions). However, numerical solutions for the seven-dimensional carrier distribution functions are very demanding. The most common solution approach is the stochastic Monte Carlo method, because the gigabytes of memory requirements of deterministic direct solution approaches has not been available until recently. As a remedy, the higher accuracy provided by solutions of the Boltzmann transport equation is often exchanged for lower computational expense by using simpler models based on macroscopic quantities such as carrier density and mean carrier velocity. Recent developments for the deterministic spherical harmonics expansion method have reduced the computational cost for solving the Boltzmann transport equation, enabling the computation of carrier distribution functions even for spatially three-dimensional device simulations within minutes to hours. We summarize recent progress for the spherical harmonics expansion method and show that small currents, reasonable execution times, and rare events such as low-frequency noise, which are all hard or even impossible to simulate with the established Monte Carlo method, can be handled in a straight-forward manner. The applicability of the method for important practical applications is demonstrated for noise simulation, small-signal analysis, hot-carrier degradation, and avalanche breakdown.

Quantum many-body theory for electron spin decoherence in nanoscale nuclear spin baths.

PubMed

Yang, Wen; Ma, Wen-Long; Liu, Ren-Bao

2017-01-01

Decoherence of electron spins in nanoscale systems is important to quantum technologies such as quantum information processing and magnetometry. It is also an ideal model problem for studying the crossover between quantum and classical phenomena. At low temperatures or in light-element materials where the spin-orbit coupling is weak, the phonon scattering in nanostructures is less important and the fluctuations of nuclear spins become the dominant decoherence mechanism for electron spins. Since the 1950s, semi-classical noise theories have been developed for understanding electron spin decoherence. In spin-based solid-state quantum technologies, the relevant systems are in the nanometer scale and nuclear spin baths are quantum objects which require a quantum description. Recently, quantum pictures have been established to understand the decoherence and quantum many-body theories have been developed to quantitatively describe this phenomenon. Anomalous quantum effects have been predicted and some have been experimentally confirmed. A systematically truncated cluster-correlation expansion theory has been developed to account for the many-body correlations in nanoscale nuclear spin baths that are built up during electron spin decoherence. The theory has successfully predicted and explained a number of experimental results in a wide range of physical systems. In this review, we will cover this recent progress. The limitations of the present quantum many-body theories and possible directions for future development will also be discussed.

Real-time Feynman path integral with Picard–Lefschetz theory and its applications to quantum tunneling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tanizaki, Yuya, E-mail: yuya.tanizaki@riken.jp; Theoretical Research Division, Nishina Center, RIKEN, Wako 351-0198; Koike, Takayuki, E-mail: tkoike@ms.u-tokyo.ac.jp

Picard–Lefschetz theory is applied to path integrals of quantum mechanics, in order to compute real-time dynamics directly. After discussing basic properties of real-time path integrals on Lefschetz thimbles, we demonstrate its computational method in a concrete way by solving three simple examples of quantum mechanics. It is applied to quantum mechanics of a double-well potential, and quantum tunneling is discussed. We identify all of the complex saddle points of the classical action, and their properties are discussed in detail. However a big theoretical difficulty turns out to appear in rewriting the original path integral into a sum of path integralsmore » on Lefschetz thimbles. We discuss generality of that problem and mention its importance. Real-time tunneling processes are shown to be described by those complex saddle points, and thus semi-classical description of real-time quantum tunneling becomes possible on solid ground if we could solve that problem. - Highlights: • Real-time path integral is studied based on Picard–Lefschetz theory. • Lucid demonstration is given through simple examples of quantum mechanics. • This technique is applied to quantum mechanics of the double-well potential. • Difficulty for practical applications is revealed, and we discuss its generality. • Quantum tunneling is shown to be closely related to complex classical solutions.« less

Restoration of four-dimensional diffeomorphism covariance in canonical general relativity: An intrinsic Hamilton-Jacobi approach

NASA Astrophysics Data System (ADS)

Salisbury, Donald; Renn, Jürgen; Sundermeyer, Kurt

2016-02-01

Classical background independence is reflected in Lagrangian general relativity through covariance under the full diffeomorphism group. We show how this independence can be maintained in a Hamilton-Jacobi approach that does not accord special privilege to any geometric structure. Intrinsic space-time curvature-based coordinates grant equal status to all geometric backgrounds. They play an essential role as a starting point for inequivalent semiclassical quantizations. The scheme calls into question Wheeler’s geometrodynamical approach and the associated Wheeler-DeWitt equation in which 3-metrics are featured geometrical objects. The formalism deals with variables that are manifestly invariant under the full diffeomorphism group. Yet, perhaps paradoxically, the liberty in selecting intrinsic coordinates is precisely as broad as is the original diffeomorphism freedom. We show how various ideas from the past five decades concerning the true degrees of freedom of general relativity can be interpreted in light of this new constrained Hamiltonian description. In particular, we show how the Kuchař multi-fingered time approach can be understood as a means of introducing full four-dimensional diffeomorphism invariants. Every choice of new phase space variables yields new Einstein-Hamilton-Jacobi constraining relations, and corresponding intrinsic Schrödinger equations. We show how to implement this freedom by canonical transformation of the intrinsic Hamiltonian. We also reinterpret and rectify significant work by Dittrich on the construction of “Dirac observables.”

An Estimation of the Logarithmic Timescale in Ergodic Dynamics

NASA Astrophysics Data System (ADS)

Gomez, Ignacio S.

An estimation of the logarithmic timescale in quantum systems having an ergodic dynamics in the semiclassical limit, is presented. The estimation is based on an extension of the Krieger’s finite generator theorem for discretized σ-algebras and using the time rescaling property of the Kolmogorov-Sinai entropy. The results are in agreement with those obtained in the literature but with a simpler mathematics and within the context of the ergodic theory. Moreover, some consequences of the Poincaré’s recurrence theorem are also explored.

Ponderomotive effects in multiphoton pair production

NASA Astrophysics Data System (ADS)

Kohlfürst, Christian; Alkofer, Reinhard

2018-02-01

The Dirac-Heisenberg-Wigner formalism is employed to investigate electron-positron pair production in cylindrically symmetric but otherwise spatially inhomogeneous, oscillating electric fields. The oscillation frequencies are hereby tuned to obtain multiphoton pair production in the nonperturbative threshold regime. An effective mass, as well as a trajectory-based semiclassical analysis, is introduced in order to interpret the numerical results for the distribution functions as well as for the particle yields and spectra. The results, including the asymptotic particle spectra, display clear signatures of ponderomotive forces.

Semiclassical analysis of spectral singularities and their applications in optics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mostafazadeh, Ali

2011-08-15

Motivated by possible applications of spectral singularities in optics, we develop a semiclassical method of computing spectral singularities. We use this method to examine the spectral singularities of a planar slab gain medium whose gain coefficient varies due to the exponential decay of the intensity of the pumping beam inside the medium. For both singly and doublypumped samples, we obtain universal upper bounds on the decay constant beyond which no lasing occurs. Furthermore, we show that the dependence of the wavelength of the spectral singularities on the value of the decay constant is extremely mild. This is an indication ofmore » the stability of optical spectral singularities.« less

Statistics of time delay and scattering correlation functions in chaotic systems. I. Random matrix theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Novaes, Marcel

2015-06-15

We consider the statistics of time delay in a chaotic cavity having M open channels, in the absence of time-reversal invariance. In the random matrix theory approach, we compute the average value of polynomial functions of the time delay matrix Q = − iħS{sup †}dS/dE, where S is the scattering matrix. Our results do not assume M to be large. In a companion paper, we develop a semiclassical approximation to S-matrix correlation functions, from which the statistics of Q can also be derived. Together, these papers contribute to establishing the conjectured equivalence between the random matrix and the semiclassical approaches.

Comparison of local exchange potentials of electron-N2 scattering

NASA Astrophysics Data System (ADS)

Rumble, J. R., Jr.; Truhlar, D. G.

1980-05-01

Vibrationally and electronically elastic electron scattering by N2 at 2-30 eV impact energy is considered. Static, static-exchange, and static-exchange-plus-polarization potentials, Cade-Sales-Wahl and INDO/1s wave functions, and semiclassical exchange and Hara free-electron-gas exchange potentials are examined. It is shown that the semiclassical exchange approximation is too attractive at low energy for N2. It is also shown quantitatively by consideration of partial and total integral cross sections how the effects of approximations to exchange become smaller as the incident energy is increased until the differences are about 8% for the total integral cross section at 30 eV.

Opening-assisted coherent transport in the semiclassical regime

NASA Astrophysics Data System (ADS)

Zhang, Yang; Celardo, G. Luca; Borgonovi, Fausto; Kaplan, Lev

2017-02-01

We study quantum enhancement of transport in open systems in the presence of disorder and dephasing. Quantum coherence effects may significantly enhance transport in open systems even in the semiclassical regime (where the decoherence rate is greater than the intersite hopping amplitude), as long as the disorder is sufficiently strong. When the strengths of disorder and dephasing are fixed, there is an optimal opening strength at which the coherent transport enhancement is optimized. Analytic results are obtained in two simple paradigmatic tight-binding models of large systems: the linear chain and the fully connected network. The physical behavior is also reflected in the Fenna-Matthews-Olson (FMO) photosynthetic complex, which may be viewed as intermediate between these paradigmatic models.

NMR lineshape equations for hindered methyl group: a comparison of the semi-classical and quantum mechanical models

NASA Astrophysics Data System (ADS)

Bernatowicz, P.; Szymański, S.

2003-09-01

The semiclassical and quantum mechanical NMR lineshape equations for a hindered methyl group are compared. In both the approaches, the stochastic dynamics can be interpreted in terms of a progressive symmetrization of the spin density matrix. However, the respective ways of achieving the same limiting symmetry can be remarkably different. From numerical lineshape simulations it is inferred that in the regime of intermediate exchange, where the conventional theory predicts occurrence of a single Lorentzian, the actual spectrum can have nontrivial features. This observation may open new perspectives in the search for nonclassical effects in the stochastic behavior of methyl groups in liquid-phase NMR.

Time dependent semiclassical tunneling through one dimensional barriers using only real valued trajectories

DOE Office of Scientific and Technical Information (OSTI.GOV)

Herman, Michael F.

2015-10-28

The time independent semiclassical treatment of barrier tunneling has been understood for a very long time. Several semiclassical approaches to time dependent tunneling through barriers have also been presented. These typically involve trajectories for which the position variable is a complex function of time. In this paper, a method is presented that uses only real valued trajectories, thus avoiding the complications that can arise when complex trajectories are employed. This is accomplished by expressing the time dependent wave packet as an integration over momentum. The action function in the exponent in this expression is expanded to second order in themore » momentum. The expansion is around the momentum, p{sub 0{sup *}}, at which the derivative of the real part of the action is zero. The resulting Gaussian integral is then taken. The stationary phase approximation requires that the derivative of the full action is zero at the expansion point, and this leads to a complex initial momentum and complex tunneling trajectories. The “pseudo-stationary phase” approximation employed in this work results in real values for the initial momentum and real valued trajectories. The transmission probabilities obtained are found to be in good agreement with exact quantum results.« less

On the Anticipatory Aspects of the Four Interactions: what the Known Classical and Semi-Classical Solutions Teach us

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lusanna, Luca

2004-08-19

The four (electro-magnetic, weak, strong and gravitational) interactions are described by singular Lagrangians and by Dirac-Bergmann theory of Hamiltonian constraints. As a consequence a subset of the original configuration variables are gauge variables, not determined by the equations of motion. Only at the Hamiltonian level it is possible to separate the gauge variables from the deterministic physical degrees of freedom, the Dirac observables, and to formulate a well posed Cauchy problem for them both in special and general relativity. Then the requirement of causality dictates the choice of retarded solutions at the classical level. However both the problems of themore » classical theory of the electron, leading to the choice of (1/2) (retarded + advanced) solutions, and the regularization of quantum field theory, leading to the Feynman propagator, introduce anticipatory aspects. The determination of the relativistic Darwin potential as a semi-classical approximation to the Lienard-Wiechert solution for particles with Grassmann-valued electric charges, regularizing the Coulomb self-energies, shows that these anticipatory effects live beyond the semi-classical approximation (tree level) under the form of radiative corrections, at least for the electro-magnetic interaction.Talk and 'best contribution' at The Sixth International Conference on Computing Anticipatory Systems CASYS'03, Liege August 11-16, 2003.« less

Semiclassical black holes expose forbidden charges and censor divergent densities

NASA Astrophysics Data System (ADS)

Brustein, Ram; Medved, A. J. M.

2013-09-01

Classically, the horizon of a Schwarzschild black hole (BH) is a rigid surface of infinite redshift; whereas the uncertainty principle dictates that the semiclassical (would-be) horizon cannot be fixed in space nor can it exhibit any divergences. We propose that this distinction underlies the BH information-loss paradox, the apparent absence of BH hair, the so-called trans-Planckian problem and the recent "firewall" controversy. We argue that the correct prescription is to first integrate out the fluctuations of the background geometry and only then evaluate matter observables. The basic idea is illustrated using a system of two strongly coupled harmonic oscillators, with the heavier oscillator representing the background. We then apply our proposal to matter fields near a BH horizon, initially treating the matter fields as classical and the background as semiclassical. In this case, the average value of the associated current does not vanish; so that it is possible, in pr inciple, to measure the global charge of the BH. Then the matter is, in addition to the background, treated quantum mechanically. We show that the average energy density of matter as seen by an asymptotic observer is finite and proportional to the BH entropy, rather than divergent. We discuss the implications of our results for the various controversial issues concerning BH physics.

Multiple choices of time in quantum cosmology

NASA Astrophysics Data System (ADS)

Małkiewicz, Przemysław

2015-07-01

It is often conjectured that a choice of time function merely sets up a frame for the quantum evolution of the gravitational field, meaning that all choices should be in some sense compatible. In order to explore this conjecture (and the meaning of compatibility), we develop suitable tools for determining the relation between quantum theories based on different time functions. First, we discuss how a time function fixes a canonical structure on the constraint surface. The presentation includes both the kinematical and the reduced perspective, and the relation between them. Second, we formulate twin theorems about the existence of two inequivalent maps between any two deparameterizations, a formal canonical and a coordinate one. They are used to separate the effects induced by choice of clock and other factors. We show, in an example, how the spectra of quantum observables are transformed under the change of clock and prove, via a general argument, the existence of choice-of-time-induced semiclassical effects. Finally, we study an example, in which we find that the semiclassical discrepancies can in fact be arbitrarily large for dynamical observables. We conclude that the values of critical energy density or critical volume in the bouncing scenarios of quantum cosmology cannot in general be at the Planck scale, and always need to be given with reference to a specific time function.

Path integral approach to the Wigner representation of canonical density operators for discrete systems coupled to harmonic baths.

PubMed

Montoya-Castillo, Andrés; Reichman, David R

2017-01-14

We derive a semi-analytical form for the Wigner transform for the canonical density operator of a discrete system coupled to a harmonic bath based on the path integral expansion of the Boltzmann factor. The introduction of this simple and controllable approach allows for the exact rendering of the canonical distribution and permits systematic convergence of static properties with respect to the number of path integral steps. In addition, the expressions derived here provide an exact and facile interface with quasi- and semi-classical dynamical methods, which enables the direct calculation of equilibrium time correlation functions within a wide array of approaches. We demonstrate that the present method represents a practical path for the calculation of thermodynamic data for the spin-boson and related systems. We illustrate the power of the present approach by detailing the improvement of the quality of Ehrenfest theory for the correlation function C zz (t)=Re⟨σ z (0)σ z (t)⟩ for the spin-boson model with systematic convergence to the exact sampling function. Importantly, the numerically exact nature of the scheme presented here and its compatibility with semiclassical methods allows for the systematic testing of commonly used approximations for the Wigner-transformed canonical density.

Kinetic isotope effects and how to describe them

PubMed Central

Karandashev, Konstantin; Xu, Zhen-Hao; Meuwly, Markus; Vaníček, Jiří; Richardson, Jeremy O.

2017-01-01

We review several methods for computing kinetic isotope effects in chemical reactions including semiclassical and quantum instanton theory. These methods describe both the quantization of vibrational modes as well as tunneling and are applied to the ⋅H + H2 and ⋅H + CH4 reactions. The absolute rate constants computed with the semiclassical instanton method both using on-the-fly electronic structure calculations and fitted potential-energy surfaces are also compared directly with exact quantum dynamics results. The error inherent in the instanton approximation is found to be relatively small and similar in magnitude to that introduced by using fitted surfaces. The kinetic isotope effect computed by the quantum instanton is even more accurate, and although it is computationally more expensive, the efficiency can be improved by path-integral acceleration techniques. We also test a simple approach for designing potential-energy surfaces for the example of proton transfer in malonaldehyde. The tunneling splittings are computed, and although they are found to deviate from experimental results, the ratio of the splitting to that of an isotopically substituted form is in much better agreement. We discuss the strengths and limitations of the potential-energy surface and based on our findings suggest ways in which it can be improved. PMID:29282447

Geometry of magnetic rotational (MR) band-crossing phenomenon in MR bands

NASA Astrophysics Data System (ADS)

Devi, K. Rojeeta; Kumar, Suresh; Palit, R.

2018-07-01

A semiclassical (SC) approach is proposed to calculate the B( M1) transition rates in the band-crossing region of two magnetic rotational (MR) bands. In the present work, a geometry is suggested for the shear blades to govern its behaviour during the band-crossing. In the crossing region, gradual alignment of two nucleons is responsible for the crossing behaviour and it must give a quantised resultant angular momentum. As an example, it is successfully implemented for the MR bands in the mass A=110 and A=200 regions. A good agreement of the present semiclassical calculations with the experimental values is presented and furthermore, it is seen that the present proposal is also helpful to see the core contribution in the MR phenomenon.

Communication: importance sampling including path correlation in semiclassical initial value representation calculations for time correlation functions.

PubMed

Pan, Feng; Tao, Guohua

2013-03-07

Full semiclassical (SC) initial value representation (IVR) for time correlation functions involves a double phase space average over a set of two phase points, each of which evolves along a classical path. Conventionally, the two initial phase points are sampled independently for all degrees of freedom (DOF) in the Monte Carlo procedure. Here, we present an efficient importance sampling scheme by including the path correlation between the two initial phase points for the bath DOF, which greatly improves the performance of the SC-IVR calculations for large molecular systems. Satisfactory convergence in the study of quantum coherence in vibrational relaxation has been achieved for a benchmark system-bath model with up to 21 DOF.

Heisenberg limit for displacements with semiclassical states

NASA Astrophysics Data System (ADS)

Luis, Alfredo

2004-04-01

We analyze the quantum limit to the sensitivity of the detection of small displacements. We focus on the case of free particles and harmonic oscillators as the systems experiencing the displacement. We show that the minimum displacement detectable is proportional to the inverse of the square root of the mean value of the energy in the state experiencing the displacement (Heisenberg limit). We present a measuring scheme that reaches this limit using semiclassical states. We examine the performance of this strategy under realistic practical conditions by computing the effect of imperfections such as losses and nonunit detection efficiencies. This analysis confirms the robustness of this measuring strategy by showing that the experimental imperfections can be suitably compensated by increasing the mean energy of the input state.

Hybrid Semiclassical Theory of Quantum Quenches in One-Dimensional Systems

NASA Astrophysics Data System (ADS)

Moca, Cǎtǎlin Paşcu; Kormos, Márton; Zaránd, Gergely

2017-09-01

We develop a hybrid semiclassical method to study the time evolution of one-dimensional quantum systems in and out of equilibrium. Our method handles internal degrees of freedom completely quantum mechanically by a modified time-evolving block decimation method while treating orbital quasiparticle motion classically. We can follow dynamics up to time scales well beyond the reach of standard numerical methods to observe the crossover between preequilibrated and locally phase equilibrated states. As an application, we investigate the quench dynamics and phase fluctuations of a pair of tunnel-coupled one-dimensional Bose condensates. We demonstrate the emergence of soliton-collision-induced phase propagation, soliton-entropy production, and multistep thermalization. Our method can be applied to a wide range of gapped one-dimensional systems.

Statistics of time delay and scattering correlation functions in chaotic systems. II. Semiclassical approximation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Novaes, Marcel

2015-06-15

We consider S-matrix correlation functions for a chaotic cavity having M open channels, in the absence of time-reversal invariance. Relying on a semiclassical approximation, we compute the average over E of the quantities Tr[S{sup †}(E − ϵ) S(E + ϵ)]{sup n}, for general positive integer n. Our result is an infinite series in ϵ, whose coefficients are rational functions of M. From this, we extract moments of the time delay matrix Q = − iħS{sup †}dS/dE and check that the first 8 of them agree with the random matrix theory prediction from our previous paper [M. Novaes, J. Math. Phys.more » 56, 062110 (2015)].« less

Quantum and semiclassical physics behind ultrafast optical nonlinearity in the midinfrared: the role of ionization dynamics within the field half cycle.

PubMed

Serebryannikov, E E; Zheltikov, A M

2014-07-25

Ultrafast ionization dynamics within the field half cycle is shown to be the key physical factor that controls the properties of optical nonlinearity as a function of the carrier wavelength and intensity of a driving laser field. The Schrödinger-equation analysis of a generic hydrogen quantum system reveals universal tendencies in the wavelength dependence of optical nonlinearity, shedding light on unusual properties of optical nonlinearities in the midinfrared. For high-intensity low-frequency fields, free-state electrons are shown to dominate over bound electrons in the overall nonlinear response of a quantum system. In this regime, semiclassical models are shown to offer useful insights into the physics behind optical nonlinearity.

Semiclassical IVR treatment of reactive collisions

NASA Astrophysics Data System (ADS)

Elran, Y.; Kay, K. G.

2002-06-01

We generalize a recently-developed semiclassical uniform initial value representation (IVR) treatment of the S-matrix [Y. Elran and K. G. Kay, J. Chem. Phys. 114, 4362 (2001)] to chaotic nonreactive and reactive collinear scattering. The present modifications allow one to determine the phase of the complex IVR integrand in a unique and practical manner even when the integrand is discontinuous or rapidly varying. The method is applied to the collinear H+H2 exchange reaction on the Porter-Karplus surface. A strategy is introduced for adapting the integration over the chaotic chattering zones to the fractal nature of the integrand. The results indicate that the technique is capable of good accuracy while requiring a relatively small number of trajectories per energy.

Two interacting Hofstadter butterflies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barelli, A.; Bellissard, J.; Jacquod, P.

1997-04-01

The problem of two interacting particles in a quasiperiodic potential is addressed. Using analytical and numerical methods, we explore the spectral properties and eigenstates structure from the weak to the strong interaction case. More precisely, a semiclassical approach based on noncommutative geometry techniques is used to understand the intricate structure of such a spectrum. An interaction induced localization effect is furthermore emphasized. We discuss the application of our results on a two-dimensional model of two particles in a uniform magnetic field with on-site interaction. {copyright} {ital 1997} {ital The American Physical Society}

Discrete sudden perturbation theory for inelastic scattering. I. Quantum and semiclassical treatment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cross, R.J.

1985-12-01

A double perturbation theory is constructed to treat rotationally and vibrationally inelastic scattering. It uses both the elastic scattering from the spherically averaged potential and the infinite-order sudden (IOS) approximation as the unperturbed solutions. First, a standard perturbation expansion is done to express the radial wave functions in terms of the elastic wave functions. The resulting coupled equations are transformed to the discrete-variable representation where the IOS equations are diagonal. Then, the IOS solutions are removed from the equations which are solved by an exponential perturbation approximation. The results for Ar+N/sub 2/ are very much more accurate than the IOSmore » and somewhat more accurate than a straight first-order exponential perturbation theory. The theory is then converted into a semiclassical, time-dependent form by using the WKB approximation. The result is an integral of the potential times a slowly oscillating factor over the classical trajectory. A method of interpolating the result is given so that the calculation is done at the average velocity for a given transition. With this procedure, the semiclassical version of the theory is more accurate than the quantum version and very much faster. Calculations on Ar+N/sub 2/ show the theory to be much more accurate than the infinite-order sudden (IOS) approximation and the exponential time-dependent perturbation theory.« less

The curious incident of multi-instantons and the necessity of Lefschetz thimbles

DOE PAGES

Behtash, Alireza; Poppitz, Erich; Sulejmanpasic, Tin; ...

2015-11-25

Here, we smore » how that compatibility of supersymmetry with exact semi-classics demands that in calculating multi-instanton amplitudes, the “separation” quasi-zeromode must be complexified and the integration cycles must be found by using complex gradient flow (or Picard-Lefschetz equations.) As a non-trivial application, we study N = 2 extended supersymmetric quantum mechanics. Even though in this case supersymmetry is unbroken, the instanton-anti-instanton amplitude (naively calculated) seems to contribute to the ground state energy. We show, however, that the instanton-anti-instanton event consists of two parts: a fermion-correlated and a scalar-correlated event. Although both of these contributions are naively of the same sign and the latter is superficially higher order in the perturbative coupling, we show that the two contributions exactly cancel when they are evaluated on Lefschetz thimbles due to their relative Hidden Topological Angles (HTAs). This gives strong evidence that the semi-classical expansion using Lefschetz thimbles is not only a meaningful prescription for higher order semi-classics, but a necessary one. This deduction seems to be universal and applicable to both supersymmetric and non-supersymmetric theories. In conclusion we speculate that similar conspiracies are responsible for the non-formation of certain molecular contributions in theories where instantons have more than two fermionic zeromodes and do not contribute to the superpotential.« less

Quantum-Classical Correspondence Principle for Work Distributions

NASA Astrophysics Data System (ADS)

Jarzynski, Christopher; Quan, H. T.; Rahav, Saar

2015-07-01

For closed quantum systems driven away from equilibrium, work is often defined in terms of projective measurements of initial and final energies. This definition leads to statistical distributions of work that satisfy nonequilibrium work and fluctuation relations. While this two-point measurement definition of quantum work can be justified heuristically by appeal to the first law of thermodynamics, its relationship to the classical definition of work has not been carefully examined. In this paper, we employ semiclassical methods, combined with numerical simulations of a driven quartic oscillator, to study the correspondence between classical and quantal definitions of work in systems with 1 degree of freedom. We find that a semiclassical work distribution, built from classical trajectories that connect the initial and final energies, provides an excellent approximation to the quantum work distribution when the trajectories are assigned suitable phases and are allowed to interfere. Neglecting the interferences between trajectories reduces the distribution to that of the corresponding classical process. Hence, in the semiclassical limit, the quantum work distribution converges to the classical distribution, decorated by a quantum interference pattern. We also derive the form of the quantum work distribution at the boundary between classically allowed and forbidden regions, where this distribution tunnels into the forbidden region. Our results clarify how the correspondence principle applies in the context of quantum and classical work distributions and contribute to the understanding of work and nonequilibrium work relations in the quantum regime.

Asymptotics of quantum weighted Hurwitz numbers

NASA Astrophysics Data System (ADS)

Harnad, J.; Ortmann, Janosch

2018-06-01

This work concerns both the semiclassical and zero temperature asymptotics of quantum weighted double Hurwitz numbers. The partition function for quantum weighted double Hurwitz numbers can be interpreted in terms of the energy distribution of a quantum Bose gas with vanishing fugacity. We compute the leading semiclassical term of the partition function for three versions of the quantum weighted Hurwitz numbers, as well as lower order semiclassical corrections. The classical limit is shown to reproduce the simple single and double Hurwitz numbers studied by Okounkov and Pandharipande (2000 Math. Res. Lett. 7 447–53, 2000 Lett. Math. Phys. 53 59–74). The KP-Toda τ-function that serves as generating function for the quantum Hurwitz numbers is shown to have the τ-function of Okounkov and Pandharipande (2000 Math. Res. Lett. 7 447–53, 2000 Lett. Math. Phys. 53 59–74) as its leading term in the classical limit, and, with suitable scaling, the same holds for the partition function, the weights and expectations of Hurwitz numbers. We also compute the zero temperature limit of the partition function and quantum weighted Hurwitz numbers. The KP or Toda τ-function serving as generating function for the quantum Hurwitz numbers are shown to give the one for Belyi curves in the zero temperature limit and, with suitable scaling, the same holds true for the partition function, the weights and the expectations of Hurwitz numbers.

Semiclassical transport in nearly symmetric quantum dots. I. Symmetry breaking in the dot.

PubMed

Whitney, Robert S; Schomerus, Henning; Kopp, Marten

2009-11-01

We apply the semiclassical theory of transport to quantum dots with exact and approximate spatial symmetries; left-right mirror symmetry, up-down mirror symmetry, inversion symmetry, or fourfold symmetry. In this work-the first of a pair of articles-we consider (a) perfectly symmetric dots and (b) nearly symmetric dots in which the symmetry is broken by the dot's internal dynamics. The second article addresses symmetry-breaking by displacement of the leads. Using semiclassics, we identify the origin of the symmetry-induced interference effects that contribute to weak localization corrections and universal conductance fluctuations. For perfect spatial symmetry, we recover results previously found using the random-matrix theory conjecture. We then go on to show how the results are affected by asymmetries in the dot, magnetic fields, and decoherence. In particular, the symmetry-asymmetry crossover is found to be described by a universal dependence on an asymmetry parameter gamma_{asym} . However, the form of this parameter is very different depending on how the dot is deformed away from spatial symmetry. Symmetry-induced interference effects are completely destroyed when the dot's boundary is globally deformed by less than an electron wavelength. In contrast, these effects are only reduced by a finite amount when a part of the dot's boundary smaller than a lead-width is deformed an arbitrarily large distance.

Kicking atoms with finite duration pulses

NASA Astrophysics Data System (ADS)

Fekete, Julia; Chai, Shijie; Daszuta, Boris; Andersen, Mikkel F.

2016-05-01

The atom optics delta-kicked particle is a paradigmatic system for experimental studies of quantum chaos and classical-quantum correspondence. It consists of a cloud of laser cooled atoms exposed to a periodically pulsed standing wave of far off-resonant laser light. A purely quantum phenomena in such systems are quantum resonances which transfers the atoms into a coherent superposition of largely separated momentum states. Using such large momentum transfer ``beamsplitters'' in atom interferometers may have applications in high precision metrology. The growth in momentum separation cannot be maintained indefinitely due to finite laser power. The largest momentum transfer is achieved by violating the usual delta-kick assumption. Therefore we explore the behavior of the atom optics kicked particle with finite pulse duration. We have developed a semi-classical model which shows good agreement with the full quantum description as well as our experiments. Furthermore we have found a simple scaling law that helps to identify optimal parameters for an atom interferometer. We verify this by measurements of the ``Talbot time'' (a measurement of h/m) which together with other well-known constants constitute a measurement of the fine structure constant.

High precision optical spectroscopy and quantum state selected photodissociation of ultracold 88Sr2 molecules in an optical lattice

NASA Astrophysics Data System (ADS)

McDonald, Mickey

2017-04-01

Over the past several decades, rapid progress has been made toward the accurate characterization and control of atoms, epitomized by the ever-increasing accuracy and precision of optical atomic lattice clocks. Extending this progress to molecules will have exciting implications for chemistry, condensed matter physics, and precision tests of physics beyond the Standard Model. My thesis describes work performed over the past six years to establish the state of the art in manipulation and quantum control of ultracold molecules. We describe a thorough set of measurements characterizing the rovibrational structure of weakly bound 88Sr2 molecules from several different perspectives, including determinations of binding energies; linear, quadratic, and higher order Zeeman shifts; transition strengths between bound states; and lifetimes of narrow subradiant states. Finally, we discuss measurements of photofragment angular distributions produced by photodissociation of molecules in single quantum states, leading to an exploration of quantum-state-resolved ultracold chemistry. The images of exploding photofragments produced in these studies exhibit dramatic interference effects and strongly violate semiclassical predictions, instead requiring a fully quantum mechanical description.

Quantum Dynamics in the HMF Model

NASA Astrophysics Data System (ADS)

Plestid, Ryan; O'Dell, Duncan

2017-04-01

The Hamiltonian Mean Field (HMF) model represents a paradigm in the study of long-range interactions but has never been realized in a lab. Recently Shutz and Morigi (PRL 113) have come close but ultimately fallen short. Their proposal relied on cavity-induced interactions between atoms. If a design using cold atoms is to be successful, an understanding of quantum effects is essential. I will outline the natural quantum generalization of the HMF assuming a BEC by using a generalized Gross-Pitaevskii equation (gGPE). I will show how quantum effects modify features which are well understood in the classical model. More specifically, by working in the semi-classical regime (strong interparticle interactions) we can identify the universal features predicted by catastrophe theory dressed with quantum interference effects. The stationary states of gGPE can be solved exactly and are found to be described by self-consistent Mathieu functions. Finally, I will discuss the connection between the classical description of the dynamics in terms of the Vlassov equation, and the gGPE. We would like to thank the Government of Ontario's OGS program, NSERC, and the Perimeter Institute of Theoretical Physics.

Semiclassical dynamics of spin density waves

NASA Astrophysics Data System (ADS)

Chern, Gia-Wei; Barros, Kipton; Wang, Zhentao; Suwa, Hidemaro; Batista, Cristian D.

2018-01-01

We present a theoretical framework for equilibrium and nonequilibrium dynamical simulation of quantum states with spin-density-wave (SDW) order. Within a semiclassical adiabatic approximation that retains electron degrees of freedom, we demonstrate that the SDW order parameter obeys a generalized Landau-Lifshitz equation. With the aid of an enhanced kernel polynomial method, our linear-scaling quantum Landau-Lifshitz dynamics (QLLD) method enables dynamical SDW simulations with N ≃105 lattice sites. Our real-space formulation can be used to compute dynamical responses, such as the dynamical structure factor, of complex and even inhomogeneous SDW configurations at zero or finite temperatures. Applying the QLLD to study the relaxation of a noncoplanar topological SDW under the excitation of a short pulse, we further demonstrate the crucial role of spatial correlations and fluctuations in the SDW dynamics.

Semi-classical approach to transitionless quantum driving: Explicitness and Locality

NASA Astrophysics Data System (ADS)

Loewe, Benjamin; Hipolito, Rafael; Goldbart, Paul M.

Berry has shown that, via a reverse engineering strategy, non-adiabatic transitions in time-dependent quantum systems can be stifled through the introduction of a specific auxiliary hamiltonian. This hamiltonian comes, however, expressed as a formal sum of outer products of the original instantaneous eigenstates and their time-derivatives. Generically, how to create such an operator in the laboratory is thus not evident. Furthermore, the operator may be non- local. By following a semi-classical approach, we obtain a recipe that yields the auxiliary hamiltonian explicitly in terms of the fundamental operators of the system (e.g., position and momentum). By using this formalism, we are able to ascertain criteria for the locality of the auxiliary hamiltonian, and also to determine its exact form in certain special cases.

Quantum theory of the far-off-resonance continuous-wave Raman laser: Heisenberg-Langevin approach

NASA Astrophysics Data System (ADS)

Roos, P. A.; Murphy, S. K.; Meng, L. S.; Carlsten, J. L.; Ralph, T. C.; White, A. G.; Brasseur, J. K.

2003-07-01

We present the quantum theory of the far-off-resonance continuous-wave Raman laser using the Heisenberg-Langevin approach. We show that the simplified quantum Langevin equations for this system are mathematically identical to those of the nondegenerate optical parametric oscillator in the time domain with the following associations: pump ↔ pump, Stokes ↔ signal, and Raman coherence ↔ idler. We derive analytical results for both the steady-state behavior and the time-dependent noise spectra, using standard linearization procedures. In the semiclassical limit, these results match with previous purely semiclassical treatments, which yield excellent agreement with experimental observations. The analytical time-dependent results predict perfect photon statistics conversion from the pump to the Stokes and nonclassical behavior under certain operational conditions.

On the total bandwidth for the rational Harper's equation

NASA Astrophysics Data System (ADS)

Helffer, Bernard; Kerdelhué, Phillippe

1995-10-01

In the last years several contributions have been done around the total bandwidth of the spectrum for the Harper's operator. In particular an interesting conjecture has been proposed by Thouless which gives also strong convincing arguments for the proof in special cases. On the other hand, in the study of the Cantor structure of the spectrum, B. Helffer and J. Sjöstrand have justified an heuristic semiclassical approach proposed by M. Wilkinson. The aim of this article is to explain how one can use the first step of this approach to give a rigorous semi-classical proof of the Thouless formula in some of the simplest cases. We shall also indicate how one can hope with more effort to prove rigorously recent results of Last and Wilkinson on the same conjecture.

Semiclassical theory of Hall viscosity

NASA Astrophysics Data System (ADS)

Biswas, Rudro

2014-03-01

Hall viscosity is an intriguing stress response in quantum Hall systems and is predicted to be observable via the conductivity in an inhomogeneous electric field. This has been studied extensively using a range of techniques, such as adiabatic transport, effective field theories, and Kubo formulae. All of these are, however, agnostic as to the distinction between strongly correlated quantum Hall states and non-interacting ones, where the effect arises due to the fundamental non-commuting nature of velocities and orbit positions in a magnetic field. In this talk I shall develop the semiclassical theory of quantized cyclotron orbits drifting in an applied inhomogeneous electric field and use it to provide a clear physical picture of how single particle properties in a magnetic field contribute to the Hall viscosity-dependence of the conductivity.

Principle of least decoherence for Newtonian semiclassical gravity

NASA Astrophysics Data System (ADS)

Tilloy, Antoine; Diósi, Lajos

2017-11-01

Recent works have proved that semiclassical theories of gravity needed not be fundamentally inconsistent, at least in the Newtonian regime. Using the machinery of continuous measurement theory and feedback, it was shown that one could construct well-behaved models of hybrid quantum-classical dynamics at the price of an imposed (nonunique) decoherence structure. We introduce a principle of least decoherence (PLD) which allows us to naturally single out a unique model from all the available options; up to some unspecified short distance regularization scale. Interestingly, the resulting model is found to coincide with the old—erstwhile only heuristically motivated—proposal of Penrose and one of us for gravity-related spontaneous decoherence and collapse. Finally, this paper suggests that it is in the submillimeter behavior of gravity that new phenomena might be found.

Quantum Chaos

NASA Astrophysics Data System (ADS)

Casati, Giulio; Chirikov, Boris

2006-11-01

Preface; Acknowledgments; Introduction: 1. The legacy of chaos in quantum mechanics G. Casati and B. V. Chirikov; Part I. Classical Chaos and Quantum Localization: 2. Stochastic behaviour of a quantum pendulum under a periodic perturbation G. Casati, B. V. Chirikov, F. M. Izrailev and J. Ford; 3. Quantum dynamics of a nonintegrable system D. R. Grempel, R. E. Prange and S. E. Fishman; 4. Excitation of molecular rotation by periodic microwave pulses. A testing ground for Anderson localization R. Blümel, S. Fishman and U. Smilansky; 5. Localization of diffusive excitation in multi-level systems D. K. Shepelyansky; 6. Classical and quantum chaos for a kicked top F. Haake, M. Kus and R. Scharf; 7. Self-similarity in quantum dynamics L. E. Reichl and L. Haoming; 8. Time irreversibility of classically chaotic quantum dynamics K. Ikeda; 9. Effect of noise on time-dependent quantum chaos E. Ott, T. M. Antonsen Jr and J. D. Hanson; 10. Dynamical localization, dissipation and noise R. F. Graham; 11. Maximum entropy models and quantum transmission in disordered systems J.-L. Pichard and M. Sanquer; 12. Solid state 'atoms' in intense oscillating fields M. S. Sherwin; Part II. Atoms in Strong Fields: 13. Localization of classically chaotic diffusion for hydrogen atoms in microwave fields J. E. Bayfield, G. Casati, I. Guarneri and D. W. Sokol; 14. Inhibition of quantum transport due to 'scars' of unstable periodic orbits R. V. Jensen, M. M. Sanders, M. Saraceno and B. Sundaram; 15. Rubidium Rydberg atoms in strong fields G. Benson, G. Raithel and H. Walther; 16. Diamagnetic Rydberg atom: confrontation of calculated and observed spectra C.-H. Iu, G. R. Welch, M. M. Kash, D. Kleppner, D. Delande and J. C. Gay; 17. Semiclassical approximation for the quantum states of a hydrogen atom in a magnetic field near the ionization limit M. Y. Kuchiev and O. P. Sushkov; 18. The semiclassical helium atom D. Wintgen, K. Richter and G. Tanner; 19. Stretched helium: a model for quantum chaos in two-electron atoms R. Blümel and W. P. Reinhardt; Part III. Semiclassical Approximations: 20. Semiclassical theory of spectral rigidity M. V. Berry; 21. Semiclassical structure of trace formulas R. G. Littlejohn; 22. h-Expansion for quantum trace formulas P. Gaspard; 23. Pinball scattering B. Eckhardt, G. Russberg, P. Cvitanovic, P. E. Rosenqvist and P. Scherer; 24. Logarithm breaking time in quantum chaos G. P. Berman and G. M. Zaslavsky; 25. Semiclassical propagation: how long can it last? M. A. Sepulveda, S. Tomsovic and E. J. Heller; 26. The quantized Baker's transformation N. L. Balazs and A. Voros; 27. Classical structures in the quantized baker transformation M. Saraceno; 28. Quantum nodal points as fingerprints of classical chaos P. Leboeuf and A. Voros; 29. Chaology of action billiards A. M. Ozorio de Almeida and M. A. M. de Aguiar; Part IV. Level Statistics and Random Matrix Theory: 30. Characterization of chaotic quantum spectra and universality of level fluctuation laws O. Bohigas, M. J. Giannono, and C. Schmit; 31. Quantum chaos, localization and band random matrices F. M. Izrailev; 32. Structural invariance in channel space: a step toward understanding chaotic scattering in quantum mechanics T. H. Seligman; 33. Spectral properties of a Fermi accelerating disk R. Badrinarayanan and J. J. José; 34. Spectral properties of systems with dynamical localization T. Dittrich and U. Smilansky; 35. Unbound quantum diffusion and fractal spectra T. Geisel, R. Ketzmerick and G. Petschel; 36. Microwave studies in irregularly shaped billiards H.-J. Stöckmann, J. Stein and M. Kollman; Index.

Quantum Chaos

NASA Astrophysics Data System (ADS)

Casati, Giulio; Chirikov, Boris

1995-04-01

Preface; Acknowledgments; Introduction: 1. The legacy of chaos in quantum mechanics G. Casati and B. V. Chirikov; Part I. Classical Chaos and Quantum Localization: 2. Stochastic behaviour of a quantum pendulum under a periodic perturbation G. Casati, B. V. Chirikov, F. M. Izrailev and J. Ford; 3. Quantum dynamics of a nonintegrable system D. R. Grempel, R. E. Prange and S. E. Fishman; 4. Excitation of molecular rotation by periodic microwave pulses. A testing ground for Anderson localization R. Blümel, S. Fishman and U. Smilansky; 5. Localization of diffusive excitation in multi-level systems D. K. Shepelyansky; 6. Classical and quantum chaos for a kicked top F. Haake, M. Kus and R. Scharf; 7. Self-similarity in quantum dynamics L. E. Reichl and L. Haoming; 8. Time irreversibility of classically chaotic quantum dynamics K. Ikeda; 9. Effect of noise on time-dependent quantum chaos E. Ott, T. M. Antonsen Jr and J. D. Hanson; 10. Dynamical localization, dissipation and noise R. F. Graham; 11. Maximum entropy models and quantum transmission in disordered systems J.-L. Pichard and M. Sanquer; 12. Solid state 'atoms' in intense oscillating fields M. S. Sherwin; Part II. Atoms in Strong Fields: 13. Localization of classically chaotic diffusion for hydrogen atoms in microwave fields J. E. Bayfield, G. Casati, I. Guarneri and D. W. Sokol; 14. Inhibition of quantum transport due to 'scars' of unstable periodic orbits R. V. Jensen, M. M. Sanders, M. Saraceno and B. Sundaram; 15. Rubidium Rydberg atoms in strong fields G. Benson, G. Raithel and H. Walther; 16. Diamagnetic Rydberg atom: confrontation of calculated and observed spectra C.-H. Iu, G. R. Welch, M. M. Kash, D. Kleppner, D. Delande and J. C. Gay; 17. Semiclassical approximation for the quantum states of a hydrogen atom in a magnetic field near the ionization limit M. Y. Kuchiev and O. P. Sushkov; 18. The semiclassical helium atom D. Wintgen, K. Richter and G. Tanner; 19. Stretched helium: a model for quantum chaos in two-electron atoms R. Blümel and W. P. Reinhardt; Part III. Semiclassical Approximations: 20. Semiclassical theory of spectral rigidity M. V. Berry; 21. Semiclassical structure of trace formulas R. G. Littlejohn; 22. h-Expansion for quantum trace formulas P. Gaspard; 23. Pinball scattering B. Eckhardt, G. Russberg, P. Cvitanovic, P. E. Rosenqvist and P. Scherer; 24. Logarithm breaking time in quantum chaos G. P. Berman and G. M. Zaslavsky; 25. Semiclassical propagation: how long can it last? M. A. Sepulveda, S. Tomsovic and E. J. Heller; 26. The quantized Baker's transformation N. L. Balazs and A. Voros; 27. Classical structures in the quantized baker transformation M. Saraceno; 28. Quantum nodal points as fingerprints of classical chaos P. Leboeuf and A. Voros; 29. Chaology of action billiards A. M. Ozorio de Almeida and M. A. M. de Aguiar; Part IV. Level Statistics and Random Matrix Theory: 30. Characterization of chaotic quantum spectra and universality of level fluctuation laws O. Bohigas, M. J. Giannono, and C. Schmit; 31. Quantum chaos, localization and band random matrices F. M. Izrailev; 32. Structural invariance in channel space: a step toward understanding chaotic scattering in quantum mechanics T. H. Seligman; 33. Spectral properties of a Fermi accelerating disk R. Badrinarayanan and J. J. José; 34. Spectral properties of systems with dynamical localization T. Dittrich and U. Smilansky; 35. Unbound quantum diffusion and fractal spectra T. Geisel, R. Ketzmerick and G. Petschel; 36. Microwave studies in irregularly shaped billiards H.-J. Stöckmann, J. Stein and M. Kollman; Index.

A quantum model of option pricing: When Black-Scholes meets Schrödinger and its semi-classical limit

NASA Astrophysics Data System (ADS)

Contreras, Mauricio; Pellicer, Rely; Villena, Marcelo; Ruiz, Aaron

2010-12-01

The Black-Scholes equation can be interpreted from the point of view of quantum mechanics, as the imaginary time Schrödinger equation of a free particle. When deviations of this state of equilibrium are considered, as a product of some market imperfection, such as: Transaction cost, asymmetric information issues, short-term volatility, extreme discontinuities, or serial correlations; the classical non-arbitrage assumption of the Black-Scholes model is violated, implying a non-risk-free portfolio. From Haven (2002) [1] we know that an arbitrage environment is a necessary condition to embedding the Black-Scholes option pricing model in a more general quantum physics setting. The aim of this paper is to propose a new Black-Scholes-Schrödinger model based on the endogenous arbitrage option pricing formulation introduced by Contreras et al. (2010) [2]. Hence, we derive a more general quantum model of option pricing, that incorporates arbitrage as an external time dependent force, which has an associated potential related to the random dynamic of the underlying asset price. This new resultant model can be interpreted as a Schrödinger equation in imaginary time for a particle of mass 1/σ2 with a wave function in an external field force generated by the arbitrage potential. As pointed out above, this new model can be seen as a more general formulation, where the perfect market equilibrium state postulated by the Black-Scholes model represent a particular case. Finally, since the Schrödinger equation is in place, we can apply semiclassical methods, of common use in theoretical physics, to find an approximate analytical solution of the Black-Scholes equation in the presence of market imperfections, as it is the case of an arbitrage bubble. Here, as a numerical illustration of the potential of this Schrödinger equation analogy, the semiclassical approximation is performed for different arbitrage bubble forms (step, linear and parabolic) and compare with the exact solution of our general quantum model of option pricing.

Can chaos be observed in quantum gravity?

NASA Astrophysics Data System (ADS)

Dittrich, Bianca; Höhn, Philipp A.; Koslowski, Tim A.; Nelson, Mike I.

2017-06-01

Full general relativity is almost certainly 'chaotic'. We argue that this entails a notion of non-integrability: a generic general relativistic model, at least when coupled to cosmologically interesting matter, likely possesses neither differentiable Dirac observables nor a reduced phase space. It follows that the standard notion of observable has to be extended to include non-differentiable or even discontinuous generalized observables. These cannot carry Poisson-algebraic structures and do not admit a standard quantization; one thus faces a quantum representation problem of gravitational observables. This has deep consequences for a quantum theory of gravity, which we investigate in a simple model for a system with Hamiltonian constraint that fails to be completely integrable. We show that basing the quantization on standard topology precludes a semiclassical limit and can even prohibit any solutions to the quantum constraints. Our proposed solution to this problem is to refine topology such that a complete set of Dirac observables becomes continuous. In the toy model, it turns out that a refinement to a polymer-type topology, as e.g. used in loop gravity, is sufficient. Basing quantization of the toy model on this finer topology, we find a complete set of quantum Dirac observables and a suitable semiclassical limit. This strategy is applicable to realistic candidate theories of quantum gravity and thereby suggests a solution to a long-standing problem which implies ramifications for the very concept of quantization. Our work reveals a qualitatively novel facet of chaos in physics and opens up a new avenue of research on chaos in gravity which hints at deep insights into the structure of quantum gravity.

Magnetoresistance of non-180° domain wall in the presence of electron-photon interaction

NASA Astrophysics Data System (ADS)

Majidi, Roya

2013-04-01

In the present paper, influence of photon on resistance of non-180° domain wall in metallic magnetic nanowires has been studied using the semiclassical approach. The analysis has been based on the Boltzmann transport equation, within the relaxation time approximation. The one-dimensional Néel-type domain wall between two ferromagnetic domains with relative magnetization angle less than 180° is considered. By increasing this angle, the contribution of the domain wall in the resistivity of the nanowire becomes considerable. It is also found that the fundamental contribution of the domain wall in resistivity can be controlled by propagating photon. These results are valuable in designing spintronic devices based on magnetic nanowires.

Two-proton pickup studies with the (6Li,8B) reaction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weisenmiller, R.B.

1976-12-03

The (/sup 6/Li,/sup 8/B) reaction has been investigated on targets of /sup 26/Mg, /sup 24/Mg, /sup 16/O, /sup 13/C, /sup 12/C, /sup 11/B, /sup 10/B, and /sup 9/Be at a bombarding energy of 80.0 MeV, and on targets of /sup 16/O, /sup 12/C, /sup 9/Be, /sup 7/Li, and /sup 6/Li at a bombarding energy of 93.3 MeV. Only levels consistent with direct, single-step two-proton pickup reaction mechanisms were observed to be strongly populated. On T/sub z/ = 0 targets, the spectroscopic selectivity of this reaction resembles that of the analogous (p,t) reaction. Additionally, these data demonstrate the dominance of spatiallymore » symmetric transfer of the two protons. On T/sub z/ greater than 0 targets the (/sup 6/Li,/sup 8/B) reaction was employed to locate two previously unreported levels (at 7.47 +- 0.05 MeV and 8.86 +- 0.07 MeV) in the T/sub z/ = 2 nuclide /sup 24/Ne and to establish the low-lying 1p-shell states in the T/sub z/ = /sup 3///sub 2/ nuclei /sup 11/Be, /sup 9/Li, and /sup 7/He. However, no evidence was seen for any narrow levels in the T/sub z/ = /sup 3///sub 2/ nuclide /sup 5/H nor for any narrow excited states in /sup 7/He. The angular distributions reported here are rather featureless and decrease monotonically with increasing angle. This behavior can be shown by a semi-classical reaction theory to be a consequence of the reaction kinematics. A semi-classical approach also suggests that the kinematic term in the transition matrix element is only weakly dependent upon the angular momentum transfer (which is consistent with simple Distorted Wave Born Approximation calculations). However, only qualitative agreement was obtained between the observed relative transition yields and semi-classical predictions, using the two-nucleon coefficients of fractional parentage of Cohen and Kurath, probably due to the limitations of the semi-classical reaction theory.« less

Semiclassical (qft) and Quantum (string) Rotating Black Holes and Their Evaporation:. New Results

NASA Astrophysics Data System (ADS)

Bouchareb, A.; Ramón Medrano, M.; Sánchez, N. G.

Combination of both quantum field theory (QFT) and string theory in curved backgrounds in a consistent framework, the string analogue model, allows us to provide a full picture of the Kerr-Newman black hole and its evaporation going beyond the current picture. We compute the quantum emission cross-section of strings by a Kerr-Newman black hole (KNbh). It shows the black hole emission at the Hawking temperature Tsem in the early stage of evaporation and the new string emission featuring a Hagedorn transition into a string state of temperature Ts at the last stages. New bounds on J and Q emerge in the quantum string regime (besides the known ones of the classical/semiclassical QFT regime). The last state of evaporation of a semiclassical Kerr-Newman black hole with mass M > mPl, angular momentum J and charge Q is a string state of temperature Ts, string mass Ms, J = 0 and Q = 0, decaying as usual quantum strings do into all kinds of particles. (Naturally, in this framework, there is no loss of information, (there is no paradox at all).) We compute the string entropy Ss(m, j) from the microscopic string density of states of mass m and spin mode j, ρ(m, j). (Besides the Hagedorn transition at Ts) we find for high j (extremal string states j → m2α‧c), a new phase transition at a temperature Tsj = √ {j/hbar }Ts, higher than Ts. By precisely identifying the semiclassical and quantum (string) gravity regimes, we find a new formula for the Kerr black hole entropy Ssem(M, J), as a function of the usual Bekenstein-Hawking entropy S sem(0). For M ≫ mPl and J < GM2/c, S sem(0) is the leading term, but for high angular momentum, (nearly extremal case J = GM2/c), a gravitational phase transition operates and the whole entropy Ssem is drastically different from the Bekenstein-Hawking entropy S sem(0). This new extremal black hole transition occurs at a temperature Tsem J = (J/ℏ)Tsem, higher than the Hawking temperature Tsem.

Relational quadrilateralland II: The Quantum Theory

NASA Astrophysics Data System (ADS)

Anderson, Edward; Kneller, Sophie

2014-04-01

We provide the quantum treatment of the relational quadrilateral. The underlying reduced configuration spaces are ℂℙ2 and the cone over this. We consider exact free and isotropic HO potential cases and perturbations about these. Moreover, our purely relational kinematical quantization is distinct from the usual one for ℂℙ2, which turns out to carry absolutist connotations instead. Thus, this paper is the first to note absolute-versus-relational motion distinctions at the kinematical rather than dynamical level. It is also an example of value to the discussion of kinematical quantization along the lines of Isham, 1984. The relational quadrilateral is the simplest RPM whose mathematics is not standard in atomic physics (the triangle and four particles on a line are both based on 𝕊2 and ℝ3 mathematics). It is far more typical of the general quantum relational N-a-gon than the previously studied case of the relational triangle. We consider useful integrals as regards perturbation theory and the peaking interpretation of quantum cosmology. We subsequently consider problem of time (PoT) applications of this: quantum Kuchař beables, the Machian version of the semiclassical approach and the timeless naïve Schrödinger interpretation. These go toward extending the combined Machian semiclassical-Histories-Timeless Approach of [Int. J. Mod. Phys. D23 (2014) 1450014] to the case of the quadrilateral, which will be treated in subsequent papers.

Quantum cosmology of a conformal multiverse

NASA Astrophysics Data System (ADS)

Robles-Pérez, Salvador J.

2017-09-01

This paper studies the cosmology of a homogeneous and isotropic spacetime endorsed with a conformally coupled massless scalar field. We find six different solutions of the Friedmann equation that represent six different types of universes, and all of them are periodically distributed along the complex time axis. From a classical point of view, they are then isolated, separated by Euclidean regions that represent quantum mechanical barriers. Quantum mechanically, however, there is a nonzero probability for the state of the universes to tunnel out through a Euclidean instanton and suffer a sudden transition to another state of the spacetime. We compute the probability of transition for this and other nonlocal processes like the creation of universes in entangled pairs and, generally speaking, in multipartite entangled states. We obtain the quantum state of a single universe within the formalism of the Wheeler-DeWitt equation and give the semiclassical state of the universes that describes the quantum mechanics of a scalar field propagating in a de Sitter background spacetime. We show that the superposition principle of the quantum mechanics of matter fields alone is an emergent feature of the semiclassical description of the universe that is not valid, for instance, in the spacetime foam. We use the third quantization formalism to describe the creation of an entangled pair of universes with opposite signs of the momentum conjugated to the scale factor. Each universe of the entangled pair represents an expanding spacetime in terms of the Wentzel-Kramers-Brillouin (WKB) time experienced by internal observers in their particle physics experiments. We compute the effective value of the Friedmann equation of the background spacetime of the two entangled universes, and thus, the effect that the entanglement would have in their expansion rates. We analyze as well the effects of the interuniversal entanglement in the properties of the scalar fields that propagate in each spacetime of the entangled pair. We find that the largest modes of the scalar field are unaware of the entanglement between the universes, but the effects can be significant for the lowest modes, allowing us to compute, in principle, detailed observational imprints of the multiverse in the properties of a single universe like ours.

General Linewidth Formula for Steady-State Multimode Lasing in Arbitrary Cavities

NASA Astrophysics Data System (ADS)

Chong, Y. D.; Stone, A. Douglas

2012-08-01

A formula for the laser linewidth of arbitrary cavities in the multimode nonlinear regime is derived from a scattering analysis of the solutions to semiclassical laser theory. The theory generalizes previous treatments of the effects of gain and openness described by the Petermann factor. The linewidth is expressed using quantities based on the nonlinear scattering matrix, which can be computed from steady-state ab initio laser theory; unlike previous treatments, no passive cavity or phenomenological parameters are involved. We find that low cavity quality factor, combined with significant dielectric dispersion, can cause substantial deviations from the Shawlow-Townes-Petermann theory.

Universality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schrödinger Equation

NASA Astrophysics Data System (ADS)

Tikan, Alexey; Billet, Cyril; El, Gennady; Tovbis, Alexander; Bertola, Marco; Sylvestre, Thibaut; Gustave, Francois; Randoux, Stephane; Genty, Goëry; Suret, Pierre; Dudley, John M.

2017-07-01

We report experimental confirmation of the universal emergence of the Peregrine soliton predicted to occur during pulse propagation in the semiclassical limit of the focusing nonlinear Schrödinger equation. Using an optical fiber based system, measurements of temporal focusing of high power pulses reveal both intensity and phase signatures of the Peregrine soliton during the initial nonlinear evolution stage. Experimental and numerical results are in very good agreement, and show that the universal mechanism that yields the Peregrine soliton structure is highly robust and can be observed over a broad range of parameters.

Stringent and efficient assessment of boson-sampling devices.

PubMed

Tichy, Malte C; Mayer, Klaus; Buchleitner, Andreas; Mølmer, Klaus

2014-07-11

Boson sampling holds the potential to experimentally falsify the extended Church-Turing thesis. The computational hardness of boson sampling, however, complicates the certification that an experimental device yields correct results in the regime in which it outmatches classical computers. To certify a boson sampler, one needs to verify quantum predictions and rule out models that yield these predictions without true many-boson interference. We show that a semiclassical model for many-boson propagation reproduces coarse-grained observables that are proposed as witnesses of boson sampling. A test based on Fourier matrices is demonstrated to falsify physically plausible alternatives to coherent many-boson propagation.

VizieR Online Data Catalog: Stark broadening of XeVIII spectral lines (Dimitrijevic+, 2015)

NASA Astrophysics Data System (ADS)

Dimitrijevic, M. S.; Simic, Z.; Kovacevic, A.; Valjarevic, A.; Sahal-Brechot, S.

2018-01-01

By means of the code based on semiclassical perturbation theory we have calculated widths and shifts for 60 transitions of Xe VIII. The needed energy levels have been taken from Saloman (2004JPCRD..33..765S). Oscillator strengths have been calculated by using the method of Bates & Damgaard (1949RSPTA.242..101B) and the tables of Oertel & Shomo (1968ApJS...16..175O). For higher levels, oscillator strengths have been calculated according to Van Regemorter, Hoang Binh & Prud'homme (1979, J. Phys. B, 12, 1073). (1 data file).

The coupled three-dimensional wave packet approach to reactive scattering

NASA Astrophysics Data System (ADS)

Marković, Nikola; Billing, Gert D.

1994-01-01

A recently developed scheme for time-dependent reactive scattering calculations using three-dimensional wave packets is applied to the D+H2 system. The present method is an extension of a previously published semiclassical formulation of the scattering problem and is based on the use of hyperspherical coordinates. The convergence requirements are investigated by detailed calculations for total angular momentum J equal to zero and the general applicability of the method is demonstrated by solving the J=1 problem. The inclusion of the geometric phase is also discussed and its effect on the reaction probability is demonstrated.

Tunnel determinants from spectral zeta functions. Instanton effects in quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Izquierdo, A. Alonso; Guilarte, J. Mateos

2014-07-23

In this paper we develop an spectral zeta function regularization procedure on the determinants of instanton fluctuation operators that describe the semi-classical order of tunnel effects between degenerate vacua.

Natural inflation from polymer quantization

NASA Astrophysics Data System (ADS)

Ali, Masooma; Seahra, Sanjeev S.

2017-11-01

We study the polymer quantization of a homogeneous massive scalar field in the early Universe using a prescription inequivalent to those previously appearing in the literature. Specifically, we assume a Hilbert space for which the scalar field momentum is well defined but its amplitude is not. This is closer in spirit to the quantization scheme of loop quantum gravity, in which no unique configuration operator exists. We show that in the semiclassical approximation, the main effect of this polymer quantization scheme is to compactify the phase space of chaotic inflation in the field amplitude direction. This gives rise to an effective scalar potential closely resembling that of hybrid natural inflation. Unlike polymer schemes in which the scalar field amplitude is well defined, the semiclassical dynamics involves a past cosmological singularity; i.e., this approach does not mitigate the big bang.

On the derivation of the semiclassical approximation to the quantum propagator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fischer, Stefan G., E-mail: stefan.fischer@physik.uni-freiburg.de; Buchleitner, Andreas

2015-07-15

In order to rigorously derive the amplitude factor of the semiclassical approximation to the quantum propagator, we extend an existing method originally devised to evaluate Gaussian path-integral expressions. Using a result which relates the determinant of symmetric block-tridiagonal matrices to the determinants of their blocks, two difference equations are obtained. The first one allows to establish the connection of the amplitude factor to Jacobi’s accessory equations in the continuous-time limit, while the second one leads to an additional factor which, however, contributes to the final result only in exceptional cases. In order to demonstrate the wide applicability of these differencemore » equations, we treat explicitly the case where the time-sliced Lagrangian is written in generalized coordinates, for which a general derivation has so far been unavailable.« less

Borel Summability of Perturbative Series in 4D N=2 and 5D N=1 Supersymmetric Theories.

PubMed

Honda, Masazumi

2016-05-27

We study weak coupling perturbative series in 4D N=2 and 5D N=1 supersymmetric gauge theories with Lagrangians. We prove that the perturbative series of these theories in the zero-instanton sector are Borel summable for various observables. Our result for the 4D N=2 case supports an expectation from a recent proposal on a semiclassical realization of infrared renormalons in QCD-like theories, where the semiclassical solution does not exist in N=2 theories and the perturbative series are unambiguous, namely, Borel summable. We also prove that the perturbative series in an arbitrary number of instanton sectors are Borel summable for a wide class of theories. It turns out that exact results can be obtained by summing over the Borel resummations with every instanton number.

Secret loss of unitarity due to the classical background

NASA Astrophysics Data System (ADS)

Yang, I.-Sheng

2017-07-01

We show that a quantum subsystem can become significantly entangled with a classical background through a process with few or no semiclassical backreactions. We study two quantum harmonic oscillators coupled to each other in a time-independent Hamiltonian. We compare it to its semiclassical approximation in which one of the oscillators is treated as the classical background. In this approximation, the remaining quantum oscillator has an effective Hamiltonian which is time-dependent, and its evolution appears to be unitary. However, in the fully quantum model, the two oscillators can entangle each other. Thus, the unitarity of either individual oscillator is never guaranteed. We derive the critical time scale after which the unitarity of either individual oscillator is irrevocably lost. In particular, we give an example that in the adiabatic limit, unitarity is lost before other relevant questions can be addressed.

Entropy production in a photovoltaic cell

NASA Astrophysics Data System (ADS)

Ansari, Mohammad H.

2017-05-01

We evaluate entropy production in a photovoltaic cell that is modeled by four electronic levels resonantly coupled to thermally populated field modes at different temperatures. We use a formalism recently proposed, the so-called multiple parallel worlds, to consistently address the nonlinearity of entropy in terms of density matrix. Our result shows that entropy production is the difference between two flows: a semiclassical flow that linearly depends on occupational probabilities, and another flow that depends nonlinearly on quantum coherence and has no semiclassical analog. We show that entropy production in the cells depends on environmentally induced decoherence time and energy detuning. We characterize regimes where reversal flow of information takes place from a cold to hot bath. Interestingly, we identify a lower bound on entropy production, which sets limitations on the statistics of dissipated heat in the cells.

Coherent and Semiclassical States of a Charged Particle in Electromagnetic Fields

NASA Astrophysics Data System (ADS)

Pereira, A. S.

2018-06-01

In the present article, we extend our study (Bagrov et al., Braz. J. Phys. 45, 369, 2015) of generalized coherent states (GCS) of a one-dimensional particle considering such important physical system as a three-dimensional charged particle in electric and magnetic fields. Constructing GCS in a many-dimensional case, we meet technical complications that make the consideration nontrivial and instructive. The GCS of the system under consideration are constructed. We study the properties of this GCS such as completeness relations, minimization of uncertainty relations, and so on. We point out which family of the obtained GCS of a charged particle in a magnetic field is related to the CS constructed first by Malkin and Man'ko. We obtain conditions under which some of the GCS can be considered as semiclassical states (SS).

Ring-polymer instanton theory of electron transfer in the nonadiabatic limit

DOE Office of Scientific and Technical Information (OSTI.GOV)

Richardson, Jeremy O., E-mail: jeremy.richardson@fau.de

We take the golden-rule instanton method derived in the previous paper [J. O. Richardson, R. Bauer, and M. Thoss, J. Chem. Phys. 143, 134115 (2015)] and reformulate it using a ring-polymer instanton approach. This gives equations which can be used to compute the rates of electron-transfer reactions in the nonadiabatic (golden-rule) limit numerically within a semiclassical approximation. The multidimensional ring-polymer instanton trajectories are obtained efficiently by minimization of the action. In this form, comparison with Wolynes’ quantum instanton method [P. G. Wolynes, J. Chem. Phys. 87, 6559 (1987)] is possible and we show that our semiclassical approach is the steepest-descentmore » limit of this method. We discuss advantages and disadvantages of both methods and give examples of where the new approach is more accurate.« less

Coherent and Semiclassical States of a Charged Particle in Electromagnetic Fields

NASA Astrophysics Data System (ADS)

Pereira, A. S.

2018-03-01

In the present article, we extend our study (Bagrov et al., Braz. J. Phys. 45, 369, 2015) of generalized coherent states (GCS) of a one-dimensional particle considering such important physical system as a three-dimensional charged particle in electric and magnetic fields. Constructing GCS in a many-dimensional case, we meet technical complications that make the consideration nontrivial and instructive. The GCS of the system under consideration are constructed. We study the properties of this GCS such as completeness relations, minimization of uncertainty relations, and so on. We point out which family of the obtained GCS of a charged particle in a magnetic field is related to the CS constructed first by Malkin and Man'ko. We obtain conditions under which some of the GCS can be considered as semiclassical states (SS).

Dynamical cluster approximation plus semiclassical approximation study for a Mott insulator and d-wave pairing

NASA Astrophysics Data System (ADS)

Kim, SungKun; Lee, Hunpyo

2017-06-01

Via a dynamical cluster approximation with N c = 4 in combination with a semiclassical approximation (DCA+SCA), we study the doped two-dimensional Hubbard model. We obtain a plaquette antiferromagnetic (AF) Mott insulator, a plaquette AF ordered metal, a pseudogap (or d-wave superconductor) and a paramagnetic metal by tuning the doping concentration. These features are similar to the behaviors observed in copper-oxide superconductors and are in qualitative agreement with the results calculated by the cluster dynamical mean field theory with the continuous-time quantum Monte Carlo (CDMFT+CTQMC) approach. The results of our DCA+SCA differ from those of the CDMFT+CTQMC approach in that the d-wave superconducting order parameters are shown even in the high doped region, unlike the results of the CDMFT+CTQMC approach. We think that the strong plaquette AF orderings in the dynamical cluster approximation (DCA) with N c = 4 suppress superconducting states with increasing doping up to strongly doped region, because frozen dynamical fluctuations in a semiclassical approximation (SCA) approach are unable to destroy those orderings. Our calculation with short-range spatial fluctuations is initial research, because the SCA can manage long-range spatial fluctuations in feasible computational times beyond the CDMFT+CTQMC tool. We believe that our future DCA+SCA calculations should supply information on the fully momentum-resolved physical properties, which could be compared with the results measured by angle-resolved photoemission spectroscopy experiments.

Experimental studies by complementary terahertz techniques and semi-classical calculations of N2- broadening coefficients of CH335Cl

NASA Astrophysics Data System (ADS)

Guinet, M.; Rohart, F.; Buldyreva, J.; Gupta, V.; Eliet, S.; Motiyenko, R. A.; Margulès, L.; Cuisset, A.; Hindle, F.; Mouret, G.

2012-07-01

Room-temperature N2-broadening coefficients of methyl chloride rotational lines are measured over a large interval of quantum numbers (6≤J≤50, 0≤K≤18) by a submillimeter frequency-multiplication chain (J≤31) and a terahertz photomixing continuous-wave spectrometer (J≥31). In order to check the accuracy of both techniques, the measurements of identical lines are compared for J=31. The pressure broadening coefficients are deduced from line fits using mainly a Voigt profile model. The excellent signal-to-noise ratio of the frequency-multiplication scheme highlights some speed dependence effect on the line shape. Theoretical values of these coefficients are calculated by a semi-classical approach with exact trajectories. An intermolecular potential including atom-atom interactions is used for the first time. It is shown that, contrary to the previous theoretical predictions, the contributions of short-range forces are important for all values of the rotational quantum numbers. Additional testing of modifications required in the semi-classical formalism for a correct application of the cumulant expansion is also performed. It is stated that the use of the cumulant average on the rotational states of the perturbing molecule leads, for high J and small K values, to slightly higher line-broadening coefficients, as expected for the relatively strong interacting CH3Cl-N2 system. The excellent agreement between the theoretical and the experimental results ensures the reliability of these data.

Non-linear non-local molecular electrodynamics with nano-optical fields.

PubMed

Chernyak, Vladimir Y; Saurabh, Prasoon; Mukamel, Shaul

2015-10-28

The interaction of optical fields sculpted on the nano-scale with matter may not be described by the dipole approximation since the fields may vary appreciably across the molecular length scale. Rather than incrementally adding higher multipoles, it is advantageous and more physically transparent to describe the optical process using non-local response functions that intrinsically include all multipoles. We present a semi-classical approach for calculating non-local response functions based on the minimal coupling Hamiltonian. The first, second, and third order response functions are expressed in terms of correlation functions of the charge and the current densities. This approach is based on the gauge invariant current rather than the polarization, and on the vector potential rather than the electric and magnetic fields.

Dissipation and traversal time in Josephson junctions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cacciari, Ilaria; Ranfagni, Anedio; Moretti, Paolo

2010-05-01

The various ways of evaluating dissipative effects in macroscopic quantum tunneling are re-examined. The results obtained by using functional integration, while confirming those of previously given treatments, enable a comparison with available experimental results relative to Josephson junctions. A criterion based on the shortening of the semiclassical traversal time tau of the barrier with regard to dissipation can be established, according to which DELTAtau/tau > or approx. N/Q, where Q is the quality factor of the junction and N is a numerical constant of order unity. The best agreement with the experiments is obtained for N=1.11, as it results frommore » a semiempirical analysis based on an increase in the potential barrier caused by dissipative effects.« less

Real time correlation function in a single phase space integral beyond the linearized semiclassical initial value representation.

PubMed

Liu, Jian; Miller, William H

2007-06-21

It is shown how quantum mechanical time correlation functions [defined, e.g., in Eq. (1.1)] can be expressed, without approximation, in the same form as the linearized approximation of the semiclassical initial value representation (LSC-IVR), or classical Wigner model, for the correlation function [cf. Eq. (2.1)], i.e., as a phase space average (over initial conditions for trajectories) of the Wigner functions corresponding to the two operators. The difference is that the trajectories involved in the LSC-IVR evolve classically, i.e., according to the classical equations of motion, while in the exact theory they evolve according to generalized equations of motion that are derived here. Approximations to the exact equations of motion are then introduced to achieve practical methods that are applicable to complex (i.e., large) molecular systems. Four such methods are proposed in the paper--the full Wigner dynamics (full WD) and the second order WD based on "Wigner trajectories" [H. W. Lee and M. D. Scully, J. Chem. Phys. 77, 4604 (1982)] and the full Donoso-Martens dynamics (full DMD) and the second order DMD based on "Donoso-Martens trajectories" [A. Donoso and C. C. Martens, Phys. Rev. Lett. 8722, 223202 (2001)]--all of which can be viewed as generalizations of the original LSC-IVR method. Numerical tests of the four versions of this new approach are made for two anharmonic model problems, and for each the momentum autocorrelation function (i.e., operators linear in coordinate or momentum operators) and the force autocorrelation function (nonlinear operators) have been calculated. These four new approximate treatments are indeed seen to be significant improvements to the original LSC-IVR approximation.

Toward simulating complex systems with quantum effects

NASA Astrophysics Data System (ADS)

Kenion-Hanrath, Rachel Lynn

Quantum effects like tunneling, coherence, and zero point energy often play a significant role in phenomena on the scales of atoms and molecules. However, the exact quantum treatment of a system scales exponentially with dimensionality, making it impractical for characterizing reaction rates and mechanisms in complex systems. An ongoing effort in the field of theoretical chemistry and physics is extending scalable, classical trajectory-based simulation methods capable of capturing quantum effects to describe dynamic processes in many-body systems; in the work presented here we explore two such techniques. First, we detail an explicit electron, path integral (PI)-based simulation protocol for predicting the rate of electron transfer in condensed-phase transition metal complex systems. Using a PI representation of the transferring electron and a classical representation of the transition metal complex and solvent atoms, we compute the outer sphere free energy barrier and dynamical recrossing factor of the electron transfer rate while accounting for quantum tunneling and zero point energy effects. We are able to achieve this employing only a single set of force field parameters to describe the system rather than parameterizing along the reaction coordinate. Following our success in describing a simple model system, we discuss our next steps in extending our protocol to technologically relevant materials systems. The latter half focuses on the Mixed Quantum-Classical Initial Value Representation (MQC-IVR) of real-time correlation functions, a semiclassical method which has demonstrated its ability to "tune'' between quantum- and classical-limit correlation functions while maintaining dynamic consistency. Specifically, this is achieved through a parameter that determines the quantumness of individual degrees of freedom. Here, we derive a semiclassical correction term for the MQC-IVR to systematically characterize the error introduced by different choices of simulation parameters, and demonstrate the ability of this approach to optimize MQC-IVR simulations.

On the generalized geometry origin of noncommutative gauge theory

NASA Astrophysics Data System (ADS)

Jurčo, Branislav; Schupp, Peter; Vysoký, Jan

2013-07-01

We discuss noncommutative gauge theory from the generalized geometry point of view. We argue that the equivalence between the commutative and semiclassically noncommutative DBI actions is naturally encoded in the generalized geometry of D-branes.

Dam break problem for the focusing nonlinear Schrödinger equation and the generation of rogue waves

NASA Astrophysics Data System (ADS)

El, G. A.; Khamis, E. G.; Tovbis, A.

2016-09-01

We propose a novel, analytically tractable, scenario of the rogue wave formation in the framework of the small-dispersion focusing nonlinear Schrödinger (NLS) equation with the initial condition in the form of a rectangular barrier (a ‘box’). We use the Whitham modulation theory combined with the nonlinear steepest descent for the semi-classical inverse scattering transform, to describe the evolution and interaction of two counter-propagating nonlinear wave trains—the dispersive dam break flows—generated in the NLS box problem. We show that the interaction dynamics results in the emergence of modulated large-amplitude quasi-periodic breather lattices whose amplitude profiles are closely approximated by the Akhmediev and Peregrine breathers within certain space-time domain. Our semi-classical analytical results are shown to be in excellent agreement with the results of direct numerical simulations of the small-dispersion focusing NLS equation.

FAST TRACK COMMUNICATION: Semiclassical Klein Kramers and Smoluchowski equations for the Brownian motion of a particle in an external potential

NASA Astrophysics Data System (ADS)

Coffey, W. T.; Kalmykov, Yu P.; Titov, S. V.; Mulligan, B. P.

2007-01-01

The quantum Brownian motion of a particle in an external potential V(x) is treated using the master equation for the Wigner distribution function W(x, p, t) in phase space (x, p). A heuristic method of determination of diffusion coefficients in the master equation is proposed. The time evolution equation so obtained contains explicit quantum correction terms up to o(planck4) and in the classical limit, planck → 0, reduces to the Klein-Kramers equation. For a quantum oscillator, the method yields an evolution equation for W(x, p, t) coinciding with that of Agarwal (1971 Phys. Rev. A 4 739). In the non-inertial regime, by applying the Brinkman expansion of the momentum distribution in Weber functions (Brinkman 1956 Physica 22 29), the corresponding semiclassical Smoluchowski equation is derived.

Diffractive paths for weak localization in quantum billiards

NASA Astrophysics Data System (ADS)

Březinová, Iva; Stampfer, Christoph; Wirtz, Ludger; Rotter, Stefan; Burgdörfer, Joachim

2008-04-01

We study the weak-localization effect in quantum transport through a clean ballistic cavity with regular classical dynamics. We address the question which paths account for the suppression of conductance through a system where disorder and chaos are absent. By exploiting both quantum and semiclassical methods, we unambiguously identify paths that are diffractively backscattered into the cavity (when approaching the lead mouths from the cavity interior) to play a key role. Diffractive scattering couples transmitted and reflected paths and is thus essential to reproduce the weak-localization peak in reflection and the corresponding antipeak in transmission. A comparison of semiclassical calculations featuring these diffractive paths yields good agreement with full quantum calculations and experimental data. Our theory provides system-specific predictions for the quantum regime of few open lead modes and can be expected to be relevant also for mixed as well as chaotic systems.

On proton excitation of forbidden lines in positive ions

NASA Astrophysics Data System (ADS)

Burgess, Alan; Tully, John A.

2005-08-01

The semi-classical impact parameter approximations used by Bahcall and Wolf and by Bely and Faucher, for proton excitation of electric quadrupole transitions in positive ions, both fail at high energies, giving cross sections which do not fall off correctly as constant/E. This is in contrast with the pioneering example of Seaton for Fe+13 and of Reid and Schwarz for S+3, both of whom achieve the correct functional form, but do not ensure the correct constant of proportionality. By combining the Born and semi-classical approximations one can obtain cross sections which have the full correct behaviour as E → ∞, and hence, rate coefficients which have the correct high temperature behaviour (~C/T1/2 with the correct value of C). We provide a computer program for calculating these. An error in Faucher's derivation of the Born formula is also discussed.

Hawking Radiation of the Charged Particle Via Tunneling from the Reissner-Nordström Black Hole

NASA Astrophysics Data System (ADS)

Pu, Jin; Han, Yan

2017-08-01

Since Parikh and Wilczek proposed a semiclassical tunneling method to investigate the Hawking radiation of static and spherically symmetric black holes, the method has been extensively developed to study various black holes. However, in almost all of the subsequent papers, there exists a important shortcoming that the geodesic equation of the massive particle is defined inconsistently with that of the massless particle. In this paper, we propose a new idea to reinvestigate the tunneling radiation from the event horizon of the Reissner-Nordström black hole. In our treatment, by starting from the Lagrangian analysis on the action, we redefine the geodesic equation of the massive and massless particle via tunneling from the event horizon of the Reissner-Nordström black hole, which overcomes the shortcoming mentioned above. The highlight of our work is a new and important development for the Parikh-Wilczek's semiclassical tunneling method.

Collisional excitation of the highly excited hydrogen atoms in the dipole form of the semiclassical impact parameter and Born approximations

NASA Technical Reports Server (NTRS)

Omidvar, K.

1971-01-01

Expressions for the excitation cross section of the highly excited states of the hydrogenlike atoms by fast charged particles have been derived in the dipole approximation of the semiclassical impact parameter and the Born approximations, making use of a formula for the asymptotic expansion of the oscillator strength of the hydrogenlike atoms given by Menzel. When only the leading term in the asymptotic expansion is retained, the expression for the cross section becomes identical to the expression obtained by the method of the classical collision and correspondence principle given by Percival and Richards. Comparisons are made between the Bethe coefficients obtained here and the Bethe coefficients of the Born approximation for transitions where the Born calculation is available. Satisfactory agreement is obtained only for n yields n + 1 transitions, with n the principal quantum number of the excited state.

Semiclassics, Goldstone bosons and CFT data

NASA Astrophysics Data System (ADS)

Monin, A.; Pirtskhalava, D.; Rattazzi, R.; Seibold, F. K.

2017-06-01

Hellerman et al. (arXiv:1505.01537) have shown that in a generic CFT the spectrum of operators carrying a large U(1) charge can be analyzed semiclassically in an expansion in inverse powers of the charge. The key is the operator state correspondence by which such operators are associated with a finite density superfluid phase for the theory quantized on the cylinder. The dynamics is dominated by the corresponding Goldstone hydrodynamic mode and the derivative expansion coincides with the inverse charge expansion. We illustrate and further clarify this situation by first considering simple quantum mechanical analogues. We then systematize the approach by employing the coset construction for non-linearly realized space-time symmetries. Focussing on CFT3 we illustrate the case of higher rank and non-abelian groups and the computation of higher point functions. Three point function coefficients turn out to satisfy universal scaling laws and correlations as the charge and spin are varied.

Virtual Antiparticle Pairs, the Unit of Charge Epsilon and the QCD Coupling Alpha(sub s)

NASA Technical Reports Server (NTRS)

Batchelor, David

2001-01-01

New semi-classical models of virtual antiparticle pairs are used to compute the pair lifetimes, and good agreement with the Heisenberg lifetimes from quantum field theory (QFT) is found. When the results of the new models and QFT are combined, formulae for e and alpha(sub s)(q) are derived in terms of only h and c. The modeling method applies to both the electromagnetic and color forces. Evaluation of the action integral of potential field fluctuation for each interaction potential yields approx. = h/2 for both electromagnetic and color fluctuations, in agreement with QFT. Thus each model is a quantized semiclassical representation for such virtual antiparticle pairs, to good approximation. This work reduces the number of arbitrary parameters of the Standard Model by two from 18 to 16. These are remarkable, unexpected results from a basically classical method.

Binding energies and modelling of nuclei in semiclassical simulations

NASA Astrophysics Data System (ADS)

Pérez-García, M. Ángeles; Tsushima, K.; Valcarce, A.

2008-03-01

We study the binding energies of spin isospin saturated nuclei with nucleon number 8⩽A⩽100 in semiclassical Monte Carlo many-body simulations. The model Hamiltonian consists of (i) nucleon kinetic energy, (ii) a nucleon nucleon interaction potential, and (iii) an effective Pauli potential which depends on density. The basic ingredients of the nucleon nucleon potential are a short-range repulsion, and a medium-range attraction. Our results demonstrate that one can always expect to obtain the empirical binding energies for a set of nuclei by introducing a proper density dependent Pauli potential in terms of a single variable, the nucleon number, A. The present work shows that in the suggested procedure there is a delicate counterbalance of kinetic and potential energetic contributions allowing a good reproduction of the experimental nuclear binding energies. This type of calculations may be of interest in further reproduction of other properties of nuclei such as radii and also exotic nuclei.

Semiclassical transport in nearly symmetric quantum dots. II. Symmetry breaking due to asymmetric leads.

PubMed

Whitney, Robert S; Schomerus, Henning; Kopp, Marten

2009-11-01

In this work-the second of a pair of articles-we consider transport through spatially symmetric quantum dots with leads whose widths or positions do not obey the spatial symmetry. We use the semiclassical theory of transport to find the symmetry-induced contributions to weak localization corrections and universal conductance fluctuations for dots with left-right, up-down, inversion, and fourfold symmetries. We show that all these contributions are suppressed by asymmetric leads; however, they remain finite whenever leads intersect with their images under the symmetry operation. For an up-down symmetric dot, this means that the contributions can be finite even if one of the leads is completely asymmetric. We find that the suppression of the contributions to universal conductance fluctuations is the square of the suppression of contributions to weak localization. Finally, we develop a random-matrix theory model which enables us to numerically confirm these results.

Gauge Physics of Spin Hall Effect

PubMed Central

Tan, Seng Ghee; Jalil, Mansoor B. A.; Ho, Cong Son; Siu, Zhuobin; Murakami, Shuichi

2015-01-01

Spin Hall effect (SHE) has been discussed in the context of Kubo formulation, geometric physics, spin orbit force, and numerous semi-classical treatments. It can be confusing if the different pictures have partial or overlapping claims of contribution to the SHE. In this article, we present a gauge-theoretic, time-momentum elucidation, which provides a general SHE equation of motion, that unifies under one theoretical framework, all contributions of SHE conductivity due to the kinetic, the spin orbit force (Yang-Mills), and the geometric (Murakami-Fujita) effects. Our work puts right an ambiguity surrounding previously partial treatments involving the Kubo, semiclassical, Berry curvatures, or the spin orbit force. Our full treatment shows the Rashba 2DEG SHE conductivity to be instead of −, and Rashba heavy hole instead of −. This renewed treatment suggests a need to re-derive and re-calculate previously studied SHE conductivity. PMID:26689260

Characteristics of Polarisation in the Ramsauer-Townsend Minima in Strongly Coupled Semiclassic Plasmas

NASA Astrophysics Data System (ADS)

Lee, Myoung-Jae; Jung, Young-Dae

2017-10-01

The influence of quantum shielding on the Ramsauer-Townsend phenomena for the total electron-atom polarisation collision cross-section is investigated in partially ionised strongly coupled semiclassic plasmas. The result shows that the quantum shielding effect changes the position of the Ramsauer energy in partially ionised strongly coupled plasmas. It is also found that the quantum shielding effect enhances the total electron-atom collision cross-section when the collision energy is greater than the Ramsauer energy; however, it suppresses the collision cross-section when the collision energy is smaller than the Ramsauer energy. In addition, it is shown that the plasma screening effect significantly changes the position of the Ramsauer energy and the influence of plasma screening on the magnitude of the collision cross-section is more significant near the Ramsauer energy domain. The variations of the Ramsauer energy and the collision cross-section due to the quantum shielding effect are also discussed.

Role of electron-electron interference in ultrafast time-resolved imaging of electronic wavepackets

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dixit, Gopal; Santra, Robin; Department of Physics, University of Hamburg, D-20355 Hamburg

2013-04-07

Ultrafast time-resolved x-ray scattering is an emerging approach to image the dynamical evolution of the electronic charge distribution during complex chemical and biological processes in real-space and real-time. Recently, the differences between semiclassical and quantum-electrodynamical (QED) theory of light-matter interaction for scattering of ultrashort x-ray pulses from the electronic wavepacket were formally demonstrated and visually illustrated by scattering patterns calculated for an electronic wavepacket in atomic hydrogen [G. Dixit, O. Vendrell, and R. Santra, Proc. Natl. Acad. Sci. U.S.A. 109, 11636 (2012)]. In this work, we present a detailed analysis of time-resolved x-ray scattering from a sample containing a mixturemore » of non-stationary and stationary electrons within both the theories. In a many-electron system, the role of scattering interference between a non-stationary and several stationary electrons to the total scattering signal is investigated. In general, QED and semiclassical theory provide different results for the contribution from the scattering interference, which depends on the energy resolution of the detector and the x-ray pulse duration. The present findings are demonstrated by means of a numerical example of x-ray time-resolved imaging for an electronic wavepacket in helium. It is shown that the time-dependent scattering interference vanishes within semiclassical theory and the corresponding patterns are dominated by the scattering contribution from the time-independent interference, whereas the time-dependent scattering interference contribution do not vanish in the QED theory and the patterns are dominated by the scattering contribution from the non-stationary electron scattering.« less

Role of electron-electron interference in ultrafast time-resolved imaging of electronic wavepackets

NASA Astrophysics Data System (ADS)

Dixit, Gopal; Santra, Robin

2013-04-01

Ultrafast time-resolved x-ray scattering is an emerging approach to image the dynamical evolution of the electronic charge distribution during complex chemical and biological processes in real-space and real-time. Recently, the differences between semiclassical and quantum-electrodynamical (QED) theory of light-matter interaction for scattering of ultrashort x-ray pulses from the electronic wavepacket were formally demonstrated and visually illustrated by scattering patterns calculated for an electronic wavepacket in atomic hydrogen [G. Dixit, O. Vendrell, and R. Santra, Proc. Natl. Acad. Sci. U.S.A. 109, 11636 (2012)], 10.1073/pnas.1202226109. In this work, we present a detailed analysis of time-resolved x-ray scattering from a sample containing a mixture of non-stationary and stationary electrons within both the theories. In a many-electron system, the role of scattering interference between a non-stationary and several stationary electrons to the total scattering signal is investigated. In general, QED and semiclassical theory provide different results for the contribution from the scattering interference, which depends on the energy resolution of the detector and the x-ray pulse duration. The present findings are demonstrated by means of a numerical example of x-ray time-resolved imaging for an electronic wavepacket in helium. It is shown that the time-dependent scattering interference vanishes within semiclassical theory and the corresponding patterns are dominated by the scattering contribution from the time-independent interference, whereas the time-dependent scattering interference contribution do not vanish in the QED theory and the patterns are dominated by the scattering contribution from the non-stationary electron scattering.

Extended linear regime of cavity-QED enhanced optical circular birefringence induced by a charged quantum dot

NASA Astrophysics Data System (ADS)

Hu, C. Y.; Rarity, J. G.

2015-02-01

Giant optical Faraday rotation (GFR) and giant optical circular birefringence (GCB) induced by a single quantum-dot spin in an optical microcavity can be regarded as linear effects in the weak-excitation approximation if the input field lies in the low-power limit [Hu et al., Phys. Rev. B 78, 085307 (2008), 10.1103/PhysRevB.78.085307; Hu et al., Phys. Rev. B 80, 205326 (2009), 10.1103/PhysRevB.80.205326]. In this work, we investigate the transition from the weak-excitation approximation moving into the saturation regime comparing a semiclassical approximation with the numerical results from a quantum optics toolbox [Tan, J. Opt. B 1, 424 (1999), 10.1088/1464-4266/1/4/312]. We find that the GFR and GCB around the cavity resonance in the strong-coupling regime are input field independent at intermediate powers and can be well described by the semiclassical approximation. Those associated with the dressed state resonances in the strong-coupling regime or merging with the cavity resonance in the Purcell regime are sensitive to input field at intermediate powers, and cannot be well described by the semiclassical approximation due to the quantum-dot saturation. As the GFR and GCB around the cavity resonance are relatively immune to the saturation effects, the rapid readout of single-electron spins can be carried out with coherent state and other statistically fluctuating light fields. This also shows that high-speed quantum entangling gates, robust against input power variations, can be built exploiting these linear effects.

Role of electron-electron interference in ultrafast time-resolved imaging of electronic wavepackets.

PubMed

Dixit, Gopal; Santra, Robin

2013-04-07

Ultrafast time-resolved x-ray scattering is an emerging approach to image the dynamical evolution of the electronic charge distribution during complex chemical and biological processes in real-space and real-time. Recently, the differences between semiclassical and quantum-electrodynamical (QED) theory of light-matter interaction for scattering of ultrashort x-ray pulses from the electronic wavepacket were formally demonstrated and visually illustrated by scattering patterns calculated for an electronic wavepacket in atomic hydrogen [G. Dixit, O. Vendrell, and R. Santra, Proc. Natl. Acad. Sci. U.S.A. 109, 11636 (2012)]. In this work, we present a detailed analysis of time-resolved x-ray scattering from a sample containing a mixture of non-stationary and stationary electrons within both the theories. In a many-electron system, the role of scattering interference between a non-stationary and several stationary electrons to the total scattering signal is investigated. In general, QED and semiclassical theory provide different results for the contribution from the scattering interference, which depends on the energy resolution of the detector and the x-ray pulse duration. The present findings are demonstrated by means of a numerical example of x-ray time-resolved imaging for an electronic wavepacket in helium. It is shown that the time-dependent scattering interference vanishes within semiclassical theory and the corresponding patterns are dominated by the scattering contribution from the time-independent interference, whereas the time-dependent scattering interference contribution do not vanish in the QED theory and the patterns are dominated by the scattering contribution from the non-stationary electron scattering.

Heat-machine control by quantum-state preparation: from quantum engines to refrigerators.

PubMed

Gelbwaser-Klimovsky, D; Kurizki, G

2014-08-01

We explore the dependence of the performance bounds of heat engines and refrigerators on the initial quantum state and the subsequent evolution of their piston, modeled by a quantized harmonic oscillator. Our goal is to provide a fully quantized treatment of self-contained (autonomous) heat machines, as opposed to their prevailing semiclassical description that consists of a quantum system alternately coupled to a hot or a cold heat bath and parametrically driven by a classical time-dependent piston or field. Here, by contrast, there is no external time-dependent driving. Instead, the evolution is caused by the stationary simultaneous interaction of two heat baths (having distinct spectra and temperatures) with a single two-level system that is in turn coupled to the quantum piston. The fully quantized treatment we put forward allows us to investigate work extraction and refrigeration by the tools of quantum-optical amplifier and dissipation theory, particularly, by the analysis of amplified or dissipated phase-plane quasiprobability distributions. Our main insight is that quantum states may be thermodynamic resources and can provide a powerful handle, or control, on the efficiency of the heat machine. In particular, a piston initialized in a coherent state can cause the engine to produce work at an efficiency above the Carnot bound in the linear amplification regime. In the refrigeration regime, the coefficient of performance can transgress the Carnot bound if the piston is initialized in a Fock state. The piston may be realized by a vibrational mode, as in nanomechanical setups, or an electromagnetic field mode, as in cavity-based scenarios.

Heat-machine control by quantum-state preparation: From quantum engines to refrigerators

NASA Astrophysics Data System (ADS)

Gelbwaser-Klimovsky, D.; Kurizki, G.

2014-08-01

We explore the dependence of the performance bounds of heat engines and refrigerators on the initial quantum state and the subsequent evolution of their piston, modeled by a quantized harmonic oscillator. Our goal is to provide a fully quantized treatment of self-contained (autonomous) heat machines, as opposed to their prevailing semiclassical description that consists of a quantum system alternately coupled to a hot or a cold heat bath and parametrically driven by a classical time-dependent piston or field. Here, by contrast, there is no external time-dependent driving. Instead, the evolution is caused by the stationary simultaneous interaction of two heat baths (having distinct spectra and temperatures) with a single two-level system that is in turn coupled to the quantum piston. The fully quantized treatment we put forward allows us to investigate work extraction and refrigeration by the tools of quantum-optical amplifier and dissipation theory, particularly, by the analysis of amplified or dissipated phase-plane quasiprobability distributions. Our main insight is that quantum states may be thermodynamic resources and can provide a powerful handle, or control, on the efficiency of the heat machine. In particular, a piston initialized in a coherent state can cause the engine to produce work at an efficiency above the Carnot bound in the linear amplification regime. In the refrigeration regime, the coefficient of performance can transgress the Carnot bound if the piston is initialized in a Fock state. The piston may be realized by a vibrational mode, as in nanomechanical setups, or an electromagnetic field mode, as in cavity-based scenarios.

Quantum State Diffusion

NASA Astrophysics Data System (ADS)

Percival, Ian

2005-10-01

1. Introduction; 2. Brownian motion and Itô calculus; 3. Open quantum systems; 4. Quantum state diffusion; 5. Localisation; 6. Numerical methods and examples; 7. Quantum foundations; 8. Primary state diffusion; 9. Classical dynamics of quantum localisation; 10. Semiclassical theory and linear dynamics.

Resonance-assisted decay of nondispersive wave packets.

PubMed

Wimberger, Sandro; Schlagheck, Peter; Eltschka, Christopher; Buchleitner, Andreas

2006-07-28

We present a quantitative semiclassical theory for the decay of nondispersive electronic wave packets in driven, ionizing Rydberg systems. Statistically robust quantities are extracted combining resonance-assisted tunneling with subsequent transport across chaotic phase space and a final ionization step.

Quantum and semiclassical spin networks: from atomic and molecular physics to quantum computing and gravity

NASA Astrophysics Data System (ADS)

Aquilanti, Vincenzo; Bitencourt, Ana Carla P.; Ferreira, Cristiane da S.; Marzuoli, Annalisa; Ragni, Mirco

2008-11-01

The mathematical apparatus of quantum-mechanical angular momentum (re)coupling, developed originally to describe spectroscopic phenomena in atomic, molecular, optical and nuclear physics, is embedded in modern algebraic settings which emphasize the underlying combinatorial aspects. SU(2) recoupling theory, involving Wigner's 3nj symbols, as well as the related problems of their calculations, general properties, asymptotic limits for large entries, nowadays plays a prominent role also in quantum gravity and quantum computing applications. We refer to the ingredients of this theory—and of its extension to other Lie and quantum groups—by using the collective term of 'spin networks'. Recent progress is recorded about the already established connections with the mathematical theory of discrete orthogonal polynomials (the so-called Askey scheme), providing powerful tools based on asymptotic expansions, which correspond on the physical side to various levels of semi-classical limits. These results are useful not only in theoretical molecular physics but also in motivating algorithms for the computationally demanding problems of molecular dynamics and chemical reaction theory, where large angular momenta are typically involved. As for quantum chemistry, applications of these techniques include selection and classification of complete orthogonal basis sets in atomic and molecular problems, either in configuration space (Sturmian orbitals) or in momentum space. In this paper, we list and discuss some aspects of these developments—such as for instance the hyperquantization algorithm—as well as a few applications to quantum gravity and topology, thus providing evidence of a unifying background structure.

An Innovative Sensing Approach Using Carbon Nanotube-Based Composites for Structural Health Monitoring of Concrete Structures

NASA Astrophysics Data System (ADS)

Dwivedi, Vatsal

This thesis presents some work on two quite disparate kinds of dynamical systems described by Hamiltonian dynamics. The first part describes a computation of gauge anomalies and their macroscopic effects in a semiclassical picture. The geometric (symplectic) formulation of classical mechanics is used to describe the dynamics of Weyl fermions in even spacetime dimensions, the only quantum input to the symplectic form being the Berry curvature that encodes the spin-momentum locking. The (semi-)classical equations of motion are used in a kinetic theory setup to compute the gauge and singlet currents, whose conservation laws reproduce the nonabelian gauge and singlet anomalies. Anomalous contributions to the hydrodynamic currents for a gas of Weyl fermions at a finite temperature and chemical potential are also calculated, and are in agreement with similar results in literature which were obtained using thermodynamic and/or quantum field theoretical arguments. The second part describes a generalized transfer matrix formalism for noninteracting tight-binding models. The formalism is used to study the bulk and edge spectra, both of which are encoded in the spectrum of the transfer matrices, for some of the common tight-binding models for noninteracting electronic topological phases of matter. The topological invariants associated with the boundary states are interpreted as winding numbers for windings around noncontractible loops on a Riemann sheet constructed using the algebraic structure of the transfer matrices, as well as with a Maslov index on a symplectic group manifold, which is the space of transfer matrices.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wagner, Albert F., E-mail: wagner@anl.gov; Dawes, Richard; Continetti, Robert E.

The measured H(D)OCO survival fractions of the photoelectron-photofragment coincidence experiments by the Continetti group are qualitatively reproduced by tunneling calculations to H(D) + CO{sub 2} on several recent ab initio potential energy surfaces for the HOCO system. The tunneling calculations involve effective one-dimensional barriers based on steepest descent paths computed on each potential energy surface. The resulting tunneling probabilities are converted into H(D)OCO survival fractions using a model developed by the Continetti group in which every oscillation of the H(D)-OCO stretch provides an opportunity to tunnel. Four different potential energy surfaces are examined with the best qualitative agreement with experimentmore » occurring for the PIP-NN surface based on UCCSD(T)-F12a/AVTZ electronic structure calculations and also a partial surface constructed for this study based on CASPT2/AVDZ electronic structure calculations. These two surfaces differ in barrier height by 1.6 kcal/mol but when matched at the saddle point have an almost identical shape along their reaction paths. The PIP surface is a less accurate fit to a smaller ab initio data set than that used for PIP-NN and its computed survival fractions are somewhat inferior to PIP-NN. The LTSH potential energy surface is the oldest surface examined and is qualitatively incompatible with experiment. This surface also has a small discontinuity that is easily repaired. On each surface, four different approximate tunneling methods are compared but only the small curvature tunneling method and the improved semiclassical transition state method produce useful results on all four surfaces. The results of these two methods are generally comparable and in qualitative agreement with experiment on the PIP-NN and CASPT2 surfaces. The original semiclassical transition state theory method produces qualitatively incorrect tunneling probabilities on all surfaces except the PIP. The Eckart tunneling method uses the least amount of information about the reaction path and produces too high a tunneling probability on PIP-NN surface, leading to survival fractions that peak at half their measured values.« less

Fully differential cross sections for Li2+-impact ionization of Li(2s) and Li(2p)

NASA Astrophysics Data System (ADS)

Ghorbani, Omid; Ghanbari-Adivi, Ebrahim; Fabian Ciappina, Marcelo

2018-05-01

A semiclassical impact parameter version of the continuum distorted wave-Eikonal initial state theory is developed to study the differential ionization of Li atoms in collisions with Li2+ ions. Both post and prior forms of the transition amplitude are considered. The fully differential cross sections are calculated for the lithium targets in their ground and their first excited states and for the projectile ions at 16 MeV impact energy. The role of the inter-nuclear interaction as well as the significance of the post-prior discrepancy in the ejected electron spectra are investigated. The obtained results for ejection of the electron into the azimuthal plane are compared with the recent measurements and with their corresponding values obtained using a fully quantum mechanical version of the theory. In most of the cases, the consistency of the present approach with the experimental and the quantum theoretical data is reasonable. However, for 2p-state ionization, in the cases where no experimental data exist, there is a considerable difference between the two theoretical approaches. This difference is questionable and further experiments are needed to judge which theory makes a more accurate description of the collision dynamics.

Ab Initio Prediction of the Structural, Electronic, Elastic, and Thermoelectric Properties of Half-Heusler Ternary Compounds TiIrX (X = As and Sb)

NASA Astrophysics Data System (ADS)

Chibani, S.; Arbouche, O.; Zemouli, M.; Amara, K.; Benallou, Y.; Azzaz, Y.; Belgoumène, B.; Bentayeb, A.; Ameri, M.

2018-01-01

The structural, electronic, elastic, and thermoelectric properties of TiIrX (X = As and Sb) half-Heusler compounds with 18 valence electrons were studied using density functional theory. The generalized gradient approximation of Perdew-Burke and Ernzerhof used for calculation of the structural parameters and elastic properties of TiIrAs and TiIrSb denotes that the computed lattice constants were in excellent agreement with the available experimental data and previous theoretical works. Furthermore, the calculated elastic constants for both compounds satisfy the Born criteria indicating their mechanical stabilities. The modified Becke-Johnson potential (TB-mBJ) was used to provide a better description of the electronic structures, which indicate that both compounds are narrow-gap semiconductors. Additionally, the investigations of thermoelectric performance were carried out using the results of ab initio band-structure calculations and the semi-classical Boltzmann theory within the constant relaxation time approximations. The predicted values of the figure of merit ZT e are close to unity at room temperature. This reveals that TiIrAs and TiIrSb compounds are excellent candidates for practical applications in the thermoelectric devices.

Event Horizon Telescope observations as probes for quantum structure of astrophysical black holes

NASA Astrophysics Data System (ADS)

Giddings, Steven B.; Psaltis, Dimitrios

2018-04-01

The need for a consistent quantum evolution for black holes has led to proposals that their semiclassical description is modified not just near the singularity, but at horizon or larger scales. If such modifications extend beyond the horizon, they influence regions accessible to distant observation. Natural candidates for these modifications behave like metric fluctuations, with characteristic length scales and timescales set by the horizon radius. We investigate the possibility of using the Event Horizon Telescope to observe these effects, if they have a strength sufficient to make quantum evolution consistent with unitarity, without introducing new scales. We find that such quantum fluctuations can introduce a strong time dependence for the shape and size of the shadow that a black hole casts on its surrounding emission. For the black hole in the center of the Milky Way, detecting the rapid time variability of its shadow will require nonimaging timing techniques. However, for the much larger black hole in the center of the M87 galaxy, a variable black-hole shadow, if present with these parameters, would be readily observable in the individual snapshots that will be obtained by the Event Horizon Telescope.

Spectral monodromy of non-self-adjoint operators

NASA Astrophysics Data System (ADS)

Phan, Quang Sang

2014-01-01

In the present paper, we build a combinatorial invariant, called the "spectral monodromy" from the spectrum of a single (non-self-adjoint) h-pseudodifferential operator with two degrees of freedom in the semi-classical limit. Our inspiration comes from the quantum monodromy defined for the joint spectrum of an integrable system of n commuting self-adjoint h-pseudodifferential operators, given by S. Vu Ngoc ["Quantum monodromy in integrable systems," Commun. Math. Phys. 203(2), 465-479 (1999)]. The first simple case that we treat in this work is a normal operator. In this case, the discrete spectrum can be identified with the joint spectrum of an integrable quantum system. The second more complex case we propose is a small perturbation of a self-adjoint operator with a classical integrability property. We show that the discrete spectrum (in a small band around the real axis) also has a combinatorial monodromy. The main difficulty in this case is that we do not know the description of the spectrum everywhere, but only in a Cantor type set. In addition, we also show that the corresponding monodromy can be identified with the classical monodromy, defined by J. Duistermaat ["On global action-angle coordinates," Commun. Pure Appl. Math. 33(6), 687-706 (1980)].

Quantum trajectory analysis of multimode subsystem-bath dynamics.

PubMed

Wyatt, Robert E; Na, Kyungsun

2002-01-01

The dynamics of a swarm of quantum trajectories is investigated for systems involving the interaction of an active mode (the subsystem) with an M-mode harmonic reservoir (the bath). Equations of motion for the position, velocity, and action function for elements of the probability fluid are integrated in the Lagrangian (moving with the fluid) picture of quantum hydrodynamics. These fluid elements are coupled through the Bohm quantum potential and as a result evolve as a correlated ensemble. Wave function synthesis along the trajectories permits an exact description of the quantum dynamics for the evolving probability fluid. The approach is fully quantum mechanical and does not involve classical or semiclassical approximations. Computational results are presented for three systems involving the interaction on an active mode with M=1, 10, and 15 bath modes. These results include configuration space trajectory evolution, flux analysis of the evolving ensemble, wave function synthesis along trajectories, and energy partitioning along specific trajectories. These results demonstrate the feasibility of using a small number of quantum trajectories to obtain accurate quantum results on some types of open quantum systems that are not amenable to standard quantum approaches involving basis set expansions or Eulerian space-fixed grids.

Radiative, nonradiative, and mixed-decay transitions of rare-earth ions in dielectric media

NASA Astrophysics Data System (ADS)

Burshtein, Zeev

2010-09-01

We present and discuss in a comprehensive, deductive, and simplified manner, issues of nonradiative transitions involvement in fluorescence of ions embedded in dielectric solid matrices. The semiclassical approach is favored over a full quantum description, and empiric quantities are introduced from the start. One issue is nonradiative single-phonon transitions when the energy gap between the adjacent electronic ion states is smaller than the cutoff matrix phonon energy. Another issue is transitions in a complex energy scheme, where some visible and near-visible transitions are radiative and others are nonradiative. A refined Füchtbauer-Ladenburg recipe for calculation of the stimulated emission spectrum on the basis of measurable absorption and fluorescence emission spectra is worked out. The last issue is multiphonon nonradiative transitions occurring when the energy gap between adjacent electronic ion states is larger than the cutoff matrix phonon energy. Transition probabilities were calculated on the basis of anharmonicity of the effective potential supporting the internal atomic basis vibrations. An expression in a closed form is obtained, similar to the empiric ``energy gap'' law, however, with parameters related to specific host material properties and the actual transition in the ion. Comparison to existing experimental evidence is presented and discussed in detail.

Properties of atomic pairs produced in the collision of Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

Ziń, Paweł; Wasak, Tomasz

2018-04-01

During a collision of Bose-Einstein condensates correlated pairs of atoms are emitted. The scattered massive particles, in analogy to photon pairs in quantum optics, might be used in the violation of Bell's inequalities, demonstration of Einstein-Podolsky-Rosen correlations, or sub-shot-noise atomic interferometry. Usually, a theoretical description of the collision relies either on stochastic numerical methods or on analytical treatments involving various approximations. Here, we investigate elastic scattering of atoms from colliding elongated Bose-Einstein condensates within the Bogoliubov method, carefully controlling performed approximations at every stage of the analysis. We derive expressions for the one- and two-particle correlation functions. The obtained formulas, which relate the correlation functions to the condensate wave function, are convenient for numerical calculations. We employ the variational approach for condensate wave functions to obtain analytical expressions for the correlation functions, whose properties we analyze in detail. We also present a useful semiclassical model of the process and compare its results with the quantum one. The results are relevant for recent experiments with excited helium atoms, as well as for planned experiments aimed at investigating the nonclassicality of the system.

On corpuscular theory of inflation

DOE PAGES

Berezhiani, Lasha

2017-02-16

In order to go beyond the mean-field approximation, commonly used in the inflationary computations, an identification of the quantum constituents of the inflationary background is made. In particular, the homogeneous scalar field configuration is represented as a Bose–Einstein condensate of the off-shell inflaton degrees of freedom, with mass significantly screened by the gravitational binding energy. The gravitational counterpart of the classical background is considered to be a degenerate state of the off-shell longitudinal gravitons with the frequency of the order of the Hubble scale. As a result, the origin of the density perturbations in the slow-roll regime is identified asmore » an uncertainty in the position of the constituent inflatons. While in the regime of eternal inflation, the scattering of the constituent gravitons becomes the relevant source of the density perturbations. The gravitational waves, on the other hand, originate from the annihilation of the constituent longitudinal gravitons at all energy scales. Lastly, this results in the quantum depletion of the classical background, leading to the upper bound on the number of e-folds, after which the semi-classical description is expected to break down; this is estimated to be of the order of the entropy of the initial Hubble patch.« less

Relative populations of excited levels within the ground configuration of Si-like Cu, Zn, Ge and Se ions

NASA Technical Reports Server (NTRS)

Datla, R. U.; Roberts, J. R.; Bhatia, A. K.

1991-01-01

Populations of 3p2 1D2, 3P1, 3P2 levels in Si-like Cu, Zn, Ge, and Se ions have been deduced from the measurements of absolute intensities of magnetic dipole transitions within the 3s2 3p2 ground configuration. The measured population ratios are compared with theoretical calculations based on the distorted-wave approximation for the electron collisions and a semiclassical approximation for the proton collisions. The observed deviation from the statistical distribution for the excited-level populations within the ground configuration along the silicon isoelectronic sequence is in agreement with theoretical prediction.

Tidal waves in 102Pd: a rotating condensate of multiple d bosons.

PubMed

Ayangeakaa, A D; Garg, U; Caprio, M A; Carpenter, M P; Ghugre, S S; Janssens, R V F; Kondev, F G; Matta, J T; Mukhopadhyay, S; Patel, D; Seweryniak, D; Sun, J; Zhu, S; Frauendorf, S

2013-03-08

Low-lying collective excitations in even-even vibrational and transitional nuclei may be described semiclassically as quadrupole running waves on the surface of the nucleus ("tidal waves"), and the observed vibrational-rotational behavior can be thought of as resulting from a rotating condensate of interacting d bosons. These concepts have been investigated by measuring lifetimes of the levels in the yrast band of the (102)Pd nucleus with the Doppler shift attenuation method. The extracted B(E2) reduced transition probabilities for the yrast band display a monotonic increase with spin, in agreement with the interpretation based on rotation-induced condensation of aligned d bosons.

Polarization effects in above-threshold ionization with a mid-infrared strong laser field

NASA Astrophysics Data System (ADS)

Kang, Hui-Peng; Xu, Song-Po; Wang, Yan-Lan; Yu, Shao-Gang; Zhao, Xiao-Yun; Hao, Xiao-Lei; Lai, Xuan-Yang; Pfeifer, Thomas; Liu, Xiao-Jun; Chen, Jing; Cheng, Ya; Xu, Zhi-Zhan

2018-05-01

Using a semiclassical approach, we theoretically study the above-threshold ionization of magnesium by intense, mid-infrared laser pulses. The formation of low-energy structures in the photoelectron spectrum is found to be enhanced by comparing with a calculation based on the single-active electron approximation. By performing electron trajectory and recollision-time distribution analysis, we demonstrate that this phenomenon is due to the laser-induced ionic core polarization effects on the recolliding electrons. We also show that the polarization effects should be experimentally detectable. Our finding provides new insight into ultrafast control of strong-field photoionization and imaging of polar molecules.

Circular and linear magnetic quantum ratchet effects in dual-grating-gate CdTe-based nanostructures

NASA Astrophysics Data System (ADS)

Faltermeier, P.; Budkin, G. V.; Hubmann, S.; Bel'kov, V. V.; Golub, L. E.; Ivchenko, E. L.; Adamus, Z.; Karczewski, G.; Wojtowicz, T.; Kozlov, D. A.; Weiss, D.; Ganichev, S. D.

2018-07-01

Circular and linear magnetic quantum ratchet effects induced by alternating electric fields in the terahertz frequency range have been observed. The ratchet current shows 1/B-periodic oscillations with an amplitude, which is much larger than the photocurrent at zero magnetic field and is sensitive to the orientation of the terahertz electric field (linear ratchet) and to the radiation helicity (circular ratchet). The ratchet effects are detected in (Cd,Mn)Te quantum well structures with dual-grating-gate lateral superlattices. Theoretical analysis performed in the framework of semiclassical approach and taking into account the Landau quantization describes well the experimental data.

Call for Papers: Cavity QED

NASA Astrophysics Data System (ADS)

Lange, W.; Gerard, J.-M.

2003-06-01

Cavity QED interactions of light and matter have been investigated in a wide range of systems covering the spectrum from microwaves to optical frequencies, using media as diverse as single atoms and semiconductors. Impressive progress has been achieved technologically as well as conceptually. This topical issue of Journal of Optics B: Quantum and Semiclassical Optics is intended to provide a comprehensive account of the current state of the art of cavity QED by uniting contributions from researchers active across this field. As Guest Editors of this topical issue, we invite manuscripts on current theoretical and experimental work on any aspects of cavity QED. The topics to be covered will include, but are not limited to: bulletCavity QED in optical microcavities bulletSemiconductor cavity QED bulletQuantum dot cavity QED bulletRydberg atoms in microwave cavities bulletPhotonic crystal cavity QED bulletMicrosphere resonators bulletMicrolasers and micromasers bulletMicrodroplets bulletDielectric cavity QED bulletCavity QED-based quantum information processing bulletQuantum state engineering in cavities The DEADLINE for submission of contributions is 31 July 2003 to allow the topical issue to appear in about February 2004. All papers will be peer-reviewed in accordance with the normal refereeing procedures and standards of Journal of Optics B: Quantum and Semiclassical Optics. Advice on publishing your work in the journal may be found at www.iop.org/journals/authors/jopb. Submissions should ideally be in either standard LaTeX form or Microsoft Word. There are no page charges for publication. In addition to the usual 50 free reprints, the corresponding author of each paper published will receive a complimentary copy of the topical issue. Contributions to the topical issue should if possible be submitted electronically at www.iop.org/journals/jopb. or by e-mail to jopb@iop.org. Authors unable to submit online or by e-mail may send hard copy contributions (enclosing the electronic code) to: Dr Claire Bedrock (Publisher), Journal of Optics B: Quantum and Semiclassical Optics, Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK. All contributions should be accompanied by a readme file or covering letter, quoting `JOPB topical issue - Cavity QED', giving the postal and e-mail addresses for correspondence. Any subsequent change of address should be notified to the publishing office. We look forward to receiving your contribution to this topical issue.

Promising thermoelectric properties of phosphorenes.

PubMed

Sevik, Cem; Sevinçli, Hâldun

2016-09-02

Electronic, phononic, and thermoelectric transport properties of single layer black- and blue-phosphorene structures are investigated with first-principles based ballistic electron and phonon transport calculations employing hybrid functionals. The maximum values of room temperature thermoelectric figure of merit, ZT corresponding to armchair and zigzag directions of black-phosphorene, ∼0.5 and ∼0.25, are calculated as rather smaller than those obtained with first-principles based semiclassical Boltzmann transport theory calculations. On the other hand, the maximum value of room temperature ZT of blue-phosphorene is predicted to be substantially high and remarkable values as high as 2.5 are obtained for elevated temperatures. Besides the fact that these figures are obtained at the ballistic limit, our findings mark the strong possibility of high thermoelectric performance of blue-phosphorene in new generation thermoelectric applications.

Semiclassical electron transport at the edge of a two-dimensional topological insulator: Interplay of protected and unprotected modes

NASA Astrophysics Data System (ADS)

Khalaf, E.; Skvortsov, M. A.; Ostrovsky, P. M.

2016-03-01

We study electron transport at the edge of a generic disordered two-dimensional topological insulator, where some channels are topologically protected from backscattering. Assuming the total number of channels is large, we consider the edge as a quasi-one-dimensional quantum wire and describe it in terms of a nonlinear sigma model with a topological term. Neglecting localization effects, we calculate the average distribution function of transmission probabilities as a function of the sample length. We mainly focus on the two experimentally relevant cases: a junction between two quantum Hall (QH) states with different filling factors (unitary class) and a relatively thick quantum well exhibiting quantum spin Hall (QSH) effect (symplectic class). In a QH sample, the presence of topologically protected modes leads to a strong suppression of diffusion in the other channels already at scales much shorter than the localization length. On the semiclassical level, this is accompanied by the formation of a gap in the spectrum of transmission probabilities close to unit transmission, thereby suppressing shot noise and conductance fluctuations. In the case of a QSH system, there is at most one topologically protected edge channel leading to weaker transport effects. In order to describe `topological' suppression of nearly perfect transparencies, we develop an exact mapping of the semiclassical limit of the one-dimensional sigma model onto a zero-dimensional sigma model of a different symmetry class, allowing us to identify the distribution of transmission probabilities with the average spectral density of a certain random-matrix ensemble. We extend our results to other symmetry classes with topologically protected edges in two dimensions.

On the substructure of the cosmological constant

NASA Astrophysics Data System (ADS)

Dvali, G.; Gomez, C.; Zell, S.

We summarize the findings of our paper arXiv:1701.08776 [hep-th]. We start by defining the quantum break-time. Once one understands a classical solution as expectation value of an underlying quantum state, it emerges as time-scale after which the true quantum evolution departs from the classical mean field evolution. We apply this idea to de Sitter space. Following earlier work, we construct a simple model of a spin-2 field, which for some time reproduces the de Sitter metric and simultaneously allows for its well-defined representation as coherent quantum state of gravitons. The mean occupation number N of background gravitons turns out to be equal to the de Sitter horizon area in Planck units, while their frequency is given by the de Sitter Hubble parameter. In the semi-classical limit, we show that the model reproduces all semi-classical calculations in de Sitter, such as thermal Gibbons-Hawking radiation, all in the language of quantum S-matrix scatterings and decays of coherent state gravitons. Most importantly, this framework allows to capture the (1/N)-effects of back reaction to which the usual semi-classical treatment is blind. They violate the de Sitter symmetry and lead to a finite quantum break-time of the de Sitter state equal to the de Sitter radius times N. We also point out that the quantum-break time is inversely proportional to the number of particle species in the theory. Thus, the quantum break-time imposes the following consistency condition: Older and species-richer universes must have smaller cosmological constants. For the maximal, phenomenologically acceptable number of species, the observed cosmological constant would saturate this bound if our Universe were 10100 years old in its entire classical history.

CALL FOR PAPERS: Optical implementation of quantum computers

NASA Astrophysics Data System (ADS)

Rarity, John; Weinfurter, Harald

2004-09-01

A topical issue of Journal of Optics B: Quantum and Semiclassical Optics will be devoted to recent advances in optical implementation of quantum computers. The topics to be covered will include, but are not limited to: bullet Linear optics quantum gates bullet Progress towards nonlinear optics quantum gates bullet Interface between optical qubits and atomic/solid state qubits bullet Novel architectures bullet Single-photon sources and detectors bullet Photonic quantum networks bullet Few-qubit applications The DEADLINE for submission of contributions is 15 January 2005 to allow the topical issue to be published in about October 2005. All contributions will be peer-reviewed in accordance with the normal refereeing procedures and standards of Journal of Optics B: Quantum and Semiclassical Optics. Submissions should preferably be in either standard LaTeX form or Microsoft Word. Advice on publishing your work in the journal may be found at www.iop.org/journals/authors/jopb. There are no page charges for publication. The corresponding author of each paper published will receive a complimentary copy of the topical issue. Contributions to the topical issue should preferably be submitted electronically at www.iop.org/journals/authors/jopb or by e-mail to jopb@iop.org. Authors unable to submit online or by e-mail may send hard copy contributions (enclosing the electronic code) to: Dr Claire Bedrock (Publisher), Journal of Optics B: Quantum and Semiclassical Optics, Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK. All contributions should be accompanied by a readme file or covering letter, quoting `JOPB Topical Issue - Optical implementation of quantum computers', giving the postal and e-mail addresses for correspondence. Any subsequent change of address should be notified to the publishing office. We look forward to receiving your contribution to this topical issue.

State-selective charge exchange in slow collisions of Si3+ ions with H atoms: A molecular state close coupling treatment*)

NASA Astrophysics Data System (ADS)

Joseph, Dwayne C.; Saha, Bidhan C.

2012-11-01

Charge transfer cross sections are calculated by employing both the quantal and semiclassical ɛ(R) molecular orbital close coupling (MOCC) approximations in the adiabatic representation and compared with other theoretical and experimental results

Detailed numerical simulations of laser cooling processes

NASA Technical Reports Server (NTRS)

Ramirez-Serrano, J.; Kohel, J.; Thompson, R.; Yu, N.

2001-01-01

We developed a detailed semiclassical numerical code of the forces applied on atoms in optical and magnetic fields to increase the understanding of the different roles that light, atomic collisions, background pressure, and number of particles play in experiments with laser cooled and trapped atoms.

Semiclassical theory of sub-Doppler forces in an asymmetric magneto-optical trap with unequal laser detunings

DOE Office of Scientific and Technical Information (OSTI.GOV)

Noh, Heung-Ryoul; Jhe, Wonho

We present a semiclassical theory of the sub-Doppler forces in an asymmetric magneto-optical trap where the trap-laser frequencies are unequal to one another. To solve the optical Bloch equations, which contain explicit time dependence, unlike in the symmetric case of equal laser detunings, we have developed a convenient and efficient method to calculate the atomic forces at various oscillating frequencies for each atomic density matrix element. In particular, the theory provides a qualitative understanding of the array of sub-Doppler traps (SDTs) recently observed in such an asymmetric trap. We find that the distances between SDTs are proportional to the relativemore » detuning differences, in good agreement with experimental results. The theory presented here can be applied to a dynamic system with multiple laser frequencies involved; the number of coupled equations to solve is much reduced and the resulting numerical calculation can be performed rather simply and efficiently.« less

Semi-classical approach to compute RABBITT traces in multi-dimensional complex field distributions.

PubMed

Lucchini, M; Ludwig, A; Kasmi, L; Gallmann, L; Keller, U

2015-04-06

We present a semi-classical model to calculate RABBITT (Reconstruction of Attosecond Beating By Interference of Two-photon Transitions) traces in the presence of a reference infrared field with a complex two-dimensional (2D) spatial distribution. The evolution of the electron spectra as a function of the pump-probe delay is evaluated starting from the solution of the classical equation of motion and incorporating the quantum phase acquired by the electron during the interaction with the infrared field. The total response to an attosecond pulse train is then evaluated by a coherent sum of the contributions generated by each individual attosecond pulse in the train. The flexibility of this model makes it possible to calculate spectrograms from non-trivial 2D field distributions. After confirming the validity of the model in a simple 1D case, we extend the discussion to describe the probe-induced phase in photo-emission experiments on an ideal metallic surface.

An assessment of mean-field mixed semiclassical approaches: Equilibrium populations and algorithm stability

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bellonzi, Nicole; Jain, Amber; Subotnik, Joseph E.

2016-04-21

We study several recent mean-field semiclassical dynamics methods, focusing on the ability to recover detailed balance for long time (equilibrium) populations. We focus especially on Miller and Cotton’s [J. Phys. Chem. A 117, 7190 (2013)] suggestion to include both zero point electronic energy and windowing on top of Ehrenfest dynamics. We investigate three regimes: harmonic surfaces with weak electronic coupling, harmonic surfaces with strong electronic coupling, and anharmonic surfaces with weak electronic coupling. In most cases, recent additions to Ehrenfest dynamics are a strong improvement upon mean-field theory. However, for methods that include zero point electronic energy, we show thatmore » anharmonic potential energy surfaces often lead to numerical instabilities, as caused by negative populations and forces. We also show that, though the effect of negative forces can appear hidden in harmonic systems, the resulting equilibrium limits do remain dependent on any windowing and zero point energy parameters.« less

The predictive accuracy of analytical formulas and semiclassical approaches for α decay half-lives of superheavy nuclei

NASA Astrophysics Data System (ADS)

Zhao, T. L.; Bao, X. J.; Guo, S. Q.

2018-02-01

Systematic calculations on the α decay half-lives are performed by using three analytical formulas and two semiclassical approaches. For the three analytical formulas, the experimental α decay half-lives and {Q}α values of the 66 reference nuclei have been used to obtain the coefficients. We get only four adjustable parameters to describe α decay half-lives for even-even, odd-A, and odd-odd nuclei. By comparison between the calculated values from ten analytical formulas and experimental data, it is shown that the new universal decay law (NUDL) foumula is the most accurate one to reproduce the experimental α decay half-lives of the superheavy nuclei (SHN). Meanwhile it is found that the experimental α decay half-lives of SHN are well reproduced by the Royer formula although many parameters are contained. The results show that the NUDL formula and the generalized liquid drop model (GLDM2) with consideration of the preformation factor can give fairly equivalent results for the superheavy nuclei.

Functional Integration

NASA Astrophysics Data System (ADS)

Cartier, Pierre; DeWitt-Morette, Cecile

2006-11-01

Acknowledgements; List symbols, conventions, and formulary; Part I. The Physical and Mathematical Environment: 1. The physical and mathematical environment; Part II. Quantum Mechanics: 2. First lesson: gaussian integrals; 3. Selected examples; 4. Semiclassical expansion: WKB; 5. Semiclassical expansion: beyond WKB; 6. Quantum dynamics: path integrals and operator formalism; Part III. Methods from Differential Geometry: 7. Symmetries; 8. Homotopy; 9. Grassmann analysis: basics; 10. Grassmann analysis: applications; 11. Volume elements, divergences, gradients; Part IV. Non-Gaussian Applications: 12. Poisson processes in physics; 13. A mathematical theory of Poisson processes; 14. First exit time: energy problems; Part V. Problems in Quantum Field Theory: 15. Renormalization 1: an introduction; 16. Renormalization 2: scaling; 17. Renormalization 3: combinatorics; 18. Volume elements in quantum field theory Bryce DeWitt; Part VI. Projects: 19. Projects; Appendix A. Forward and backward integrals: spaces of pointed paths; Appendix B. Product integrals; Appendix C. A compendium of gaussian integrals; Appendix D. Wick calculus Alexander Wurm; Appendix E. The Jacobi operator; Appendix F. Change of variables of integration; Appendix G. Analytic properties of covariances; Appendix H. Feynman's checkerboard; Bibliography; Index.

Functional Integration

NASA Astrophysics Data System (ADS)

Cartier, Pierre; DeWitt-Morette, Cecile

2010-06-01

Acknowledgements; List symbols, conventions, and formulary; Part I. The Physical and Mathematical Environment: 1. The physical and mathematical environment; Part II. Quantum Mechanics: 2. First lesson: gaussian integrals; 3. Selected examples; 4. Semiclassical expansion: WKB; 5. Semiclassical expansion: beyond WKB; 6. Quantum dynamics: path integrals and operator formalism; Part III. Methods from Differential Geometry: 7. Symmetries; 8. Homotopy; 9. Grassmann analysis: basics; 10. Grassmann analysis: applications; 11. Volume elements, divergences, gradients; Part IV. Non-Gaussian Applications: 12. Poisson processes in physics; 13. A mathematical theory of Poisson processes; 14. First exit time: energy problems; Part V. Problems in Quantum Field Theory: 15. Renormalization 1: an introduction; 16. Renormalization 2: scaling; 17. Renormalization 3: combinatorics; 18. Volume elements in quantum field theory Bryce DeWitt; Part VI. Projects: 19. Projects; Appendix A. Forward and backward integrals: spaces of pointed paths; Appendix B. Product integrals; Appendix C. A compendium of gaussian integrals; Appendix D. Wick calculus Alexander Wurm; Appendix E. The Jacobi operator; Appendix F. Change of variables of integration; Appendix G. Analytic properties of covariances; Appendix H. Feynman's checkerboard; Bibliography; Index.

Unified semiclassical theory for the two-state system: an analytical solution for general nonadiabatic tunneling.

PubMed

Zhu, Chaoyuan; Lin, Sheng Hsien

2006-07-28

Unified semiclasical solution for general nonadiabatic tunneling between two adiabatic potential energy surfaces is established by employing unified semiclassical solution for pure nonadiabatic transition [C. Zhu, J. Chem. Phys. 105, 4159 (1996)] with the certain symmetry transformation. This symmetry comes from a detailed analysis of the reduced scattering matrix for Landau-Zener type of crossing as a special case of nonadiabatic transition and nonadiabatic tunneling. Traditional classification of crossing and noncrossing types of nonadiabatic transition can be quantitatively defined by the rotation angle of adiabatic-to-diabatic transformation, and this rotational angle enters the analytical solution for general nonadiabatic tunneling. The certain two-state exponential potential models are employed for numerical tests, and the calculations from the present general nonadiabatic tunneling formula are demonstrated in very good agreement with the results from exact quantum mechanical calculations. The present general nonadiabatic tunneling formula can be incorporated with various mixed quantum-classical methods for modeling electronically nonadiabatic processes in photochemistry.

Quantum localization for a kicked rotor with accelerator mode islands.

PubMed

Iomin, A; Fishman, S; Zaslavsky, G M

2002-03-01

Dynamical localization of classical superdiffusion for the quantum kicked rotor is studied in the semiclassical limit. Both classical and quantum dynamics of the system become more complicated under the conditions of mixed phase space with accelerator mode islands. Recently, long time quantum flights due to the accelerator mode islands have been found. By exploration of their dynamics, it is shown here that the classical-quantum duality of the flights leads to their localization. The classical mechanism of superdiffusion is due to accelerator mode dynamics, while quantum tunneling suppresses the superdiffusion and leads to localization of the wave function. Coupling of the regular type dynamics inside the accelerator mode island structures to dynamics in the chaotic sea proves increasing the localization length. A numerical procedure and an analytical method are developed to obtain an estimate of the localization length which, as it is shown, has exponentially large scaling with the dimensionless Planck's constant (tilde)h<1 in the semiclassical limit. Conditions for the validity of the developed method are specified.

Influence of quantum diffraction and shielding on electron-ion collision in two-component semiclassical plasmas

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hong, Woo-Pyo; Jung, Young-Dae, E-mail: ydjung@hanyang.ac.kr; Department of Applied Physics and Department of Bionanotechnology, Hanyang University, Ansan, Kyunggi-Do 426-791

2015-01-15

The influence of quantum diffraction and shielding on the electron-ion collision process is investigated in two-component semiclassical plasmas. The eikonal method and micropotential taking into account the quantum diffraction and shielding are used to obtain the eikonal scattering phase shift and the eikonal collision cross section as functions of the collision energy, density parameter, Debye length, electron de Broglie wavelength, and the impact parameter. The result shows that the quantum diffraction and shielding effects suppress the eikonal scattering phase shift as well as the differential eikonal collision cross section, especially, in small-impact parameter regions. It is also shown that themore » quantum shielding effect on the eikonal collision cross section is more important in low-collision energies. In addition, it is found that the eikonal collision cross section increases with an increase in the density parameter. The variations of the eikonal cross section due to the quantum diffraction and shielding effects are also discussed.« less

Applicability of Quantum Thermal Baths to Complex Many-Body Systems with Various Degrees of Anharmonicity.

PubMed

Hernández-Rojas, Javier; Calvo, Florent; Noya, Eva Gonzalez

2015-03-10

The semiclassical method of quantum thermal baths by colored noise thermostats has been used to simulate various atomic systems in the molecular and bulk limits, at finite temperature and in moderately to strongly anharmonic regimes. In all cases, the method performs relatively well against alternative approaches in predicting correct energetic properties, including in the presence of phase changes, provided that vibrational delocalization is not too strong-neon appearing already as an upper limiting case. In contrast, the dynamical behavior inferred from global indicators such as the root-mean-square bond length fluctuation index or the vibrational spectrum reveals more marked differences caused by zero-point energy leakage, except in the case of isolated molecules with well separated vibrational modes. To correct for such deficiencies and reduce the undesired transfer among modes, empirical modifications of the noise power spectral density were attempted to better describe thermal equilibrium but still failed when used as semiclassical preparation for microcanonical trajectories.

An investigation of one- versus two-dimensional semiclassical transition state theory for H atom abstraction and exchange reactions.

PubMed

Greene, Samuel M; Shan, Xiao; Clary, David C

2016-02-28

We investigate which terms in Reduced-Dimensionality Semiclassical Transition State Theory (RD SCTST) contribute most significantly in rate constant calculations of hydrogen extraction and exchange reactions of hydrocarbons. We also investigate the importance of deep tunneling corrections to the theory. In addition, we introduce a novel formulation of the theory in Jacobi coordinates. For the reactions of H atoms with methane, ethane, and cyclopropane, we find that a one-dimensional (1-D) version of the theory without deep tunneling corrections compares well with 2-D SCTST results and accurate quantum scattering results. For the "heavy-light-heavy" H atom exchange reaction between CH3 and CH4, deep tunneling corrections are needed to yield 1-D results that compare well with 2-D results. The finding that accurate rate constants can be obtained from derivatives of the potential along only one dimension further validates RD SCTST as a computationally efficient yet accurate rate constant theory.

Dissipation and decoherence in nanodevices: a generalized Fermi's golden rule

NASA Astrophysics Data System (ADS)

Taj, D.; Iotti, R. C.; Rossi, F.

2009-06-01

We shall revisit the conventional adiabatic or Markov approximation, which—in contrast to the semiclassical case—does not preserve the positive-definite character of the corresponding density matrix, thus leading to highly non-physical results. To overcome this serious limitation, originally pointed out and partially solved by Davies and co-workers almost three decades ago, we shall propose an alternative more general adiabatic procedure, which (i) is physically justified under the same validity restrictions of the conventional Markov approach, (ii) in the semiclassical limit reduces to the standard Fermi's golden rule and (iii) describes a genuine Lindblad evolution, thus providing a reliable/robust treatment of energy-dissipation and dephasing processes in electronic quantum devices. Unlike standard master-equation formulations, the dependence of our approximation on the specific choice of the subsystem (that includes the common partial trace reduction) does not threaten positivity, and quantum scattering rates are well defined even in the case the subsystem is infinitely extended/has a continuous spectrum.

Higher curvature self-interaction corrections to Hawking radiation

NASA Astrophysics Data System (ADS)

Fairoos, C.; Sarkar, Sudipta; Yogendran, K. P.

2017-07-01

The purely thermal nature of Hawking radiation from evaporating black holes leads to the information loss paradox. A possible route to its resolution could be if (enough) correlations are shown to be present in the radiation emitted from evaporating black holes. A reanalysis of Hawking's derivation including the effects of self-interactions in general relativity shows that the emitted radiation does deviate from pure thermality; however no correlations exist between successively emitted Hawking quanta. We extend the calculations to Einstein-Gauss-Bonnet gravity and investigate if higher curvature corrections to the action lead to some new correlations in the Hawking spectra. The effective trajectory of a massless shell is determined by solving the constraint equations and the semiclassical tunneling probability is calculated. As in the case of general relativity, the radiation is no longer thermal and there is no correlation between successive emissions. The absence of any extra correlations in the emitted radiations even in Gauss-Bonnet gravity suggests that the resolution of the paradox is beyond the scope of semiclassical gravity.

Entangled photons from single atoms and molecules

NASA Astrophysics Data System (ADS)

Nordén, Bengt

2018-05-01

The first two-photon entanglement experiment performed 50 years ago by Kocher and Commins (KC) provided isolated pairs of entangled photons from an atomic three-state fluorescence cascade. In view of questioning of Bell's theorem, data from these experiments are re-analyzed and shown sufficiently precise to confirm quantum mechanical and dismiss semi-classical theory without need for Bell's inequalities. Polarization photon correlation anisotropy (A) is useful: A is near unity as predicted quantum mechanically and well above the semi-classic range, 0 ⩽ A ⩽ 1 / 2 . Although yet to be found, one may envisage a three-state molecule emitting entangled photon pairs, in analogy with the KC atomic system. Antibunching in fluorescence from single molecules in matrix and entangled photons from quantum dots promise it be possible. Molecules can have advantages to parametric down-conversion as the latter photon distribution is Poissonian and unsuitable for producing isolated pairs of entangled photons. Analytical molecular applications of entangled light are also envisaged.

Footprints of electron correlation in strong-field double ionization of Kr close to the sequential-ionization regime

NASA Astrophysics Data System (ADS)

Li, Xiaokai; Wang, Chuncheng; Yuan, Zongqiang; Ye, Difa; Ma, Pan; Hu, Wenhui; Luo, Sizuo; Fu, Libin; Ding, Dajun

2017-09-01

By combining kinematically complete measurements and a semiclassical Monte Carlo simulation we study the correlated-electron dynamics in the strong-field double ionization of Kr. Interestingly, we find that, as we step into the sequential-ionization regime, there are still signatures of correlation in the two-electron joint momentum spectrum and, more intriguingly, the scaling law of the high-energy tail is completely different from early predictions on the low-Z atom (He). These experimental observations are well reproduced by our generalized semiclassical model adapting a Green-Sellin-Zachor potential. It is revealed that the competition between the screening effect of inner-shell electrons and the Coulomb focusing of nuclei leads to a non-inverse-square central force, which twists the returned electron trajectory at the vicinity of the parent core and thus significantly increases the probability of hard recollisions between two electrons. Our results might have promising applications ranging from accurately retrieving atomic structures to simulating celestial phenomena in the laboratory.

Berry phase effect on electronic properties

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xiao, Di; Chang, Ming-Che; Niu, Qian

2010-01-01

Ever since its discovery, the Berry phase has permeated through all branches of physics. Over the last three decades, it was gradually realized that the Berry phase of the electronic wave function can have a profound effect on material properties and is responsible for a spectrum of phenomena, such as ferroelectricity, orbital magnetism, various (quantum/anomalous/spin) Hall effects, and quantum charge pumping. This progress is summarized in a pedagogical manner in this review. We start with a brief summary of necessary background, followed by a detailed discussion of the Berry phase effect in a variety of solid state applications. A commonmore » thread of the review is the semiclassical formulation of electron dynamics, which is a versatile tool in the study of electron dynamics in the presence of electromagnetic fields and more general perturbations. Finally, we demonstrate a re-quantization method that converts a semiclassical theory to an effective quantum theory. It is clear that the Berry phase should be added as a basic ingredient to our understanding of basic material properties.« less

Numerical solutions of ideal quantum gas dynamical flows governed by semiclassical ellipsoidal-statistical distribution.

PubMed

Yang, Jaw-Yen; Yan, Chih-Yuan; Diaz, Manuel; Huang, Juan-Chen; Li, Zhihui; Zhang, Hanxin

2014-01-08

The ideal quantum gas dynamics as manifested by the semiclassical ellipsoidal-statistical (ES) equilibrium distribution derived in Wu et al. (Wu et al . 2012 Proc. R. Soc. A 468 , 1799-1823 (doi:10.1098/rspa.2011.0673)) is numerically studied for particles of three statistics. This anisotropic ES equilibrium distribution was derived using the maximum entropy principle and conserves the mass, momentum and energy, but differs from the standard Fermi-Dirac or Bose-Einstein distribution. The present numerical method combines the discrete velocity (or momentum) ordinate method in momentum space and the high-resolution shock-capturing method in physical space. A decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. Computations of two-dimensional Riemann problems are presented, and various contours of the quantities unique to this ES model are illustrated. The main flow features, such as shock waves, expansion waves and slip lines and their complex nonlinear interactions, are depicted and found to be consistent with existing calculations for a classical gas.

Periodic Toda lattice in quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Matsuyama, A.

The quantum mechanical periodic Toda lattice is studied by the direct diagonalization of the Hamiltonian. The eigenstates are classified according to the irreducible representations of the dihedral group D[sub N]. It is shown that Gutzwiller's quantization conditions are satisfied and they have a one-to-one correspondence to the irreducible representation of the D[sub N] group. The authors have also carried out the semiclassical quantization of the periodic Toda lattice by the EBK formulation. The eigenvalues of the semiclassical quantization have a one-to-one correspondence to the integer quantum numbers, and those quantum numbers also have a close relationship to the symmetry ofmore » the state. Numerical calculations have been done for N = 3, 4, 5, and 6 particle periodic Toda lattices. The distributions of the eigenvalues are systematic and distinguished by the symmetry of the state. As illustrative examples, amplitudes of the wave functions and density distributions are shown. 14 refs., 8 figs., 11 tabs.« less

Semiclassical multi-phonon theory for atom-surface scattering: Application to the Cu(111) system

NASA Astrophysics Data System (ADS)

Daon, Shauli; Pollak, Eli

2015-05-01

The semiclassical perturbation theory of Hubbard and Miller [J. Chem. Phys. 80, 5827 (1984)] is further developed to include the full multi-phonon transitions in atom-surface scattering. A practically applicable expression is developed for the angular scattering distribution by utilising a discretized bath of oscillators, instead of the continuum limit. At sufficiently low surface temperature good agreement is found between the present multi-phonon theory and the previous one-, and two-phonon theory derived in the continuum limit in our previous study [Daon, Pollak, and Miret-Artés, J. Chem. Phys. 137, 201103 (2012)]. The theory is applied to the measured angular distributions of Ne, Ar, and Kr scattered from a Cu(111) surface. We find that the present multi-phonon theory substantially improves the agreement between experiment and theory, especially at the higher surface temperatures. This provides evidence for the importance of multi-phonon transitions in determining the angular distribution as the surface temperature is increased.

First-principles binary diffusion coefficients for H, H 2 and four normal alkanes + N 2

DOE PAGES

Jasper, Ahren W.; Kamarchik, Eugene; Miller, James A.; ...

2014-09-30

Collision integrals related to binary (dilute gas) diffusion are calculated classically for six species colliding with N 2. The most detailed calculations make no assumptions regarding the complexity of the potential energy surface, and the resulting classical collision integrals are in excellent agreement with previous semiclassical results for H + N 2 and H 2 + N 2 and with recent experimental results for C n H 2n+2 + N 2, n = 2–4. The detailed classical results are used to test the accuracy of three simplifying assumptions typically made when calculating collision integrals: (1) approximating the intermolecular potential asmore » isotropic, (2) neglecting the internal structure of the colliders (i.e., neglecting inelasticity), and (3) employing unphysical R –12 repulsive interactions. The effect of anisotropy is found to be negligible for H + N 2 and H 2 + N 2 (in agreement with previous quantum mechanical and semiclassical results for systems involving atomic and diatomic species) but is more significant for larger species at low temperatures. For example, the neglect of anisotropy decreases the diffusion coefficient for butane + N 2 by 15% at 300 K. The neglect of inelasticity, in contrast, introduces only very small errors. Approximating the repulsive wall as an unphysical R –12 interaction is a significant source of error at all temperatures for the weakly interacting systems H + N 2 and H 2 + N 2, with errors as large as 40%. For the normal alkanes in N 2, which feature stronger interactions, the 12/6 Lennard–Jones approximation is found to be accurate, particularly at temperatures above –700 K where it predicts the full-dimensional result to within 5% (although with somewhat different temperature dependence). Overall, the typical practical approach of assuming isotropic 12/6 Lennard–Jones interactions is confirmed to be suitable for combustion applications except for weakly interacting systems, such as H + N 2. For these systems, anisotropy and inelasticity can safely be neglected but a more detailed description of the repulsive wall is required for quantitative predictions. Moreover, a straightforward approach for calculating effective isotropic potentials with realistic repulsive walls is described. An analytic expression for the calculated diffusion coefficient for H + N 2 is presented and is estimated to have a 2-sigma error bar of only 0.7%.« less

Communication: Charge-transfer rate constants in zinc-porphyrin-porphyrin-derived dyads: A Fermi golden rule first-principles-based study

NASA Astrophysics Data System (ADS)

Manna, Arun K.; Dunietz, Barry D.

2014-09-01

We investigate photoinduced charge transfer (CT) processes within dyads consisting of porphyrin derivatives in which one ring ligates a Zn metal center and where the rings vary by their degree of conjugation. Using a first-principles approach, we show that molecular-scale means can tune CT rates through stabilization affected by the polar environment. Such means of CT tuning are important for achieving high efficiency optoelectronic applications using organic semiconducting materials. Our fully quantum mechanical scheme is necessary for reliably modeling the CT process across different regimes, in contrast to the pervading semi-classical Marcus picture that grossly underestimates transfer in the far-inverted regime.

The effect of dynamical Bloch oscillations on optical-field-induced current in a wide-gap dielectric

NASA Astrophysics Data System (ADS)

Földi, P.; Benedict, M. G.; Yakovlev, V. S.

2013-06-01

We consider the motion of charge carriers in a bulk wide-gap dielectric interacting with a few-cycle laser pulse. A semiclassical model based on Bloch equations is applied to describe the emerging time-dependent macroscopic currents for laser intensities close to the damage threshold. At such laser intensities, electrons can reach edges of the first Brillouin zone even for electron-phonon scattering rates as high as those known for SiO2. We find that, whenever this happens, Bragg-like reflections of electron waves, also known as Bloch oscillations, affect the dependence of the charge displaced by the laser pulse on its carrier-envelope phase.

Effect of strain on thermoelectric properties of SrTiO3: First-principles calculations

NASA Astrophysics Data System (ADS)

Zou, Daifeng; Liu, Yunya; Xie, Shuhong; Lin, Jianguo; Li, Jiangyu

2013-10-01

The electronic structures of strained SrTiO3 were investigated by using first-principles calculations, and the anisotropic thermoelectric properties of n-type SrTiO3 under biaxial strain were calculated on the base of the semi-classical Boltzmann transport theory. It was theoretically found that the in-plane and out-of-plane power factors of n-type SrTiO3 can be increased under compressive and tensile strains, respectively, and such dependence can be explained by the strain-induced redistribution of electrons. To further optimize the thermoelectric performance of n-type SrTiO3, the maximum power factors and the corresponding optimal n-type doping levels were evaluated.

Multiband corrections for the semi-classical simulation of interband tunneling in GaAs tunnel junctions

NASA Astrophysics Data System (ADS)

Louarn, K.; Claveau, Y.; Hapiuk, D.; Fontaine, C.; Arnoult, A.; Taliercio, T.; Licitra, C.; Piquemal, F.; Bounouh, A.; Cavassilas, N.; Almuneau, G.

2017-09-01

The aim of this study is to investigate the impact of multiband corrections on the current density in GaAs tunnel junctions (TJs) calculated with a refined yet simple semi-classical interband tunneling model (SCITM). The non-parabolicity of the considered bands and the spin-orbit effects are considered by using a recently revisited SCITM available in the literature. The model is confronted to experimental results from a series of molecular beam epitaxy grown GaAs TJs and to numerical results obtained with a full quantum model based on the non-equilibrium Green’s function formalism and a 6-band k.p Hamiltonian. We emphasize the importance of considering the non-parabolicity of the conduction band by two different measurements of the energy-dependent electron effective mass in N-doped GaAs. We also propose an innovative method to compute the non-uniform electric field in the TJ for the SCITM simulations, which is of prime importance for a successful operation of the model. We demonstrate that, when considering the multiband corrections and this new computation of the non-uniform electric field, the SCITM succeeds in predicting the electrical characteristics of GaAs TJs, and are also in agreement with the quantum model. Besides the fundamental study of the tunneling phenomenon in TJs, the main benefit of this SCITM is that it can be easily embedded into drift-diffusion software, which are the most widely-used simulation tools for electronic and opto-electronic devices such as multi-junction solar cells, tunnel field-effect transistors, or vertical-cavity surface-emitting lasers.

Higher spin gauge theory on fuzzy \\boldsymbol {S^4_N}

NASA Astrophysics Data System (ADS)

Sperling, Marcus; Steinacker, Harold C.

2018-02-01

We examine in detail the higher spin fields which arise on the basic fuzzy sphere S^4N in the semi-classical limit. The space of functions can be identified with functions on classical S 4 taking values in a higher spin algebra associated to \

Behavior of Tachyon in String Cosmology Based on Gauged WZW Model

NASA Astrophysics Data System (ADS)

Lee, Sunggeun; Nam, Soonkeon

We investigate a string theoretic cosmological model in the context of the gauged Wess-Zumino-Witten model. Our model is based on a product of non-compact coset space and a spectator flat space; [SL(2, R)/U(1)]k × ℝ2. We extend the formerly studied semiclassical consideration with infinite Kac-Moody level k to a finite one. In this case, the tachyon field appears in the effective action, and we solve the Einstein equation to determine the behavior of tachyon as a function of time. We find that tachyon field dominates over dilaton field in early times. In particular, we consider the energy conditions of the matter fields consisting of the dilaton and the tachyon which affect the initial singularity. We find that not only the strong energy but also the null energy condition is violated.

On the hadron mass decomposition

NASA Astrophysics Data System (ADS)

Lorcé, Cédric

2018-02-01

We argue that the standard decompositions of the hadron mass overlook pressure effects, and hence should be interpreted with great care. Based on the semiclassical picture, we propose a new decomposition that properly accounts for these pressure effects. Because of Lorentz covariance, we stress that the hadron mass decomposition automatically comes along with a stability constraint, which we discuss for the first time. We show also that if a hadron is seen as made of quarks and gluons, one cannot decompose its mass into more than two contributions without running into trouble with the consistency of the physical interpretation. In particular, the so-called quark mass and trace anomaly contributions appear to be purely conventional. Based on the current phenomenological values, we find that in average quarks exert a repulsive force inside nucleons, balanced exactly by the gluon attractive force.

The isentropic quantum drift-diffusion model in two or three space dimensions

NASA Astrophysics Data System (ADS)

Chen, Xiuqing

2009-05-01

We investigate the isentropic quantum drift-diffusion model, a fourth order parabolic system, in space dimensions d = 2, 3. First, we establish the global weak solutions with large initial value and periodic boundary conditions. Then we show the semiclassical limit by delicate interpolation estimates and compactness argument.

Dependence of Fusion Barrier Heights on the Difference of Proton and Neutron Radii

NASA Astrophysics Data System (ADS)

Dobrowolski, A.; Pomorski, K.; Bartel, J.

2005-04-01

Using the Skyrme effective nucleon--nucleon interaction together with the semiclassical Extended Thomas--Fermi approach (ETF) we investigate the relative change of the fusion barrier heights for the reaction 16O+208Pb as function of the nuclear proton or neutron radii of the colliding nuclei.

A simple expression for the cold compression curve.

NASA Astrophysics Data System (ADS)

Čelebonović, V.

1996-10-01

The aim of this contribution is to present expressions for the bulk modulus of a material and its pressure derivative obtained by using the semi-classical theory of dense matter proposed by P. Savić and R. Kašanin. Some possibilities for the application of these expressions are briefly discussed.

Reply to the 'Comment on "Proton transport in barium stannate: classical, semi-classical and quantum regime"'.

PubMed

Geneste, Grégory; Hermet, Jessica; Dezanneau, Guilhem

2017-08-09

We respond to the erroneous criticisms about our modeling of proton transport in barium stannate [G. Geneste et al., Phys. Chem. Chem. Phys., 2015, 17, 19104]. In this previous work, we described, on the basis of density-functional calculations, proton transport in the classical and semi-classical regimes, and provided arguments in favor of an adiabatic picture for proton transfer at low temperature. We re-explain here our article (with more detail and precision), the content of which has been distorted in the Comment, and reiterate our arguments in this reply. We refute all criticisms. They are completely wrong in the context of our article. Even though a few of them are based on considerations probably true in some metals, they make no sense here since they do not correspond to the content of our work. It has not been understood in the Comment that two competitive configurations, associated with radically different transfer mechanisms, have been studied in our work. It has also not been understood in the Comment that the adiabatic regime described for transfer occurs in the protonic ground state, in a very-low barrier configuration with the protonic ground state energy larger than the barrier. Serious confusion has been made in the Comment with the case of H in metals like Nb or Ta, leading to the introduction of the notion of (protonic) "excited-state proton transfer", relevant for H in some metals, but (i) that does not correspond to the (ground state) adiabatic transfers here described, and (ii) that does not correspond to what is commonly described as the "adiabatic limit for proton transfer" in the scientific literature. We emphasize, accordingly, the large differences between proton transfer in the present oxide and hydrogen jumps in metals like Nb or Ta, and the similarities between proton transfer in the present oxide and in acid-base solutions. We finally describe a scenario for proton transfer in the present oxide regardless of the temperature regime.

Charge Transfer Rate in Collisions of H + Ions with Si Atoms

NASA Astrophysics Data System (ADS)

Kimura, M.; Sannigrahi, A. B.; Gu, J. P.; Hirsch, G.; Buenker, R. J.; Shimamura, I.

1996-12-01

Charge transfer in Si(3P, 1D) + H+ collisions is studied theoretically by using a semiclassical molecular representation with six molecular channels for the triplet manifold and four channels for the singlet manifold at collision energies above 30 eV, and by using a fully quantum mechanical approach with two molecular channels for both triplet and singlet manifolds below 30 eV. The ab initio potential curves and nonadiabatic coupling matrix elements for the HSi+ system are obtained from multireference single- and double-excitation configuration interaction (MRD-CI) calculations employing a relatively large basis set. The present rate coefficients for charge transfer to Si+(4P) formation resulting from H+ + Si(3P) collisions are found to be large with values from 1 x 10-10 cm-3 s-1 at 1000 K to 1 x 10-8 cm-3 s-1 at 100,000 K. The rate coefficient for Si+(2P) formation, resulting from H+ + Si(3P) collisions, is found to be much smaller because of a larger energy defect from the initial state. These calculated rates are much larger than those reported by Baliunas & Butler, who estimated a value of 10-11 cm-3 s-1 in their coronal plasma study. The present result may be relevant to the description of the silicon ionization equilibrium.

The Quantum Focussing Conjecture and Quantum Null Energy Condition

NASA Astrophysics Data System (ADS)

Koeller, Jason

Evidence has been gathering over the decades that spacetime and gravity are best understood as emergent phenomenon, especially in the context of a unified description of quantum mechanics and gravity. The Quantum Focussing Conjecture (QFC) and Quantum Null Energy Condition (QNEC) are two recently-proposed relationships between entropy and geometry, and energy and entropy, respectively, which further strengthen this idea. In this thesis, we study the QFC and the QNEC. We prove the QNEC in a variety of contexts, including free field theories on Killing horizons, holographic theories on Killing horizons, and in more general curved spacetimes. We also consider the implications of the QFC and QNEC in asymptotically flat space, where they constrain the information content of gravitational radiation arriving at null infinity, and in AdS/CFT, where they are related to other semiclassical inequalities and properties of boundary-anchored extremal area surfaces. It is shown that the assumption of validity and vacuum-state saturation of the QNEC for regions of flat space defined by smooth cuts of null planes implies a local formula for the modular Hamiltonian of these regions. We also demonstrate that the QFC as originally conjectured can be violated in generic theories in d ≥ 5, which led the way to an improved formulation subsequently suggested by Stefan Leichenauer.

Gauge-invariant formulation of high-field transport in semiconductors

NASA Astrophysics Data System (ADS)

Ciancio, Emanuele; Iotti, Rita C.; Rossi, Fausto

2004-04-01

In this paper we revisit the conventional description of carrier-phonon scattering in the presence of high electric fields by means of a gauge-invariant density-matrix approach. The proposed formulation of the transport problem allows us, on the one hand, to provide a gauge-independent formulation of Fermi’s golden rule; on the other hand, our analysis clearly shows that in the standard treatments of high-field carrier-phonon scattering—also referred to as intracollisional field effect—the possible variation of the basis states has been usually neglected. This is recognized to be the origin of the apparent discrepancy between scalar- and vector-potential treatments of the problem; indeed, a proper account of such contributions leads, in general, to an ill-defined Markov limit in the carrier-phonon interaction process, assigning to the scalar-potential or Wannier-Stark picture a privileged role. The neglect of such Zener-like contributions in the transport equation leads to a wrong estimation of the high-field voltage-current characteristics, and may partially account for the surprisingly good agreement between semiclassical and rigorous quantum-transport calculations previously reported. This is confirmed by fully three-dimensional simulations of charge transport in state-of-the-art semiconductor superlattices, which show a significant current overestimation.

Coupled channels description of the α-decay fine structure

NASA Astrophysics Data System (ADS)

Delion, D. S.; Ren, Zhongzhou; Dumitrescu, A.; Ni, Dongdong

2018-05-01

We review the coupled channels approach of α transitions to excited states. The α-decaying states are identified as narrow outgoing Gamow resonances in an α-daughter potential. The real part of the eigenvalue corresponds to the Q-value, while the imaginary part determines the half of the total α-decay width. We first review the calculations describing transitions to rotational states treated by the rigid rotator model, in even–even, odd-mass and odd–odd nuclei. It is found that the semiclassical method overestimates the branching ratios to excited 4+ for some even–even α-emitters and fails in explaining the unexpected inversion of branching ratios of some odd-mass nuclei, while the coupled-channels results show good agreement with the experimental data. Then, we review the coupled channels method for α-transitions to 2+ vibrational and transitional states. We present the results of the Coherent State Model that describes in a unified way the spectra of vibrational, transitional and rotational nuclei. We evidence general features of the α-decay fine structure, namely the linear dependence between α-intensities and excitation energy, the linear correlation between the strength of the α-core interaction and spectroscopic factor, and the inverse correlation between the nuclear collectivity, given by electromagnetic transitions, and α-clustering.

Discrete quantum spectrum of black holes

NASA Astrophysics Data System (ADS)

Lochan, Kinjalk; Chakraborty, Sumanta

2016-04-01

The quantum genesis of Hawking radiation is a long-standing puzzle in black hole physics. Semi-classically one can argue that the spectrum of radiation emitted by a black hole look very much sparse unlike what is expected from a thermal object. It was demonstrated through a simple quantum model that a quantum black hole will retain a discrete profile, at least in the weak energy regime. However, it was suggested that this discreteness might be an artifact of the simplicity of eigen-spectrum of the model considered. Different quantum theories can, in principle, give rise to different complicated spectra and make the radiation from black hole dense enough in transition lines, to make them look continuous in profile. We show that such a hope from a geometry-quantized black hole is not realized as long as large enough black holes are dubbed with a classical mass area relation in any gravity theory ranging from GR, Lanczos-Lovelock to f(R) gravity. We show that the smallest frequency of emission from black hole in any quantum description, is bounded from below, to be of the order of its inverse mass. That leaves the emission with only two possibilities. It can either be non-thermal, or it can be thermal only with the temperature being much larger than 1/M.

Transport coefficients of a hot QCD medium and their relative significance in heavy-ion collisions

NASA Astrophysics Data System (ADS)

Mitra, Sukanya; Chandra, Vinod

2017-11-01

The main focus of this article is to obtain various transport coefficients for a hot QCD medium that is likely to be produced while colliding two heavy nuclei ultra-relativistically. The technical approach adopted here is the semiclassical transport theory. The away-from-equilibrium linearized transport equation has been set up by employing the Chapman-Enskog technique from the kinetic theory of a many-particle system with a collision term that includes the binary collisions of quarks/antiquarks and gluons. In order to include the effects of a strongly interacting, thermal medium, a quasi-particle description of a realistic hot QCD equation of state has been employed through the equilibrium modeling of the momentum distributions of gluons and quarks with nontrivial dispersion relations while extending the model for finite but small quark chemical potential. The effective coupling for strong interaction has been redefined following the charge renormalization under the scheme of the quasi-particle model. The consolidated effects on transport coefficients are seen to have a significant impact on their temperature dependence. Finally, the relative significances of momentum and heat transfer, as well as the charge diffusion processes in hot QCD, have been investigated by studying the ratios of the respective transport coefficients indicating different physical laws.

Theoretical/experimental comparison of deep tunneling decay of quasi-bound H(D)OCO to H(D) + CO₂.

PubMed

Wagner, Albert F; Dawes, Richard; Continetti, Robert E; Guo, Hua

2014-08-07

The measured H(D)OCO survival fractions of the photoelectron-photofragment coincidence experiments by the Continetti group are qualitatively reproduced by tunneling calculations to H(D) + CO2 on several recent ab initio potential energy surfaces for the HOCO system. The tunneling calculations involve effective one-dimensional barriers based on steepest descent paths computed on each potential energy surface. The resulting tunneling probabilities are converted into H(D)OCO survival fractions using a model developed by the Continetti group in which every oscillation of the H(D)-OCO stretch provides an opportunity to tunnel. Four different potential energy surfaces are examined with the best qualitative agreement with experiment occurring for the PIP-NN surface based on UCCSD(T)-F12a/AVTZ electronic structure calculations and also a partial surface constructed for this study based on CASPT2/AVDZ electronic structure calculations. These two surfaces differ in barrier height by 1.6 kcal/mol but when matched at the saddle point have an almost identical shape along their reaction paths. The PIP surface is a less accurate fit to a smaller ab initio data set than that used for PIP-NN and its computed survival fractions are somewhat inferior to PIP-NN. The LTSH potential energy surface is the oldest surface examined and is qualitatively incompatible with experiment. This surface also has a small discontinuity that is easily repaired. On each surface, four different approximate tunneling methods are compared but only the small curvature tunneling method and the improved semiclassical transition state method produce useful results on all four surfaces. The results of these two methods are generally comparable and in qualitative agreement with experiment on the PIP-NN and CASPT2 surfaces. The original semiclassical transition state theory method produces qualitatively incorrect tunneling probabilities on all surfaces except the PIP. The Eckart tunneling method uses the least amount of information about the reaction path and produces too high a tunneling probability on PIP-NN surface, leading to survival fractions that peak at half their measured values.

Phase control of attosecond pulses in a train

NASA Astrophysics Data System (ADS)

Guo, Chen; Harth, Anne; Carlström, Stefanos; Cheng, Yu-Chen; Mikaelsson, Sara; Mårsell, Erik; Heyl, Christoph; Miranda, Miguel; Gisselbrecht, Mathieu; Gaarde, Mette B.; Schafer, Kenneth J.; Mikkelsen, Anders; Mauritsson, Johan; Arnold, Cord L.; L'Huillier, Anne

2018-02-01

Ultrafast processes in matter can be captured and even controlled by using sequences of few-cycle optical pulses, which need to be well characterized, both in amplitude and phase. The same degree of control has not yet been achieved for few-cycle extreme ultraviolet pulses generated by high-order harmonic generation (HHG) in gases, with duration in the attosecond range. Here, we show that by varying the spectral phase and carrier-envelope phase (CEP) of a high-repetition rate laser, using dispersion in glass, we achieve a high degree of control of the relative phase and CEP between consecutive attosecond pulses. The experimental results are supported by a detailed theoretical analysis based upon the semi-classical three-step model for HHG.

Optical solitons and modulation instability analysis of an integrable model of (2+1)-Dimensional Heisenberg ferromagnetic spin chain equation

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru

2017-12-01

This paper addresses the nonlinear Schrödinger type equation (NLSE) in (2+1)-dimensions which describes the nonlinear spin dynamics of Heisenberg ferromagnetic spin chains (HFSC) with anisotropic and bilinear interactions in the semiclassical limit. Two integration schemes are employed to study the equation. These are the complex envelope function ansatz and the generalized tanh methods. Dark, dark-bright or combined optical and singular soliton solutions of the equation are derived. Furthermore, the modulational instability (MI) is studied based on the standard linear-stability analysis and the MI gain is got. Numerical simulation of the obtained results are analyzed with interesting figures showing the physical meaning of the solutions.

Kinetics of the chiral phase transition in a linear σ model

NASA Astrophysics Data System (ADS)

Wesp, Christian; van Hees, Hendrik; Meistrenko, Alex; Greiner, Carsten

2018-02-01

We study the dynamics of the chiral phase transition in a linear quark-meson σ model using a novel approach based on semiclassical wave-particle duality. The quarks are treated as test particles in a Monte Carlo simulation of elastic collisions and the coupling to the σ meson, which is treated as a classical field, via a kinetic approach motivated by wave-particle duality. The exchange of energy and momentum between particles and fields is described in terms of appropriate Gaussian wave packets. It has been demonstrated that energy-momentum conservation and the principle of detailed balance are fulfilled, and that the dynamics leads to the correct equilibrium limit. First schematic studies of the dynamics of matter produced in heavy-ion collisions are presented.

Phase-space analysis of the Schwinger effect in inhomogeneous electromagnetic fields

NASA Astrophysics Data System (ADS)

Kohlfürst, Christian

2018-05-01

Schwinger pair production in spatially and temporally inhomogeneous electric and magnetic fields is studied. The focus is on the particle phase-space distribution within a high-intensity few-cycle pulse. Accurate numerical solutions of a quantum kinetic theory (DHW formalism) are presented in momentum space and, with the aid of coarse-graining techniques, in a mixed spatial-momentum representation. Additionally, signatures of the carrier-envelope phase as well as spin-field interactions are discussed on the basis of a trajectory-based model taking into account instantaneous pair production and relativistic single-particle dynamics. Although our simple semi-classical single-particle model cannot describe every aspect of the particle production process (quantum interferences), essential features such as spin-field interactions are captured.

Competing magnetostructural phases in a semiclassical system

NASA Astrophysics Data System (ADS)

O'Neal, Kenneth R.; Lee, Jun Hee; Kim, Maeng-Suk; Manson, Jamie L.; Liu, Zhenxian; Fishman, Randy S.; Musfeldt, Janice L.

2017-11-01

The interplay between charge, structure, and magnetism gives rise to rich phase diagrams in complex materials with exotic properties emerging when phases compete. Molecule-based materials are particularly advantageous in this regard due to their low energy scales, flexible lattices, and chemical tunability. Here, we bring together high pressure Raman scattering, modeling, and first principles calculations to reveal the pressure-temperature-magnetic field phase diagram of Mn[N(CN)2]2. We uncover how hidden soft modes involving octahedral rotations drive two pressure-induced transitions triggering the low → high magnetic anisotropy crossover and a unique reorientation of exchange planes. These magnetostructural transitions and their mechanisms highlight the importance of spin-lattice interactions in establishing phases with novel magnetic properties in Mn(II)-containing systems.

Commensurability resonances in two-dimensional magnetoelectric lateral superlattices

NASA Astrophysics Data System (ADS)

Schluck, J.; Fasbender, S.; Heinzel, T.; Pierz, K.; Schumacher, H. W.; Kazazis, D.; Gennser, U.

2015-05-01

Hybrid lateral superlattices composed of a square array of antidots and a periodic one-dimensional magnetic modulation are prepared in Ga [Al ]As heterostructures. The two-dimensional electron gases exposed to these superlattices are characterized by magnetotransport experiments in vanishing average perpendicular magnetic fields. Despite the absence of closed orbits, the diagonal magnetoresistivity in the direction perpendicular to the magnetic modulation shows pronounced classical resonances. They are located at magnetic fields where snake trajectories exist which are quasicommensurate with the antidot lattice. The diagonal magnetoresistivity in the direction of the magnetic modulation increases sharply above a threshold magnetic field and shows no fine structure. The experimental results are interpreted with the help of numerical simulations based on the semiclassical Kubo model.

Effects of spatial nonuniformity on laser dynamics.

PubMed

Deych, L I

2005-07-22

Semiclassical equations of lasing dynamics are rederived for a lasing medium in a cavity with a spatially nonuniform dielectric constant. The nonuniformity causes a radiative coupling between modes of the empty cavity, which results in a renormalization of self- and cross-saturation coefficients. Possible manifestations of these effects in random lasers are discussed.

Modeling Synchronization in Networks of Delay-Coupled Fiber Ring Lasers

DTIC Science & Technology

2011-11-21

synchronication of delay-couple oscillators,” Chaos 20, 043127 (2010). 10. J. Mulet , C. Mirasso, T. Heil, and I. Fischer, “Synchronication scenario of two...distant mutually coupled semi- conductor lasers,” J. Opt. B: Quantum Semiclassical Opt. 6, 97–105 (2004). 11. T. Heil, I. Fischer, W. Elsasser, J. Mulet

Vibrational effects in x-ray absorption and resonant inelastic x-ray scattering using a semiclassical scheme

NASA Astrophysics Data System (ADS)

Ljungberg, Mathias P.

2017-12-01

A method is presented for describing vibrational effects in x-ray absorption spectroscopy and resonant inelastic x-ray scattering (RIXS) using a combination of the classical Franck-Condon (FC) approximation and classical trajectories run on the core-excited state. The formulation of RIXS is an extension of the semiclassical Kramers-Heisenberg formalism of Ljungberg et al. [Phys. Rev. B 82, 245115 (2010), 10.1103/PhysRevB.82.245115] to the resonant case, retaining approximately the same computational cost. To overcome difficulties with connecting the absorption and emission processes in RIXS, the classical FC approximation is used for the absorption, which is seen to work well provided that a zero-point-energy correction is included. In the case of core-excited states with dissociative character, the method is capable of closely reproducing the main features for one-dimensional test systems, compared to the quantum-mechanical formulation. Due to the good accuracy combined with the relatively low computational cost, the method has great potential of being used for complex systems with many degrees of freedom, such as liquids and surface adsorbates.

Global hybrids from the semiclassical atom theory satisfying the local density linear response.

PubMed

Fabiano, Eduardo; Constantin, Lucian A; Cortona, Pietro; Della Sala, Fabio

2015-01-13

We propose global hybrid approximations of the exchange-correlation (XC) energy functional which reproduce well the modified fourth-order gradient expansion of the exchange energy in the semiclassical limit of many-electron neutral atoms and recover the full local density approximation (LDA) linear response. These XC functionals represent the hybrid versions of the APBE functional [Phys. Rev. Lett. 2011, 106, 186406] yet employing an additional correlation functional which uses the localization concept of the correlation energy density to improve the compatibility with the Hartree-Fock exchange as well as the coupling-constant-resolved XC potential energy. Broad energetic and structural testing, including thermochemistry and geometry, transition metal complexes, noncovalent interactions, gold clusters and small gold-molecule interfaces, as well as an analysis of the hybrid parameters, show that our construction is quite robust. In particular, our testing shows that the resulting hybrid, including 20% of Hartree-Fock exchange and named hAPBE, performs remarkably well for a broad palette of systems and properties, being generally better than popular hybrids (PBE0 and B3LYP). Semiempirical dispersion corrections are also provided.

Big-bounce cosmology from quantum gravity: The case of a cyclical Bianchi I universe

NASA Astrophysics Data System (ADS)

Moriconi, Riccardo; Montani, Giovanni; Capozziello, Salvatore

2016-07-01

We analyze the classical and quantum dynamics of a Bianchi I model in the presence of a small negative cosmological constant characterizing its evolution in term of the dust-time dualism. We demonstrate that in a canonical metric approach, the cosmological singularity is removed in correspondence to a positive defined value of the dust energy density. Furthermore, the quantum big bounce is connected to the Universe's turning point via a well-defined semiclassical limit. Then we can reliably infer that the proposed scenario is compatible with a cyclical universe picture. We also show how, when the contribution of the dust energy density is sufficiently high, the proposed scenario can be extended to the Bianchi IX cosmology and therefore how it can be regarded as a paradigm for the generic cosmological model. Finally, we investigate the origin of the observed cutoff on the cosmological dynamics, demonstrating how the big-bounce evolution can be mimicked by the same semiclassical scenario, where the negative cosmological constant is replaced via a polymer discretization of the Universe's volume. A direct proportionality law between these two parameters is then established.

Semiclassical theory for liquidlike behavior of the frustrated magnet Ca10Cr7O28

NASA Astrophysics Data System (ADS)

Biswas, Sounak; Damle, Kedar

2018-03-01

We identify the low energy effective Hamiltonian that is expected to describe the low temperature properties of the frustrated magnet Ca10Cr7O28 . Motivated by the fact that this effective Hamiltonian has S =3 /2 effective moments as its degrees of freedom, we use semiclassical spin-wave theory to study the T =0 physics of this effective model and argue that singular spin-wave fluctuations destabilize the spiral order favored by the exchange couplings of this effective Hamiltonian. We also use a combination of classical Monte-Carlo simulations and molecular dynamics, as well as analytical approximations, to study the physics at low, nonzero temperatures. The results of these nonzero temperature calculations capture the liquidlike structure factors observed in the temperature range accessed by recent experiments. Additionally, at still lower temperatures, they predict that a transition to nematic order in the bond energies reflects itself in the spin channel in the form of a crossover to a regime with large but finite correlation length for spiral spin correlations and a corresponding slowing down of spin dynamics.

Pre-Hawking radiation cannot prevent the formation of apparent horizon

NASA Astrophysics Data System (ADS)

Chen, Pisin; Unruh, William G.; Wu, Chih-Hung; Yeom, Dong-Han

2018-03-01

As an attempt to solve the black hole information loss paradox, recently there has been the suggestion that, due to semiclassical effects, a pre-Hawking radiation must exist during the gravitational collapse of matter, which in turn prevents the apparent horizon from forming. Assuming the pre-Hawking radiation does exist, here we argue the opposite. First we note that the stress energy tensor near the horizon for the pre-Hawking radiation is far too small to do anything to the motion of a collapsing shell. Thus the shell will always cross the apparent horizon within a finite proper time. Moreover, the amount of energy that can be radiated must be less than half of the total initial energy (if the particle starts at rest at infinity) before the shell becomes a null shell and cannot radiate any more without becoming tachyonic. We conclude that for any gravitational collapsing process within Einstein gravity and semiclassical quantum field theory, the formation of the apparent horizon is inevitable. Pre-Hawking radiation is therefore not a valid solution to the information paradox.

Projective loop quantum gravity. II. Searching for semi-classical states

NASA Astrophysics Data System (ADS)

Lanéry, Suzanne; Thiemann, Thomas

2017-05-01

In the first paper of this series, an extension of the Ashtekar-Lewandowski state space of loop quantum gravity was set up with the help of a projective formalism introduced by Kijowski. The motivation for this work was to achieve a more balanced treatment of the position and momentum variables (also known as holonomies and fluxes). While this is the first step toward the construction of states semi-classical with respect to a full set of observables, one uncovers a deeper issue, which we analyse in the present article in the case of real-valued holonomies. Specifically, we show that, in this case, there does not exist any state on the holonomy-flux algebra in which the variances of the holonomy and flux observables would all be finite, let alone small. It is important to note that this obstruction cannot be bypassed by further enlarging the quantum state space, for it arises from the structure of the algebra itself. A way out would be to suitably restrict the algebra of observables: we take the first step in this direction in a companion paper.

Tunneling method for Hawking radiation in the Nariai case

NASA Astrophysics Data System (ADS)

Belgiorno, F.; Cacciatori, S. L.; Dalla Piazza, F.

2017-08-01

We revisit the tunneling picture for the Hawking effect in light of the charged Nariai manifold, because this general relativistic solution, which displays two horizons, provides the bonus to allow the knowledge of exact solutions of the field equations. We first perform a revisitation of the tunneling ansatz in the framework of particle creation in external fields à la Nikishov, which corroborates the interpretation of the semiclassical emission rate Γ_{emission} as the conditional probability rate for the creation of a couple of particles from the vacuum. Then, particle creation associated with the Hawking effect on the Nariai manifold is calculated in two ways. On the one hand, we apply the Hamilton-Jacobi formalism for tunneling, in the case of a charged scalar field on the given background. On the other hand, the knowledge of the exact solutions for the Klein-Gordon equations on Nariai manifold, and their analytic properties on the extended manifold, allow us a direct computation of the flux of particles leaving the horizon, and, as a consequence, we obtain a further corroboration of the semiclassical tunneling picture from the side of S-matrix formalism.

Pre-Hawking radiation cannot prevent the formation of apparent horizon

DOE PAGES

Chen, Pisin; Unruh, William G.; Wu, Chih-Hung; ...

2018-03-30

As an attempt to solve the black hole information loss paradox, recently there has been the suggestion that, due to semiclassical effects, a pre-Hawking radiation must exist during the gravitational collapse of matter, which in turn prevents the apparent horizon from forming. Assuming the pre-Hawking radiation does exist, here we argue the opposite. First we note that the stress energy tensor near the horizon for the pre-Hawking radiation is far too small to do anything to the motion of a collapsing shell. Thus the shell will always cross the apparent horizon within a finite proper time. Moreover, the amount ofmore » energy that can be radiated must be less than half of the total initial energy (if the particle starts at rest at infinity) before the shell becomes a null shell and cannot radiate any more without becoming tachyonic. Here, we conclude that for any gravitational collapsing process within Einstein gravity and semiclassical quantum field theory, the formation of the apparent horizon is inevitable. Pre-Hawking radiation is therefore not a valid solution to the information paradox.« less

Pre-Hawking radiation cannot prevent the formation of apparent horizon

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Pisin; Unruh, William G.; Wu, Chih-Hung

As an attempt to solve the black hole information loss paradox, recently there has been the suggestion that, due to semiclassical effects, a pre-Hawking radiation must exist during the gravitational collapse of matter, which in turn prevents the apparent horizon from forming. Assuming the pre-Hawking radiation does exist, here we argue the opposite. First we note that the stress energy tensor near the horizon for the pre-Hawking radiation is far too small to do anything to the motion of a collapsing shell. Thus the shell will always cross the apparent horizon within a finite proper time. Moreover, the amount ofmore » energy that can be radiated must be less than half of the total initial energy (if the particle starts at rest at infinity) before the shell becomes a null shell and cannot radiate any more without becoming tachyonic. Here, we conclude that for any gravitational collapsing process within Einstein gravity and semiclassical quantum field theory, the formation of the apparent horizon is inevitable. Pre-Hawking radiation is therefore not a valid solution to the information paradox.« less

What is dynamics in quantum gravity?

NASA Astrophysics Data System (ADS)

Małkiewicz, Przemysław

2017-10-01

The appearance of the Hamiltonian constraint in the canonical formalism for general relativity reflects the lack of a fixed external time. The dynamics of general relativistic systems can be expressed with respect to an arbitrarily chosen internal degree of freedom, the so-called internal clock. We investigate the way in which the choice of internal clock determines the quantum dynamics and how much different quantum dynamics induced by different clocks are. We develop our method of comparison by extending the Hamilton-Jacobi theory of contact transformations to include a new type of transformation which transforms both the canonical variables and the internal clock. We employ our method to study the quantum dynamics of the Friedmann-Lemaitre model and obtain semiclassical corrections to the classical dynamics, which depend on the choice of internal clock. For a unique quantisation map we find the abundance of inequivalent semiclassical corrections induced by quantum dynamics taking place in different internal clocks. It follows that the concepts like minimal volume, maximal curvature and the number of quantum bounces, often used to describe quantum effects in cosmological models, depend on the choice of internal clock.

Numerical solutions of ideal quantum gas dynamical flows governed by semiclassical ellipsoidal-statistical distribution

PubMed Central

Yang, Jaw-Yen; Yan, Chih-Yuan; Diaz, Manuel; Huang, Juan-Chen; Li, Zhihui; Zhang, Hanxin

2014-01-01

The ideal quantum gas dynamics as manifested by the semiclassical ellipsoidal-statistical (ES) equilibrium distribution derived in Wu et al. (Wu et al. 2012 Proc. R. Soc. A 468, 1799–1823 (doi:10.1098/rspa.2011.0673)) is numerically studied for particles of three statistics. This anisotropic ES equilibrium distribution was derived using the maximum entropy principle and conserves the mass, momentum and energy, but differs from the standard Fermi–Dirac or Bose–Einstein distribution. The present numerical method combines the discrete velocity (or momentum) ordinate method in momentum space and the high-resolution shock-capturing method in physical space. A decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. Computations of two-dimensional Riemann problems are presented, and various contours of the quantities unique to this ES model are illustrated. The main flow features, such as shock waves, expansion waves and slip lines and their complex nonlinear interactions, are depicted and found to be consistent with existing calculations for a classical gas. PMID:24399919

Simulations of terahertz pulse emission from thin-film semiconductor structures

NASA Astrophysics Data System (ADS)

Semichaevsky, Andrey

The photo-Dember effect is the formation of transient electric dipoles due to the interaction of semiconductors with ultrashort optical pulses. Typically the optically-induced dipole moments vary on the ns- or ps- scales, leading to the emission of electromagnetic pulses with terahertz (THz) bandwidths. One of the applications of the photo-Dember effect is a photoconductive dipole antenna (PDA). This work presents a computational model of a PDA based on Maxwell's equations coupled to the Boltzmann transport equation. The latter is solved semiclassically for the doped GaAs using a continuum approach. The emphasis is on the accurate prediction of the emitted THz pulse shape and bandwidth, particularly when materials are doped with a rare-earth metal such as erbium or terbium that serve as carrier recombination centers. Field-dependent carrier mobility is determined from particle-based simulations. Some of the previous experimental results are used as a basis for comparison with our model.

Semiclassical analysis of angular differential cross sections for single-electron capture in 250-eV H++H collisions

NASA Astrophysics Data System (ADS)

Frémont, F.

2015-05-01

A classical model based on the resolution of Hamilton equations of motion is used to determine the angular distribution of H projectiles following single-electron capture in H++H collisions at an incident projectile energy of 250 eV. At such low energies, the experimental charge-exchange probability and angular differential cross sections exhibit oscillatory structures that are classically related to the number of swaps the electron experiences between the target and the projectile during the collision. These oscillations are well reproduced by models based on quantum mechanics. In the present paper, the angular distribution of H projectiles is determined classically, at angles varying from 0.1° up to 7°. The variation in intensity due to interferences caused by the indiscernibility between different trajectories is calculated, and the role of these interferences is discussed.

Experimental investigation of terahertz quantum cascade laser with variable barrier heights

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiang, Aiting; Vijayraghavan, Karun; Belkin, Mikhail A., E-mail: mbelkin@ece.utexas.edu

2014-04-28

We report an experimental study of terahertz quantum cascade lasers with variable barrier heights based on the Al{sub x}Ga{sub 1–x}As/GaAs material system. Two new designs are developed based on semiclassical ensemble Monte Carlo simulations using state-of-the-art Al{sub 0.15}Ga{sub 0.85}As/GaAs three-quantum-well resonant phonon depopulation active region design as a reference. The new designs achieved maximum lasing temperatures of 188 K and 172 K, as compared to the maximum lasing temperature of 191 K for the reference structure. These results demonstrate that terahertz quantum cascade laser designs with variable barrier heights provide a viable alternative to the traditional active region designs with fixed barrier composition.more » Additional design space offered by using variable barriers may lead to future improvements in the terahertz quantum cascade laser performance.« less

HZE reactions and data-base development

NASA Technical Reports Server (NTRS)

Townsend, Lawrence W.; Cucinotta, Francis A.; Wilson, John W.

1993-01-01

The primary cosmic rays are dispersed over a large range of linear energy transfer (LET) values and their distribution over LET is a determinant of biological response. This LET distribution is modified by radiation shielding thickness and shield material composition. The current uncertainties in nuclear cross sections will not allow the composition of the shield material to be distinguished in order to minimize biological risk. An overview of the development of quantum mechanical models of heavy ion reactions will be given and computational results compared with experiments. A second approach is the development of phenomenological models from semi-classical considerations. These models provide the current data base in high charge and energy (HZE) shielding studies. They will be compared with available experimental data. The background material for this lecture will be available as a review document of over 30 years of research at Langley but will include new results obtained over the last year.

Pressure broadening of the electric dipole and Raman lines of CO2 by argon: Stringent test of the classical impact theory at different temperatures on a benchmark system

NASA Astrophysics Data System (ADS)

Ivanov, Sergey V.; Buzykin, Oleg G.

2016-12-01

A classical approach is applied to calculate pressure broadening coefficients of CO2 vibration-rotational spectral lines perturbed by Ar. Three types of spectra are examined: electric dipole (infrared) absorption; isotropic and anisotropic Raman Q branches. Simple and explicit formulae of the classical impact theory are used along with exact 3D Hamilton equations for CO2-Ar molecular motion. The calculations utilize vibrationally independent most accurate ab initio potential energy surface (PES) of Hutson et al. expanded in Legendre polynomial series up to lmax = 24. New improved algorithm of classical rotational frequency selection is applied. The dependences of CO2 half-widths on rotational quantum number J up to J=100 are computed for the temperatures between 77 and 765 K and compared with available experimental data as well as with the results of fully quantum dynamical calculations performed on the same PES. To make the picture complete, the predictions of two independent variants of the semi-classical Robert-Bonamy formalism for dipole absorption lines are included. This method. however, has demonstrated poor accuracy almost for all temperatures. On the contrary, classical broadening coefficients are in excellent agreement both with measurements and with quantum results at all temperatures. The classical impact theory in its present variant is capable to produce quickly and accurately the pressure broadening coefficients of spectral lines of linear molecules for any J value (including high Js) using full-dimensional ab initio - based PES in the cases where other computational methods are either extremely time consuming (like the quantum close coupling method) or give erroneous results (like semi-classical methods).

Interface or bulk scattering in the semiclassical theory for spin valves

NASA Astrophysics Data System (ADS)

Wang, L.; McMahon, W. J.; Liu, B.; Wu, Y. H.; Chong, C. T.

2004-06-01

By taking into account spin asymmetries of the interface transmissions and the bulk mean free paths, we have treated pure interface, non-pure interface, bulk, and interface plus bulk scattering within the semiclassical Boltzmann theory. First, the optimizations of NOL (nano-oxide-layers) insertions in bottom, synthetic, and dual spin valves and the variations of the giant magnetoresistance (GMR) with the thickness of the free layer have been examined. For non-pure interface, bulk, and interface plus bulk scattering, qualitative trends of GMR versus NOL positions in spin valves are similar to each other. For pure interface scattering, there is no optimized NOL insertion positions and the blocking effect of the NOL inserted in the spacer remains effective as other three kinds of scattering. The GMR ratio for bulk scattering simply approaches zero when the free layer thickness becomes short; in contrast, for interface scattering or interface plus bulk scattering, the GMR ratio is nonzero at zero thickness of the free layer. Second, the relationships between GMR and specular and diffusive scattering have been explored. As far as specular reflection is concerned, our results imply that for a realistic bottom spin filter spin valve, Ta/NiFe/IrMn/CoFe/Cu/CoFe/Cu/Ta, roughness of the surfaces of Ta and the interfaces of Ta/NiFe, NiFe/IrMn, pinned layer/spacer, and spacer/free layer may lead to large GMR. We also find that the enhancement of GMR due to surface specular reflection is only a pure interface effect. The dependences of GMR on the specular transmissions roughly follow square relations. The trends of GMR against the spin-down diffusive scattering depend on the values of the spin-up transmission. Finally, impurity scattering was investigated and our semiclassical results are in qualitative agreement with the experiments and the quantum theory.

No rescue for the no boundary proposal: Pointers to the future of quantum cosmology

NASA Astrophysics Data System (ADS)

Feldbrugge, Job; Lehners, Jean-Luc; Turok, Neil

2018-01-01

In recent work [J. Feldbrugge et al. Phys. Rev. D 95, 103508 (2017)., 10.1103/PhysRevD.95.103508 and J. Feldbrugge et al. Phys. Rev. Lett. 119, 171301 (2017)., 10.1103/PhysRevLett.119.171301], we introduced Picard-Lefschetz theory as a tool for defining the Lorentzian path integral for quantum gravity in a systematic semiclassical expansion. This formulation avoids several pitfalls occurring in the Euclidean approach. Our method provides, in particular, a more precise formulation of the Hartle-Hawking no boundary proposal, as a sum over real Lorentzian four-geometries interpolating between an initial three-geometry of zero size, i.e., a point, and a final three-geometry. With this definition, we calculated the no boundary amplitude for a closed universe with a cosmological constant, assuming cosmological symmetry for the background and including linear perturbations. We found the opposite semiclassical exponent to that obtained by Hartle and Hawking for the creation of a de Sitter spacetime "from nothing." Furthermore, we found the linearized perturbations to be governed by an inverse Gaussian distribution, meaning they are unsuppressed and out of control. Recently, Diaz Dorronsoro et al. [Phys. Rev. D 96, 043505 (2017), 10.1103/PhysRevD.96.043505] followed our methods but attempted to rescue the no boundary proposal by integrating the lapse over a different, intrinsically complex contour. Here, we show that, in addition to the desired Hartle-Hawking saddle point contribution, their contour yields extra, nonperturbative corrections which again render the perturbations unsuppressed. We prove there is no choice of complex contour for the lapse which avoids this problem. We extend our discussion to include backreaction in the leading semiclassical approximation, fully nonlinearly for the lowest tensor harmonic and to second order for all higher modes. Implications for quantum de Sitter spacetime and for cosmic inflation are briefly discussed.

EDITORIAL: Squeeze transformation and optics after Einstein

NASA Astrophysics Data System (ADS)

Kim, Young S.; Man'ko, Margarita A.; Planat, Michel

2005-12-01

With this special issue, Journal of Optics B: Quantum and Semiclassical Optics contributes to the celebration of the World Year of Physics held in recognition of five brilliant papers written by Albert Einstein in 1905. There is no need to explain to the readers of this journal the content and importance of these papers, which are cornerstones of modern physics. The 51 contributions in this special issue represent current trends in quantum optics —100 years after the concept of light quanta was introduced. At first glance, in his famous papers of 1905, Einstein treated quite independent subjects—special relativity, the nature and statistical properties of light, electrodynamics of moving bodies and Brownian motion. We now know that all these phenomena are deeply related, and these relations are clearly shown in many papers in this issue. Most of the papers are based on the talks and poster contributions from participants of the 9th International Conference on Squeezed States and Uncertainty Relations (ICSSUR'05), which took place in Besançon, France, 2-6 May, 2005. This was the continuation of a series of meetings, originating with the first workshops organized by Professor Y S Kim at the University of Maryland, College Park, USA, in 1991 and by Professor V I Man'ko at the Lebedev Physical Institute, Moscow in 1992. One of the main topics of ICSSUR'05 and this special issue is the theory and applications of squeezed states and their generalizations. At first glance, one could think that this subject has no relation to Einstein's papers. However, this is not true: the theory of squeezed states is deeply related to special relativity, as far as it is based on the representations of the Lorentz group (see the paper by Kim Y S and Noz M E, S458-S467), which also links the current concepts of entanglement and decoherence with Lorentz-covariance. Besides, studies of the different quantum states of light imply, after all, the study of photon (or photo-electron) statistics and fluctuations of the electromagnetic field, whose importance was first emphasized by Einstein in 1905. The squeezed states can also be considered as a generalization of the concept of coherent states, which turned out to be one of the most important theoretical tools for solving the numerous problems of quantum optics. It seems highly symbolical that the printed version of this special issue will appear in the same month when one of the prominent creators of the theory of coherent states and modern quantum optics—Professor Roy J Glauber—will receive his Nobel Prize in Stockholm. ICSSUR'05 was opened by the invited talk of R J Glauber, `What makes a quantum jump?', and we take great pleasure in congratulating him on this well deserved award. We are sure that all participants of ICSSUR'05 and all readers of this special issue share our feelings. Two other Nobel Prize winners of 2005—Professor J L Hall and Professor T W H\\"ansch—also made great contributions to quantum optics. In particular, in 1986, J L Hall with collaborators, performed the first experiments on the generation of squeezed states by parametric down conversion, having obtained squeezing at the 50% level (Wu L A, Kimble H J, Hall J L and Wu H 1986 Phys. Rev. Lett. 57 2520). Another area, which has attracted the attention of many researchers in the past decade and which is well represented in this special issue, is related to the problems of quantum correlations, entanglement and quantum nonlocality. It is also connected with the name of Einstein due to his famous `EPR' paper of 1935 written together with Podolsky and Rosen. For several decades this was an area of `thought experiments' only, but now this field is becoming a new part of physics, known as `quantum information'. The reader can find several papers which introduce new concepts in this area, such as applications of the Galois algebras and discrete Wigner functions. Solutions of different problems of the interaction between light and matter (which also take their origin in Einstein's paper of 1905), stationary and nonstationary Casimir effect, decoherence, new forms of uncertainty relations and their experimental verification, etc, can also be found in this issue. Many other contributions will be published in another special issue of the International Journal of Modern Physics B entitled `Quantum Information in Modern Optics'. This special issue is also the last issue of Journal of Optics B: Quantum and Semiclassical Optics. For the past 15 years this journal and its predecessors—Quantum Optics and Quantum and Semiclassical Optics—gained great respect among the quantum optics community. Many breakthrough papers were published in its pages during this period (see, for example, Schrade G, Man'ko V I, Schleich W P and Glauber R J 1995 Wigner Functions in the Paul trap Quantum Semiclass. Opt. 7 307). Since 1999, Journal of Optics B: Quantum and Semiclassical Optics has published a special issue for each ICSSUR meeting. This is the fourth issue of this series. We would like to thank Institute of Physics Publishing and the staff of Journal of Optics B: Quantum and Semiclassical Optics for providing the opportunity to pursue this programme, hoping that such a cooperation will continue in the future. We would also like to thank the many colleagues, who served as referees and whose efforts helped immensely in the preparation of this issue at such a high standard. The 10th ICSSUR conference will be organized for 2007 in Bradford, UK, by Professor A Vourdas. We invite readers to join us in two years.

On mini-superspace limit of boundary three-point function in Liouville field theory

NASA Astrophysics Data System (ADS)

Apresyan, Elena; Sarkissian, Gor

2017-12-01

We study the mini-superspace semiclassical limit of the boundary three-point function in the Liouville field theory. We compute also matrix elements for the Morse potential quantum mechanics. An exact agreement between the former and the latter is found. We show that both of them are given by the generalized hypergeometric functions.

Bell's Theorem and Einstein's "Spooky Actions" from a Simple Thought Experiment

ERIC Educational Resources Information Center

Kuttner, Fred; Rosenblum, Bruce

2010-01-01

In 1964 John Bell proved a theorem allowing the experimental test of whether what Einstein derided as "spooky actions at a distance" actually exist. We will see that they "do". Bell's theorem can be displayed with a simple, nonmathematical thought experiment suitable for a physics course at "any" level. And a simple, semi-classical derivation of…

Aspects of String Dualities

NASA Astrophysics Data System (ADS)

Orgera, Jacopo

In this thesis we investigate some aspects of String Dualities. In particular, in the context of Twistor-String/Field Theories duality, we present some partial results toward the understanding of Conformal Supergravity amplitudes. Also, in the context of AdS/CFT duality, we investigate: the role of Euclidean Wormholes in quantum de-coherence and the semiclassical decay of certain non-supersimmetric vacua.

Black Hole Interior in Quantum Gravity.

PubMed

Nomura, Yasunori; Sanches, Fabio; Weinberg, Sean J

2015-05-22

We discuss the interior of a black hole in quantum gravity, in which black holes form and evaporate unitarily. The interior spacetime appears in the sense of complementarity because of special features revealed by the microscopic degrees of freedom when viewed from a semiclassical standpoint. The relation between quantum mechanics and the equivalence principle is subtle, but they are still consistent.

Cross-Over Between Different Symmetries

NASA Astrophysics Data System (ADS)

Frauendorf, S.

2014-09-01

The yrast states of even even vibrational and transitional nuclei are interpreted as a rotating condensate of interacting d-bosons. The corresponding semi-classical tidal wave concept is used for microscopic calculations of energies and E2 transition probabilities. The strong octupole correlations in the light rare earth and actinide nuclides are interpreted as rotation-induced condensation of interacting f-bosons.

Possibility of observation of polaron normal modes at the far-infrared spectrum of acetanilide and related organics

NASA Astrophysics Data System (ADS)

Kalosakas, G.; Aubry, S.; Tsironis, G. P.

1998-10-01

We use a stationary and normal mode analysis of the semiclassical Holstein model in order to connect the low-frequency linear polaron modes to low-lying far-infrared lines of the acetanilide spectrum and through parameter fitting we comment on the validity of the polaron results in this system.

Prebifurcation periodic ghost orbits in semiclassical quantization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kus, M.; Haake, F.; Delande, D.

1993-10-04

Classical periodic orbits are stationary-phase points in path integral representations of quantum propagators. We show that complex solutions of the stationary-phase equation, not corresponding to real classical periodic orbits, give additional contributions to the propagator which can be important, especially near bifurcations. We reveal the existence and relevance of such periodic ghost orbits for a kicked top.

Solving the Nose-Hoover thermostat for Nuclear Pasta

DOE Office of Scientific and Technical Information (OSTI.GOV)

Perez Garcia, M. Angeles

2006-06-19

At densities just below nuclear saturation density, there may be possible non-uniform spatial configurations of neutron rich matter. In this work we present a calculation using molecular dynamics techniques for a nuclear system interacting via a semiclassical potential depending on both positions and momenta and kept at fixed temperature by using the Nose-Hoover Thermostat.

Quasiparticle motion in some classical and quantum mechanical systems: Investigations of nanoscale friction and polaron mobility

NASA Astrophysics Data System (ADS)

Tiwari, Mukesh

In this thesis, we investigate some topics of transport in classical and quantum systems. The classical system under study is related to friction at the nanoscale. The first model we consider is that of a dimer moving on a 1-dimensional periodic substrate; we study the role of an internal channel of dissipation on the effective damping experienced by the dimer during its motion. With the view that understanding of the processes at the microscopic scale can shed some light on the origin of frictional forces, we undertake a systematic study of the scattering of a free particle by a harmonic oscillator. This study starts from a Hamiltonian description of the system, without any phenomenological damping. The dissipation in this system results from an exchange of energy between the particle and the oscillator when they are in close proximity. This classical scattering problem becomes chaotic as a result of exchange of energy. We present, in detail, a study of the chaotic scattering process for an initially static oscillator. In the case of an initially excited oscillator, extraction of information about the chaotic set requires the construction of Smale horseshoe on an appropriate Poincare surface of section. A discussion on the construction of this chaotic invariant set is also provided in this thesis. Interacting quasiparticle-boson systems form an important part of condensed matter physics. Various approximation schemes are often employed in the study of these systems. In order to understand the response of a quasi-particle to externally applied electric fields, we study in the second part of this thesis, the 2-site quantum dimer under the semiclassical approximation. The role of initial phases and effects of resonance between phonon frequency and the frequency due to the Stark splitting of states is investigated. This thesis also contains discussions regarding the frequency response of both degenerate and nondegenerate adiabatic semiclassical models and self-trapping observed in these systems. A review of the derivation of the generalized master equation and the relationship of the memory function to bath spectra is also provided. The formal theory is then applied to the 2-site nondegenerate quantum mechanical polaron model and the effect of a constant electric field on the evolution is studied both in the short and long time limit. The role of temperature and of coupling to the bath on the spectrum, and ultimately on the evolution, are also discussed.

Topics in quantum chaos

NASA Astrophysics Data System (ADS)

Jordan, Andrew Noble

2002-09-01

In this dissertation, we study the quantum mechanics of classically chaotic dynamical systems. We begin by considering the decoherence effects a quantum chaotic system has on a simple quantum few state system. Typical time evolution of a quantum system whose classical limit is chaotic generates structures in phase space whose size is much smaller than Planck's constant. A naive application of Heisenberg's uncertainty principle indicates that these structures are not physically relevant. However, if we take the quantum chaotic system in question to be an environment which interacts with a simple two state quantum system (qubit), we show that these small phase-space structures cause the qubit to generically lose quantum coherence if and only if the environment has many degrees of freedom, such as a dilute gas. This implies that many-body environments may be crucial for the phenomenon of quantum decoherence. Next, we turn to an analysis of statistical properties of time correlation functions and matrix elements of quantum chaotic systems. A semiclassical evaluation of matrix elements of an operator indicates that the dominant contribution will be related to a classical time correlation function over the energy surface. For a highly chaotic class of dynamics, these correlation functions may be decomposed into sums of Ruelle resonances, which control exponential decay to the ergodic distribution. The theory is illustrated both numerically and theoretically on the Baker map. For this system, we are able to isolate individual Ruelle modes. We further consider dynamical systems whose approach to ergodicity is given by a power law rather than an exponential in time. We propose a billiard with diffusive boundary conditions, whose classical solution may be calculated analytically. We go on to compare the exact solution with an approximation scheme, as well calculate asympotic corrections. Quantum spectral statistics are calculated assuming the validity of the Again, Altshuler and Andreev ansatz. We find singular behavior of the two point spectral correlator in the limit of small spacing. Finally, we analyse the effect that slow decay to ergodicity has on the structure of the quantum propagator, as well as wavefunction localization. We introduce a statistical quantum description of systems that are composed of both an orderly region and a random region. By averaging over the random region only, we find that measures of localization in momentum space semiclassically diverge with the dimension of the Hilbert space. We illustrate this numerically with quantum maps and suggest various other systems where this behavior should be important.

Evaluation of the photoionization probability of H2+ by the trajectory semiclassical method

NASA Astrophysics Data System (ADS)

Arkhipov, D. N.; Astashkevich, S. A.; Mityureva, A. A.; Smirnov, V. V.

2018-07-01

The trajectory-based method for calculating the probabilities of transitions in the quantum system developed in our previous works and tested for atoms is applied to calculating the photoionization probability for the simplest molecule - hydrogen molecular ion. In a weak field it is established a good agreement between our photoionization cross section and the data obtained by other theoretical methods for photon energy in the range from one-photon ionization threshold up to 25 a.u. Photoionization cross section in the range 25 < ω ≤ 100 a.u. was calculated for the first time judging by the literature known to us. It is also confirmed that the trajectory method works in a wide range of the field magnitudes including superatomic values up to relativistic intensity.

Electronic excitation and quenching of atoms at insulator surfaces

NASA Technical Reports Server (NTRS)

Swaminathan, P. K.; Garrett, Bruce C.; Murthy, C. S.

1988-01-01

A trajectory-based semiclassical method is used to study electronically inelastic collisions of gas atoms with insulator surfaces. The method provides for quantum-mechanical treatment of the internal electronic dynamics of a localized region involving the gas/surface collision, and a classical treatment of all the nuclear degrees of freedom (self-consistently and in terms of stochastic trajectories), and includes accurate simulation of the bath-temperature effects. The method is easy to implement and has a generality that holds promise for many practical applications. The problem of electronically inelastic dynamics is solved by computing a set of stochastic trajectories that on thermal averaging directly provide electronic transition probabilities at a given temperature. The theory is illustrated by a simple model of a two-state gas/surface interaction.

The Influence of the Optical Phonons on the Non-equilibrium Spin Current in the Presence of Spin-Orbit Couplings

NASA Astrophysics Data System (ADS)

Hasanirokh, K.; Phirouznia, A.; Majidi, R.

2016-02-01

The influence of the electron coupling with non-polarized optical phonons on magnetoelectric effects of a two-dimensional electron gas system has been investigated in the presence of the Rashba and Dresselhaus spin-orbit couplings. Numerical calculations have been performed in the non-equilibrium regime. In the previous studies in this field, it has been shown that the Rashba and Dresselhaus couplings cannot generate non-equilibrium spin current and the spin current vanishes identically in the absence of other relaxation mechanisms such as lattice vibrations. However, in the current study, based on a semiclassical approach, it was demonstrated that in the presence of electron-phonon coupling, the spin current and other magnetoelectric quantities have been modulated by the strength of the spin-orbit interactions.

Scaling of Rényi entanglement entropies of the free fermi-gas ground state: a rigorous proof.

PubMed

Leschke, Hajo; Sobolev, Alexander V; Spitzer, Wolfgang

2014-04-25

In a remarkable paper [Phys. Rev. Lett. 96, 100503 (2006)], Gioev and Klich conjectured an explicit formula for the leading asymptotic growth of the spatially bipartite von Neumann entanglement entropy of noninteracting fermions in multidimensional Euclidean space at zero temperature. Based on recent progress by one of us (A. V. S.) in semiclassical functional calculus for pseudodifferential operators with discontinuous symbols, we provide here a complete proof of that formula and of its generalization to Rényi entropies of all orders α>0. The special case α=1/2 is also known under the name logarithmic negativity and often considered to be a particularly useful quantification of entanglement. These formulas exhibiting a "logarithmically enhanced area law" have been used already in many publications.

On the theory of Carriers's Electrostatic Interaction near an Interface

NASA Astrophysics Data System (ADS)

Waters, Michael; Hashemi, Hossein; Kieffer, John

2015-03-01

Heterojunction interfaces are common in non-traditional photovoltaic device designs, such as those based small molecules, polymers, and perovskites. We have examined a number of the effects of the heterojunction interface region on carrier/exciton energetics using a mixture of both semi-classical and quantum electrostatic methods, ab initio methods, and statistical mechanics. Our theoretical analysis has yielded several useful relationships and numerical recipes that should be considered in device design regardless of the particular materials system. As a demonstration, we highlight these formalisms as applied to carriers and polaron pairs near a C60/subphthalocyanine interface. On the regularly ordered areas of the heterojunction, the effect of the interface is a significant set of corrections to the carrier energies, which in turn directly affects device performance.

Superconformal Baryon-Meson Symmetry and Light-Front Holographic QCD

DOE PAGES

Dosch, Hans Guenter; de Teramond, Guy F.; Brodsky, Stanley J.

2015-04-10

We construct an effective QCD light-front Hamiltonian for both mesons and baryons in the chiral limit based on the generalized supercharges of a superconformal graded algebra. The superconformal construction is shown to be equivalent to a semi-classical approximation to light-front QCD and its embedding in AdS space. The specific breaking of conformal invariance inside the graded algebra uniquely determines the effective confinement potential. The generalized supercharges connect the baryon and meson spectra to each other in a remarkable manner. In particular, the π/b 1 Regge trajectory is identified as the superpartner of the nucleon trajectory. However, the lowest-lying state onmore » this trajectory, the π-meson is massless in the chiral limit and has no supersymmetric partner.« less

Jacobi Shape Transitions Within the LSD Model and the Skyrme-Etf Approach

NASA Astrophysics Data System (ADS)

Bartel, Johann; Pomorski, Krzysztof

The "Modified Funny-Hills parametrisation" is used together with the Lublin-Strasbourg Drop Model to evaluate the stability of rotating nuclei. The Jacobi transition into triaxial shapes is studied. By a comparison with selfconsistent semiclassical calculations in the framework of the Extended Thomas-Fermi method, the validity of the present approach is demonstrated and possible improvements are indicated.

Conditional symmetries in axisymmetric quantum cosmologies with scalar fields and the fate of the classical singularities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zampeli, Adamantia; Pailas, Theodoros; Terzis, Petros A.

2016-05-01

In this paper, the classical and quantum solutions of some axisymmetric cosmologies coupled to a massless scalar field are studied in the context of minisuperspace approximation. In these models, the singular nature of the Lagrangians entails a search for possible conditional symmetries. These have been proven to be the simultaneous conformal symmetries of the supermetric and the superpotential. The quantization is performed by adopting the Dirac proposal for constrained systems, i.e. promoting the first-class constraints to operators annihilating the wave function. To further enrich the approach, we follow [1] and impose the operators related to the classical conditional symmetries onmore » the wave function. These additional equations select particular solutions of the Wheeler-DeWitt equation. In order to gain some physical insight from the quantization of these cosmological systems, we perform a semiclassical analysis following the Bohmian approach to quantum theory. The generic result is that, in all but one model, one can find appropriate ranges of the parameters, so that the emerging semiclassical geometries are non-singular. An attempt for physical interpretation involves the study of the effective energy-momentum tensor which corresponds to an imperfect fluid.« less

Time-dependent importance sampling in semiclassical initial value representation calculations for time correlation functions. II. A simplified implementation.

PubMed

Tao, Guohua; Miller, William H

2012-09-28

An efficient time-dependent (TD) Monte Carlo (MC) importance sampling method has recently been developed [G. Tao and W. H. Miller, J. Chem. Phys. 135, 024104 (2011)] for the evaluation of time correlation functions using the semiclassical (SC) initial value representation (IVR) methodology. In this TD-SC-IVR method, the MC sampling uses information from both time-evolved phase points as well as their initial values, and only the "important" trajectories are sampled frequently. Even though the TD-SC-IVR was shown in some benchmark examples to be much more efficient than the traditional time-independent sampling method (which uses only initial conditions), the calculation of the SC prefactor-which is computationally expensive, especially for large systems-is still required for accepted trajectories. In the present work, we present an approximate implementation of the TD-SC-IVR method that is completely prefactor-free; it gives the time correlation function as a classical-like magnitude function multiplied by a phase function. Application of this approach to flux-flux correlation functions (which yield reaction rate constants) for the benchmark H + H(2) system shows very good agreement with exact quantum results. Limitations of the approximate approach are also discussed.

Charge Transfer Processes in Collisions of Si4+ Ions with He Atoms at Intermediate Energies

NASA Astrophysics Data System (ADS)

Suzuki, R.; Watanabe, A.; Sato, H.; Gu, J. P.; Hirsch, G.; Buenker, R. J.; Kimura, M.; Stancil, P. C.

Charge transfer in collisions of Si4+ ions with He atoms below 100 keV/u is studied by using a molecular orbital representation within both the semiclassical and quantal representations. Single transfer reaction Si4++He →Si3++He+ has been studied by a number of theoretical investigations. In addition to the reaction (1), the first semiclassical MOCC calculations are performed for the double transfer channel Si4++HE→Si2++He2+ Nine molecular states that connect both with single and double electron transfer processes are considered in the present model. Electronic states and corresponding couplings are determined by the multireference single- and double- excitation configuration interaction method. The present cross sections tie well with the earlier calculations of Stancil et al., Phys. Rev. A 55, 1064 (1997) at lower energies, but show a rather different magnitude from those of Bacchus-Montabonel and Ceyzeriat, Phys. Rev. A 58, 1162 (1998). The present rate constant is found to be significantly different from the experimental finding of Fang and Kwong, Phys. Rev. A 59, 342 (1996) at 4,600 K, and hence does not support the experiment.

Fluctuations of the gluon distribution from the small- x effective action

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dumitru, Adrian; Skokov, Vladimir

The computation of observables in high-energy QCD involves an average over stochastic semiclassical small-x gluon fields. The weight of various configurations is determined by the effective action. We introduce a method to study fluctuations of observables, functionals of the small-x fields, which does not explicitly involve dipoles. We integrate out those fluctuations of the semiclassical gluon field under which a given observable is invariant. Thereby we obtain the effective potential for that observable describing its fluctuations about the average. Here, we determine explicitly the effective potential for the covariant gauge gluon distribution both for the McLerran-Venugopalan (MV) model and formore » a (nonlocal) Gaussian approximation for the small-x effective action. This provides insight into the correlation of fluctuations of the number of hard gluons versus their typical transverse momentum. We find that the spectral shape of the fluctuations of the gluon distribution is fundamentally different in the MV model, where there is a pileup of gluons near the saturation scale, versus the solution of the small-x JIMWLK renormalization group, which generates essentially scale-invariant fluctuations above the absorptive boundary set by the saturation scale.« less

Fluctuations of the gluon distribution from the small- x effective action

DOE PAGES

Dumitru, Adrian; Skokov, Vladimir

2017-09-29

The computation of observables in high-energy QCD involves an average over stochastic semiclassical small-x gluon fields. The weight of various configurations is determined by the effective action. We introduce a method to study fluctuations of observables, functionals of the small-x fields, which does not explicitly involve dipoles. We integrate out those fluctuations of the semiclassical gluon field under which a given observable is invariant. Thereby we obtain the effective potential for that observable describing its fluctuations about the average. Here, we determine explicitly the effective potential for the covariant gauge gluon distribution both for the McLerran-Venugopalan (MV) model and formore » a (nonlocal) Gaussian approximation for the small-x effective action. This provides insight into the correlation of fluctuations of the number of hard gluons versus their typical transverse momentum. We find that the spectral shape of the fluctuations of the gluon distribution is fundamentally different in the MV model, where there is a pileup of gluons near the saturation scale, versus the solution of the small-x JIMWLK renormalization group, which generates essentially scale-invariant fluctuations above the absorptive boundary set by the saturation scale.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bianchi, Eugenio; Speziale, Simone; Dona, Pietro

Intertwiners are the building blocks of spin-network states. The space of intertwiners is the quantization of a classical symplectic manifold introduced by Kapovich and Millson. Here we show that a theorem by Minkowski allows us to interpret generic configurations in this space as bounded convex polyhedra in R{sup 3}: A polyhedron is uniquely described by the areas and normals to its faces. We provide a reconstruction of the geometry of the polyhedron: We give formulas for the edge lengths, the volume, and the adjacency of its faces. At the quantum level, this correspondence allows us to identify an intertwiner withmore » the state of a quantum polyhedron, thus generalizing the notion of the quantum tetrahedron familiar in the loop quantum gravity literature. Moreover, coherent intertwiners result to be peaked on the classical geometry of polyhedra. We discuss the relevance of this result for loop quantum gravity. In particular, coherent spin-network states with nodes of arbitrary valence represent a collection of semiclassical polyhedra. Furthermore, we introduce an operator that measures the volume of a quantum polyhedron and examine its relation with the standard volume operator of loop quantum gravity. We also comment on the semiclassical limit of spin foams with nonsimplicial graphs.« less

Reduced-Dimensionality Semiclassical Transition State Theory: Application to Hydrogen Atom Abstraction and Exchange Reactions of Hydrocarbons.

PubMed

Greene, Samuel M; Shan, Xiao; Clary, David C

2015-12-17

Quantum mechanical methods for calculating rate constants are often intractable for reactions involving many atoms. Semiclassical transition state theory (SCTST) offers computational advantages over these methods but nonetheless scales exponentially with the number of degrees of freedom (DOFs) of the system. Here we present a method with more favorable scaling, reduced-dimensionality SCTST (RD SCTST), that treats only a subset of DOFs of the system explicitly. We apply it to three H abstraction and exchange reactions for which two-dimensional potential energy surfaces (PESs) have previously been constructed and evaluated using RD quantum scattering calculations. We differentiated these PESs to calculate harmonic frequencies and anharmonic constants, which were then used to calculate cumulative reaction probabilities and rate constants by RD SCTST. This method yielded rate constants in good agreement with quantum scattering results. Notably, it performed well for a heavy-light-heavy reaction, even though it does not explicitly account for corner-cutting effects. Recent extensions to SCTST that improve its treatment of deep tunneling were also evaluated within the reduced-dimensionality framework. The success of RD SCTST in this study suggests its potential applicability to larger systems.

Semiclassical gravitational effects on the gravitational lensing in the spacetime of topological defects

NASA Astrophysics Data System (ADS)

Jusufi, Kimet; Rahaman, Farook; Banerjee, Ayan

2018-02-01

The theory of gravitational lensing has revealed many generic and fundamental properties of compact objects like black holes and wormholes. In this article, we utilize a recent formulation to compute the quantum effects on the deflection angle of a light ray, namely, the Gauss-Bonnet theorem (GBT) to explore the semiclassical gravitational effects in the spacetime of a point-like global monopole and a cosmic string. Previously, the Gauss-Bonnet theorem (Gibbons and Werner, 2008) was proposed as an alternative way to compute the deflection angle of light in a static, spherically symmetric and asymptotically flat spacetime. In the present article we have used the celebrated GBT that applied to the optical metric as well as the geodesic method in computing the deflection angle. Interestingly one can observe that we have found an exact result between GBT and the standard approach up to the third-order contributions terms by modifying the domain of integration for cosmic string and global monopole deflection angles. Finally we have considered the time delay in the cosmic string/global monopole spacetime and found that the delay in time is proportional to the linear mass density of the cosmic string and global monopole parameter, respectively.

Quantum propagation across cosmological singularities

NASA Astrophysics Data System (ADS)

Gielen, Steffen; Turok, Neil

2017-05-01

The initial singularity is the most troubling feature of the standard cosmology, which quantum effects are hoped to resolve. In this paper, we study quantum cosmology with conformal (Weyl) invariant matter. We show that it is natural to extend the scale factor to negative values, allowing a large, collapsing universe to evolve across a quantum "bounce" into an expanding universe like ours. We compute the Feynman propagator for Friedmann-Robertson-Walker backgrounds exactly, identifying curious pathologies in the case of curved (open or closed) universes. We then include anisotropies, fixing the operator ordering of the quantum Hamiltonian by imposing covariance under field redefinitions and again finding exact solutions. We show how complex classical solutions allow one to circumvent the singularity while maintaining the validity of the semiclassical approximation. The simplest isotropic universes sit on a critical boundary, beyond which there is qualitatively different behavior, with potential for instability. Additional scalars improve the theory's stability. Finally, we study the semiclassical propagation of inhomogeneous perturbations about the flat, isotropic case, at linear and nonlinear order, showing that, at least at this level, there is no particle production across the bounce. These results form the basis for a promising new approach to quantum cosmology and the resolution of the big bang singularity.

Noncommutative spherically symmetric spacetimes at semiclassical order

NASA Astrophysics Data System (ADS)

Fritz, Christopher; Majid, Shahn

2017-07-01

Working within the recent formalism of Poisson-Riemannian geometry, we completely solve the case of generic spherically symmetric metric and spherically symmetric Poisson-bracket to find a unique answer for the quantum differential calculus, quantum metric and quantum Levi-Civita connection at semiclassical order O(λ) . Here λ is the deformation parameter, plausibly the Planck scale. We find that r, t, d r, d t are all forced to be central, i.e. undeformed at order λ, while for each value of r, t we are forced to have a fuzzy sphere of radius r with a unique differential calculus which is necessarily nonassociative at order λ2 . We give the spherically symmetric quantisation of the FLRW cosmology in detail and also recover a previous analysis for the Schwarzschild black hole, now showing that the quantum Ricci tensor for the latter vanishes at order λ. The quantum Laplace-Beltrami operator for spherically symmetric models turns out to be undeformed at order λ while more generally in Poisson-Riemannian geometry we show that it deforms to □f+λ2ωαβ(Ricγα-Sγα)(∇^βdf)γ+O(λ2) in terms of the classical Levi-Civita connection \\widehat\

Computational comparison of quantum-mechanical models for multistep direct reactions

NASA Astrophysics Data System (ADS)

Koning, A. J.; Akkermans, J. M.

1993-02-01

We have carried out a computational comparison of all existing quantum-mechanical models for multistep direct (MSD) reactions. The various MSD models, including the so-called Feshbach-Kerman-Koonin, Tamura-Udagawa-Lenske and Nishioka-Yoshida-Weidenmüller models, have been implemented in a single computer system. All model calculations thus use the same set of parameters and the same numerical techniques; only one adjustable parameter is employed. The computational results have been compared with experimental energy spectra and angular distributions for several nuclear reactions, namely, 90Zr(p,p') at 80 MeV, 209Bi(p,p') at 62 MeV, and 93Nb(n,n') at 25.7 MeV. In addition, the results have been compared with the Kalbach systematics and with semiclassical exciton model calculations. All quantum MSD models provide a good fit to the experimental data. In addition, they reproduce the systematics very well and are clearly better than semiclassical model calculations. We furthermore show that the calculated predictions do not differ very strongly between the various quantum MSD models, leading to the conclusion that the simplest MSD model (the Feshbach-Kerman-Koonin model) is adequate for the analysis of experimental data.

Thermal Transport in Crystals as a Kinetic Theory of Relaxons

NASA Astrophysics Data System (ADS)

Cepellotti, Andrea; Marzari, Nicola

2016-10-01

Thermal conductivity in dielectric crystals is the result of the relaxation of lattice vibrations described by the phonon Boltzmann transport equation. Remarkably, an exact microscopic definition of the heat carriers and their relaxation times is still missing: Phonons, typically regarded as the relevant excitations for thermal transport, cannot be identified as the heat carriers when most scattering events conserve momentum and do not dissipate heat flux. This is the case for two-dimensional or layered materials at room temperature, or three-dimensional crystals at cryogenic temperatures. In this work, we show that the eigenvectors of the scattering matrix in the Boltzmann equation define collective phonon excitations, which are termed here "relaxons". These excitations have well-defined relaxation times, directly related to heat-flux dissipation, and they provide an exact description of thermal transport as a kinetic theory of the relaxon gas. We show why Matthiessen's rule is violated, and we construct a procedure for obtaining the mean free paths and relaxation times of the relaxons. These considerations are general and would also apply to other semiclassical transport models, such as the electronic Boltzmann equation. For heat transport, they remain relevant even in conventional crystals like silicon, but they are of the utmost importance in the case of two-dimensional materials, where they can revise, by several orders of magnitude, the relevant time and length scales for thermal transport in the hydrodynamic regime.

Theoretical Studies of Spectroscopic Line Mixing in Remote Sensing Applications

NASA Astrophysics Data System (ADS)

Ma, Q.

2015-12-01

The phenomenon of collisional transfer of intensity due to line mixing has an increasing importance for atmospheric monitoring. From a theoretical point of view, all relevant information about the collisional processes is contained in the relaxation matrix where the diagonal elements give half-widths and shifts, and the off-diagonal elements correspond to line interferences. For simple systems such as those consisting of diatom-atom or diatom-diatom, accurate fully quantum calculations based on interaction potentials are feasible. However, fully quantum calculations become unrealistic for more complex systems. On the other hand, the semi-classical Robert-Bonamy (RB) formalism, which has been widely used to calculate half-widths and shifts for decades, fails in calculating the off-diagonal matrix elements. As a result, in order to simulate atmospheric spectra where the effects from line mixing are important, semi-empirical fitting or scaling laws such as the ECS and IOS models are commonly used. Recently, while scrutinizing the development of the RB formalism, we have found that these authors applied the isolated line approximation in their evaluating matrix elements of the Liouville scattering operator given in exponential form. Since the criterion of this assumption is so stringent, it is not valid for many systems of interest in atmospheric applications. Furthermore, it is this assumption that blocks the possibility to calculate the whole relaxation matrix at all. By eliminating this unjustified application, and accurately evaluating matrix elements of the exponential operators, we have developed a more capable formalism. With this new formalism, we are now able not only to reduce uncertainties for calculated half-widths and shifts, but also to remove a once insurmountable obstacle to calculate the whole relaxation matrix. This implies that we can address the line mixing with the semi-classical theory based on interaction potentials between molecular absorber and molecular perturber. We have applied this formalism to address the line mixing for Raman and infrared spectra of molecules such as N2, C2H2, CO2, NH3, and H2O. By carrying out rigorous calculations, our calculated relaxation matrices are in good agreement with both experimental data and results derived from the ECS model.

Book Review:

NASA Astrophysics Data System (ADS)

Israel, W.

2006-07-01

The evaporation of a black hole formed by the collapse of matter is a nonunitary process involving loss of information. At least, this is how it appears in Hawking's semiclassical description, in which gravity is not quantized and the emergent radiation appears thermal. Since unitarity is one of the pillars of quantum mechanics there has been an understandable reluctance to accept this as an ironclad conclusion. Conformal field theories in flat space are manifestly unitary, and the AdS/CFT correspondence therefore suggests that the information trapped in the depths of the hole must find some way to escape—a conclusion almost universally accepted today, at least among particle theorists. Just how it could escape remains a mystery, however, since nothing can escape without violating causality until the black hole has shrunk too far to hold much information. Gerard 't Hooft and the senior author of this book, Leonard Susskind, have been vocal advocates of the view that the information paradox poses a real crisis for physics requiring significant paradigm shifts. They suggest that locality must be given up as an objective property of physical phenomena (even on large scales) and replaced by a new principle of 'black hole complementarity'. Specifically, there are two very different ways to view the process of collapse and evaporation. To a free-falling observer, nothing unusual happens at the horizon and matter and information fall deep into the hole. To a stationary observer hovering just outside the hole it appears instead that the matter and information are deposited on the horizon (which he experiences as very hot because of his large acceleration), to be eventually re-emitted from there as Hawking radiation. According to 't Hooft and Susskind, these must be viewed as equally valid, 'complementary' descriptions of the same process. Black hole complementarity is essentially the statement (supported by operational arguments) that their simultaneous validity cannot lead to inconsistencies. Students and non-specialists will welcome this book, which provides an entry into this fascinating realm at a level that can be enjoyed by an enterprising undergraduate. The first chapter introduces the Schwarzschild black hole and the various coordinate systems used for its description. In four brief chapters (29 pages) the authors then manage a clear presentation of the thermal properties of quantum fields in Rindler and Schwarzschild space that skirts the operator formalism of QFT. Two further chapters treat charged black holes and the stretched-horizon description of black hole electrodynamics. Chapter 8, 'The Laws of Nature', explains how information is quantified, the quantum xerox principle and the entanglement entropy of black holes, with a detailed account of how this evolves as the hole evaporates. This sets the stage for a discussion of the black hole information puzzle and the complementarity principle in chapter 9. The pace heats up in the second part of the book, which in 48 pages sketches a variety of topics: Bousso's entropy bound and holography, the AdS/CFT correspondence, a 13 page introduction to string theory and the ideas underlying the string-based derivations of the entropy area relation for higher-dimensional black holes. This well-planned, stimulating and sometimes provocative book can be enthusiastically recommended.

Classical and quantum entropy of parton distributions

NASA Astrophysics Data System (ADS)

Hagiwara, Yoshikazu; Hatta, Yoshitaka; Xiao, Bo-Wen; Yuan, Feng

2018-05-01

We introduce the semiclassical Wehrl entropy for the nucleon as a measure of complexity of the multiparton configuration in phase space. This gives a new perspective on the nucleon tomography. We evaluate the entropy in the small-x region and compare with the quantum von Neumann entropy. We also argue that the growth of entropy at small x is eventually slowed down due to the Pomeron loop effect.

Quantum and classical chaos in kicked coupled Jaynes-Cummings cavities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hayward, A. L. C.; Greentree, Andrew D.

2010-06-15

We consider two Jaynes-Cummings cavities coupled periodically with a photon hopping term. The semiclassical phase space is chaotic, with regions of stability over some ranges of the parameters. The quantum case exhibits dynamic localization and dynamic tunneling between classically forbidden regions. We explore the correspondence between the classical and quantum phase space and propose an implementation in a circuit QED system.

Irregular wave functions of a hydrogen atom in a uniform magnetic field

NASA Technical Reports Server (NTRS)

Wintgen, D.; Hoenig, A.

1989-01-01

The highly excited irregular wave functions of a hydrogen atom in a uniform magnetic field are investigated analytically, with wave function scarring by periodic orbits considered quantitatively. The results obtained confirm that the contributions of closed classical orbits to the spatial wave functions vanish in the semiclassical limit. Their disappearance, however, is slow. This discussion is illustrated by numerical examples.

Model for Ultrafast Carrier Scattering in Semiconductors

DTIC Science & Technology

2012-11-14

energy transfer between semi-classical carrier drift-diffusion under an electric field and quantum kinetics of interband /intersubband transitions...from an electron during each phonon-emission event. The net rate of phonon emission is determined by the Boltzmann scattering equation which depends ...energy-drift term under a strong dc field was demonstrated to reduce the field- dependent drift velocity and mobility. The Doppler shift in the energy

CALL FOR PAPERS: Optical solitons

NASA Astrophysics Data System (ADS)

Drummond, P. D.; Haelterman, Marc; Vilaseca, R.

2003-06-01

A topical issue of Journal of Optics B: Quantum and Semiclassical Optics will be devoted to recent advances in optical solitons. The topics to be covered will include, but are not limited to: bulletProperties, control and dynamics of temporal solitons bulletProperties, control and dynamics of spatial solitons bulletCavity solitons in passive and active resonators bulletThree-dimensional spatial solitons bulletDark, bright, grey solitons; interface dynamics bulletCompound or vector solitons; incoherent solitons bulletLight and matter solitons in BEC bulletNonlinear localized structures in microstructured and nanostructured materials (photonic crystals, etc) bulletAngular momentum effects associated with localized light structures; vortex solitons bulletQuantum effects associated with localized light structures bulletInteraction of solitons with atoms and other media bulletApplications of optical solitons The DEADLINE for submission of contributions is 31 July 2003 to allow the topical issue to appear in about February 2004. All papers will be peer-reviewed in accordance with the normal refereeing procedures and standards of Journal of Optics B: Quantum and Semiclassical Optics. Advice on publishing your work in the journal may be found at www.iop.org/journals/authors/jopb. Submissions should ideally be in either standard LaTeX form or Microsoft Word. There are no page charges for publication. In addition to the usual 50 free reprints, the corresponding author of each paper published will receive a complimentary copy of the topical issue. Contributions to the topical issue should if possible be submitted electronically at www.iop.org/journals/jopb. or by e-mail to jopb@iop.org. Authors unable to submit online or by e-mail may send hard copy contributions (enclosing the electronic code) to: Dr Claire Bedrock (Publisher), Journal of Optics B: Quantum and Semiclassical Optics, Institute of Physics Publishing, Dirac House, Temple Back, Bristol BS1 6BE, UK. All contributions should be accompanied by a readme file or covering letter, quoting `JOPB topical issue - Optical Solitons', giving the postal and e-mail addresses for correspondence. Any subsequent change of address should be notified to the publishing office. We look forward to receiving your contribution to this topical issue.

The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schroedinger equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Leung Shingyu, E-mail: masyleung@ust.h; Qian Jianliang, E-mail: qian@math.msu.ed

2010-11-20

We propose the backward phase flow method to implement the Fourier-Bros-Iagolnitzer (FBI)-transform-based Eulerian Gaussian beam method for solving the Schroedinger equation in the semi-classical regime. The idea of Eulerian Gaussian beams has been first proposed in . In this paper we aim at two crucial computational issues of the Eulerian Gaussian beam method: how to carry out long-time beam propagation and how to compute beam ingredients rapidly in phase space. By virtue of the FBI transform, we address the first issue by introducing the reinitialization strategy into the Eulerian Gaussian beam framework. Essentially we reinitialize beam propagation by applying themore » FBI transform to wavefields at intermediate time steps when the beams become too wide. To address the second issue, inspired by the original phase flow method, we propose the backward phase flow method which allows us to compute beam ingredients rapidly. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithms.« less

The backward phase flow and FBI-transform-based Eulerian Gaussian beams for the Schrödinger equation

NASA Astrophysics Data System (ADS)

Leung, Shingyu; Qian, Jianliang

2010-11-01

We propose the backward phase flow method to implement the Fourier-Bros-Iagolnitzer (FBI)-transform-based Eulerian Gaussian beam method for solving the Schrödinger equation in the semi-classical regime. The idea of Eulerian Gaussian beams has been first proposed in [12]. In this paper we aim at two crucial computational issues of the Eulerian Gaussian beam method: how to carry out long-time beam propagation and how to compute beam ingredients rapidly in phase space. By virtue of the FBI transform, we address the first issue by introducing the reinitialization strategy into the Eulerian Gaussian beam framework. Essentially we reinitialize beam propagation by applying the FBI transform to wavefields at intermediate time steps when the beams become too wide. To address the second issue, inspired by the original phase flow method, we propose the backward phase flow method which allows us to compute beam ingredients rapidly. Numerical examples demonstrate the efficiency and accuracy of the proposed algorithms.

A note on Boltzmann brains

DOE PAGES

Nomura, Yasunori

2015-08-14

Understanding the observed arrow of time is equivalent, under general assumptions, to explaining why Boltzmann brains do not overwhelm ordinary observers. It is usually thought that this provides a condition on the decay rate of every cosmologically accessible de Sitter vacuum, and that this condition is determined by the production rate of Boltzmann brains calculated using semiclassical theory built on each such vacuum. Here, we argue, based on a recently developed picture of microscopic quantum gravitational degrees of freedom, that this thinking needs to be modified. In particular, depending on the structure of the fundamental theory, the decay rate ofmore » a de Sitter vacuum may not have to satisfy any condition except for the one imposed by the Poincaré recurrence. Finally, the framework discussed here also addresses the question of whether a Minkowski vacuum may produce Boltzmann brains.« less

Violations of K-Conservation in 178Hf

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hayes, A. B.; Cline, D.; Wu, C. Y.

2006-03-13

Coulomb excitation of K{pi}=6+(t1/2=77 ns), 8-(t1/2=4.0 s) and 16+(t1/2=31 y) 178Hf isomers has led to the measurement of a set of E{lambda} matrix elements, coupling the isomer bands to the {gamma}- and ground state bands. The resulting matrix elements, derived using a coupled-channel semiclassical Coulomb excitation search code, have been used to probe the K-components in the wave functions and revealed the onset and saturation of K-mixing in low-K bands, whereas K-mixing is negligible in the high-K bands. The implications can be applied to other quadrupole-deformed nuclei. An upper limit on the Coulomb depopulation yield of the 16+ isomer wasmore » calculated based on the present set of matrix elements.« less

Quantized Faraday and Kerr rotation and axion electrodynamics of a 3D topological insulator

NASA Astrophysics Data System (ADS)

Wu, Liang; Salehi, M.; Koirala, N.; Moon, J.; Oh, S.; Armitage, N. P.

2016-12-01

Topological insulators have been proposed to be best characterized as bulk magnetoelectric materials that show response functions quantized in terms of fundamental physical constants. Here, we lower the chemical potential of three-dimensional (3D) Bi2Se3 films to ~30 meV above the Dirac point and probe their low-energy electrodynamic response in the presence of magnetic fields with high-precision time-domain terahertz polarimetry. For fields higher than 5 tesla, we observed quantized Faraday and Kerr rotations, whereas the dc transport is still semiclassical. A nontrivial Berry’s phase offset to these values gives evidence for axion electrodynamics and the topological magnetoelectric effect. The time structure used in these measurements allows a direct measure of the fine-structure constant based on a topological invariant of a solid-state system.

Enhancing high-order harmonic generation by sculpting waveforms with chirp

NASA Astrophysics Data System (ADS)

Peng, Dian; Frolov, M. V.; Pi, Liang-Wen; Starace, Anthony F.

2018-05-01

We present a theoretical analysis showing how chirp can be used to sculpt two-color driving laser field waveforms in order to enhance high-order harmonic generation (HHG) and/or extend HHG cutoff energies. Specifically, we consider driving laser field waveforms composed of two ultrashort pulses having different carrier frequencies in each of which a linear chirp is introduced. Two pairs of carrier frequencies of the component pulses are considered: (ω , 2 ω ) and (ω , 3 ω ). Our results show how changing the signs of the chirps in each of the two component pulses leads to drastic changes in the HHG spectra. Our theoretical analysis is based on numerical solutions of the time-dependent Schrödinger equation and on a semiclassical analytical approach that affords a clear physical interpretation of how our optimized waveforms lead to enhanced HHG spectra.

Coupled wave-packets for non-adiabatic molecular dynamics: a generalization of Gaussian wave-packet dynamics to multiple potential energy surfaces

DOE PAGES

White, Alexander James; Tretiak, Sergei; Mozyrsky, Dima V.

2016-04-25

Accurate simulation of the non-adiabatic dynamics of molecules in excited electronic states is key to understanding molecular photo-physical processes. Here we present a novel method, based on a semiclassical approximation, that is as efficient as the commonly used mean field Ehrenfest or ad hoc surface hopping methods and properly accounts for interference and decoherence effects. This novel method is an extension of Heller's thawed Gaussian wave-packet dynamics that includes coupling between potential energy surfaces. By studying several standard test problems we demonstrate that the accuracy of the method can be systematically improved while maintaining high efficiency. The method is suitablemore » for investigating the role of quantum coherence in the non-adiabatic dynamics of many-atom molecules.« less

Simplified Formulae System for Resonant Inverse Compton Scattering of a Fast Electron in an Intense Magnetic Field

NASA Technical Reports Server (NTRS)

You, J. H.; Chen, W. P.; Zhang, S. N.; Chen, L.; Liu, D.; Chou, C. K.

2003-01-01

We present simple analytical formulae for the emission spectrum and total power of a special kind of resonant inverse Compton scattering (RICS) of a relativistic electron in an intense magnetic field. In contrast with the available formulae system, we obtain a markedly simplified one based on the semiclassical quantum theory, which is more understandable for people who are unfamiliar with quantum electrodynamics. We show that the RICS process, under an appropriate 'accommodation condition' derived in this paper, is predominantly much more efficient than the coexistent ordinary inverse Compton scattering, and produces highly beamed high-frequency radiation with moderately good monochromaticity. Our formulae are simple to use - thus offering a lucid physical intuition for the theory - and may find wide applications in hard X-ray and gamma-ray astrophysics.

Buckling of stiff polymers: Influence of thermal fluctuations

NASA Astrophysics Data System (ADS)

Emanuel, Marc; Mohrbach, Hervé; Sayar, Mehmet; Schiessel, Helmut; Kulić, Igor M.

2007-12-01

The buckling of biopolymers is a frequently studied phenomenon The influence of thermal fluctuations on the buckling transition is, however, often ignored and not completely understood. A quantitative theory of the buckling of a wormlike chain based on a semiclassical approximation of the partition function is presented. The contribution of thermal fluctuations to the force-extension relation that allows one to go beyond the classical Euler buckling is derived in the linear and nonlinear regimes as well. It is shown that the thermal fluctuations in the nonlinear buckling regime increase the end-to-end distance of the semiflexible rod if it is confined to two dimensions as opposed to the three-dimensional case. The transition to a buckled state softens at finite temperature. We derive the scaling behavior of the transition shift with increasing ratio of contour length versus persistence length.

Investigation on phase noise of the signal from a singly resonant optical parametric oscillator

NASA Astrophysics Data System (ADS)

Jinxia, Feng; Yuanji, Li; Kuanshou, Zhang

2018-04-01

The phase noise of the signal from a singly resonant optical parametric oscillator (SRO) is investigated theoretically and experimentally. An SRO based on periodically poled lithium niobate is built up that generates the signal with a maximum power of 5.2 W at 1.5 µm. The intensity noise of the signal reaches the shot noise level for frequencies above 5 MHz. The phase noise of the signal oscillates depending on the analysis frequency, and there are phase noise peaks above the shot noise level at the peak frequencies. To explain the phase noise feature of the signal, a semi-classical theoretical model of SROs including the guided acoustic wave Brillouin scattering effect within the nonlinear crystal is developed. The theoretical predictions are in good agreement with the experimental results.

Modeling of coherent ultrafast magneto-optical experiments: Light-induced molecular mean-field model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hinschberger, Y.; Hervieux, P.-A.

2015-12-28

We present calculations which aim to describe coherent ultrafast magneto-optical effects observed in time-resolved pump-probe experiments. Our approach is based on a nonlinear semi-classical Drude-Voigt model and is used to interpret experiments performed on nickel ferromagnetic thin film. Within this framework, a phenomenological light-induced coherent molecular mean-field depending on the polarizations of the pump and probe pulses is proposed whose microscopic origin is related to a spin-orbit coupling involving the electron spins of the material sample and the electric field of the laser pulses. Theoretical predictions are compared to available experimental data. The model successfully reproduces the observed experimental trendsmore » and gives meaningful insight into the understanding of magneto-optical rotation behavior in the ultrafast regime. Theoretical predictions for further experimental studies are also proposed.« less

Classical Limit and Quantum Logic

NASA Astrophysics Data System (ADS)

Losada, Marcelo; Fortin, Sebastian; Holik, Federico

2018-02-01

The analysis of the classical limit of quantum mechanics usually focuses on the state of the system. The general idea is to explain the disappearance of the interference terms of quantum states appealing to the decoherence process induced by the environment. However, in these approaches it is not explained how the structure of quantum properties becomes classical. In this paper, we consider the classical limit from a different perspective. We consider the set of properties of a quantum system and we study the quantum-to-classical transition of its logical structure. The aim is to open the door to a new study based on dynamical logics, that is, logics that change over time. In particular, we appeal to the notion of hybrid logics to describe semiclassical systems. Moreover, we consider systems with many characteristic decoherence times, whose sublattices of properties become distributive at different times.

Interaction of Rydberg atoms in circular states with the alkaline-earth Ca(4s{sup 2}) and Sr(5s{sup 2}) atoms

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mironchuk, E. S.; Narits, A. A.; Lebedev, V. S., E-mail: vlebedev@sci.lebedev.ru

2015-11-15

The resonant mechanism of interaction of alkaline-earth atoms having a low electron affinity to Rydberg atoms in circular (l = vertical bar m vertical bar = n–1) and near-circular states has been studied. To describe the dynamics of resonant processes accompanied by nonadiabatic transitions between ionic and Rydberg covalent terms of a quasimolecule, an approach based on the integration of coupled equations for the probability amplitudes has been developed taking into account the possibility of the decay of an anion in the Coulomb field of the positive ionic core of a highly excited atom. The approach involves the specific featuresmore » of the problem associated with the structure of the wavefunction of a Rydberg electron in states with high orbital angular momenta l ∼ n–1. This approach provides a much more accurate description of the dynamics of electronic transitions at collisions between atoms than that within the modified semiclassical Landau–Zener model. In addition, this approach makes it possible to effectively take into account many channels of the problem. The cross sections for resonant quenching of Rydberg states of the Li(nlm) atom with given principal n, orbital l = n–1, and magnetic m quantum numbers at thermal collisions with the Ca(4s{sup 2}) and Sr(5s{sup 2}) atoms have been calculated. The dependences of the results on n, m, and angle α between the relative velocity of the atoms and the normal to the plane of the orbit of the Rydberg electron have been obtained. The influence of orientational effects on the efficiency of the collisional destruction of circular and near-circular states has been studied. The results indicate a higher stability of such states to their perturbations by neutral particles as compared to usually studied nl states with low values of l (l ≪ n)« less

A numerical study of adaptive space and time discretisations for Gross–Pitaevskii equations

PubMed Central

Thalhammer, Mechthild; Abhau, Jochen

2012-01-01

As a basic principle, benefits of adaptive discretisations are an improved balance between required accuracy and efficiency as well as an enhancement of the reliability of numerical computations. In this work, the capacity of locally adaptive space and time discretisations for the numerical solution of low-dimensional nonlinear Schrödinger equations is investigated. The considered model equation is related to the time-dependent Gross–Pitaevskii equation arising in the description of Bose–Einstein condensates in dilute gases. The performance of the Fourier-pseudo spectral method constrained to uniform meshes versus the locally adaptive finite element method and of higher-order exponential operator splitting methods with variable time stepsizes is studied. Numerical experiments confirm that a local time stepsize control based on a posteriori local error estimators or embedded splitting pairs, respectively, is effective in different situations with an enhancement either in efficiency or reliability. As expected, adaptive time-splitting schemes combined with fast Fourier transform techniques are favourable regarding accuracy and efficiency when applied to Gross–Pitaevskii equations with a defocusing nonlinearity and a mildly varying regular solution. However, the numerical solution of nonlinear Schrödinger equations in the semi-classical regime becomes a demanding task. Due to the highly oscillatory and nonlinear nature of the problem, the spatial mesh size and the time increments need to be of the size of the decisive parameter 0<ε≪1, especially when it is desired to capture correctly the quantitative behaviour of the wave function itself. The required high resolution in space constricts the feasibility of numerical computations for both, the Fourier pseudo-spectral and the finite element method. Nevertheless, for smaller parameter values locally adaptive time discretisations facilitate to determine the time stepsizes sufficiently small in order that the numerical approximation captures correctly the behaviour of the analytical solution. Further illustrations for Gross–Pitaevskii equations with a focusing nonlinearity or a sharp Gaussian as initial condition, respectively, complement the numerical study. PMID:25550676

A numerical study of adaptive space and time discretisations for Gross-Pitaevskii equations.

PubMed

Thalhammer, Mechthild; Abhau, Jochen

2012-08-15

As a basic principle, benefits of adaptive discretisations are an improved balance between required accuracy and efficiency as well as an enhancement of the reliability of numerical computations. In this work, the capacity of locally adaptive space and time discretisations for the numerical solution of low-dimensional nonlinear Schrödinger equations is investigated. The considered model equation is related to the time-dependent Gross-Pitaevskii equation arising in the description of Bose-Einstein condensates in dilute gases. The performance of the Fourier-pseudo spectral method constrained to uniform meshes versus the locally adaptive finite element method and of higher-order exponential operator splitting methods with variable time stepsizes is studied. Numerical experiments confirm that a local time stepsize control based on a posteriori local error estimators or embedded splitting pairs, respectively, is effective in different situations with an enhancement either in efficiency or reliability. As expected, adaptive time-splitting schemes combined with fast Fourier transform techniques are favourable regarding accuracy and efficiency when applied to Gross-Pitaevskii equations with a defocusing nonlinearity and a mildly varying regular solution. However, the numerical solution of nonlinear Schrödinger equations in the semi-classical regime becomes a demanding task. Due to the highly oscillatory and nonlinear nature of the problem, the spatial mesh size and the time increments need to be of the size of the decisive parameter [Formula: see text], especially when it is desired to capture correctly the quantitative behaviour of the wave function itself. The required high resolution in space constricts the feasibility of numerical computations for both, the Fourier pseudo-spectral and the finite element method. Nevertheless, for smaller parameter values locally adaptive time discretisations facilitate to determine the time stepsizes sufficiently small in order that the numerical approximation captures correctly the behaviour of the analytical solution. Further illustrations for Gross-Pitaevskii equations with a focusing nonlinearity or a sharp Gaussian as initial condition, respectively, complement the numerical study.

Fusion reaction cross-sections using the Wong model within Skyrme energy density based semiclassical extended Thomas Fermi approach

NASA Astrophysics Data System (ADS)

Kumar, Raj; Sharma, Manoj K.; Gupta, Raj K.

2011-11-01

First, the nuclear proximity potential, obtained by using the semiclassical extended Thomas Fermi (ETF) approach in Skyrme energy density formalism (SEDF), is shown to give more realistic barriers in frozen density approximation, as compared to the sudden approximation. Then, taking advantage of the fact that, in ETF method, different Skyrme forces give different barriers (height, position and curvature), we use the ℓ-summed extended-Wong model of Gupta and collaborators (2009) [1] under frozen densities approximation for calculating the cross-sections, where the Skyrme force is chosen with proper barrier characteristics, not-requiring additional "barrier modification" effects (lowering or narrowing, etc.), for a best fit to data at sub-barrier energies. The method is applied to capture cross-section data from 48Ca + 238U, 244Pu, and 248Cm reactions and to fusion-evaporation cross-sections from 58Ni + 58Ni, 64Ni + 64Ni, and 64Ni + 100Mo reactions, with effects of deformations and orientations of nuclei included, wherever required. Interestingly, whereas the capture cross-sections in Ca-induced reactions could be fitted to any force, such as SIII, SV and GSkI, by allowing a small change of couple of units in deduced ℓ-values at below-barrier energies, the near-barrier data point of 48Ca + 248Cm reaction could not be fitted to ℓ-values deduced for below-barrier energies, calling for a check of data. On the other hand, the fusion-evaporation cross-sections in Ni-induced reactions at sub-barrier energies required different Skyrme forces, representing "modifications of the barrier", for the best fit to data at all incident center-of-mass energies E's, displaying a kind of fusion hindrance at sub-barrier energies. This barrier modification effect is taken into care here by using different Skyrme forces for reactions belonging to different regions of the periodic table. Note that more than one Skyrme force (with identical barrier characteristics) could equally well fit the same data.

Physical theories, eternal inflation, and the quantum universe

NASA Astrophysics Data System (ADS)

Nomura, Yasunori

2011-11-01

Infinities in eternal inflation have long been plaguing cosmology, making any predictions highly sensitive to how they are regulated. The problem exists already at the level of semi-classical general relativity, and has a priori nothing to do with quantum gravity. On the other hand, we know that certain problems in semi-classical gravity, for example physics of black holes and their evaporation, have led to understanding of surprising, quantum natures of spacetime and gravity, such as the holographic principle and horizon complementarity. In this paper, we present a framework in which well-defined predictions are obtained in an eternally inflating multiverse, based on the principles of quantum mechanics. We propose that the entire multiverse is described purely from the viewpoint of a single "observer," who describes the world as a quantum state defined on his/her past light cones bounded by the (stretched) apparent horizons. We find that quantum mechanics plays an essential role in regulating infinities. The framework is "gauge invariant," i.e. predictions do not depend on how spacetime is parametrized, as it should be in a theory of quantum gravity. Our framework provides a fully unified treatment of quantum measurement processes and the multiverse. We conclude that the eternally inflating multiverse and many worlds in quantum mechanics are the same. Other important implications include: global spacetime can be viewed as a derived concept; the multiverse is a transient phenomenon during the world relaxing into a supersymmetric Minkowski state. We also present a model of "initial conditions" for the multiverse. By extrapolating our framework to the extreme, we arrive at a picture that the entire multiverse is a fluctuation in the stationary, fractal "mega-multiverse," in which an infinite sequence of multiverse productions occurs. The framework discussed here does not suffer from problems/paradoxes plaguing other measures proposed earlier, such as the youngness paradox and the Boltzmann brain problem.

Prediction and Real-Time Compensation of Qubit Decoherence Via Machine Learning (Open Access, Publisher’s Version)

DTIC Science & Technology

2017-01-16

ARTICLE Received 24 Sep 2016 | Accepted 29 Nov 2016 | Published 16 Jan 2017 Prediction and real- time compensation of qubit decoherence via machine...information to suppress stochastic, semiclassical decoherence, even when access to measurements is limited. First, we implement a time -division...quantum information experiments. Second, we employ predictive feedback during sequential but time delayed measurements to reduce the Dick effect as