Quantum chaotic scattering in graphene systems in the absence of invariant classical dynamics
NASA Astrophysics Data System (ADS)
Wang, Guang-Lei; Ying, Lei; Lai, Ying-Cheng; Grebogi, Celso
2013-05-01
Quantum chaotic scattering is referred to as the study of quantum behaviors of open Hamiltonian systems that exhibit transient chaos in the classical limit. Traditionally a central issue in this field is how the elements of the scattering matrix or their functions fluctuate as a system parameter, e.g., the electron Fermi energy, is changed. A tacit hypothesis underlying previous works was that the underlying classical phase-space structure remains invariant as the parameter varies, so semiclassical theory can be used to explain various phenomena in quantum chaotic scattering. There are, however, experimental situations where the corresponding classical chaotic dynamics can change characteristically with some physical parameter. Multiple-terminal quantum dots are one such example where, when a magnetic field is present, the classical chaotic-scattering dynamics can change between being nonhyperbolic and being hyperbolic as the Fermi energy is changed continuously. For such systems semiclassical theory is inadequate to account for the characteristics of conductance fluctuations with the Fermi energy. To develop a general framework for quantum chaotic scattering associated with variable classical dynamics, we use multi-terminal graphene quantum-dot systems as a prototypical model. We find that significant conductance fluctuations occur with the Fermi energy even for fixed magnetic field strength, and the characteristics of the fluctuation patterns depend on the energy. We propose and validate that the statistical behaviors of the conductance-fluctuation patterns can be understood by the complex eigenvalue spectrum of the generalized, complex Hamiltonian of the system which includes self-energies resulted from the interactions between the device and the semi-infinite leads. As the Fermi energy is increased, complex eigenvalues with extremely smaller imaginary parts emerge, leading to sharp resonances in the conductance.
CALL FOR PAPERS: Special Issue on `Trends in Quantum Chaotic Scattering'
NASA Astrophysics Data System (ADS)
Fyodorov, Y. V.; Kottos, T.; Stöckmann, H.-J.
2005-04-01
Quantum scattering of waves in classically chaotic systems has been the subject of rather intensive research activity for more than two decades, both theoretically and experimentally. This interest was motivated by phenomena discovered in various areas, ranging from nuclear, atomic and molecular physics, to mesoscopics and theory of electron transport, quantum chaos, and classical wave scattering. Recently, the interest in this subject was renewed due to technological developments in quantum optics (in particular the ability to construct microlasers with chaotic resonators which produce high-power directional emission) as well as the experimental realizations of the so-called random lasers where the feedback is due to multiple scattering within the medium. The articles collected in this special issue, which contains both review-style contributions and regular research papers, should give an up-to-date, fairly representative (but definitely not complete) picture of current activity related to the various facets of chaotic wave scattering, and its diverse manifestations. We hope that this will serve as a good basis for boosting the research in this fascinating area to a new level of understanding.
Universal Impedance, Admittance and Scattering Fluctuations in Quantum-chaotic Systems
NASA Astrophysics Data System (ADS)
Hemmady, Sameer
2006-03-01
We experimentally investigate fluctuations in the eigenvalues of the impedance, admittance and scattering matrices of wave chaotic systems using a microwave analog of a quantum chaotic infinite square well potential. We consider a 2-D, time-reversal symmetric chaotic microwave resonator driven by two non-ideally coupled ports. The system-specific coupling effects are removed using the measured radiation impedance matrix (3pt<->Z Rad) [1] of the two ports. A normalized impedance matrix (3pt<->z ) is thus obtained, and the Probability Density Function (PDF) of its eigenvalues is predicted to be universal depending only on the cavity loss. We observe remarkable agreement between the statistical properties of 3pt<->z and 3pt<->y =3pt<->z -1 for all degrees of loss, which is in accordance with [1, 2] and Random Matrix Theory (RMT). We compare the joint PDF of the eigenphases of the normalized scattering matrix (3pt<->s ) with that obtained from RMT for varying degrees of loss. We study the joint PDF of the eigenvalues of 3pt<->s 3pt<->s ^ and find good agreement with [3]. [1] X. Zheng, et al., -- Electromagnetics (in press); condmat/0408317; S. Hemmady, et al., Phys. Rev. Lett. 94, 014102 (2005).[2] Y. V. Fyodorov, et al.,-- condmat/0507016.[3] P. W. Brouwer and C. W. J Beenakker -- PRB 55, 4695 (1997). Work supported by DOD MURI AFOSR Grant F496200110374, DURIP Grants FA95500410295 and FA95500510240.
Universal Impedance, Admittance and Scattering Fluctuations in Quantum-chaotic Systems.
NASA Astrophysics Data System (ADS)
Hemmady, Sameer; Zheng, Xing; Antonsen, Thomas; Ott, Edward; Anlage, Steven M.
2006-03-01
We experimentally investigate fluctuations in the eigenvalues of the impedance, admittance and scattering matrices of wave chaotic systems using a microwave analog of a quantum chaotic infinite square well potential. We consider a 2-D, time-reversal symmetric chaotic microwave resonator driven by two non-ideally coupled ports. The system-specific coupling effects are removed using the measured radiation impedance matrix (3pt<->Z Rad) [1] of the two ports. A normalized impedance matrix (3pt<->z ) is thus obtained, and the Probability Density Function (PDF) of its eigenvalues is predicted to be universal depending only on the cavity loss. We observe remarkable agreement between the statistical properties of 3pt<->z and 3pt<->y =3pt<->z -1 for all degrees of loss, which is in accordance with [1, 2] and Random Matrix Theory (RMT). We compare the joint PDF of the eigenphases of the normalized scattering matrix (3pt<->s ) with that obtained from RMT for varying degrees of loss. We study the joint PDF of the eigenvalues of 3pt<->s 3pt<->s ^ and find good agreement with [3]. [1] X. Zheng, et al., -- Electromagnetics (in press); condmat/0408317; S. Hemmady, et al., Phys. Rev. Lett. 94, 014102 (2005).[2] Y. V. Fyodorov, et al.,-- condmat/0507016.[3] P. W. Brouwer and C. W. J Beenakker -- PRB 55, 4695 (1997). Work supported by DOD MURI AFOSR Grant F496200110374, DURIP Grants FA95500410295 and FA95500510240.
NASA Astrophysics Data System (ADS)
Ramos, J. G. G. S.; Barbosa, A. L. R.; Carlson, B. V.; Frederico, T.; Hussein, M. S.
2016-01-01
We derive analytical expressions for the correlation functions of the electronic conductance fluctuations of an open quantum dot under several conditions. Both the variation of energy and that of an external parameter, such as an applied perpendicular or parallel magnetic fields, are considered in the general case of partial openness. These expressions are then used to obtain the ensemble-averaged density of maxima, a measure recently suggested to contain invaluable information concerning the correlation widths of chaotic systems. The correlation width is then calculated for the case of energy variation, and a significant deviation from the Weisskopf estimate is found in the case of two terminals. The results are extended to more than two terminals. All of our results are analytical. The use of these results in other fields, such as nuclei, where the system can only be studied through a variation of the energy, is then discussed.
Ramos, J G G S; Barbosa, A L R; Carlson, B V; Frederico, T; Hussein, M S
2016-01-01
We derive analytical expressions for the correlation functions of the electronic conductance fluctuations of an open quantum dot under several conditions. Both the variation of energy and that of an external parameter, such as an applied perpendicular or parallel magnetic fields, are considered in the general case of partial openness. These expressions are then used to obtain the ensemble-averaged density of maxima, a measure recently suggested to contain invaluable information concerning the correlation widths of chaotic systems. The correlation width is then calculated for the case of energy variation, and a significant deviation from the Weisskopf estimate is found in the case of two terminals. The results are extended to more than two terminals. All of our results are analytical. The use of these results in other fields, such as nuclei, where the system can only be studied through a variation of the energy, is then discussed. PMID:26871076
Chaotic Scattering and Anomalous Transport
NASA Astrophysics Data System (ADS)
Hu, B.; Horton, W.; Petrosky, T.
2002-11-01
The non-relativistic classical electron scattering by a fixed ion in a uniform magnetic field exhibits chaotic scattering feature of fractal dependence of the final pitch angle on the impact parameter. We have constructed a discrete map(B. Hu, W. Horton and T. Petrosky, Phys. Rev. E 65, 056212 (2002).) for the region v>> 3.5 × 10^4 B^1/3, where v is the electron velocity in m/s and B is the magnetic field in Tesla. The map agrees quite well with the numerical integration of the equation of motion. For neutron star atmosphere and white dwarf atmosphere, the Debye length and the average distance between ions are much greater than the electron gyroradius, but the deBroglie wavelength is comparable or smaller than the electron gyroradius, thus quantum effect should be considered. We create ensembles for the initial conditions in different parameter regions, and study the transition between the asymptotic states, the distribution of some quantities, e.g., final pitch angles, trapping times and bouncing numbers. We shall also consider multi-ion scattering and transport problem, and search for possible anomalies in the electric resistivity and thermal conductivity.
Equilibration of quantum chaotic systems.
Zhuang, Quntao; Wu, Biao
2013-12-01
The quantum ergordic theorem for a large class of quantum systems was proved by von Neumann [Z. Phys. 57, 30 (1929)] and again by Reimann [Phys. Rev. Lett. 101, 190403 (2008)] in a more practical and well-defined form. However, it is not clear whether the theorem applies to quantum chaotic systems. With a rigorous proof still elusive, we illustrate and verify this theorem for quantum chaotic systems with examples. Our numerical results show that a quantum chaotic system with an initial low-entropy state will dynamically relax to a high-entropy state and reach equilibrium. The quantum equilibrium state reached after dynamical relaxation bears a remarkable resemblance to the classical microcanonical ensemble. However, the fluctuations around equilibrium are distinct: The quantum fluctuations are exponential while the classical fluctuations are Gaussian. PMID:24483425
Driving trajectories in chaotic scattering.
Macau, Elbert E N; Caldas, Iberê L
2002-02-01
In this work we introduce a general approach for targeting in chaotic scattering that can be used to find a transfer trajectory between any two points located inside the scattering region. We show that this method can be used in association with a control of chaos strategy to drive around and keep a particle inside the scattering region. As an illustration of how powerful this approach is, we use it in a case of practical interest in celestial mechanics in which it is desired to control the evolution of two satellites that evolve around a large central body. PMID:11863640
Quantum stress in chaotic billiards.
Berggren, Karl-Fredrik; Maksimov, Dmitrii N; Sadreev, Almas F; Höhmann, Ruven; Kuhl, Ulrich; Stöckmann, Hans-Jürgen
2008-06-01
This paper reports on a joint theoretical and experimental study of the Pauli quantum-mechanical stress tensor T_{alphabeta}(x,y) for open two-dimensional chaotic billiards. In the case of a finite current flow through the system the interior wave function is expressed as psi=u+iv . With the assumption that u and v are Gaussian random fields we derive analytic expressions for the statistical distributions for the quantum stress tensor components T_{alphabeta} . The Gaussian random field model is tested for a Sinai billiard with two opposite leads by analyzing the scattering wave functions obtained numerically from the corresponding Schrödinger equation. Two-dimensional quantum billiards may be emulated from planar microwave analogs. Hence we report on microwave measurements for an open two-dimensional cavity and how the quantum stress tensor analog is extracted from the recorded electric field. The agreement with the theoretical predictions for the distributions for T_{alphabeta}(x,y) is quite satisfactory for small net currents. However, a distinct difference between experiments and theory is observed at higher net flow, which could be explained using a Gaussian random field, where the net current was taken into account by an additional plane wave with a preferential direction and amplitude. PMID:18643352
New developments in classical chaotic scattering.
Seoane, Jesús M; Sanjuán, Miguel A F
2013-01-01
Classical chaotic scattering is a topic of fundamental interest in nonlinear physics due to the numerous existing applications in fields such as celestial mechanics, atomic and nuclear physics and fluid mechanics, among others. Many new advances in chaotic scattering have been achieved in the last few decades. This work provides a current overview of the field, where our attention has been mainly focused on the most important contributions related to the theoretical framework of chaotic scattering, the fractal dimension, the basins boundaries and new applications, among others. Numerical techniques and algorithms, as well as analytical tools used for its analysis, are also included. We also show some of the experimental setups that have been implemented to study diverse manifestations of chaotic scattering. Furthermore, new theoretical aspects such as the study of this phenomenon in time-dependent systems, different transitions and bifurcations to chaotic scattering and a classification of boundaries in different types according to symbolic dynamics are also shown. Finally, some recent progress on chaotic scattering in higher dimensions is also described. PMID:23242261
Fractal dimension in nonhyperbolic chaotic scattering
NASA Technical Reports Server (NTRS)
Lau, Yun-Tung; Finn, John M.; Ott, Edward
1991-01-01
In chaotic scattering there is a Cantor set of input-variable values of zero Lebesgue measure (i.e., zero total length) on which the scattering function is singular. For cases where the dynamics leading to chaotic scattering is nonhyperbolic (e.g., there are Kolmogorov-Arnol'd-Moser tori), the nature of this singular set is fundamentally different from that in the hyperbolic case. In particular, for the nonhyperbolic case, although the singular set has zero total length, strong evidence is presented to show that its fractal dimension is 1.
Basin topology in dissipative chaotic scattering.
Seoane, Jesús M; Aguirre, Jacobo; Sanjuán, Miguel A F; Lai, Ying-Cheng
2006-06-01
Chaotic scattering in open Hamiltonian systems under weak dissipation is not only of fundamental interest but also important for problems of current concern such as the advection and transport of inertial particles in fluid flows. Previous work using discrete maps demonstrated that nonhyperbolic chaotic scattering is structurally unstable in the sense that the algebraic decay of scattering particles immediately becomes exponential in the presence of weak dissipation. Here we extend the result to continuous-time Hamiltonian systems by using the Henon-Heiles system as a prototype model. More importantly, we go beyond to investigate the basin structure of scattering dynamics. A surprising finding is that, in the common case where multiple destinations exist for scattering trajectories, Wada basin boundaries are common and they appear to be structurally stable under weak dissipation, even when other characteristics of the nonhyperbolic scattering dynamics are not. We provide numerical evidence and a geometric theory for the structural stability of the complex basin topology. PMID:16822004
Exploring Classically Chaotic Potentials with a Matter Wave Quantum Probe
Gattobigio, G. L.; Couvert, A.; Georgeot, B.; Guery-Odelin, D.
2011-12-16
We study an experimental setup in which a quantum probe, provided by a quasimonomode guided atom laser, interacts with a static localized attractive potential whose characteristic parameters are tunable. In this system, classical mechanics predicts a transition from regular to chaotic behavior as a result of the coupling between the different degrees of freedom. Our experimental results display a clear signature of this transition. On the basis of extensive numerical simulations, we discuss the quantum versus classical physics predictions in this context. This system opens new possibilities for investigating quantum scattering, provides a new testing ground for classical and quantum chaos, and enables us to revisit the quantum-classical correspondence.
Will Quantum Cosmology Resurrect Chaotic Inflation Model?
NASA Astrophysics Data System (ADS)
Kim, Sang Pyo; Kim, Won
2016-07-01
The single field chaotic inflation model with a monomial power greater than one seems to be ruled out by the recent Planck and WMAP CMB data while Starobinsky model with a higher curvature term seems to be a viable model. Higher curvature terms being originated from quantum fluctuations, we revisit the quantum cosmology of the Wheeler-DeWitt equation for the chaotic inflation model. The semiclassical cosmology emerges from quantum cosmology with fluctuations of spacetimes and matter when the wave function is peaked around the semiclassical trajectory with quantum corrections a la the de Broglie-Bohm pilot theory.
Chaotic scattering of two vortex pairs
NASA Astrophysics Data System (ADS)
Tophøj, Laust; Aref, Hassan
2008-11-01
Chaotic scattering of two vortex pairs with slightly different circulations was considered by Eckhardt & Aref in 1988. A new numerical exploration suggests that the motion of two vortex pairs, with constituent vortices all of the same absolute circulation, also displays chaotic scattering regimes. The mechanisms leading to chaotic scattering are different from the ``slingshot effect'' identified by Price [Phys. Fluids A, 5, 2479 (1993)] and occur in a different region of the four-vortex phase space. They may in many cases be understood by appealing to the solutions of the three-vortex problem obtained by merging two like-signed vortices into one of twice the strength, and by assuming that the four-vortex problem has unstable, periodic solutions similar to those seen in the thereby associated three-vortex problems. The integrals of motion, linear impulse and Hamiltonian, are recast in a form appropriate for vortex pair scattering interactions that provides constraints on the parameters characterizing the outgoing vortex pairs in terms of the initial conditions.
Conductance fluctuations in chaotic bilayer graphene quantum dots.
Bao, Rui; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso
2015-07-01
Previous studies of quantum chaotic scattering established a connection between classical dynamics and quantum transport properties: Integrable or mixed classical dynamics can lead to sharp conductance fluctuations but chaos is capable of smoothing out the conductance variations. Relativistic quantum transport through single-layer graphene systems, for which the quasiparticles are massless Dirac fermions, exhibits, due to scarring, this classical-quantum correspondence, but sharp conductance fluctuations persist to a certain extent even when the classical system is fully chaotic. There is an open issue regarding the effect of finite mass on relativistic quantum transport. To address this issue, we study quantum transport in chaotic bilayer graphene quantum dots for which the quasiparticles have a finite mass. An interesting phenomenon is that, when traveling along the classical ballistic orbit, the quasiparticle tends to hop back and forth between the two layers, exhibiting a Zitterbewegung-like effect. We find signatures of abrupt conductance variations, indicating that the mass has little effect on relativistic quantum transport. In solid-state electronic devices based on Dirac materials, sharp conductance fluctuations are thus expected, regardless of whether the quasiparticle is massless or massive and whether there is chaos in the classical limit. PMID:26274258
Conductance fluctuations in chaotic bilayer graphene quantum dots
NASA Astrophysics Data System (ADS)
Bao, Rui; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso
2015-07-01
Previous studies of quantum chaotic scattering established a connection between classical dynamics and quantum transport properties: Integrable or mixed classical dynamics can lead to sharp conductance fluctuations but chaos is capable of smoothing out the conductance variations. Relativistic quantum transport through single-layer graphene systems, for which the quasiparticles are massless Dirac fermions, exhibits, due to scarring, this classical-quantum correspondence, but sharp conductance fluctuations persist to a certain extent even when the classical system is fully chaotic. There is an open issue regarding the effect of finite mass on relativistic quantum transport. To address this issue, we study quantum transport in chaotic bilayer graphene quantum dots for which the quasiparticles have a finite mass. An interesting phenomenon is that, when traveling along the classical ballistic orbit, the quasiparticle tends to hop back and forth between the two layers, exhibiting a Zitterbewegung-like effect. We find signatures of abrupt conductance variations, indicating that the mass has little effect on relativistic quantum transport. In solid-state electronic devices based on Dirac materials, sharp conductance fluctuations are thus expected, regardless of whether the quasiparticle is massless or massive and whether there is chaos in the classical limit.
Effects of periodic forcing in chaotic scattering.
Blesa, Fernando; Seoane, Jesús M; Barrio, Roberto; Sanjuán, Miguel A F
2014-04-01
The effects of a periodic forcing on chaotic scattering are relevant in certain situations of physical interest. We investigate the effects of the forcing amplitude and the external frequency in both the survival probability of the particles in the scattering region and the exit basins associated to phase space. We have found an exponential decay law for the survival probability of the particles in the scattering region. A resonant-like behavior is uncovered where the critical values of the frequencies ω≃1 and ω≃2 permit the particles to escape faster than for other different values. On the other hand, the computation of the exit basins in phase space reveals the existence of Wada basins depending of the frequency values. We provide some heuristic arguments that are in good agreement with the numerical results. Our results are expected to be relevant for physical phenomena such as the effect of companion galaxies, among others. PMID:24827315
Association of scattering matrices in quantum networks
Almeida, F.A.G.; Macêdo, A.M.S.
2013-06-15
Algorithms based on operations that associate scattering matrices in series or in parallel (analogous to impedance association in a classical circuit) are developed here. We exemplify their application by calculating the total scattering matrix of several types of quantum networks, such as star graphs and a chain of chaotic quantum dots, obtaining results with good agreement with the literature. Through a computational-time analysis we compare the efficiency of two algorithms for the simulation of a chain of chaotic quantum dots based on series association operations of (i) two-by-two centers and (ii) three-by-three ones. Empirical results point out that the algorithm (ii) is more efficient than (i) for small number of open scattering channels. A direct counting of floating point operations justifies quantitatively the superiority of the algorithm (i) for large number of open scattering channels.
Parametric number covariance in quantum chaotic spectra
NASA Astrophysics Data System (ADS)
Vinayak, Kumar, Sandeep; Pandey, Akhilesh
2016-03-01
We study spectral parametric correlations in quantum chaotic systems and introduce the number covariance as a measure of such correlations. We derive analytic results for the classical random matrix ensembles using the binary correlation method and obtain compact expressions for the covariance. We illustrate the universality of this measure by presenting the spectral analysis of the quantum kicked rotors for the time-reversal invariant and time-reversal noninvariant cases. A local version of the parametric number variance introduced earlier is also investigated.
Parametric number covariance in quantum chaotic spectra.
Vinayak; Kumar, Sandeep; Pandey, Akhilesh
2016-03-01
We study spectral parametric correlations in quantum chaotic systems and introduce the number covariance as a measure of such correlations. We derive analytic results for the classical random matrix ensembles using the binary correlation method and obtain compact expressions for the covariance. We illustrate the universality of this measure by presenting the spectral analysis of the quantum kicked rotors for the time-reversal invariant and time-reversal noninvariant cases. A local version of the parametric number variance introduced earlier is also investigated. PMID:27078354
Sensing small changes in a wave chaotic scattering system
Taddese, Biniyam Tesfaye; Antonsen, Thomas M.; Ott, Edward; Anlage, Steven M.
2010-12-01
Classical analogs of the quantum mechanical concepts of the Loschmidt Echo and quantum fidelity are developed with the goal of detecting small perturbations in a closed wave chaotic region. Sensing techniques that employ a one-recording-channel time-reversal-mirror, which in turn relies on time reversal invariance and spatial reciprocity of the classical wave equation, are introduced. In analogy with quantum fidelity, we employ scattering fidelity techniques which work by comparing response signals of the scattering region, by means of cross correlation and mutual information of signals. The performance of the sensing techniques is compared for various perturbations induced experimentally in an acoustic resonant cavity. The acoustic signals are parametrically processed to mitigate the effect of dissipation and to vary the spatial diversity of the sensing schemes. In addition to static boundary condition perturbations at specified locations, perturbations to the medium of wave propagation are shown to be detectable, opening up various real world sensing applications in which a false negative cannot be tolerated.
Quantum-Behaved Particle Swarm Optimization with Chaotic Search
NASA Astrophysics Data System (ADS)
Yang, Kaiqiao; Nomura, Hirosato
The chaotic search is introduced into Quantum-behaved Particle Swarm Optimization (QPSO) to increase the diversity of the swarm in the latter period of the search, so as to help the system escape from local optima. Taking full advantages of the characteristics of ergodicity and randomicity of chaotic variables, the chaotic search is carried out in the neighborhoods of the particles which are trapped into local optima. The experimental results on test functions show that QPSO with chaotic search outperforms the Particle Swarm Optimization (PSO) and QPSO.
Chaotic scattering of two identical point vortex pairs revisited
NASA Astrophysics Data System (ADS)
Tophøj, Laust; Aref, Hassan
2008-09-01
A new numerical exploration suggests that the motion of two vortex pairs, with constituent vortices all of the same absolute circulation, displays chaotic scattering regimes. The mechanisms leading to chaotic scattering are different from the "slingshot effect" identified by Price [Phys. Fluids A 5, 2479 (1993)] and occur in a different region of the four-vortex phase space. They may, in many cases, be understood by appealing to the solutions of the three-vortex problem obtained by merging two like-signed vortices into one of twice the strength and by assuming that the four-vortex problem has unstable periodic solutions similar to those seen in the thereby associated three-vortex problems. The integrals of motion, linear impulse and Hamiltonian are recast in a form appropriate for vortex pair scattering interactions that provides constraints on the parameters characterizing the outgoing vortex pairs in terms of the initial conditions.
Chaotic scattering in a molecular system
NASA Astrophysics Data System (ADS)
Barr, Alex M.; Na, Kyungsun; Reichl, L. E.; Jung, Christof
2009-02-01
We study the classical dynamics of bound state and scattering trajectories of the chlorine atom interacting with the HO molecule using a two-dimensional model in which the HO bond length is held fixed. The bound state system forms the HOCl molecule and at low energies is predominantly integrable. Below dissociation a number of bifurcations are observed, most notably a series of saddle-center bifurcations related to a 2:1 and at higher energies 3:1 resonance between bend and stretch motions. At energies above dissociation the classical phase space becomes dominated by a homoclinic tangle which induces a fractal distribution of singularities in all scattering functions. The structure of the homoclinic tangle is examined directly using Poincaré surfaces of section as well as indirectly through its influence on the time delay of the scattered chlorine atom and the angular momentum of the scattered HO molecule.
Emergence of Chaotic Scattering in Ultracold Er and Dy
NASA Astrophysics Data System (ADS)
Maier, T.; Kadau, H.; Schmitt, M.; Wenzel, M.; Ferrier-Barbut, I.; Pfau, T.; Frisch, A.; Baier, S.; Aikawa, K.; Chomaz, L.; Mark, M. J.; Ferlaino, F.; Makrides, C.; Tiesinga, E.; Petrov, A.; Kotochigova, S.
2015-10-01
We show that for ultracold magnetic lanthanide atoms chaotic scattering emerges due to a combination of anisotropic interaction potentials and Zeeman coupling under an external magnetic field. This scattering is studied in a collaborative experimental and theoretical effort for both dysprosium and erbium. We present extensive atom-loss measurements of their dense magnetic Feshbach-resonance spectra, analyze their statistical properties, and compare to predictions from a random-matrix-theory-inspired model. Furthermore, theoretical coupled-channels simulations of the anisotropic molecular Hamiltonian at zero magnetic field show that weakly bound, near threshold diatomic levels form overlapping, uncoupled chaotic series that when combined are randomly distributed. The Zeeman interaction shifts and couples these levels, leading to a Feshbach spectrum of zero-energy bound states with nearest-neighbor spacings that changes from randomly to chaotically distributed for increasing magnetic field. Finally, we show that the extreme temperature sensitivity of a small, but sizable fraction of the resonances in the Dy and Er atom-loss spectra is due to resonant nonzero partial-wave collisions. Our threshold analysis for these resonances indicates a large collision-energy dependence of the three-body recombination rate.
Binary black hole shadows, chaotic scattering and the Cantor set
NASA Astrophysics Data System (ADS)
Shipley, Jake O.; Dolan, Sam R.
2016-09-01
We investigate the qualitative features of binary black hole shadows using the model of two extremally charged black holes in static equilibrium (a Majumdar–Papapetrou solution). Our perspective is that binary spacetimes are natural exemplars of chaotic scattering, because they admit more than one fundamental null orbit, and thus an uncountably infinite set of perpetual null orbits which generate scattering singularities in initial data. Inspired by the three-disc model, we develop an appropriate symbolic dynamics to describe planar null geodesics on the double black hole spacetime. We show that a one-dimensional (1D) black hole shadow may be constructed through an iterative procedure akin to the construction of the Cantor set; thus the 1D shadow is self-similar. Next, we study non-planar rays, to understand how angular momentum affects the existence and properties of the fundamental null orbits. Taking slices through 2D shadows, we observe three types of 1D shadow: regular, Cantor-like, and highly chaotic. The switch from Cantor-like to regular occurs where outer fundamental orbits are forbidden by angular momentum. The highly chaotic part is associated with an unexpected feature: stable and bounded null orbits, which exist around two black holes of equal mass M separated by {a}1\\lt a\\lt \\sqrt{2}{a}1, where {a}1=4M/\\sqrt{27}. To show how this possibility arises, we define a certain potential function and classify its stationary points. We conjecture that the highly chaotic parts of the 2D shadow possess the Wada property. Finally, we consider the possibility of following null geodesics through event horizons, and chaos in the maximally extended spacetime.
Electric circuit networks equivalent to chaotic quantum billiards
Bulgakov, Evgeny N.; Maksimov, Dmitrii N.; Sadreev, Almas F.
2005-04-01
We consider two electric RLC resonance networks that are equivalent to quantum billiards. In a network of inductors grounded by capacitors, the eigenvalues of the quantum billiard correspond to the squared resonant frequencies. In a network of capacitors grounded by inductors, the eigenvalues of the billiard are given by the inverse of the squared resonant frequencies. In both cases, the local voltages play the role of the wave function of the quantum billiard. However, unlike for quantum billiards, there is a heat power because of the resistance of the inductors. In the equivalent chaotic billiards, we derive a distribution of the heat power which describes well the numerical statistics.
Quantum localization of chaotic eigenstates and the level spacing distribution
NASA Astrophysics Data System (ADS)
Batistić, Benjamin; Robnik, Marko
2013-11-01
The phenomenon of quantum localization in classically chaotic eigenstates is one of the main issues in quantum chaos (or wave chaos), and thus plays an important role in general quantum mechanics or even in general wave mechanics. In this work we propose two different localization measures characterizing the degree of quantum localization, and study their relation to another fundamental aspect of quantum chaos, namely the (energy) spectral statistics. Our approach and method is quite general, and we apply it to billiard systems. One of the signatures of the localization of chaotic eigenstates is a fractional power-law repulsion between the nearest energy levels in the sense that the probability density to find successive levels on a distance S goes like ∝Sβ for small S, where 0≤β≤1, and β=1 corresponds to completely extended states. We show that there is a clear functional relation between the exponent β and the two different localization measures. One is based on the information entropy and the other one on the correlation properties of the Husimi functions. We show that the two definitions are surprisingly linearly equivalent. The approach is applied in the case of a mixed-type billiard system [M. Robnik, J. Phys. A: Math. Gen.JPHAC50305-447010.1088/0305-4470/16/17/014 16, 3971 (1983)], in which the separation of regular and chaotic eigenstates is performed.
Quantum localization of chaotic eigenstates and the level spacing distribution.
Batistić, Benjamin; Robnik, Marko
2013-11-01
The phenomenon of quantum localization in classically chaotic eigenstates is one of the main issues in quantum chaos (or wave chaos), and thus plays an important role in general quantum mechanics or even in general wave mechanics. In this work we propose two different localization measures characterizing the degree of quantum localization, and study their relation to another fundamental aspect of quantum chaos, namely the (energy) spectral statistics. Our approach and method is quite general, and we apply it to billiard systems. One of the signatures of the localization of chaotic eigenstates is a fractional power-law repulsion between the nearest energy levels in the sense that the probability density to find successive levels on a distance S goes like [proportionality]S(β) for small S, where 0≤β≤1, and β=1 corresponds to completely extended states. We show that there is a clear functional relation between the exponent β and the two different localization measures. One is based on the information entropy and the other one on the correlation properties of the Husimi functions. We show that the two definitions are surprisingly linearly equivalent. The approach is applied in the case of a mixed-type billiard system [M. Robnik, J. Phys. A: Math. Gen. 16, 3971 (1983)], in which the separation of regular and chaotic eigenstates is performed. PMID:24329337
A review of sigma models for quantum chaotic dynamics
NASA Astrophysics Data System (ADS)
Altland, Alexander; Gnutzmann, Sven; Haake, Fritz; Micklitz, Tobias
2015-07-01
We review the construction of the supersymmetric sigma model for unitary maps, using the color-flavor transformation. We then illustrate applications by three case studies in quantum chaos. In two of these cases, general Floquet maps and quantum graphs, we show that universal spectral fluctuations arise provided the pertinent classical dynamics are fully chaotic (ergodic and with decay rates sufficiently gapped away from zero). In the third case, the kicked rotor, we show how the existence of arbitrarily long-lived modes of excitation (diffusion) precludes universal fluctuations and entails quantum localization.
A review of sigma models for quantum chaotic dynamics.
Altland, Alexander; Gnutzmann, Sven; Haake, Fritz; Micklitz, Tobias
2015-07-01
We review the construction of the supersymmetric sigma model for unitary maps, using the color-flavor transformation. We then illustrate applications by three case studies in quantum chaos. In two of these cases, general Floquet maps and quantum graphs, we show that universal spectral fluctuations arise provided the pertinent classical dynamics are fully chaotic (ergodic and with decay rates sufficiently gapped away from zero). In the third case, the kicked rotor, we show how the existence of arbitrarily long-lived modes of excitation (diffusion) precludes universal fluctuations and entails quantum localization. PMID:26181515
Quantum manifestations of chaos in elastic atom-surface scattering
Guantes, R.; Miret-Artes, S.; Borondo, F.
2001-06-15
Quantum manifestations of chaos in the diffraction of atoms from corrugated surfaces, for a range of initial conditions easily attainable in scattering experiments, are presented and discussed. The appearance of strong oscillations in diffraction patterns is shown to be directly related to the presence of classical chaos and threshold effects. We also show that the autocorrelation function for some of the collision S-matrix elements over incident angles is sensitive to the character, hyperbolic or nonhyperbolic, of the underlying chaotic dynamics, in agreement with general semiclassical arguments for unbound chaotic systems.
Characterization of fluctuations of impedance and scattering matrices in wave chaotic scattering
Zheng Xing; Hemmady, Sameer; Antonsen, Thomas M. Jr.; Anlage, Steven M.; Ott, Edward
2006-04-15
In wave chaotic scattering, statistical fluctuations of the scattering matrix S and the impedance matrix Z depend both on universal properties and on nonuniversal details of how the scatterer is coupled to external channels. This paper considers the impedance and scattering variance ratios, {xi}{sub z} and {xi}{sub s}, where {xi}{sub z}=Var[Z{sub ij}]/{l_brace}Var[Z{sub ii}]Var[Z{sub jj}]{r_brace}{sup 1/2}, {xi}{sub s}=Var[S{sub ij}]/{l_brace}Var[S{sub ii}]Var[S{sub jj}]{r_brace}{sup 1/2}, and Var[{center_dot}] denotes variance. {xi}{sub z} is shown to be a universal function of distributed losses within the scatterer. That is, {xi}{sub z} is independent of nonuniversal coupling details. This contrasts with {xi}{sub s} for which universality applies only in the large loss limit. Explicit results are given for {xi}{sub z} for time reversal symmetric and broken time reversal symmetric systems. Experimental tests of the theory are presented using data taken from scattering measurements on a chaotic microwave cavity.
Numerical experiments on quantum chaotic billiards
NASA Astrophysics Data System (ADS)
de Menezes, D. D.; Jar e Silva, M.; de Aguiar, F. M.
2007-06-01
A recently proposed numerical technique for generation of high-quality unstructured meshes is combined with a finite-element method to solve the Helmholtz equation that describes the quantum mechanics of a particle confined in two-dimensional cavities. Different shapes are treated on equal footing, including Sinai, stadium, annular, threefold symmetric, mushroom, cardioid, triangle, and coupled billiards. The results are shown to be in excellent agreement with available measurements in flat microwave resonator counterparts with nonintegrable geometries.
Numerical experiments on quantum chaotic billiards.
de Menezes, D D; Jar e Silva, M; de Aguiar, F M
2007-06-01
A recently proposed numerical technique for generation of high-quality unstructured meshes is combined with a finite-element method to solve the Helmholtz equation that describes the quantum mechanics of a particle confined in two-dimensional cavities. Different shapes are treated on equal footing, including Sinai, stadium, annular, threefold symmetric, mushroom, cardioid, triangle, and coupled billiards. The results are shown to be in excellent agreement with available measurements in flat microwave resonator counterparts with nonintegrable geometries. PMID:17614670
Relativistic wavepackets in classically chaotic quantum cosmological billiards
NASA Astrophysics Data System (ADS)
Koehn, Michael
2012-03-01
Close to a spacelike singularity, pure gravity and supergravity in 4 to 11 spacetime dimensions admit a cosmological billiard description based on hyperbolic Kac-Moody groups. We investigate the quantum cosmological billiards of relativistic wavepackets towards the singularity, employing flat and hyperbolic space descriptions for the quantum billiards. We find that the strongly chaotic classical billiard motion of four-dimensional pure gravity corresponds to a spreading wavepacket subject to successive redshifts and tending to zero as the singularity is approached. We discuss the possible implications of these results in the context of singularity resolution and compare them with those of known semiclassical approaches. As an aside, we obtain exact solutions for the one-dimensional relativistic quantum billiards with moving walls.
Symmetry breaking: a tool to unveil the topology of chaotic scattering with three degrees of freedom
Jung, Christof; Zapfe, W. P. Karel; Seligman, T. H.
2010-12-23
We shall use symmetry breaking as a tool to attack the problem of identifying the topology of chaotic scatteruing with more then two degrees of freedom. specifically we discuss the structure of the homoclinic/heteroclinic tangle and the connection between the chaotic invariant set, the scattering functions and the singularities in the cross section for a class of scattering systems with one open and two closed degrees of freedom.
Chaotic scattering in an open vase-shaped cavity: Topological, numerical, and experimental results
NASA Astrophysics Data System (ADS)
Novick, Jaison Allen
We present a study of trajectories in a two-dimensional, open, vase-shaped cavity in the absence of forces The classical trajectories freely propagate between elastic collisions. Bound trajectories, regular scattering trajectories, and chaotic scattering trajectories are present in the vase. Most importantly, we find that classical trajectories passing through the vase's mouth escape without return. In our simulations, we propagate bursts of trajectories from point sources located along the vase walls. We record the time for escaping trajectories to pass through the vase's neck. Constructing a plot of escape time versus the initial launch angle for the chaotic trajectories reveals a vastly complicated recursive structure or a fractal. This fractal structure can be understood by a suitable coordinate transform. Reducing the dynamics to two dimensions reveals that the chaotic dynamics are organized by a homoclinic tangle, which is formed by the union of infinitely long, intersecting stable and unstable manifolds. This study is broken down into three major components. We first present a topological theory that extracts the essential topological information from a finite subset of the tangle and encodes this information in a set of symbolic dynamical equations. These equations can be used to predict a topologically forced minimal subset of the recursive structure seen in numerically computed escape time plots. We present three applications of the theory and compare these predictions to our simulations. The second component is a presentation of an experiment in which the vase was constructed from Teflon walls using an ultrasound transducer as a point source. We compare the escaping signal to a classical simulation and find agreement between the two. Finally, we present an approximate solution to the time independent Schrodinger Equation for escaping waves. We choose a set of points at which to evaluate the wave function and interpolate trajectories connecting the source
Wave scattering from cavities with both regular and chaotic ray trajectories
NASA Astrophysics Data System (ADS)
Lee, Ming-Jer; Antonsen, Thomas; Ott, Edward
2013-03-01
The random plane wave hypothesis has been used to characterize fields inside chaotic cavities where all ray trajectories are chaotic and visit the available phase space uniformly. We consider incident and reflected waves in channels connecting to a chaotic cavity. From Random Matrix Theory, the impedance, obtained from the scattering matrix, for pure chaotic cavities can be described as a Lorentzian random variable with predictable mean and width. For some shapes of cavities, called mixed systems, some rays are chaotic and visit subregions of phase space ergodically, while some rays are regular staying on invariant troi. We generalize the previous chaotic cavity theory to mixed systems by separating the impedance into regular and chaotic parts. We test the theory by numerically solving for eigenmodes of the Helmholtz equation in a mushroom shaped cavity where there is a clear separation between regular and chaotic regions of phase space. We compare our theoretical predictions with numerical calculations for one-port and two-ports cases with different port positions.
Scattering in Quantum Lattice Gases
NASA Astrophysics Data System (ADS)
O'Hara, Andrew; Love, Peter
2009-03-01
Quantum Lattice Gas Automata (QLGA) are of interest for their use in simulating quantum mechanics on both classical and quantum computers. QLGAs are an extension of classical Lattice Gas Automata where the constraint of unitary evolution is added. In the late 1990s, David A. Meyer as well as Bruce Boghosian and Washington Taylor produced similar models of QLGAs. We start by presenting a unified version of these models and study them from the point of view of the physics of wave-packet scattering. We show that the Meyer and Boghosian-Taylor models are actually the same basic model with slightly different parameterizations and limits. We then implement these models computationally using the Python programming language and show that QLGAs are able to replicate the analytic results of quantum mechanics (for example reflected and transmitted amplitudes for step potentials and the Klein paradox).
Quantum theory of Thomson scattering
NASA Astrophysics Data System (ADS)
Crowley, B. J. B.; Gregori, G.
2014-12-01
The general theory of the scattering of electromagnetic radiation in atomic plasmas and metals, in the non-relativistic regime, in which account is taken of the Kramers-Heisenberg polarization terms in the Hamiltonian, is described from a quantum mechanical viewpoint. As well as deriving the general formula for the double differential Thomson scattering cross section in an isotropic finite temperature multi-component system, this work also considers closely related phenomena such as absorption, refraction, Raman scattering, resonant (Rayleigh) scattering and Bragg scattering, and derives many essential relationships between these quantities. In particular, the work introduces the concept of scattering strength and the strength-density field which replaces the normal particle density field in the standard treatment of scattering by a collection of similar particles and it is the decomposition of the strength-density correlation function into more familiar-looking components that leads to the final result. Comparisons are made with previous work, in particular that of Chihara [1].
NASA Astrophysics Data System (ADS)
Pecora, Louis; Wu, Dong Ho; Kim, Christopher
Tunneling rates in closed, double well quantum or wave systems in two dimensions or higher are radically different between wells with classically regular or chaotic behavior. Wells with regular dynamics have tunneling rates that fluctuate by several orders of magnitude as a function of energy or frequency. Wells with chaotic dynamics have fluctuations smaller than one order of magnitude (a regularization of the fluctuations). We examine a more realistic experimental system, a single well with two channels with tunneling barriers at their junctions with the wells. Former theories for conductance in quantum dots will not apply here. We developed a theory, which uses proper boundary conditions at the barriers and yields the scattering matrix. Results show that the transmission rates fluctuate by orders of magnitude in the regular-shaped well, but are greatly reduced (regularized) for the chaotic-shaped well. We will show experimental results that test these theoretical findings for microwave transmission through a chaotic-shaped cavity, which is made of copper and has two ports with tunneling barriers.
Classical and quantum chaotic angular-momentum pumps.
Dittrich, T; Dubeibe, F L
2015-03-01
We study directed transport of charge and intrinsic angular momentum by periodically driven scattering in the regime of fast and strong driving. A spin-orbit coupling through a kicked magnetic field confined to a compact region in space leads to irregular scattering and triggers spin flips in a spatially asymmetric manner which allows us to generate polarized currents. The dynamical mechanisms responsible for the spin separation carry over to the quantum level and give rise to spin pumping. Our theory based on the Floquet formalism is confirmed by numerical solutions of the time-dependent inhomogeneous Schrödinger equation with a continuous source term. PMID:25793818
Huang, Yu; Guo, Feng; Li, Yongling; Liu, Yufeng
2015-01-01
Parameter estimation for fractional-order chaotic systems is an important issue in fractional-order chaotic control and synchronization and could be essentially formulated as a multidimensional optimization problem. A novel algorithm called quantum parallel particle swarm optimization (QPPSO) is proposed to solve the parameter estimation for fractional-order chaotic systems. The parallel characteristic of quantum computing is used in QPPSO. This characteristic increases the calculation of each generation exponentially. The behavior of particles in quantum space is restrained by the quantum evolution equation, which consists of the current rotation angle, individual optimal quantum rotation angle, and global optimal quantum rotation angle. Numerical simulation based on several typical fractional-order systems and comparisons with some typical existing algorithms show the effectiveness and efficiency of the proposed algorithm. PMID:25603158
Huang, Yu; Guo, Feng; Li, Yongling; Liu, Yufeng
2015-01-01
Parameter estimation for fractional-order chaotic systems is an important issue in fractional-order chaotic control and synchronization and could be essentially formulated as a multidimensional optimization problem. A novel algorithm called quantum parallel particle swarm optimization (QPPSO) is proposed to solve the parameter estimation for fractional-order chaotic systems. The parallel characteristic of quantum computing is used in QPPSO. This characteristic increases the calculation of each generation exponentially. The behavior of particles in quantum space is restrained by the quantum evolution equation, which consists of the current rotation angle, individual optimal quantum rotation angle, and global optimal quantum rotation angle. Numerical simulation based on several typical fractional-order systems and comparisons with some typical existing algorithms show the effectiveness and efficiency of the proposed algorithm. PMID:25603158
Coexistence of regular and chaotic scattering in heavy-ion collisions
Rapisarda, A.; Baldo, M. Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Corso Italia 57, 95129 Catania, Italy)
1991-05-20
Classical dynamics of heavy-ion scattering is investigated in the case of a collision between a supposed spherical nucleus, {sup 28}Si, and a deformed one, {sup 24}Mg, at energies above the Coulomb barrier. Evidence of regular and irregular motion is found. The chaotic behavior justifies the presence of Ericson's fluctuations observed for this reaction, while the presence of regular motion embedded in the chaotic region could be the crucial point to explain the nature of the observed isolated resonances, once the semiclassical theory is applied.
Quantum-classical correspondence principle for work distributions in a chaotic system
NASA Astrophysics Data System (ADS)
Zhu, Long; Gong, Zongping; Wu, Biao; Quan, H. T.
2016-06-01
We numerically study the work distributions in a chaotic system and examine the relationship between quantum work and classical work. Our numerical results suggest that there exists a correspondence principle between quantum and classical work distributions in a chaotic system. This correspondence was proved for one-dimensional integrable systems in a recent work [Jarzynski, Quan, and Rahav, Phys. Rev. X 5, 031038 (2015), 10.1103/PhysRevX.5.031038]. Our investigation further justifies the definition of quantum work via two-point energy measurements.
Classical singularities in chaotic atom-surface scattering
Miret-Artes, S.; Margalef-Roig, J.; Guantes, R.; Borondo, F.; Jaffe, C.
1996-10-01
In this paper we show that the diffraction condition for the scattering of atoms from surfaces leads to the appearance of a distinct type of classical singularity. Moreover, it is also shown that the onset of classical trapping or classical chaos is closely related to the bifurcation set of the diffraction-order function around the surface points presenting the rainbow effect. As an illustration of this dynamic, application to the scattering of He atoms by the stepped Cu(115) surface is presented using both a hard corrugated one-dimensional wall and a soft corrugated Morse potential. {copyright} {ital 1996 The American Physical Society.}
NASA Astrophysics Data System (ADS)
Drótos, G.; Jung, C.
2016-06-01
The topic of this paper is hyperbolic chaotic scattering in a three degrees of freedom system. We generalize how shadows in the domain of the doubly differential cross-section are found: they are traced out by the appropriately filtered unstable manifolds of the periodic trajectories in the chaotic saddle. These shadows are related to the rainbow singularities in the doubly differential cross-section. As a result of this relation, we discover a method of how to recognize in the cross section a smoothly deformed image of the chaotic saddle, allowing the reconstruction of the symbolic dynamics of the chaotic saddle, its topology and its scaling factors.
Quantum Mechanical Scattering in Nanoscale Systems
NASA Astrophysics Data System (ADS)
Gianfrancesco, A. G.; Ilyashenko, A.; Boucher, C. R.; Ram-Mohan, L. R.
2012-02-01
We investigate quantum scattering using the finite element method. Unlike textbook treatments employing asymptotic boundary conditions (BCs), we use modified BCs, which permits computation close to the near-field region and reduces the Cauchy BCs to Dirichlet BCs, greatly simplifying the analysis. Scattering from any finite quantum mechanical potential can be modeled, including scattering in a finite waveguide geometry and in the open domain. Being numerical, our analysis goes beyond the Born Approximation, and the finite element approach allows us to transcend geometric constraints. Results of the formulation will be presented with several case studies, including spin dependent scattering, demonstrating the high accuracy and flexibility attained in this approach.
Quantum dot microlasers with external feedback: a chaotic system close to the quantum limit
NASA Astrophysics Data System (ADS)
Albert, Ferdinand; Hopfmann, Caspar; Schneider, Christian; Höfling, Sven; Worschech, Lukas; Kamp, Martin; Kinzel, Wolfgang; Forchel, Alfred; Reitzenstein, Stephan; Kanter, Ido
2012-06-01
Studying cavity quantum electrodynamical effects is an emerging and important field of research for the understanding of the many body quantum theory as well as for the generation of a new type of efficient lasers. Here we report a dramatic change in the photon statistics of quantum dot based micropillar lasers where a finite fraction of the emission is reflected back into the microcavity after a roundtrip time τ in an external cavity, where τ greatly exceeds the coherence time. Photon bunching was observed above the threshold current where the second order autocorrelation function g(2)(τ) at zero-lag can reach values up to 3.51+/-0.06. The change in the photon statistics of the two non-degenerated fundamental modes were found to be correlated, indicating non-trivial interactions between both cavity modes. Furthermore the optical feedback led to revivals of the bunching signal in integer multiples of the round trip time of the external cavity and to a decrease in the coherence time of the laser. These phenomena compare well with milliwatt chaotic lasers induced by an external feedback, indicating that chaos might occur in the nanowatt lasing regime where fluctuations in the photon statistics are in the leading order.
Inverse scattering problem for quantum graph vertices
Cheon, Taksu; Turek, Ondrej; Exner, Pavel
2011-06-15
We demonstrate how the inverse scattering problem of a quantum star graph can be solved by means of diagonalization of the Hermitian unitary matrix when the vertex coupling is of the scale-invariant (or Fueloep-Tsutsui) form. This enables the construction of quantum graphs with desired properties in a tailor-made fashion. The procedure is illustrated on the example of quantum vertices with equal transmission probabilities.
Quantum rainbow scattering at tunable velocities
NASA Astrophysics Data System (ADS)
Strebel, M.; Müller, T.-O.; Ruff, B.; Stienkemeier, F.; Mudrich, M.
2012-12-01
Elastic scattering cross sections are measured for lithium atoms colliding with rare-gas atoms and SF6 molecules at tunable relative velocities down to ˜50 m/s. Our scattering apparatus combines a velocity-tunable molecular beam with a magneto-optic trap which provides an ultracold cloud of lithium atoms as a scattering target. Comparison with theory reveals the quantum nature of the collision dynamics in the studied regime, including rainbows as well as orbiting resonances.
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.
Quantum Ergodicity for Quantum Graphs without Back-Scattering
NASA Astrophysics Data System (ADS)
Brammall, Matthew; Winn, B.
2016-06-01
We give an estimate of the quantum variance for $d$-regular graphs quantised with boundary scattering matrices that prohibit back-scattering. For families of graphs that are expanders, with few short cycles, our estimate leads to quantum ergodicity for these families of graphs. Our proof is based on a uniform control of an associated random walk on the bonds of the graph. We show that recent constructions of Ramanujan graphs, and asymptotically almost surely, random $d$-regular graphs, satisfy the necessary conditions to conclude that quantum ergodicity holds.
Regular and chaotic quantum dynamics in atom-diatom reactive collisions
Gevorkyan, A. S.; Nyman, G.
2008-05-15
A new microirreversible 3D theory of quantum multichannel scattering in the three-body system is developed. The quantum approach is constructed on the generating trajectory tubes which allow taking into account influence of classical nonintegrability of the dynamical quantum system. When the volume of classical chaos in phase space is larger than the quantum cell in the corresponding quantum system, quantum chaos is generated. The probability of quantum transitions is constructed for this case. The collinear collision of the Li + (FH) {sup {yields}}(LiF) + H system is used for numerical illustration of a system generating quantum (wave) chaos.
Quantum smearing in hybrid inflation with chaotic potentials
NASA Astrophysics Data System (ADS)
Ahmed, Waqas; Ishaque, Ommair; Rehman, Mansoor Ur
2016-01-01
We study the impact of 1-loop radiative corrections in a nonsupersymmetric model of hybrid inflation (HI) with chaotic (polynomial-like) potential, V0 + λpϕp. These corrections can arise from the possible couplings of inflaton with other fields which can play an active role in the reheating process. The tree-level predictions of these models are shown to lie outside of the Planck’s latest bounds on the scalar spectral index ns and the tensor to scalar ratio r. However, the radiatively corrected version of these models, V0 + λpϕp + Aϕ4ln ϕ, is fully consistent with the Planck’s data. More specifically, fermionic radiative correction (A < 0) reduces the tensor to scalar ratio significantly and a red-tilted spectral index ns < 1, consistent with Planck’s data, is obtained even for sub-Planckian field-values.
Quantum reactive scattering on innovative computing platforms
NASA Astrophysics Data System (ADS)
Pacifici, Leonardo; Nalli, Danilo; Laganà, Antonio
2013-05-01
The possibility of implementing quantum reactive scattering programs on cheap platforms, originally used for graphic purposes only, has been investigated using a NVIDIA GPU. After a conversion of the code considered from Fortran to C and its deep restructuring for exploiting the GPU key features, significant speedups have been obtained for RWAVEPR, a time dependent quantum reactive scattering code propagating in time a complex wavepacket. As benchmark calculations those concerned with the evaluation of the reactive probabilities of the Cl+H2 and the N+N2 reactions have been considered.
Semiclassical matrix model for quantum chaotic transport with time-reversal symmetry
Novaes, Marcel
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.
A chaotic view of behavior change: a quantum leap for health promotion
Resnicow, Ken; Vaughan, Roger
2006-01-01
Background The study of health behavior change, including nutrition and physical activity behaviors, has been rooted in a cognitive-rational paradigm. Change is conceptualized as a linear, deterministic process where individuals weigh pros and cons, and at the point at which the benefits outweigh the cost change occurs. Consistent with this paradigm, the associated statistical models have almost exclusively assumed a linear relationship between psychosocial predictors and behavior. Such a perspective however, fails to account for non-linear, quantum influences on human thought and action. Consider why after years of false starts and failed attempts, a person succeeds at increasing their physical activity, eating healthier or losing weight. Or, why after years of success a person relapses. This paper discusses a competing view of health behavior change that was presented at the 2006 annual ISBNPA meeting in Boston. Discussion Rather than viewing behavior change from a linear perspective it can be viewed as a quantum event that can be understood through the lens of Chaos Theory and Complex Dynamic Systems. Key principles of Chaos Theory and Complex Dynamic Systems relevant to understanding health behavior change include: 1) Chaotic systems can be mathematically modeled but are nearly impossible to predict; 2) Chaotic systems are sensitive to initial conditions; 3) Complex Systems involve multiple component parts that interact in a nonlinear fashion; and 4) The results of Complex Systems are often greater than the sum of their parts. Accordingly, small changes in knowledge, attitude, efficacy, etc may dramatically alter motivation and behavioral outcomes. And the interaction of such variables can yield almost infinite potential patterns of motivation and behavior change. In the linear paradigm unaccounted for variance is generally relegated to the catch all "error" term, when in fact such "error" may represent the chaotic component of the process. The linear and
Zurek, W.H.; Pas, J.P. |
1995-08-01
Violation of correspondence principle may occur for very macroscopic byt isolated quantum systems on rather short timescales as illustrated by the case of Hyperion, the chaotically tumbling moon of Saturn, for which quantum and classical predictions are expected to diverge on a timescale of approximately 20 years. Motivated by Hyperion, we review salient features of ``quantum chaos`` and show that decoherence is the essential ingredient of the classical limit, as it enables one to solve the apparent paradox caused by the breakdown of the correspondence principle for classically chaotic systems.
Jacobs, E.W.; Bulsara, A.R.; Schieve, W.C.
1989-06-01
We consider a simple model of the flux in an rf superconducting quantum-interference device (SQUID) subjected to an external periodic magnetic field. The dynamic equation describing the flux response of the SQUID is solved analytically in the absence of damping and external driving terms. These terms are then introduced as perturbations, and the Melnikov function for the system is constructed. The transition from periodic to chaotic behavior is studied through a calculation of the Lyapunov exponents for the systems, and the dimension of the strange attracting set is calculated.
NASA Astrophysics Data System (ADS)
Rotter, Stefan; Aigner, Florian; Burgdörfer, Joachim
2007-03-01
We investigate the statistical distribution of transmission eigenvalues in phase-coherent transport through quantum dots. In two-dimensional ab initio simulations for both clean and disordered two-dimensional cavities, we find markedly different quantum-to-classical crossover scenarios for these two cases. In particular, we observe the emergence of “noiseless scattering states” in clean cavities, irrespective of sharp-edged entrance and exit lead mouths. We find the onset of these “classical” states to be largely independent of the cavity’s classical chaoticity, but very sensitive with respect to bulk disorder. Our results suggest that for weakly disordered cavities, the transmission eigenvalue distribution is determined both by scattering at the disorder potential and the cavity walls. To properly account for this intermediate parameter regime, we introduce a hybrid crossover scheme, which combines previous models that are valid in the ballistic and the stochastic limit, respectively.
NASA Astrophysics Data System (ADS)
Flambaum, Victor; Berengut, Julian; Dzuba, Vladimir; Gribakin, Gleb; Harabati, Celal; Kozlov, Michael
2016-05-01
Level density of many-body states exponentially increases with the number of excited particles. When residual interaction exceeds the interval between these levels, the eigenstates (compound states) become chaotic superpositions of of thousands, or even millions of Slater determinant basis states.This situation takes place in highly excited nuclei, rare-earth and actinide atoms, open f-shell ions excited by the electron recombination and in ultracold collisions of open f-shell atoms. We derived formulas for the resonant multi-electron recombination via di-electron doorway states leading to the many-electron compound resonances and performed numerical calculations for the electron recombination with gold (Au+25) and tungsten ions (W+1724). A recent experiment showed that the electron recombination of tungsten ion W20+exceeds the direct recombination by three order of magnitude. Our calculations agree with the experimental results for Au+25 and W20+. Other manifestation of chaos are enhancement of weak interactions and Raman photon scattering, and suppression of the photoionization.
Complex quantum trajectories for barrier scattering
NASA Astrophysics Data System (ADS)
Rowland, Bradley Allen
We have directed much attention towards developing quantum trajectory methods which can accurately predict the transmission probabilities for a variety of quantum mechanical barrier scattering processes. One promising method involves solving the complex quantum Hamilton-Jacobi equation with the Derivative Propagation Method (DPM). We present this method, termed complex valued DPM (CVDPM(n)). CVDPM(n) has been successfully employed in the Lagrangian frame to accurately compute transmission probabilities on 'thick' one dimensional Eckart and Gaussian potential surfaces. CVDPM(n) is able to reproduce accurate results with a much lower order of approximation than is required by real valued quantum trajectory methods, from initial wave packet energies ranging from the tunneling case (Eo = 0) to high energy cases (twice the barrier height). We successfully extended CVDPM(n) to two-dimensional problems (one translational degree of freedom representing an Eckart or Gaussian barrier coupled to a vibrational degree of freedom) in the Lagrangian framework with great success. CVDPM helps to explain why barrier scattering from "thick" barriers is a much more well posed problem than barrier scattering from "thin" barriers. Though results in these two cases are in very good agreement with grid methods, the search for an appropriate set of initial conditions (termed an 'isochrone) from which to launch the trajectories leads to a time-consuming search problem that is reminiscent of the root-searching problem from semi-classical dynamics. In order to circumvent the isochrone problem, we present CVDPM(n) equations of motion which are derived and implemented in the arbitrary Lagrangian-Eulerian frame for a metastable potential as well as the Eckart and Gaussian surfaces. In this way, the isochrone problem can be circumvented but at the cost of introducing other computational difficulties. In order to understand why CVDPM may give better transmission probabilities than real valued
NASA Astrophysics Data System (ADS)
Hur, Gwang-Ok
The -kicked rotor is a paradigm of quantum chaos. Its realisation with clouds of cold atoms in pulsed optical lattices demonstrated the well-known quantum chaos phenomenon of 'dynamical localisation'. In those experi ments by several groups world-wide, the £-kicks were applied at equal time intervals. However, recent theoretical and experimental work by the cold atom group at UCL Monteiro et al 2002, Jonckheere et al 2003, Jones et al 2004 showed that novel quantum and classical dynamics arises if the atomic cloud is pulsed with repeating sequences of unequally spaced kicks. In Mon teiro et al 2002 it was found that the energy absorption rates depend on the momentum of the atoms relative to the optical lattice hence a type of chaotic ratchet was proposed. In Jonckheere et al and Jones et al, a possible mechanism for selecting atoms according to their momenta (velocity filter) was investigated. The aim of this thesis was to study the properties of the underlying eigen values and eigenstates. Despite the unequally-spaced kicks, these systems are still time-periodic, so we in fact investigated the Floquet states, which are eigenstates of U(T), the one-period time evolution operator. The Floquet states and corresponding eigenvalues were obtained by diagonalising a ma trix representation of the operator U(T). It was found that the form of the eigenstates enables us to analyse qual itatively the atomic momentum probability distributions, N(p) measured experimentally. In particular, the momentum width of the individual eigen states varies strongly with < p > as expected from the theoretical and ex- perimental results obtained previously. In addition, at specific < p > close to values which in the experiment yield directed motion (ratchet transport), the probability distribution of the individual Floquet states is asymmetric, mirroring the asymmetric N(p) measured in clouds of cesium atoms. In the penultimate chapter, the spectral fluctuations (eigenvalue statis tics) are
Quantum chaotic tunneling in graphene systems with electron-electron interactions
NASA Astrophysics Data System (ADS)
Ying, Lei; Wang, Guanglei; Huang, Liang; Lai, Ying-Cheng
2014-12-01
An outstanding and fundamental problem in contemporary physics is to include and probe the many-body effect in the study of relativistic quantum manifestations of classical chaos. We address this problem using graphene systems described by the Hubbard Hamiltonian in the setting of resonant tunneling. Such a system consists of two symmetric potential wells separated by a potential barrier, and the geometric shape of the whole domain can be chosen to generate integrable or chaotic dynamics in the classical limit. Employing a standard mean-field approach to calculating a large number of eigenenergies and eigenstates, we uncover a class of localized states with near-zero tunneling in the integrable systems. These states are not the edge states typically seen in graphene systems, and as such they are the consequence of many-body interactions. The physical origin of the non-edge-state type of localized states can be understood by the one-dimensional relativistic quantum tunneling dynamics through the solutions of the Dirac equation with appropriate boundary conditions. We demonstrate that, when the geometry of the system is modified to one with chaos, the localized states are effectively removed, implying that in realistic situations where many-body interactions are present, classical chaos is capable of facilitating greatly quantum tunneling. This result, besides its fundamental importance, can be useful for the development of nanoscale devices such as graphene-based resonant-tunneling diodes.
Conductance stability in chaotic and integrable quantum dots with random impurities.
Wang, Guanglei; Ying, Lei; Lai, Ying-Cheng
2015-08-01
For a quantum dot system of fixed geometry, in the presence of random impurities the average conductance over an appropriate range of the Fermi energy decreases as the impurity strength is increased. Can the nature of the corresponding classical dynamics in the dot region affect the rate of decrease? Utilizing graphene quantum dots with two semi-infinite, single-mode leads as a prototypical model, we address the device stability issue by investigating the combined effects of classical dynamics and impurities on the average conductance over the energy range of the first transverse mode. We find that, for chaotic dot systems, the rate of decrease in the average conductance with the impurity strength is in general characteristically smaller than that for integrable dots. We develop a semiclassical analysis for the phenomenon and also obtain an understanding based on the random matrix theory. Our results demonstrate that classical chaos can generally lead to a stronger stability in the device performance, strongly advocating exploiting chaos in the development of nanoscale quantum transport devices. PMID:26382470
Suppression of Quantum Scattering in Strongly Confined Systems
Kim, J. I.; Melezhik, V. S.; Schmelcher, P.
2006-11-10
We demonstrate that scattering of particles strongly interacting in three dimensions (3D) can be suppressed at low energies in a quasi-one-dimensional (1D) confinement. The underlying mechanism is the interference of the s- and p-wave scattering contributions with large s- and p-wave 3D scattering lengths being a necessary prerequisite. This low-dimensional quantum scattering effect might be useful in 'interacting' quasi-1D ultracold atomic gases, guided atom interferometry, and impurity scattering in strongly confined quantum wire-based electronic devices.
Deep Wavelet Scattering for Quantum Energy Regression
NASA Astrophysics Data System (ADS)
Hirn, Matthew
Physical functionals are usually computed as solutions of variational problems or from solutions of partial differential equations, which may require huge computations for complex systems. Quantum chemistry calculations of ground state molecular energies is such an example. Indeed, if x is a quantum molecular state, then the ground state energy E0 (x) is the minimum eigenvalue solution of the time independent Schrödinger Equation, which is computationally intensive for large systems. Machine learning algorithms do not simulate the physical system but estimate solutions by interpolating values provided by a training set of known examples {(xi ,E0 (xi) } i <= n . However, precise interpolations may require a number of examples that is exponential in the system dimension, and are thus intractable. This curse of dimensionality may be circumvented by computing interpolations in smaller approximation spaces, which take advantage of physical invariants. Linear regressions of E0 over a dictionary Φ ={ϕk } k compute an approximation E 0 as: E 0 (x) =∑kwkϕk (x) , where the weights {wk } k are selected to minimize the error between E0 and E 0 on the training set. The key to such a regression approach then lies in the design of the dictionary Φ. It must be intricate enough to capture the essential variability of E0 (x) over the molecular states x of interest, while simple enough so that evaluation of Φ (x) is significantly less intensive than a direct quantum mechanical computation (or approximation) of E0 (x) . In this talk we present a novel dictionary Φ for the regression of quantum mechanical energies based on the scattering transform of an intermediate, approximate electron density representation ρx of the state x. The scattering transform has the architecture of a deep convolutional network, composed of an alternating sequence of linear filters and nonlinear maps. Whereas in many deep learning tasks the linear filters are learned from the training data, here
Quantum double pendulum: study of an autonomous classically chaotic quantum system.
Perotti, Luca
2004-12-01
A numerical study of the quantum double pendulum is conducted. A suitable quantum scaling is found which allows us to have as the only parameters the ratios of the lengths and masses of the two pendula and a (quantum) gravity parameter containing Planck's constant. Comparison with classical and semiclassical results is used to understand the behavior of the energy curves of the levels, to define regimes in terms of the gravity parameter, and to classify the (resonant) interactions among levels by connecting them to various classical phase space structures (resonance islands). PMID:15697495
Macek, M. Leviatan, A.
2014-12-15
We present a comprehensive analysis of the emerging order and chaos and enduring symmetries, accompanying a generic (high-barrier) first-order quantum phase transition (QPT). The interacting boson model Hamiltonian employed, describes a QPT between spherical and deformed shapes, associated with its U(5) and SU(3) dynamical symmetry limits. A classical analysis of the intrinsic dynamics reveals a rich but simply-divided phase space structure with a Hénon–Heiles type of chaotic dynamics ascribed to the spherical minimum and a robustly regular dynamics ascribed to the deformed minimum. The simple pattern of mixed but well-separated dynamics persists in the coexistence region and traces the crossing of the two minima in the Landau potential. A quantum analysis discloses a number of regular low-energy U(5)-like multiplets in the spherical region, and regular SU(3)-like rotational bands extending to high energies and angular momenta, in the deformed region. These two kinds of regular subsets of states retain their identity amidst a complicated environment of other states and both occur in the coexistence region. A symmetry analysis of their wave functions shows that they are associated with partial U(5) dynamical symmetry (PDS) and SU(3) quasi-dynamical symmetry (QDS), respectively. The pattern of mixed but well-separated dynamics and the PDS or QDS characterization of the remaining regularity, appear to be robust throughout the QPT. Effects of kinetic collective rotational terms, which may disrupt this simple pattern, are considered.
NASA Astrophysics Data System (ADS)
Eyre, T. M. W.
Given a polynomial function f of classical stochastic integrator processes whose differentials satisfy a closed Ito multiplication table, we can express the stochastic derivative of f as
Lee, Gyeong Won; Jung, Young-Dae; Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 Eighth Street, Troy, New York 12180-3590
2013-06-15
The influence of the electron-exchange and quantum screening on the Thomson scattering process is investigated in degenerate quantum Fermi plasmas. The Thomson scattering cross section in quantum plasmas is obtained by the plasma dielectric function and fluctuation-dissipation theorem as a function of the electron-exchange parameter, Fermi energy, plasmon energy, and wave number. It is shown that the electron-exchange effect enhances the Thomson scattering cross section in quantum plasmas. It is also shown that the differential Thomson scattering cross section has a minimum at the scattering angle Θ=π/2. It is also found that the Thomson scattering cross section increases with an increase of the Fermi energy. In addition, the Thomson scattering cross section is found to be decreased with increasing plasmon energy.
A modified Lax-Phillips scattering theory for quantum mechanics
NASA Astrophysics Data System (ADS)
Strauss, Y.
2015-07-01
The Lax-Phillips scattering theory is an appealing abstract framework for the analysis of scattering resonances. Quantum mechanical adaptations of the theory have been proposed. However, since these quantum adaptations essentially retain the original structure of the theory, assuming the existence of incoming and outgoing subspaces for the evolution and requiring the spectrum of the generator of evolution to be unbounded from below, their range of applications is rather limited. In this paper, it is shown that if we replace the assumption regarding the existence of incoming and outgoing subspaces by the assumption of the existence of Lyapunov operators for the quantum evolution (the existence of which has been proved for certain classes of quantum mechanical scattering problems), then it is possible to construct a structure analogous to the Lax-Phillips structure for scattering problems for which the spectrum of the generator of evolution is bounded from below.
A modified Lax-Phillips scattering theory for quantum mechanics
Strauss, Y.
2015-07-15
The Lax-Phillips scattering theory is an appealing abstract framework for the analysis of scattering resonances. Quantum mechanical adaptations of the theory have been proposed. However, since these quantum adaptations essentially retain the original structure of the theory, assuming the existence of incoming and outgoing subspaces for the evolution and requiring the spectrum of the generator of evolution to be unbounded from below, their range of applications is rather limited. In this paper, it is shown that if we replace the assumption regarding the existence of incoming and outgoing subspaces by the assumption of the existence of Lyapunov operators for the quantum evolution (the existence of which has been proved for certain classes of quantum mechanical scattering problems), then it is possible to construct a structure analogous to the Lax-Phillips structure for scattering problems for which the spectrum of the generator of evolution is bounded from below.
Ponderomotive potential and backward Raman scattering in dense quantum plasmas
Son, S.
2014-03-15
The backward Raman scattering is studied in dense quantum plasmas. The coefficients in the backward Raman scattering is found to be underestimated (overestimated) in the classical theory if the excited Langmuir wave has low-wave vector (high-wave vector). The second-order quantum perturbation theory shows that the second harmonic of the ponderomotive potential arises naturally even in a single particle motion contrary to the classical prediction.
Initial-state dependence of the quench dynamics in integrable quantum systems. III. Chaotic states
NASA Astrophysics Data System (ADS)
He, Kai; Rigol, Marcos
2013-04-01
We study sudden quantum quenches in which the initial states are selected to be either eigenstates of an integrable Hamiltonian that is nonmappable to a noninteracting one or a nonintegrable Hamiltonian, while the Hamiltonian after the quench is always integrable and mappable to a noninteracting one. By studying weighted energy densities and entropies, we show that quenches starting from nonintegrable (chaotic) eigenstates lead to an “ergodic” sampling of the eigenstates of the final Hamiltonian, while those starting from the integrable eigenstates do not (or at least it is not apparent for the system sizes accessible to us). This goes in parallel with the fact that the distribution of conserved quantities in the initial states is thermal in the nonintegrable cases and nonthermal in the integrable ones, and means that, in general, thermalization occurs in integrable systems when the quench starts form an eigenstate of a nonintegrable Hamiltonian (away from the edges of the spectrum), while it fails (or requires larger system sizes than those studied here to become apparent) for quenches starting at integrable points. We test those conclusions by studying the momentum distribution function of hard-core bosons after a quench.
Quantum transport in chaotic and integrable ballistic cavities with tunable shape
NASA Astrophysics Data System (ADS)
Lee, Y.; Faini, G.; Mailly, D.
1997-10-01
We have performed magnetotransport measurements in ballistic cavities and obtained the average by small modulations on the shapes and/or on the Fermi level. We work with cavities whose underlying classical dynamics is chaotic (stadia and Sinaï billiards) and integrable (circles and rectangles). The former show a Lorentzian weak-localization peak, in agreement with semiclassical predictions and other averaging methods that have been used in recent measurements. For integrable cavities our measurements show that the shape of the weak localization is very sensitive to the exact geometry of the sample: a linear magnetoconductance has been observed for rectangles as expected by the theory for integrable cavities, whereas for circles the shape is always Lorentzian. These discrepancies illustrate the nongeneric behavior of scattering through integrable geometries, that we analyze taking into account the interplay of integrability with smooth disorder and geometrical effects. The power spectra of the conductance fluctuations are also analyzed, the deduced typical areas are in good agreement with those obtained from the weak localization. Periodic orbits in nonaveraged Fourier transforms of the magnetoconductance for regular cavities are clearly identified indicating the good quality of our samples.
Chaotic scattering in solitary wave interactions: A singular iterated-map description
Goodman, Roy H.
2008-06-15
We derive a family of singular iterated maps--closely related to Poincare maps--that describe chaotic interactions between colliding solitary waves. The chaotic behavior of such solitary-wave collisions depends on the transfer of energy to a secondary mode of oscillation, often an internal mode of the pulse. This map allows us to go beyond previous analyses and to understand the interactions in the case when this mode is excited prior to the first collision. The map is derived using Melnikov integrals and matched asymptotic expansions and generalizes a ''multipulse'' Melnikov integral. It allows one to find not only multipulse heteroclinic orbits, but exotic periodic orbits. The maps exhibit singular behavior, including regions of infinite winding. These maps are shown to be singular versions of the conservative Ikeda map from laser physics and connections are made with problems from celestial mechanics and fluid mechanics.
Chaotic scattering in solitary wave interactions: a singular iterated-map description.
Goodman, Roy H
2008-06-01
We derive a family of singular iterated maps--closely related to Poincare maps--that describe chaotic interactions between colliding solitary waves. The chaotic behavior of such solitary-wave collisions depends on the transfer of energy to a secondary mode of oscillation, often an internal mode of the pulse. This map allows us to go beyond previous analyses and to understand the interactions in the case when this mode is excited prior to the first collision. The map is derived using Melnikov integrals and matched asymptotic expansions and generalizes a "multipulse" Melnikov integral. It allows one to find not only multipulse heteroclinic orbits, but exotic periodic orbits. The maps exhibit singular behavior, including regions of infinite winding. These maps are shown to be singular versions of the conservative Ikeda map from laser physics and connections are made with problems from celestial mechanics and fluid mechanics. PMID:18601480
Scattering asymptotic conditions in Euclidean relativistic quantum theory
NASA Astrophysics Data System (ADS)
Aiello, Gordon J.; Polyzou, W. N.
2016-03-01
We discuss the formulation of the scattering asymptotic condition as a strong limit in Euclidean quantum theories satisfying the Osterwalder-Schrader axioms. When used with the invariance principle this provides a constructive method to compute scattering observables directly in the Euclidean formulation of the theory, without an explicit analytic continuation.
Quantum scattering in the strip: From ballistic to localized regimes
NASA Astrophysics Data System (ADS)
Gebarowski, R.; Šeba, P.; Życzkowski, K.; Zakrzewski, J.
1998-11-01
Quantum scattering is studied in a system consisting of randomly distributed point scatterers in the strip. The model is continuous yet exactly solvable. Varying the number of scatterers (the sample length) we investigate a transition between the ballistic and the localized regimes. By considering the cylinder geometry and introducing the magnetic flux we are able to study time reversal symmetry breaking in the system. Both macroscopic (conductance) and microscopic (eigenphases distribution, statistics of S-matrix elements) characteristics of the system are examined.
Loss of quantum coherence through scattering off virtual black holes
NASA Astrophysics Data System (ADS)
Hawking, S. W.; Ross, Simon F.
1997-11-01
In quantum gravity, fields may lose quantum coherence by scattering off vacuum fluctuations in which virtual black hole pairs appear and disappear. Although it is not possible to properly compute the scattering off such fluctuations, we argue that one can get useful qualitative results, which provide a guide to the possible effects of such scattering, by considering a quantum field on the C metric, which has the same topology as a virtual black hole pair. We study a scalar field on the Lorentzian C metric background, with the scalar field in the analytically continued Euclidean vacuum state. We find that there are a finite number of particles at infinity in this state, contrary to recent claims made by Yi. Thus, this state is not determined by data at infinity, and there is loss of quantum coherence in this semiclassical calculation.
Resonant scattering of surface plasmon polaritons by dressed quantum dots
Huang, Danhong; Cardimona, Dave; Easter, Michelle; Gumbs, Godfrey; Maradudin, A. A.; Lin, Shawn-Yu; Zhang, Xiang
2014-06-23
The resonant scattering of surface plasmon-polariton waves (SPP) by embedded semiconductor quantum dots above the dielectric/metal interface is explored in the strong-coupling regime. In contrast to non-resonant scattering by a localized dielectric surface defect, a strong resonant peak in the spectrum of the scattered field is predicted that is accompanied by two side valleys. The peak height depends nonlinearly on the amplitude of SPP waves, reflecting the feedback dynamics from a photon-dressed electron-hole plasma inside the quantum dots. This unique behavior in the scattered field peak strength is correlated with the occurrence of a resonant dip in the absorption spectrum of SPP waves due to the interband photon-dressing effect. Our result on the scattering of SPP waves may be experimentally observable and applied to spatially selective illumination and imaging of individual molecules.
Superpersistent currents and whispering gallery modes in relativistic quantum chaotic systems.
Xu, Hongya; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso
2015-01-01
Persistent currents (PCs), one of the most intriguing manifestations of the Aharonov-Bohm (AB) effect, are known to vanish for Schrödinger particles in the presence of random scatterings, e.g., due to classical chaos. But would this still be the case for Dirac fermions? Addressing this question is of significant value due to the tremendous recent interest in two-dimensional Dirac materials. We investigate relativistic quantum AB rings threaded by a magnetic flux and find that PCs are extremely robust. Even for highly asymmetric rings that host fully developed classical chaos, the amplitudes of PCs are of the same order of magnitude as those for integrable rings, henceforth the term superpersistent currents (SPCs). A striking finding is that the SPCs can be attributed to a robust type of relativistic quantum states, i.e., Dirac whispering gallery modes (WGMs) that carry large angular momenta and travel along the boundaries. We propose an experimental scheme using topological insulators to observe and characterize Dirac WGMs and SPCs, and speculate that these features can potentially be the base for a new class of relativistic qubit systems. Our discovery of WGMs in relativistic quantum systems is remarkable because, although WGMs are common in photonic systems, they are relatively rare in electronic systems. PMID:25758591
Superpersistent currents and whispering gallery modes in relativistic quantum chaotic systems
Xu, Hongya; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso
2015-01-01
Persistent currents (PCs), one of the most intriguing manifestations of the Aharonov-Bohm (AB) effect, are known to vanish for Schrödinger particles in the presence of random scatterings, e.g., due to classical chaos. But would this still be the case for Dirac fermions? Addressing this question is of significant value due to the tremendous recent interest in two-dimensional Dirac materials. We investigate relativistic quantum AB rings threaded by a magnetic flux and find that PCs are extremely robust. Even for highly asymmetric rings that host fully developed classical chaos, the amplitudes of PCs are of the same order of magnitude as those for integrable rings, henceforth the term superpersistent currents (SPCs). A striking finding is that the SPCs can be attributed to a robust type of relativistic quantum states, i.e., Dirac whispering gallery modes (WGMs) that carry large angular momenta and travel along the boundaries. We propose an experimental scheme using topological insulators to observe and characterize Dirac WGMs and SPCs, and speculate that these features can potentially be the base for a new class of relativistic qubit systems. Our discovery of WGMs in relativistic quantum systems is remarkable because, although WGMs are common in photonic systems, they are relatively rare in electronic systems. PMID:25758591
Quantum Radiation Reaction Effects in Multiphoton Compton Scattering
Di Piazza, A.; Hatsagortsyan, K. Z.; Keitel, C. H.
2010-11-26
Radiation reaction effects in the interaction of an electron and a strong laser field are investigated in the realm of quantum electrodynamics. We identify the quantum radiation reaction with the multiple photon recoils experienced by the laser-driven electron due to consecutive incoherent photon emissions. After determining a quantum radiation dominated regime, we demonstrate how in this regime quantum signatures of the radiation reaction strongly affect multiphoton Compton scattering spectra and that they could be measurable in principle with presently available laser technology.
Chakraborty, Debdutta; Kar, Susmita; Chattaraj, Pratim Kumar
2015-12-21
The orbital free density functional theory and the single density equation approach are formally equivalent. An orbital free density based quantum dynamical strategy is used to study the quantum-classical correspondence in both weakly and strongly coupled van der Pol and Duffing oscillators in the presence of an external electric field in one dimension. The resulting quantum hydrodynamic equations of motion are solved through an implicit Euler type real space method involving a moving weighted least square technique. The Lagrangian framework used here allows the numerical grid points to follow the wave packet trajectory. The associated classical equations of motion are solved using a sixth order Runge-Kutta method and the Ehrenfest dynamics is followed through the solution of the time dependent Schrodinger equation using a time dependent Fourier Grid Hamiltonian technique. Various diagnostics reveal a close parallelism between classical regular as well as chaotic dynamics and that obtained from the Bohmian mechanics. PMID:26033095
NASA Astrophysics Data System (ADS)
Aguilar-López, Ricardo; López-Pérez, Pablo A.; Lara-Cisneros, Gerardo; Femat, Ricardo
2016-09-01
In this paper, a robust nonlinear feedback control scheme with adaptive gain is proposed to control the chaotic behavior in a Bose-Einstein condensate (BEC). The control goal concerns the track or regulation purposes. The BEC system is represented as stochastic ordinary differential equations with measured output perturbed by Gaussian noise, which represents the nature of the quantum systems. The convergence of the BEC control law is analyzed under the frame of the Lyapunov stability theory. Numerical experiments show an adequate performance of the proposed methodology under the required conditions. The results are applicable when the shape of the condensate is sufficiently simple.
NASA Astrophysics Data System (ADS)
Novaes, Marcel
2015-06-01
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†(E - ɛ) S(E + ɛ)]n, for general positive integer n. Our result is an infinite series in ɛ, whose coefficients are rational functions of M. From this, we extract moments of the time delay matrix Q = - iħS†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. 56, 062110 (2015)].
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. 56, 062110 (2015)].
Classical And Quantum Rainbow Scattering From Surfaces
Winter, H.; Schueller, A.; Busch, M.; Seifert, J.; Wethekam, S.
2011-06-01
The structure of clean and adsorbate covered surfaces as well as of ultrathin films can be investigated by grazing scattering of fast atoms. We present two recent experimental techniques which allow one to study the structure of ordered arrangements of surface atoms in detail. (1) Rainbow scattering under axial surface channeling conditions, and (2) fast atom diffraction. Our examples demonstrate the attractive features of grazing fast atom scattering as a powerful analytical tool in studies on the structure of surfaces. We will concentrate our discussion on the structure of ultrathin silica films on a Mo(112) surface and of adsorbed oxygen atoms on a Fe(110) surface.
Quasi-soliton scattering in quantum spin chains
NASA Astrophysics Data System (ADS)
Fioretto, Davide; Vljim, Rogier; Ganahl, Martin; Brockmann, Michael; Haque, Masud; Evertz, Hans-Gerd; Caux, Jean-Sébastien
The quantum scattering of magnon bound states in the anisotropic Heisenberg spin chain is shown to display features similar to the scattering of solitons in classical exactly solvable models. Localized colliding Gaussian wave packets of bound magnons are constructed from string solutions of the Bethe equations and subsequently evolved in time, relying on an algebraic Bethe ansatz based framework for the computation of local expectation values in real space-time. The local magnetization profile shows the trajectories of colliding wave packets of bound magnons, which obtain a spatial displacement upon scattering. Analytic predictions on the displacements for various values of anisotropy and string lengths are derived from scattering theory and Bethe ansatz phase shifts, matching time evolution fits on the displacements. The TEBD algorithm allows for the study of scattering displacements from spin-block states, showing similar displacement scattering features.
Evaluation of Quantum Scattering Time in Ultra-High Quality GaAs Quantum Wells
NASA Astrophysics Data System (ADS)
Qian, Qi; Mondal, Sumit; Gardner, Geoffrey C.; Watson, John D.; Manfra, Michael J.
2015-03-01
We present a critical analysis of the extraction of quantum scattering time from Shubnikov-de Haas oscillations in ultra-high quality GaAs quantum wells. In the regime of temperature and magnetic field study here (T ~0.3K, B <=0.3T) we find the canonical method for determination of quantum scattering time yields unreliable results (cf.). We elaborate a formalism that allows extraction of the quantum scattering time in a regime in which the normalized modulation of the density of states Δg /g0 is greater than unity. This approach describes well low-field data for samples that display very large excitation gaps for fragile fractional quantum Hall states at large magnetic field.
Scattering through a straight quantum waveguide with combined boundary conditions
Briet, Ph. Soccorsi, E.; Dittrich, J.
2014-11-15
Scattering through a straight two-dimensional quantum waveguide R×(0,d) with Dirichlet boundary conditions on (R{sub −}{sup *}×(y=0))∪(R{sub +}{sup *}×(y=d)) and Neumann boundary condition on (R{sub −}{sup *}×(y=d))∪(R{sub +}{sup *}×(y=0)) is considered using stationary scattering theory. The existence of a matching conditions solution at x = 0 is proved. The use of stationary scattering theory is justified showing its relation to the wave packets motion. As an illustration, the matching conditions are also solved numerically and the transition probabilities are shown.
Scattering bright solitons: Quantum versus mean-field behavior
NASA Astrophysics Data System (ADS)
Gertjerenken, Bettina; Billam, Thomas P.; Khaykovich, Lev; Weiss, Christoph
2012-09-01
We investigate scattering bright solitons off a potential using both analytical and numerical methods. Our paper focuses on low kinetic energies for which differences between the mean-field description via the Gross-Pitaevskii equation (GPE) and the quantum behavior are particularly large. On the N-particle quantum level, adding an additional harmonic confinement leads to a simple signature to distinguish quantum superpositions from statistical mixtures. While the nonlinear character of the GPE does not allow quantum superpositions, the splitting of GPE solitons takes place only partially. When the potential strength is increased, the fraction of the soliton which is transmitted or reflected jumps noncontinuously. We explain these jumps via energy conservation and interpret them as indications for quantum superpositions on the N-particle level. On the GPE level, we also investigate the transition from this stepwise behavior to the continuous case.
Cavity-enhanced coherent light scattering from a quantum dot
Bennett, Anthony J.; Lee, James P.; Ellis, David J. P.; Meany, Thomas; Murray, Eoin; Floether, Frederik F.; Griffths, Jonathan P.; Farrer, Ian; Ritchie, David A.; Shields, Andrew J.
2016-01-01
The generation of coherent and indistinguishable single photons is a critical step for photonic quantum technologies in information processing and metrology. A promising system is the resonant optical excitation of solid-state emitters embedded in wavelength-scale three-dimensional cavities. However, the challenge here is to reject the unwanted excitation to a level below the quantum signal. We demonstrate this using coherent photon scattering from a quantum dot in a micropillar. The cavity is shown to enhance the fraction of light that is resonantly scattered toward unity, generating antibunched indistinguishable photons that are 16 times narrower than the time-bandwidth limit, even when the transition is near saturation. Finally, deterministic excitation is used to create two-photon N00N states with which we make superresolving phase measurements in a photonic circuit. PMID:27152337
Cavity-enhanced coherent light scattering from a quantum dot.
Bennett, Anthony J; Lee, James P; Ellis, David J P; Meany, Thomas; Murray, Eoin; Floether, Frederik F; Griffths, Jonathan P; Farrer, Ian; Ritchie, David A; Shields, Andrew J
2016-04-01
The generation of coherent and indistinguishable single photons is a critical step for photonic quantum technologies in information processing and metrology. A promising system is the resonant optical excitation of solid-state emitters embedded in wavelength-scale three-dimensional cavities. However, the challenge here is to reject the unwanted excitation to a level below the quantum signal. We demonstrate this using coherent photon scattering from a quantum dot in a micropillar. The cavity is shown to enhance the fraction of light that is resonantly scattered toward unity, generating antibunched indistinguishable photons that are 16 times narrower than the time-bandwidth limit, even when the transition is near saturation. Finally, deterministic excitation is used to create two-photon N00N states with which we make superresolving phase measurements in a photonic circuit. PMID:27152337
Asymptotic neutron scattering laws for anomalously diffusing quantum particles
NASA Astrophysics Data System (ADS)
Kneller, Gerald R.
2016-07-01
The paper deals with a model-free approach to the analysis of quasielastic neutron scattering intensities from anomalously diffusing quantum particles. All quantities are inferred from the asymptotic form of their time-dependent mean square displacements which grow ∝tα, with 0 ≤ α < 2. Confined diffusion (α = 0) is here explicitly included. We discuss in particular the intermediate scattering function for long times and the Fourier spectrum of the velocity autocorrelation function for small frequencies. Quantum effects enter in both cases through the general symmetry properties of quantum time correlation functions. It is shown that the fractional diffusion constant can be expressed by a Green-Kubo type relation involving the real part of the velocity autocorrelation function. The theory is exact in the diffusive regime and at moderate momentum transfers.
Asymptotic neutron scattering laws for anomalously diffusing quantum particles.
Kneller, Gerald R
2016-07-28
The paper deals with a model-free approach to the analysis of quasielastic neutron scattering intensities from anomalously diffusing quantum particles. All quantities are inferred from the asymptotic form of their time-dependent mean square displacements which grow ∝t(α), with 0 ≤ α < 2. Confined diffusion (α = 0) is here explicitly included. We discuss in particular the intermediate scattering function for long times and the Fourier spectrum of the velocity autocorrelation function for small frequencies. Quantum effects enter in both cases through the general symmetry properties of quantum time correlation functions. It is shown that the fractional diffusion constant can be expressed by a Green-Kubo type relation involving the real part of the velocity autocorrelation function. The theory is exact in the diffusive regime and at moderate momentum transfers. PMID:27475344
Quantum error correction of photon-scattering errors
NASA Astrophysics Data System (ADS)
Akerman, Nitzan; Glickman, Yinnon; Kotler, Shlomi; Ozeri, Roee
2011-05-01
Photon scattering by an atomic ground-state superposition is often considered as a source of decoherence. The same process also results in atom-photon entanglement which had been directly observed in various experiments using single atom, ion or a diamond nitrogen-vacancy center. Here we combine these two aspects to implement a quantum error correction protocol. We encode a qubit in the two Zeeman-splitted ground states of a single trapped 88 Sr+ ion. Photons are resonantly scattered on the S1 / 2 -->P1 / 2 transition. We study the process of single photon scattering i.e. the excitation of the ion to the excited manifold followed by a spontaneous emission and decay. In the absence of any knowledge on the emitted photon, the ion-qubit coherence is lost. However the joined ion-photon system still maintains coherence. We show that while scattering events where spin population is preserved (Rayleigh scattering) do not affect coherence, spin-changing (Raman) scattering events result in coherent amplitude exchange between the two qubit states. By applying a unitary spin rotation that is dependent on the detected photon polarization we retrieve the ion-qubit initial state. We characterize this quantum error correction protocol by process tomography and demonstrate an ability to preserve ion-qubit coherence with high fidelity.
Density fluctuations due to Raman forward scattering in quantum plasma
NASA Astrophysics Data System (ADS)
Kumar, Punit; Singh, Shiv; Rathore, Nisha Singh
2016-05-01
Density fluctuations due Raman forward scattering (RFS) is analysed in the interaction of a high intensity laser pulse with high density quantum plasma. The interaction model is developed using the quantum hydrodynamic (QHD) model which consist of a set of equations describing the transport of charge, density, momentum and energy of a charged particle system interacting through a self-consistent electrostatic potential. The nonlinear source current has been obtained incorporating the effects of quantum Bohm potential, Fermi pressure and electron spin. The laser spectrum is strongly modulated by the interaction, showing sidebands at the plasma frequency. Furthermore, as the quiver velocity of the electrons in the high electric field of the laser beam is quit large, various quantum effects are observed which can be attributed to the variation of electron mass with laser intensity.
Quantum scattering of neon from a nanotextured surface.
Levi, A C; Huang, C; Allison, W; Maclaren, D A
2009-06-01
Phonon exchange is the usual cause of decoherence in atom-surface scattering. By including quantum effects in the treatment of Debye-Waller scattering, we show that phonon exchange becomes ineffective when the relevant phonon frequencies are high. The result explains the surprising observation of strong elastic scattering of Ne from a Cu(100) surface nanotextured with a c(2 × 2) Li adsorbate structure. We extend a previous model to describe the phonon spectra by an Einstein oscillator component with an admixture of a Debye spectrum. The Einstein oscillator represents the dominant, high frequency vibration of the adsorbate, normal to the surface, while the Debye spectrum represents the substrate contribution. Neon scattering is so slow that exciting the adsorbate mode has a low probability and is impossible if the incident energy is below the threshold. Thus, adsorbate vibrations are averaged out. A theoretical discussion and calculation shows that under such circumstances the vibrations of a light adsorbate do not contribute to the Debye-Waller effect, with the result that Ne scattering at thermal energies is quantum mechanical and largely elastic, explaining the high reflectivity and the diffraction peaks observed experimentally. PMID:21715773
Green-function approach for scattering quantum walks
Andrade, F. M.; Luz, M. G. E. da
2011-10-15
In this work a Green-function approach for scattering quantum walks is developed. The exact formula has the form of a sum over paths and always can be cast into a closed analytic expression for arbitrary topologies and position-dependent quantum amplitudes. By introducing the step and path operators, it is shown how to extract any information about the system from the Green function. The method's relevant features are demonstrated by discussing in detail an example, a general diamond-shaped graph.
Quantum Markovian master equation for scattering from surfaces
Li, Haifeng; Shao, Jiushu; Azuri, Asaf; Pollak, Eli Alicki, Robert
2014-01-07
We propose a semi-phenomenological Markovian Master equation for describing the quantum dynamics of atom-surface scattering. It embodies the Lindblad-like structure and can describe both damping and pumping of energy between the system and the bath. It preserves positivity and correctly accounts for the vanishing of the interaction of the particle with the surface when the particle is distant from the surface. As a numerical test, we apply it to a model of an Ar atom scattered from a LiF surface, allowing for interaction only in the vertical direction. At low temperatures, we find that the quantum mechanical average energy loss is smaller than the classical energy loss. The numerical results obtained from the space dependent friction master equation are compared with numerical simulations for a discretized bath, using the multi-configurational time dependent Hartree methodology. The agreement between the two simulations is quantitative.
Landau retardation on the occurrence scattering time in quantum electron-hole plasmas
NASA Astrophysics Data System (ADS)
Hong, Woo-Pyo; Jung, Young-Dae
2016-03-01
The Landau damping effects on the occurrence scattering time in electron collisions are investigated in a quantum plasma composed of electrons and holes. The Shukla-Stenflo-Bingham effective potential model is employed to obtain the occurrence scattering time in a quantum electron-hole plasma. The result shows that the influence of Landau damping produces the imaginary term in the scattering amplitude. It is then found that the Landau damping generates the retardation effect on the occurrence scattering time. It is found that the occurrence scattering time increases in forward scattering domains and decreases in backward scattering domains with an increase of the Landau parameter. It is also found that the occurrence scattering time decreases with increasing collision energy. In addition, it is found that the quantum shielding effect enhances the occurrence scattering time in the forward scattering and, however, suppresses the occurrence scattering time in the backward scattering.
Quantum random bit generation using stimulated Raman scattering.
Bustard, Philip J; Moffatt, Doug; Lausten, Rune; Wu, Guorong; Walmsley, Ian A; Sussman, Benjamin J
2011-12-01
Random number sequences are a critical resource in a wide variety of information systems, including applications in cryptography, simulation, and data sampling. We introduce a quantum random number generator based on the phase measurement of Stokes light generated by amplification of zero-point vacuum fluctuations using stimulated Raman scattering. This is an example of quantum noise amplification using the most noise-free process possible: near unitary quantum evolution. The use of phase offers robustness to classical pump noise and the ability to generate multiple bits per measurement. The Stokes light is generated with high intensity and as a result, fast detectors with high signal-to-noise ratios can be used for measurement, eliminating the need for single-photon sensitive devices. The demonstrated implementation uses optical phonons in bulk diamond. PMID:22273908
Quantum Monte Carlo Calculations of Nucleon-Nucleus Scattering
NASA Astrophysics Data System (ADS)
Wiringa, R. B.; Nollett, Kenneth M.; Pieper, Steven C.; Brida, I.
2009-10-01
We report recent quantum Monte Carlo (variational and Green's function) calculations of elastic nucleon-nucleus scattering. We are adding the cases of proton-^4He, neutron-^3H and proton-^3He scattering to a previous GFMC study of neutron-^4He scattering [1]. To do this requires generalizing our methods to include long-range Coulomb forces and to treat coupled channels. The two four-body cases can be compared to other accurate four-body calculational methods such as the AGS equations and hyperspherical harmonic expansions. We will present results for the Argonne v18 interaction alone and with Urbana and Illinois three-nucleon potentials. [4pt] [1] K.M. Nollett, S. C. Pieper, R.B. Wiringa, J. Carlson, and G.M. Hale, Phys. Rev. Lett. 99, 022502 (2007)
The pilot-wave perspective on quantum scattering and tunneling
NASA Astrophysics Data System (ADS)
Norsen, Travis
2013-04-01
The de Broglie-Bohm "pilot-wave" theory replaces the paradoxical wave-particle duality of ordinary quantum theory with a more mundane and literal kind of duality: each individual photon or electron comprises a quantum wave (evolving in accordance with the usual quantum mechanical wave equation) and a particle that, under the influence of the wave, traces out a definite trajectory. The definite particle trajectory allows the theory to account for the results of experiments without the usual recourse to additional dynamical axioms about measurements. Instead, one need simply assume that particle detectors click when particles arrive at them. This alternative understanding of quantum phenomena is illustrated here for two elementary textbook examples of one-dimensional scattering and tunneling. We introduce a novel approach to reconcile standard textbook calculations (made using unphysical plane-wave states) with the need to treat such phenomena in terms of normalizable wave packets. This approach allows for a simple but illuminating analysis of the pilot-wave theory's particle trajectories and an explicit demonstration of the equivalence of the pilot-wave theory predictions with those of ordinary quantum theory.
Positron scattering from hydrogen atom embedded in dense quantum plasma
Bhattacharya, Arka; Kamali, M. Z. M.; Ghoshal, Arijit; Ratnavelu, K.
2013-08-15
Scattering of positrons from the ground state of hydrogen atoms embedded in dense quantum plasma has been investigated by applying a formulation of the three-body collision problem in the form of coupled multi-channel two-body Lippmann-Schwinger equations. The interactions among the charged particles in dense quantum plasma have been represented by exponential cosine-screened Coulomb potentials. Variationally determined hydrogenic wave function has been employed to calculate the partial-wave scattering amplitude. Plasma screening effects on various possible mode of fragmentation of the system e{sup +}+H(1s) during the collision, such as 1s→1s and 2s→2s elastic collisions, 1s→2s excitation, positronium formation, elastic proton-positronium collisions, have been reported in the energy range 13.6-350 eV. Furthermore, a comparison has been made on the plasma screening effect of a dense quantum plasma with that of a weakly coupled plasma for which the plasma screening effect has been represented by the Debye model. Our results for the unscreened case are in fair agreement with some of the most accurate results available in the literature.
Communication: Heavy atom quantum diffraction by scattering from surfaces.
Moix, Jeremy M; Pollak, Eli
2011-01-01
Typically one expects that when a heavy particle collides with a surface, the scattered angular distribution will follow classical mechanics. The heavy mass usually assures that the coherence length of the incident particle in the direction of the propagation of the particle (the parallel direction) will be much shorter than the characteristic lattice length of the surface, thus leading to a classical description. Recent work on molecular interferometry has shown that extreme collimation of the beam creates a perpendicular coherence length which is sufficiently long so as to observe interference of very heavy species passing through a grating. Here we show, using quantum mechanical simulations, that the same effect will lead to quantum diffraction of heavy particles colliding with a surface. The effect is robust with respect to the incident energy, the angle of incidence, and the mass of the particle. PMID:21218990
Scattering assisted injection based injectorless mid infrared quantum cascade laser
Singh, Siddharth Kamoua, Ridha
2014-06-07
An injectorless five-well mid infrared quantum cascade laser is analyzed which relies on phonon scattering injection in contrast to resonant tunneling injection, which has been previously used for injectorless designs. A Monte Carlo based self-consistent electron and photon transport simulator is used to analyze the performance of the analyzed design and compare it to existing injectorless designs. The simulation results show that the analyzed design could greatly enhance the optical gain and the characteristic temperatures of injectorless quantum cascade lasers (QCLs) which have typically been hindered by low characteristic temperatures and significant temperature related performance degradation. Simulations of the analyzed device predict threshold current densities of 0.85 kA/cm{sup 2} and 1.95 kA/cm{sup 2} at 77 K and 300 K, respectively, which are comparable to the threshold current densities of conventional injector based QCLs.
Single quantum dot controls a plasmonic cavity's scattering and anisotropy.
Hartsfield, Thomas; Chang, Wei-Shun; Yang, Seung-Cheol; Ma, Tzuhsuan; Shi, Jinwei; Sun, Liuyang; Shvets, Gennady; Link, Stephan; Li, Xiaoqin
2015-10-01
Plasmonic cavities represent a promising platform for controlling light-matter interaction due to their exceptionally small mode volume and high density of photonic states. Using plasmonic cavities for enhancing light's coupling to individual two-level systems, such as single semiconductor quantum dots (QD), is particularly desirable for exploring cavity quantum electrodynamic (QED) effects and using them in quantum information applications. The lack of experimental progress in this area is in part due to the difficulty of precisely placing a QD within nanometers of the plasmonic cavity. Here, we study the simplest plasmonic cavity in the form of a spherical metallic nanoparticle (MNP). By controllably positioning a semiconductor QD in the close proximity of the MNP cavity via atomic force microscope (AFM) manipulation, the scattering spectrum of the MNP is dramatically modified due to Fano interference between the classical plasmonic resonance of the MNP and the quantized exciton resonance in the QD. Moreover, our experiment demonstrates that a single two-level system can render a spherical MNP strongly anisotropic. These findings represent an important step toward realizing quantum plasmonic devices. PMID:26372957
NASA Astrophysics Data System (ADS)
Stuchlík, Zdeněk; Kološ, Martin
2016-01-01
To test the role of large-scale magnetic fields in accretion processes, we study the dynamics of the charged test particles in the vicinity of a black hole immersed into an asymptotically uniform magnetic field. Using the Hamiltonian formalism of the charged particle dynamics, we examine chaotic scattering in the effective potential related to the black hole gravitational field combined with the uniform magnetic field. Energy interchange between the translational and oscillatory modes of the charged particle dynamics provides a mechanism for charged particle acceleration along the magnetic field lines. This energy transmutation is an attribute of the chaotic charged particle dynamics in the combined gravitational and magnetic fields only, the black hole rotation is not necessary for such charged particle acceleration. The chaotic scatter can cause a transition to the motion along the magnetic field lines with small radius of the Larmor motion or vanishing Larmor radius, when the speed of the particle translational motion is largest and it can be ultra-relativistic. We discuss the consequences of the model of ionization of test particles forming a neutral accretion disc, or heavy ions following off-equatorial circular orbits, and we explore the fate of heavy charged test particles after ionization where no kick of heavy ions is assumed and only the switch-on effect of the magnetic field is relevant. We demonstrate that acceleration and escape of the ionized particles can be efficient along the Kerr black hole symmetry axis parallel to the magnetic field lines. We show that a strong acceleration of the ionized particles to ultra-relativistic velocities is preferred in the direction close to the magnetic field lines. Therefore, the process of ionization of Keplerian discs around the Kerr black holes can serve as a model of relativistic jets.
Towards a Social Theory of School Administrative Practice in a Complex, Chaotic, Quantum World.
ERIC Educational Resources Information Center
Beavis, Allan K.
Educational administration, like many other social sciences, has traditionally followed the rubrics of classical science with its emphasis on prediction and control and attempts to understand the whole by understanding in ever finer detail how the parts fit together. However, the "new" science (especially quantum mechanics, complexity, and chaos…
Quantum optics with quantum gases: Controlled state reduction by designed light scattering
Mekhov, Igor B.; Ritsch, Helmut
2009-07-15
Cavity-enhanced light scattering from an ultracold gas in an optical lattice constitutes a quantum measurement with a controllable form of the measurement backaction. Time-resolved counting of scattered photons alters the state of the atoms without particle loss implementing a quantum nondemolition measurement. The conditional dynamics is given by the interplay between photodetection events (quantum jumps) and no-count processes. The class of emerging atomic many-body states can be chosen via the optical geometry and light frequencies. Light detection along the angle of a diffraction maximum (Bragg angle) creates an atom-number-squeezed state, while light detection at diffraction minima leads to the macroscopic superposition states (Schroedinger cat states) of different atom numbers in the cavity mode. A measurement of the cavity transmission intensity can lead to atom-number-squeezed or macroscopic superposition states depending on its outcome. We analyze the robustness of the superposition with respect to missed counts and find that a transmission measurement yields more robust and controllable superposition states than the ones obtained by scattering at a diffraction minimum.
Inelastic neutron scattering studies of novel quantum magnets
NASA Astrophysics Data System (ADS)
Plumb, Kemp W.
Inelastic neutron scattering was used to study the magnetic excitation spectrum of three quantum magnets: (i) the double perovskite Ba2FeReO 6; (ii) the two-dimensional square lattice Heisenberg antiferromagnet Sr2CuO2Cl2; and (iii) the quasi-two-dimensional frustrated two-leg ladder BiCu2PO6. We have conducted inelastic neutron scattering measurements on powder samples of the double perovskite compound Ba2FeReO6. The measurements revealed two well defined dispersing spin wave modes. No excitation gap was observable and the spectrum can be explained with a local moment model incorporating the interactions of Fe spins with spin-orbital locked degrees of freedom on the Re site. The results reveal that both significant electronic correlations and spin-orbit coupling on the Re site play a significant role in the spin dynamics of Ba2FeReO6. High resolution neutron scattering measurements of magnetic excitations in the parent cuprate Sr2CuO2Cl2 reveal a significant dispersion and momentum dependent damping of the zone boundary magnons. We directly compare our measurements with previous resonant inelastic x-ray scattering measurements and find a ~25 meV discrepancy between the two techniques for the measured zone boundary energy at (1/2, 0). The deviations are greatest precisely in the region of phase space where the magnon damping is strongest. This comparison shows that the inelastic x-ray spectrum must contain significant contributions from higher energy excitations not previously considered. Our measurements demonstrate that the high energy continuum of magnetic fluctuations is a ubiquitous feature of the magnetic spectrum among insulating monolayer cuprates, and that these excitations couple to both inelastic neutron and light scattering. A comprehensive series of inelastic neutron scattering measurements was used to investigate spin excitations in the frustrated two-leg ladder compound BiCu2PO6. The measurements revealed six branches of steeply dispersing triplon
Coverage-dependent quantum versus classical scattering of thermal neon atoms from Li/Cu(100).
Maclaren, D A; Huang, C; Levi, A C; Allison, W
2008-09-01
We show that subtle variations in surface structure can enhance quantum scattering and quench atom-surface energy transfer. The scattering of thermal energy neon atoms from a lithium overlayer on a copper substrate switches between a classical regime, dominated by multiphonon interactions, and a quantum regime, dominated by elastic diffraction. The transition is achieved by simple tailoring of the lithium coverage and quantum scattering dominates only in the narrow coverage range of theta=0.3-0.6 ML. The results are described qualitatively using a modified Debye-Waller model that incorporates an approximate quantum treatment of the adsorbate-substrate vibration. PMID:19044885
On the optical theorem and non-plane-wave scattering in quantum mechanics
NASA Astrophysics Data System (ADS)
Gouesbet, G.
2009-11-01
In quantum mechanics, the optical theorem states that the extinction cross section is equal (within a prefactor 4π/k, in which k is a quantum wave number) to the imaginary part of the forward scattering angular function. This theorem is valid for plane wave scattering. We discuss modifications required for non-plane-wave scattering and establish a generalized expression for the extinction cross section in quantum mechanics. Examples are provided for two kinds of quantum shaped beams, namely, Gaussian and Bessel beams.
Numerical Aspects of Eigenvalue and Eigenfunction Computations for Chaotic Quantum Systems
NASA Astrophysics Data System (ADS)
Bäcker, A.
Summary: We give an introduction to some of the numerical aspects in quantum chaos. The classical dynamics of two-dimensional area-preserving maps on the torus is illustrated using the standard map and a perturbed cat map. The quantization of area-preserving maps given by their generating function is discussed and for the computation of the eigenvalues a computer program in Python is presented. We illustrate the eigenvalue distribution for two types of perturbed cat maps, one leading to COE and the other to CUE statistics. For the eigenfunctions of quantum maps we study the distribution of the eigenvectors and compare them with the corresponding random matrix distributions. The Husimi representation allows for a direct comparison of the localization of the eigenstates in phase space with the corresponding classical structures. Examples for a perturbed cat map and the standard map with different parameters are shown. Billiard systems and the corresponding quantum billiards are another important class of systems (which are also relevant to applications, for example in mesoscopic physics). We provide a detailed exposition of the boundary integral method, which is one important method to determine the eigenvalues and eigenfunctions of the Helmholtz equation. We discuss several methods to determine the eigenvalues from the Fredholm equation and illustrate them for the stadium billiard. The occurrence of spurious solutions is discussed in detail and illustrated for the circular billiard, the stadium billiard, and the annular sector billiard. We emphasize the role of the normal derivative function to compute the normalization of eigenfunctions, momentum representations or autocorrelation functions in a very efficient and direct way. Some examples for these quantities are given and discussed.
Time Delay for Dispersive Systems in Quantum Scattering Theory
NASA Astrophysics Data System (ADS)
Tiedra de Aldecoa, Rafael
We consider time delay and symmetrized time delay (defined in terms of sojourn times) for quantum scattering pairs {H0 = h(P), H}, where h(P) is a dispersive operator of hypoelliptic-type. For instance, h(P) can be one of the usual elliptic operators such as the Schrödinger operator h(P) = P2 or the square-root Klein-Gordon operator h(P) = √ {1 + P2}. We show under general conditions that the symmetrized time delay exists for all smooth even localization functions. It is equal to the Eisenbud-Wigner time delay plus a contribution due to the non-radial component of the localization function. If the scattering operator S commutes with some function of the velocity operator ∇h(P), then the time delay also exists and is equal to the symmetrized time delay. As an illustration of our results, we consider the case of a one-dimensional Friedrichs Hamiltonian perturbed by a finite rank potential. Our study puts into evidence an integral formula relating the operator of differentiation with respect to the kinetic energy h(P) to the time evolution of localization operators.
Quantum tunneling and scattering of a composite object
NASA Astrophysics Data System (ADS)
Ahsan, Naureen
Reaction physics involving composite objects with internal degrees of freedom is an important subject since it is encountered in the context of nuclear processes like fusion, fission, particle decay, as well as many other branches of science. Quantum tunneling and scattering of a composite object are explored in this work. A few model Hamiltonians are chosen as examples where a two-particle system interacts, in one dimension, with a target that poses a delta-potential or an infinite wall potential. It is assumed that only one of the two components interacts with the target. The study includes the harmonic oscillator and the infinite square well as examples of intrinsic Hamiltonians that do not allow the projectile to break up, and a finite square well and a delta-well as examples of Hamiltonians that do. The Projection Method and the Variable Phase Method are applied with the aim of an exact solution to the relevant scattering problems. These methods are discussed in the context of the pertinent convergence issues related thereto, and of their applicability. Virtual excitations of the projectile into the classically forbidden energy-domain are found to play a dominant and non-perturbative role in shaping reaction observables, giving rise to enhanced or reduced tunneling in various situations. Cusps and discontinuities are found to appear in observables as manifestations of unitarity and redistribution of flux at the thresholds. The intrinsic structure gives rise to resonancelike behavior in tunneling probabilities. It is also shown that there is charge asymmetry in the scattering of a composite object, unlike in the case of a structureless particle.
Regular and Chaotic Quantum Dynamics of Two-Level Atoms in a Selfconsistent Radiation Field
NASA Technical Reports Server (NTRS)
Konkov, L. E.; Prants, S. V.
1996-01-01
Dynamics of two-level atoms interacting with their own radiation field in a single-mode high-quality resonator is considered. The dynamical system consists of two second-order differential equations, one for the atomic SU(2) dynamical-group parameter and another for the field strength. With the help of the maximal Lyapunov exponent for this set, we numerically investigate transitions from regularity to deterministic quantum chaos in such a simple model. Increasing the collective coupling constant b is identical with 8(pi)N(sub 0)(d(exp 2))/hw, we observed for initially unexcited atoms a usual sharp transition to chaos at b(sub c) approx. equal to 1. If we take the dimensionless individual Rabi frequency a = Omega/2w as a control parameter, then a sequence of order-to-chaos transitions has been observed starting with the critical value a(sub c) approx. equal to 0.25 at the same initial conditions.
Subband Quantum Scattering Times for Algaas/GaAs Obtained Using Digital Filtering
NASA Technical Reports Server (NTRS)
Mena, R. A.; Schacham, S. E.; Haughland, E. J.; Alterovitz, S. A.; Bibyk, S. B.; Ringel, S. A.
1995-01-01
In this study we investigate both the transport and quantum scattering times as a function of the carrier concentration for a modulation doped Al(0.3)Ga(0.7)As/GaAs structure. Carriers in the well are generated as a result of the persistent photoconductivity effect. When more than one subband becomes populated, digital filtering is used to separate the components for each of the excited subbands. We find that the quantum scattering time for the ground subband increases initially as the carrier concentration is increased. However, once the second subband becomes populated, the ground subband scattering time begins to decrease. The quantum scattering time for the excited subband is also observed to decrease as the concentration is increased. From the ratio of the transport and quantum scattering times, it is seen that the transport in the well becomes more isotropic also as the concentration is increased.
Quantum diffraction grating: A possible new description of nuclear elastic scattering
NASA Astrophysics Data System (ADS)
Wojciechowski, H.
2016-02-01
The problem of discontinuous functions and their representations in the form of Legendre polynomial series in quantum nuclear scattering theory is presented briefly. The problem is quite old yet not adequately explained in numerous Quantum Theory textbooks and sometimes not correctly understood by physicists. Introduction of the generalized functions into the quantum scattering theory clarifies the problem and allows to propose new interpretations of nuclear elastic scattering phenomenon. The derived new forms of the full elastic scattering amplitudes and possibility of splitting them suggest existence of dynamical quantum diffraction grating around the nuclei. Particularly important fact is that this grating existing in the space around the nucleus makes considerable contribution to the experimental elastic differential cross-section. All these might be quite important in analyses of nuclear elastic scattering data and so require to be stated in a more detailed and clear way.
NASA Astrophysics Data System (ADS)
Martienssen, W.; Hübinger, B.; Doerner, R.
A method to transfer secret information using chaotic dynamical systems is proposed. It is based on modulating a chaotic system with the message such that its time evolution contains the hidden information. Decryption of the cipher is achieved by chaos control. Operation of the scheme is demonstrated by en- and decoding a short german text.
Quantum trajectories in complex space: one-dimensional stationary scattering problems.
Chou, Chia-Chun; Wyatt, Robert E
2008-04-21
One-dimensional time-independent scattering problems are investigated in the framework of the quantum Hamilton-Jacobi formalism. The equation for the local approximate quantum trajectories near the stagnation point of the quantum momentum function is derived, and the first derivative of the quantum momentum function is related to the local structure of quantum trajectories. Exact complex quantum trajectories are determined for two examples by numerically integrating the equations of motion. For the soft potential step, some particles penetrate into the nonclassical region, and then turn back to the reflection region. For the barrier scattering problem, quantum trajectories may spiral into the attractors or from the repellers in the barrier region. Although the classical potentials extended to complex space show different pole structures for each problem, the quantum potentials present the same second-order pole structure in the reflection region. This paper not only analyzes complex quantum trajectories and the total potentials for these examples but also demonstrates general properties and similar structures of the complex quantum trajectories and the quantum potentials for one-dimensional time-independent scattering problems. PMID:18433189
Analysis of the scatter effect on detective quantum efficiency of digital mammography
NASA Astrophysics Data System (ADS)
Park, Jiwoong; Yun, Seungman; Kim, Dong Woon; Baek, Cheol-Ha; Youn, Hanbean; Jeon, Hosang; Kim, Ho Kyung
2016-03-01
The scatter effect on detective quantum efficiency (DQE) of digital mammography is investigated using the cascaded-systems model. The cascaded-systems model includes a scatter-reduction device as a binomial selection stage. Quantum-noise-limited operation approximates the system DQE into the multiplication form of the scatter-reduction device DQE and the conventional detector DQE. The developed DQE model is validated in comparisons with the measured results using a CMOS flat-panel detector under scatter environments. For various scatter-reduction devices, the slot-scan method shows the best scatter-cleanup performance in terms of DQE, and the scatter-cleanup performance of the conventional one-dimensional grid is rather worse than the air gap. The developed model can also be applied to general radiography and will be very useful for a better design of imaging chain.
The study of effects of small perturbations on chaotic systems
Grebogi, C.; Yorke, J.A.
1991-12-01
This report discusses the following topics: controlling chaotic dynamical systems; embedding of experimental data; effect of noise on critical exponents of crises; transition to chaotic scattering; and distribution of floaters on a fluid surface. (LSP)
Forward scattering approximation and bosonization in integer quantum Hall systems
Rosenau da Costa, M. Westfahl, H.; Caldeira, A.O.
2008-03-15
In this work, we present a model and a method to study integer quantum Hall (IQH) systems. Making use of the Landau levels structure we divide these two-dimensional systems into a set of interacting one-dimensional gases, one for each guiding center. We show that the so-called strong field approximation, used by Kallin and Halperin and by MacDonald, is equivalent, in first order, to a forward scattering approximation and analyze the IQH systems within this approximation. Using an appropriate variation of the Landau level bosonization method we obtain the dispersion relations for the collective excitations and the single-particle spectral functions. For the bulk states, these results evidence a behavior typical of non-normal strongly correlated systems, including the spin-charge splitting of the single-particle spectral function. We discuss the origin of this behavior in the light of the Tomonaga-Luttinger model and the bosonization of two-dimensional electron gases.
Scattering theory of nonlinear thermoelectricity in quantum coherent conductors.
Meair, Jonathan; Jacquod, Philippe
2013-02-27
We construct a scattering theory of weakly nonlinear thermoelectric transport through sub-micron scale conductors. The theory incorporates the leading nonlinear contributions in temperature and voltage biases to the charge and heat currents. Because of the finite capacitances of sub-micron scale conducting circuits, fundamental conservation laws such as gauge invariance and current conservation require special care to be preserved. We do this by extending the approach of Christen and Büttiker (1996 Europhys. Lett. 35 523) to coupled charge and heat transport. In this way we write relations connecting nonlinear transport coefficients in a manner similar to Mott's relation between the linear thermopower and the linear conductance. We derive sum rules that nonlinear transport coefficients must satisfy to preserve gauge invariance and current conservation. We illustrate our theory by calculating the efficiency of heat engines and the coefficient of performance of thermoelectric refrigerators based on quantum point contacts and resonant tunneling barriers. We identify, in particular, rectification effects that increase device performance. PMID:23343784
Neutron Scattering Study of Low Dimensional Quantum Magnets
NASA Astrophysics Data System (ADS)
Broholm, Collin
1997-03-01
I review three neutron scattering experiments which have uncovered unusual magnetic phenomena in non-metallic low dimensional quantum antiferromagnets. (Work done in collaboration with M. Adams, G. Aeppli, C. Carlile, S.-W. Cheong, D. Davidović), D. C. Dender, J. F. DiTusa, P. R. Hammar, B. Hessen, T. Ito, S. H. Lee, K. Lefmann, K. Oka, T. G. Perring, A. P. Ramirez, Daniel H. Reich, H. Takagi, A. Taylor, and Guangyong Xu. I present evidence that the low temperature short-range ordered spin configuration in the kagomé bi-layer system SrCr_9pGa_12-9pO_19 is composed of small groups of spins whose dipole moments cancel. I report the first observation of field induced incommensurate spin correlations in the uniform spin 1/2 antiferromagnetic chain copper benzoate, and I discuss new results concerning sub-gap excitations in a spin 1 antiferromagnetic chain with impurity bonds, (Y_1-xCa_x)_2BaNiO_5.
Modern integral equation techniques for quantum reactive scattering theory
Auerbach, S.M.
1993-11-01
Rigorous calculations of cross sections and rate constants for elementary gas phase chemical reactions are performed for comparison with experiment, to ensure that our picture of the chemical reaction is complete. We focus on the H/D+H{sub 2} {yields} H{sub 2}/DH + H reaction, and use the time independent integral equation technique in quantum reactive scattering theory. We examine the sensitivity of H+H{sub 2} state resolved integral cross sections {sigma}{sub v{prime}j{prime},vj}(E) for the transitions (v = 0,j = 0) to (v{prime} = 1,j{prime} = 1,3), to the difference between the Liu-Siegbahn-Truhlar-Horowitz (LSTH) and double many body expansion (DMBE) ab initio potential energy surfaces (PES). This sensitivity analysis is performed to determine the origin of a large discrepancy between experimental cross sections with sharply peaked energy dependence and theoretical ones with smooth energy dependence. We find that the LSTH and DMBE PESs give virtually identical cross sections, which lends credence to the theoretical energy dependence.
Review of the inverse scattering problem at fixed energy in quantum mechanics
NASA Technical Reports Server (NTRS)
Sabatier, P. C.
1972-01-01
Methods of solution of the inverse scattering problem at fixed energy in quantum mechanics are presented. Scattering experiments of a beam of particles at a nonrelativisitic energy by a target made up of particles are analyzed. The Schroedinger equation is used to develop the quantum mechanical description of the system and one of several functions depending on the relative distance of the particles. The inverse problem is the construction of the potentials from experimental measurements.
A semiclassical method in the theory of light scattering by semiconductor quantum dots
Lang, I. G.; Korovin, L. I. Pavlov, S. T.
2008-06-15
A semiclassical method is proposed for the theoretical description of elastic light scattering by arbitrary semiconductor quantum dots under conditions of size quantization. This method involves retarded potentials and allows one to dispense with boundary conditions for electric and magnetic fields. Exact results for the Umov-Poynting vector at large distances from quantum dots in the case of monochromatic and pulsed irradiation and formulas for differential scattering cross sections are obtained.
Quantum Theory of (H,H{Sub 2}) Scattering: Approximate Treatments of Reactive Scattering
DOE R&D Accomplishments Database
Tang, K. T.; Karplus, M.
1970-10-01
A quantum mechanical study is made of reactive scattering in the (H, H{sub 2}) system. The problem is formulated in terms of a form of the distorted-wave Born approximation (DWBA) suitable for collisions in which all particles have finite mass. For certain incident energies, differential and total cross sections, as well as other attributes of the reactive collisions, (e.g. reaction configuration), are determined. Two limiting models in the DWBA formulation are compared; in one, the molecule is unperturbed by the incoming atom and in the other, the molecule adiabatically follows the incoming atom. For thermal incident energies and semi-empirical interaction potential employed, the adiabatic model seems to be more appropriate. Since the DWBA method is too complicated for a general study of the (H, H{sub 2}) reaction, a much simpler approximation method, the “linear model” is developed. This model is very different in concept from treatments in which the three atoms are constrained to move on a line throughout the collision. The present model includes the full three-dimensional aspect of the collision and it is only the evaluation of the transition matrix element itself that is simplified. It is found that the linear model, when appropriately normalized, gives results in good agreement with that of the DWBA method. By application of this model, the energy dependence, rotational state of dependence and other properties of the total and differential reactions cross sections are determined. These results of the quantum mechanical treatment are compared with the classical calculation for the same potential surface. The most important result is that, in agreement with the classical treatment, the differential cross sections are strongly backward peaked at low energies and shifts in the forward direction as the energy increases. Finally, the implications of the present calculations for a theory of chemical kinetics are discussed.
Fermion-fermion scattering in quantum field theory with superconducting circuits.
García-Álvarez, L; Casanova, J; Mezzacapo, A; Egusquiza, I L; Lamata, L; Romero, G; Solano, E
2015-02-20
We propose an analog-digital quantum simulation of fermion-fermion scattering mediated by a continuum of bosonic modes within a circuit quantum electrodynamics scenario. This quantum technology naturally provides strong coupling of superconducting qubits with a continuum of electromagnetic modes in an open transmission line. In this way, we propose qubits to efficiently simulate fermionic modes via digital techniques, while we consider the continuum complexity of an open transmission line to simulate the continuum complexity of bosonic modes in quantum field theories. Therefore, we believe that the complexity-simulating-complexity concept should become a leading paradigm in any effort towards scalable quantum simulations. PMID:25763944
NASA Astrophysics Data System (ADS)
Figarova, S. R.; Hasiyeva, G. N.; Figarov, V. R.
2016-04-01
The effect of phonon scattering on electrical conductivity (EC) of 2D electron gas in quantum well (QW) systems with a complicated potential profile is described. Dependence of QW electrical conductivity on QW parameters (such as QW width, Fermi level positions etc.) when phonon scattering is employed has been calculated. NDC in EC when it varies with width of the QW has been found.
Modern Integral Equation Techniques for Quantum Reactive Scattering Theory.
NASA Astrophysics Data System (ADS)
Auerbach, Scott Michael
Rigorous calculations of cross sections and rate constants for elementary gas phase chemical reactions are performed for comparison with experiment, to ensure that our picture of the chemical reaction is complete. We focus on the H/D + H_2 to H _2/DH + H reaction, and use the time independent integral equation technique in quantum reactive scattering theory. We examine the sensitivity of H + H_2 state resolved integral cross sections sigma_{v^' j^ ',vj}(E) for the transitions (v = 0, j = 0) to (v^' = 1,j^ ' = 1,3), to the difference between the Liu-Siegbahn-Truhlar-Horowitz (LSTH) and double many body expansion (DMBE) ab initio potential energy surfaces (PES). This sensitivity analysis is performed to determine the origin of a large discrepancy between experimental cross sections with sharply peaked energy dependence and theoretical ones with smooth energy dependence. We find that the LSTH and DMBE PESs give virtually identical cross sections, which lends credence to the theoretical energy dependence. To facilitate quantum calculations on more complex reactive systems, we develop a new method to compute the energy Green's function with absorbing boundary conditions (ABC), for use in calculating the cumulative reaction probability. The method is an iterative technique to compute the inverse of a non-Hermitian matrix which is based on Fourier transforming time dependent dynamics, and which requires very little core memory. The Hamiltonian is evaluated in a sinc-function based discrete variable representation (DVR) which we argue may often be superior to the fast Fourier transform method for reactive scattering. We apply the resulting power series Green's function to the benchmark collinear H + H_2 system over the energy range 3.37 to 1.27 eV. The convergence of the power series is stable at all energies, and is accelerated by the use of a stronger absorbing potential. The practicality of computing the ABC-DVR Green's function in a polynomial of the Hamiltonian is
Miyake, Hirokazu; Siviloglou, Georgios A; Puentes, Graciana; Pritchard, David E; Ketterle, Wolfgang; Weld, David M
2011-10-21
We have observed Bragg scattering of photons from quantum degenerate ^{87}Rb atoms in a three-dimensional optical lattice. Bragg scattered light directly probes the microscopic crystal structure and atomic wave function whose position and momentum width is Heisenberg limited. The spatial coherence of the wave function leads to revivals in the Bragg scattered light due to the atomic Talbot effect. The decay of revivals across the superfluid to Mott insulator transition indicates the loss of superfluid coherence. PMID:22107532
Angle-resolved scattering spectroscopy of explosives using an external cavity quantum cascade laser
Suter, Jonathan D.; Bernacki, Bruce E.; Phillips, Mark C.
2012-04-01
Investigation of angle-resolved scattering from solid explosives residues on a car door for non-contact sensing geometries. Illumination with a mid-infrared external cavity quantum cascade laser tuning between 7 and 8 microns was detected both with a sensitive single point detector and a hyperspectral imaging camera. Spectral scattering phenomena were discussed and possibilities for hyperspectral imaging at large scattering angles were outlined.
Quantum correlations of magnetic impurities by a multiple electron scattering in carbon nanotubes
NASA Astrophysics Data System (ADS)
Gamboa Angulo, Didier; Cordourier Maruri, Guillermo; de Coss Gómez, Romeo
In this work we analyze the quantum correlations and polarizations states of magnetic impurities spins, when a multiple electron scattering was taken place. A sequence of non-correlated electrons interacts through scattering producing quantum correlation which will have an impact on the electronic transmission. We consider a short range Heisenberg interaction between ballistic electron and static impurities. We analyze the cases when the electron scattering is produce by one and two impurities, obtaining the electronic transmission rates. Concurrence and fidelity calculations are performed to obtain the level of quantum entanglement and polarization correlations. We also discuss the possible application of this model to metallic and semiconductor carbon nanotubes, which could have important implications on spintronics and quantum information devices.
Programmable two-photon quantum interference in 103 channels in opaque scattering media
NASA Astrophysics Data System (ADS)
Wolterink, Tom A. W.; Uppu, Ravitej; Ctistis, Georgios; Vos, Willem L.; Boller, Klaus-J.; Pinkse, Pepijn W. H.
2016-05-01
We investigate two-photon quantum interference in an opaque scattering medium that intrinsically supports a large number of transmission channels. By adaptive spatial phase modulation of the incident wave fronts, the photons are directed at targeted speckle spots or output channels. From 103 experimentally available coupled channels, we select two channels and enhance their transmission to realize the equivalent of a fully programmable 2 ×2 beam splitter. By sending pairs of single photons from a parametric down-conversion source through the opaque scattering medium, we observe two-photon quantum interference. The programed beam splitter need not fulfill energy conservation over the two selected output channels and hence could be nonunitary. Consequently, we have the freedom to tune the quantum interference from bunching (Hong-Ou-Mandel-like) to antibunching. Our results establish opaque scattering media as a platform for high-dimensional quantum interference that is notably relevant for boson sampling and physical-key-based authentication.
Electron-interface-phonon scattering in graded quantum wells of Ga1-xAlxAs
NASA Astrophysics Data System (ADS)
Duan, Wenhui; Zhu, Jia-Lin; Gu, Bing-Lin
1994-05-01
Using the method of series expansion, interface-phonon vibrational modes are calculated in the dielectric continuum model for the graded quantum well of Ga1-xAlxAs with a Ga0.6Al0.4As barrier. The intrasubband and intersubband scattering rates are obtained as functions of quantum-well width. The results reveal that the behavior of interface phonon modes is very different from that in a square quantum-well structure. It is found that the electron-interface-phonon scattering rates can be changed remarkably in a graded quantum-well structure compared with those in a square quantum-well structure, which is useful for some device applications.
Quantum Monte Carlo calculations of neutron-alpha scattering.
Nollett, K. M.; Pieper, S. C.; Wiringa, R. B.; Carlson, J.; Hale, G. M.; Physics
2007-07-13
We describe a new method to treat low-energy scattering problems in few-nucleon systems, and we apply it to the five-body case of neutron-alpha scattering. The method allows precise calculations of low-lying resonances and their widths. We find that a good three-nucleon interaction is crucial to obtain an accurate description of neutron-alpha scattering.
Quantum Monte Carlo Calculations of Neutron-{alpha} Scattering
Nollett, Kenneth M.; Pieper, Steven C.; Wiringa, R. B.; Carlson, J.; Hale, G. M.
2007-07-13
We describe a new method to treat low-energy scattering problems in few-nucleon systems, and we apply it to the five-body case of neutron-alpha scattering. The method allows precise calculations of low-lying resonances and their widths. We find that a good three-nucleon interaction is crucial to obtain an accurate description of neutron-alpha scattering.
Light-scattering detection of quantum phases of ultracold atoms in optical lattices
Ye Jinwu; Zhang, J. M.; Liu, W. M.; Zhang Keye; Li Yan; Zhang Weiping
2011-05-15
Ultracold atoms loaded on optical lattices can provide unprecedented experimental systems for the quantum simulations and manipulations of many quantum phases. However, so far, how to detect these quantum phases effectively remains an outstanding challenge. Here, we show that the optical Bragg scattering of cold atoms loaded on optical lattices can be used to detect many quantum phases, which include not only the conventional superfluid and Mott insulating phases, but also other important phases, such as various kinds of charge density wave (CDW), valence bond solid (VBS), CDW supersolid (CDW-SS) and Valence bond supersolid (VB-SS).
Effect of an electric field on electron-interface-phonon scattering in a graded quantum well
NASA Astrophysics Data System (ADS)
Zhu, Jia-Lin; Duan, Wenhui; Gu, Bing-Lin; Wu, Jian
1996-02-01
Within the dielectric continuum model, the effect of an applied longitudinal electric field on electron-interface-phonon scattering is studied for the graded quantum well of Ga 1- xAl xAs with a Ga 0.6Al 0.4As barrier, and compared with that in a staircase-like square quantum well structure. The electron subband and interface phonon modes are calculated using the method of series expansion. The intrasubband and intersubband scattering rates are obtained as functions of the applied electric field, and the influence of the composition gradient of a graded quantum well on the scattering rates is shown. It is found that the variation of the interface-phonon scattering rates with the applied electric field in a graded quantum well structure is significantly different from that in a staircase-like square quantum well structure. However, there is much less difference in the variation of the total scattering rates between the two structures.
NASA Astrophysics Data System (ADS)
Prabhu-Gaunkar, S.; Grayson, M.
2011-03-01
Valley degenerate systems have an extra scattering channel not present in single valley systems, namely inter-valley scattering. To help classify anisotropic inter-valley scattering in degenerate multi-valley systems, such as AlAs quantum wells (QWs), we define a valley scattering primitive unit cell in momentum space which allows one to distinguish purely in-plane momentum scattering from scattering requiring an out-of-plane momentum component. The standard depiction of a 2D Brillouin zone of a quantum confined valley-degenerate system projects all valleys to a single plane and this depiction loses information about the momentum scattering component that was projected out. Because QW confinement potentials are inherently anisotropic, the disorder potential characteristic of quantum confinement can create anisotropic short-wavelength inter- valley scattering potentials favoring in-plane momentum scattering. We demonstrate that the valley scattering cell for AlAs QWs grown along various orientations is particularly useful in identifying relevant scattering vectors. Initial estimates will be shown of the role of strong electron-electron interactions in AlAs QWs on inter-valley scattering parameters such as inter-valley scattering time, probabilities and rates.
Scattering in the Euclidean formulation of relativistic quantum mechanics
NASA Astrophysics Data System (ADS)
Polyzou, Wayne
2013-10-01
Euclidean relativistic quantum mechanics is a formulation of relativistic quantum mechanics based on the Osterwalder-Schrader reconstruction theorem that exploits the logical independence of locality from the rest of the axioms of Euclidean field theory. I discuss the properties of Euclidean Green functions necessary for the existence of Møller wave operators and the construction of these wave operators in this formalism. Supported by the US Department of Energy, Grant - DE-AC02-81ER40038.
Resonances in positron-hydrogen scattering in dense quantum plasmas
Jiang, Zishi; Zhang, Yong-Zhi; Kar, Sabyasachi
2015-05-15
We have investigated the S-wave resonance states in positron-hydrogen system embedded in dense quantum plasmas using Hylleraas-type wave functions within the framework of the stabilization method. The effect of quantum plasmas has been incorporated using the exponential-cosine-screened Coulomb (modified Yukawa-type) potential. Resonance parameters (both position and width) below the Ps n = 2 threshold are reported as functions of plasma screening parameters.
Polarization State of Light Scattered from Quantum Plasmonic Dimer Antennas.
Yang, Longkun; Wang, Hancong; Fang, Yan; Li, Zhipeng
2016-01-26
Plasmonic antennas are able to concentrate and re-emit light in a controllable manner through strong coupling between metallic nanostructures. Only recently has it found that quantum mechanical effects can drastically change the coupling strength as the feature size approaches atomic scales. Here, we present a comprehensive experimental and theoretical study of the evolution of the resonance peak and its polarization state as the dimer-antenna gap narrows to subnanometer scale. We clearly can identify the classical plasmonic regime, a crossover regime where nonlocal screening plays an important role, and the quantum regime where a charge transfer plasmon appears due to interparticle electron tunneling. Moreover, as the gap decreases from tens of to a few nanometers, the bonding dipole mode tends to emit photons with increasing polarizability. When the gap narrows to quantum regime, a significant depolarization of the mode emission is observed due to the reduction of the charge density of coupled quantum plasmons. These results would be beneficial for the understanding of quantum effects on emitting-polarization of nanoantennas and the development of quantum-based photonic nanodevices. PMID:26700823
Exact scattering matrix of graphs in magnetic field and quantum noise
Caudrelier, Vincent; Mintchev, Mihail; Ragoucy, Eric
2014-08-15
We consider arbitrary quantum wire networks modelled by finite, noncompact, connected quantum graphs in the presence of an external magnetic field. We find a general formula for the total scattering matrix of the network in terms of its local scattering properties and its metric structure. This is applied to a quantum ring with N external edges. Connecting the external edges of the ring to heat reservoirs, we study the quantum transport on the graph in ambient magnetic field. We consider two types of dynamics on the ring: the free Schrödinger and the free massless Dirac equations. For each case, a detailed study of the thermal noise is performed analytically. Interestingly enough, in presence of a magnetic field, the standard linear Johnson-Nyquist law for the low temperature behaviour of the thermal noise becomes nonlinear. The precise regime of validity of this effect is discussed and a typical signature of the underlying dynamics is observed.
NASA Astrophysics Data System (ADS)
Ticknor, Christopher; Kendrick, Brian
2016-05-01
We report progress towards including excited vibrational states in quantum scattering calculations of NaK-NaK at ultracold temperatures. We systematically use all pair potentials to build a complete 4 body potential energy surface. We study this 4-body potential and the asymptotic ro-vibrational 2-body basis. This allows for a more complete interaction as two molecules approach each other. We study where and how vibrationally excited states influence the asymptotic 2-body ro-vibrational scattering potentials. This work is an intermediate step in performing the complete scattering calculations as we develop tools to bring together the long range, ultracold 2-body scattering problem and the short range 4-body quantum chemistry problem.
Cavity-Enhanced Light Scattering in Optical Lattices to Probe Atomic Quantum Statistics
Mekhov, Igor B.; Maschler, Christoph; Ritsch, Helmut
2007-03-09
Different quantum states of atoms in optical lattices can be nondestructively monitored by off-resonant collective light scattering into a cavity. Angle resolved measurements of photon number and variance give information about atom-number fluctuations and pair correlations without single-site access. Observation at angles of diffraction minima provides information on quantum fluctuations insensitive to classical noise. For transverse probing, no photon is scattered into a cavity from a Mott insulator phase, while the photon number is proportional to the atom number for a superfluid.
Inelastic microwave photon scattering off a quantum impurity in a Josephson-junction array.
Goldstein, Moshe; Devoret, Michel H; Houzet, Manuel; Glazman, Leonid I
2013-01-01
Quantum fluctuations in an anharmonic superconducting circuit enable frequency conversion of individual incoming photons. This effect, linear in the photon beam intensity, leads to ramifications for the standard input-output circuit theory. We consider an extreme case of anharmonicity in which photons scatter off a small set of weak links within a Josephson junction array. We show that this quantum impurity displays Kondo physics and evaluate the elastic and inelastic photon scattering cross sections. These cross sections reveal many-body properties of the Kondo problem that are hard to access in its traditional fermionic version. PMID:23383827
Stimulated Brillouin scattering of laser radiation in a piezoelectric semiconductor: Quantum effect
Uzma, Ch.; Zeba, I.; Shah, H. A.; Salimullah, M.
2009-01-01
Using quantum-hydrodynamic model, the phenomenon of the stimulated Brillouin scattering of a laser radiation in an unmagnetized piezoelectric semiconductor has been examined in detail. It is noticed that the Bohm potential in the electron dynamics of the semiconductor plasma enhances drastically the growth rate of the stimulated Brillouin scattering at higher values of the electron number density of the semiconductor plasma and the wave number of the electron-acoustic wave in the semiconductor.
Resonances in Coupled πK-ηK Scattering from Quantum Chromodynamics
Dudek, Jozef J.; Edwards, Robert G.; Thomas, Christopher E.; Wilson, David J.
2014-10-01
Using first-principles calculation within Quantum Chromodynamics, we are able to reproduce the pattern of experimental strange resonances which appear as complex singularities within coupled πK, ηK scattering amplitudes. We make use of numerical computation within the lattice discretized approach to QCD, extracting the energy dependence of scattering amplitudes through their relation- ship to the discrete spectrum of the theory in a finite-volume, which we map out in unprecedented detail.
NASA Astrophysics Data System (ADS)
Chatzidimitriou-Dreismann, C. A.; Dreismann, A.
2014-10-01
The interactions between physical systems generally lead to the formation of correlations. In this paper we consider the phenomena of entanglement and "quantumness of correlations", such as quantum discord, with particular emphasis on their energetic consequences for the participating systems. We describe a number of theoretical models that are commonly employed in this context, highlighting the general character of one of their most intriguing results: In contradiction to conventional expectations, erasure (decay, consumption) of quantum correlations may be a source of work, i.e. may have "negative energetic costs". We report experimental evidence of this surprising effect obtained within the framework of an elementary scattering experiment, namely ultrafast neutron Compton scattering from normal-state liquid 4He. The general theory of quantumness of correlations provides a natural way of interpreting the reported results, which stand in blatant contrast to the conventional theory of scattering, where neutron-atom-environment quantum correlations and decoherence play no role. Moreover, they provide a new operational meaning of discord and related measures of quantumness.
Light scattering from ultracold atoms in optical lattices as an optical probe of quantum statistics
Mekhov, Igor B.; Maschler, Christoph; Ritsch, Helmut
2007-11-15
We study off-resonant collective light scattering from ultracold atoms trapped in an optical lattice. Scattering from different atomic quantum states creates different quantum states of the scattered light, which can be distinguished by measurements of the spatial intensity distribution, quadrature variances, photon statistics, or spectral measurements. In particular, angle-resolved intensity measurements reflect global statistics of atoms (total number of radiating atoms) as well as local statistical quantities (single-site statistics even without optical access to a single site) and pair correlations between different sites. As a striking example we consider scattering from transversally illuminated atoms into an optical cavity mode. For the Mott-insulator state, similar to classical diffraction, the number of photons scattered into a cavity is zero due to destructive interference, while for the superfluid state it is nonzero and proportional to the number of atoms. Moreover, we demonstrate that light scattering into a standing-wave cavity has a nontrivial angle dependence, including the appearance of narrow features at angles, where classical diffraction predicts zero. The measurement procedure corresponds to the quantum nondemolition measurement of various atomic variables by observing light.
NASA Astrophysics Data System (ADS)
Altmann, Eduardo G.; Portela, Jefferson S. E.; Tél, Tamás
2015-02-01
We investigate chaotic dynamical systems for which the intensity of trajectories might grow unlimited in time. We show that i) the intensity grows exponentially in time and is distributed spatially according to a fractal measure with an information dimension smaller than that of the phase space, ii) such exploding cases can be described by an operator formalism similar to the one applied to chaotic systems with absorption (decaying intensities), but iii) the invariant quantities characterizing explosion and absorption are typically not directly related to each other, e.g., the decay rate and fractal dimensions of absorbing maps typically differ from the ones computed in the corresponding inverse (exploding) maps. We illustrate our general results through numerical simulation in the cardioid billiard mimicking a lasing optical cavity, and through analytical calculations in the baker map.
Dirac quantum cellular automaton in one dimension: Zitterbewegung and scattering from potential
NASA Astrophysics Data System (ADS)
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Tosini, Alessandro
2013-09-01
We study the dynamical behavior of a quantum cellular automaton which reproduces the Dirac dynamics in the limit of small wave vectors and masses. We present analytical evaluations along with computer simulations, showing that the automaton exhibits typical Dirac dynamical features, such as the Zitterbewegung and, considering the scattering from potential, the so-called Klein paradox. The motivation is to show concretely how pure processing of quantum information can lead to particle mechanics as an emergent feature, an issue that has been the focus of solid-state, optical, and atomic-physics quantum simulators.
NASA Astrophysics Data System (ADS)
Casati, Giulio; Chirikov, Boris
2006-11-01
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.
NASA Astrophysics Data System (ADS)
Casati, Giulio; Chirikov, Boris
1995-04-01
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.
Interference Swapping in Scattering from a Nonlocal Quantum Target
Rohrlich, Daniel; Neiman, Yakov; Japha, Yonathan; Folman, Ron
2006-05-05
We describe a new and distinctive interferometry in which a probe particle scatters off a superposition of locations of a single free target particle. Probe particles scattering off a single free 'mirror' (in one dimension) or a single free 'slit' (in two dimensions) can 'swap' interference with the superposed target states. The condition for interference is loss of orthogonality of the target states and reduces, in simple examples, to transfer of orthogonality from target to probe states. We analyze experimental parameters and conditions necessary for interference to be observed.
Stimulated scattering of electromagnetic waves carrying orbital angular momentum in quantum plasmas.
Shukla, P K; Eliasson, B; Stenflo, L
2012-07-01
We investigate stimulated scattering instabilities of coherent circularly polarized electromagnetic (CPEM) waves carrying orbital angular momentum (OAM) in dense quantum plasmas with degenerate electrons and nondegenerate ions. For this purpose, we employ the coupled equations for the CPEM wave vector potential and the driven (by the ponderomotive force of the CPEM waves) equations for the electron and ion plasma oscillations. The electrons are significantly affected by the quantum forces (viz., the quantum statistical pressure, the quantum Bohm potential, as well as the electron exchange and electron correlations due to electron spin), which are included in the framework of the quantum hydrodynamical description of the electrons. Furthermore, our investigation of the stimulated Brillouin instability of coherent CPEM waves uses the generalized ion momentum equation that includes strong ion coupling effects. The nonlinear equations for the coupled CPEM and quantum plasma waves are then analyzed to obtain nonlinear dispersion relations which exhibit stimulated Raman, stimulated Brillouin, and modulational instabilities of CPEM waves carrying OAM. The present results are useful for understanding the origin of scattered light off low-frequency density fluctuations in high-energy density plasmas where quantum effects are eminent. PMID:23005546
Dynamical fractional chaotic inflation
NASA Astrophysics Data System (ADS)
Harigaya, Keisuke; Ibe, Masahiro; Schmitz, Kai; Yanagida, Tsutomu T.
2014-12-01
Chaotic inflation based on a simple monomial scalar potential, V (ϕ )∝ϕp, is an attractive large-field model of inflation capable of generating a sizable tensor-to-scalar ratio r . Therefore, assuming that future cosmic microwave background observations will confirm the large r value reported by BICEP2, it is important to determine what kind of dynamical mechanism could possibly endow the inflaton field with such a simple effective potential. In this paper, we answer this question in the context of field theory, i.e. in the framework of dynamical chaotic inflation, where strongly interacting supersymmetric gauge dynamics around the scale of grand unification dynamically generate a fractional power-law potential via the quantum effect of dimensional transmutation. In constructing explicit models, we significantly extend our previous work, as we now consider a large variety of possible underlying gauge dynamics and relax our conditions on the field content of the model. This allows us to realize almost arbitrary rational values for the power p in the inflaton potential. The present paper may hence be regarded as a first step toward a more complete theory of dynamical chaotic inflation.
Rotationally Inelastic Scattering of Quantum-State-Selected ND3 with Ar.
Tkáč, Ondřej; Saha, Ashim K; Loreau, Jérôme; Parker, David H; van der Avoird, Ad; Orr-Ewing, Andrew J
2015-06-11
Rotationally inelastic scattering of ND3 with Ar is studied at mean collision energies of 410 and 310 cm(–1). In the experimental component of the study, ND3 molecules are prepared by supersonic expansion and subsequent hexapole state selection in the ground electronic and vibrational levels and in the jk(±) = 1(1) rotational level. A beam of state-selected ND3 molecules is crossed with a beam of Ar, and scattered ND3 molecules are detected in single final j′k′(±) quantum states using resonance enhanced multiphoton ionization spectroscopy. State-to-state differential cross sections for rotational-level changing collisions are obtained by velocity map imaging. The experimental measurements are compared with close-coupling quantum-mechanical scattering calculations performed using an ab initio potential energy surface. The computed DCSs agree well with the experimental measurements, confirming the high quality of the potential energy surface. The angular distributions are dominated by forward scattering for all measured final rotational and vibrational inversion symmetry states. This outcome is in contrast to our recent results for inelastic scattering of ND3 with He, where we observed significant amount of sideways and backward scattering for some final rotational levels of ND3. The differences between He and Ar collision partners are explained by differences in the potential energy surfaces that govern the scattering dynamics. PMID:25532415
How quantum impenetrability affects Aharonov-Bohm scattering?
NASA Astrophysics Data System (ADS)
Afanasev, G. N.; Shilov, V. M.
It is shown that different forms of quantum impenetrability lead to different physical consequences. This should be kept in mind in analyzing experimental data. The relativistic impenetrability conditions are considered and the corresponding relativistic Aharonov-Bohm cross-sections are obtained. The possibility of the AB effect occurrence in simply-connected space regions is discussed.
NASA Astrophysics Data System (ADS)
Mani, Arjun; Benjamin, Colin
2016-04-01
On the surface of 2D topological insulators, 1D quantum spin Hall (QSH) edge modes occur with Dirac-like dispersion. Unlike quantum Hall (QH) edge modes, which occur at high magnetic fields in 2D electron gases, the occurrence of QSH edge modes is due to spin-orbit scattering in the bulk of the material. These QSH edge modes are spin-dependent, and chiral-opposite spins move in opposing directions. Electronic spin has a larger decoherence and relaxation time than charge. In view of this, it is expected that QSH edge modes will be more robust to disorder and inelastic scattering than QH edge modes, which are charge-dependent and spin-unpolarized. However, we notice no such advantage accrues in QSH edge modes when subjected to the same degree of contact disorder and/or inelastic scattering in similar setups as QH edge modes. In fact we observe that QSH edge modes are more susceptible to inelastic scattering and contact disorder than QH edge modes. Furthermore, while a single disordered contact has no effect on QH edge modes, it leads to a finite charge Hall current in the case of QSH edge modes, and thus a vanishing of the pure QSH effect. For more than a single disordered contact while QH states continue to remain immune to disorder, QSH edge modes become more susceptible—the Hall resistance for the QSH effect changes sign with increasing disorder. In the case of many disordered contacts with inelastic scattering included, while quantization of Hall edge modes holds, for QSH edge modes a finite charge Hall current still flows. For QSH edge modes in the inelastic scattering regime we distinguish between two cases: with spin-flip and without spin-flip scattering. Finally, while asymmetry in sample geometry can have a deleterious effect in the QSH case, it has no impact in the QH case.
Solution of coupled integral equations for quantum scattering in the presence of complex potentials
Franz, Jan
2015-01-15
In this paper, we present a method to compute solutions of coupled integral equations for quantum scattering problems in the presence of a complex potential. We show how the elastic and absorption cross sections can be obtained from the numerical solution of these equations in the asymptotic region at large radial distances.
Quantum superposition principle and gravitational collapse: Scattering times for spherical shells
Ambrus, M.; Hajicek, P.
2005-09-15
A quantum theory of spherically symmetric thin shells of null dust and their gravitational field is studied. In Nucl. Phys. B603, 555 (2001), it has been shown how superpositions of quantum states with different geometries can lead to a solution of the singularity problem and black hole information paradox: the shells bounce and re-expand and the evolution is unitary. The corresponding scattering times will be defined in the present paper. To this aim, a spherical mirror of radius R{sub m} is introduced. The classical formula for scattering times of the shell reflected from the mirror is extended to quantum theory. The scattering times and their spreads are calculated. They have a regular limit for R{sub m}{yields}0 and they reveal a resonance at E{sub m}=c{sup 4}R{sub m}/2G. Except for the resonance, they are roughly of the order of the time the light needs to cross the flat space distance between the observer and the mirror. Some ideas are discussed of how the construction of the quantum theory could be changed so that the scattering times become considerably longer.
Dissipation in deforming chaotic billiards
NASA Astrophysics Data System (ADS)
Barnett, Alexander Harvey
Chaotic billiards (hard-walled cavities) in two or more dimensions are paradigm systems in the fields of classical and quantum chaos. We study the dissipation (irreversible heating) rate in such billiard systems due to general shape deformations which are periodic in time. We are motivated by older studies of one-body nuclear dissipation and by anticipated mesoscopic applications. We review the classical and quantum linear response theories of dissipation rate and demonstrate their correspondence in the semiclassical limit. In both pictures, heating is a result of stochastic energy spreading. The heating rate can be expressed as a frequency-dependent friction coefficient μ(ω), which depends on billiard shape and deformation choice. We show that there is a special class of deformations for which μ vanishes as like a power law in the small- ω limit. Namely, for deformations which cause translations and dilations μ ~ ω4 whereas for those which cause rotations μ ~ ω2. This contrasts the generic case for which μ ~ ω4 We show how a systematic treatment of this special class leads to an improved version of the `wall formula' estimate for μ(0). We show that the special nature of dilation (a new result) is semiclassically equivalent to a quasi- orthogonality relation between the (undeformed) billiard quantum eigenstates on the boundary. This quasi- orthogonality forms the heart of a `scaling method' for the numerical calculation of quantum eigenstates, invented recently by Vergini and Saraceno. The scaling method is orders of magnitude more efficient than any other known billiard quantization method, however an adequate explanation for its success has been lacking until now. We explain the scaling method, its errors, and applications. We also present improvements to Heller's plane wave method. Two smaller projects conclude the thesis. Firstly, we give a new formalism for quantum point contact (QPC) conductance in terms of scattering cross-section in the half
Tkach, N. V. Seti, Ju.
2009-03-15
In the effective mass approximation in the model of rectangular potentials, the scattering cross section of electrons in an open spherical quantum dot is calculated for the first time. It is shown that, for such a nanosystem with a barrier of several monolayers, the experimental measurements of the scattering cross section allow adequate identification of the resonance energies and the widths of resonance states in the low-energy region of the quasi-stationary electron spectrum. It is also shown that, for an open spherical quantum dot with a low-strength potential barrier, the adequate spectral parameters of the quasi-stationary spectrum are the generalized resonance energies and widths determined via the probability of an electron being inside the quantum dot.
Universal quantum computation by scattering in the Fermi-Hubbard model
NASA Astrophysics Data System (ADS)
Bao, Ning; Hayden, Patrick; Salton, Grant; Thomas, Nathaniel
2015-09-01
The Hubbard model may be the simplest model of particles interacting on a lattice, but simulation of its dynamics remains beyond the reach of current numerical methods. In this article, we show that general quantum computations can be encoded into the physics of wave packets propagating through a planar graph, with scattering interactions governed by the fermionic Hubbard model. Therefore, simulating the model on planar graphs is as hard as simulating quantum computation. We give two different arguments, demonstrating that the simulation is difficult both for wave packets prepared as excitations of the fermionic vacuum, and for hole wave packets at filling fraction one-half in the limit of strong coupling. In the latter case, which is described by the t-J model, there is only reflection and no transmission in the scattering events, as would be the case for classical hard spheres. In that sense, the construction provides a quantum mechanical analog of the Fredkin-Toffoli billiard ball computer.
Implementing quantum gates through scattering between a static and a flying qubit
Cordourier-Maruri, G.; Coss, R. de; Ciccarello, F.; Zarcone, M.; Omar, Y.; Bose, S.
2010-11-15
We investigate whether a two-qubit quantum gate can be implemented in a scattering process involving a flying and a static qubit. To this end, we focus on a paradigmatic setup made out of a mobile particle and a quantum impurity, whose respective spin degrees of freedom couple to each other during a one-dimensional scattering process. Once a condition for the occurrence of quantum gates is derived in terms of spin-dependent transmission coefficients, we show that this can be actually fulfilled through the insertion of an additional narrow potential barrier. An interesting observation is that under resonance conditions this procedure enables a gate only for isotropic Heisenberg (exchange) interactions and fails for an XY interaction. We show the existence of parameter regimes for which gates able to establish a maximum amount of entanglement can be implemented. The gates are found to be robust to variations of the optimal parameters.
NASA Astrophysics Data System (ADS)
Sassoli de Bianchi, Massimiliano
2012-04-01
We present a step by step introduction to the notion of time-delay in classical and quantum mechanics, with the aim of clarifying its foundation at a conceptual level. In doing so, we motivate the introduction of the concepts of "fuzzy" and "free-flight" sojourn times that we use to provide the most general possible definition for the quantum time-delay, valid for simple and multichannel scattering systems, with or without conditions on the observation of the scattering particle, and for incoming wave packets whose energy can be smeared out or sharply peaked (fixed energy). We conclude our conceptual analysis by presenting what we think is the right interpretation of the concepts of sojourn and delay times in quantum mechanics, explaining why, in ultimate analysis, they should not be called "times."
Quantum statistics of Raman scattering model with Stokes mode generation
NASA Technical Reports Server (NTRS)
Tanatar, Bilal; Shumovsky, Alexander S.
1994-01-01
The model describing three coupled quantum oscillators with decay of Rayleigh mode into the Stokes and vibration (phonon) modes is examined. Due to the Manley-Rowe relations the problem of exact eigenvalues and eigenstates is reduced to the calculation of new orthogonal polynomials defined both by the difference and differential equations. The quantum statistical properties are examined in the case when initially: the Stokes mode is in the vacuum state; the Rayleigh mode is in the number state; and the vibration mode is in the number of or squeezed states. The collapses and revivals are obtained for different initial conditions as well as the change in time the sub-Poisson distribution by the super-Poisson distribution and vice versa.
Non-Perturbative, Unitary Quantum-Particle Scattering Amplitudes from Three-Particle Equations
Lindesay, James V
2002-03-19
We here use our non-perturbative, cluster decomposable relativistic scattering formalism to calculate photon-spinor scattering, including the related particle-antiparticle annihilation amplitude. We start from a three-body system in which the unitary pair interactions contain the kinematic possibility of single quantum exchange and the symmetry properties needed to identify and substitute antiparticles for particles. We extract from it unitary two-particle amplitude for quantum-particle scattering. We verify that we have done this correctly by showing that our calculated photon-spinor amplitude reduces in the weak coupling limit to the usual lowest order, manifestly covariant (QED) result with the correct normalization. That we are able to successfully do this directly demonstrates that renormalizability need not be a fundamental requirement for all physically viable models.
A Model of Resonance Scattering on Curved Quantum Wires
NASA Astrophysics Data System (ADS)
Exner, Pavel
A model of electron motion in a curved quantum wire of a finite length 2D attached to a pair of macroscopic electrodes is studied. Regarding the problem as a two-dimensional one, we model the electrodes as halfplanes and the quantum wire as a line segment joining them; it supports a potential which is a combination of a constant transversal-mode energy and an attractive curvature-induced term. We show that the bound states which may be present at an infinite quantum wire turn into resonances and that spectral concentration is valid as D .Translated AbstractEin Modell der Resonanzstreuung auf gekrümmten, dünnen DrähtenDas Modell einer Elektronenbewegung in einem gekrümmten, ultradünnen Draht der Länge 2D, der zwei makroskopische Elektroden verbindet, wird untersucht. Das Modell als zweidimensional betrachtend, nehmen wir die Elektroden als Halbebenen und den Draht als verbindendes Liniensegment. Das Potential ist eine Kombination aus konstanter Transversalmoden-energie und einem anziehenden, von der Krümmung hervorgerufenen Term. Wir zeigen, daß der gebundene Zustand, der im unendlich langen Draht auftreten kann, in Resonanzen übergeht, und die Spektraldichte für D gilt.
NASA Astrophysics Data System (ADS)
Huang, Danhong; Gumbs, Godfrey
2010-05-01
When impurity and phonon scattering coexist, the Boltzmann equation has been solved accurately for nonlinear electron transport in a quantum wire. Based on the calculated nonequilibrium distribution of electrons in momentum space, the scattering effects on both the nondifferential (for a fixed dc field) and differential (for a fixed temperature) mobilities of electrons as functions of temperature and dc field have been demonstrated. The nondifferential mobility of electrons is switched from a linearly increasing function of temperature to a paraboliclike temperature dependence as the quantum wire is tuned from an impurity-dominated system to a phonon-dominated one, as described by Fang et al. [Phys. Rev. B 78, 205403 (2008)]. In addition, a maximum has been obtained in the dc field dependence of the differential mobility of electrons. The low-field differential mobility is dominated by the impurity scattering, whereas the high-field differential mobility is limited by the phonon scattering as described by Hauser et al. [Semicond. Sci. Technol. 9, 951 (1994)]. Once a quantum wire is dominated by quasielastic scattering, the peak of the momentum-space distribution function becomes sharpened and both tails of the equilibrium electron distribution centered at the Fermi edges are raised by the dc field after a redistribution of the electrons is fulfilled in a symmetric way in the low-field regime. If a quantum wire is dominated by inelastic scattering, on the other hand, the peak of the momentum-space distribution function is unchanged while both shoulders centered at the Fermi edges shift leftward correspondingly with increasing dc field through an asymmetric redistribution of the electrons even in low-field regime as described by Wirner et al. [Phys. Rev. Lett. 70, 2609 (1993)].
Silver, R.N.; Clark, J.W.
1988-01-01
The impulse approximation (IA) predicts that momentum distributions, n/sub k/, in many-body systems should be measurable by inclusive quasielastic scattering at high energy and momentum (w,Q) transfer. The observations that the cross section appears to satisfy ''Y-scaling'' (i.e., is a function not of both w and Q of a single variable, Y) is usually taken as a signature of the IA. In nuclear physics, inelastic electron scattering at GeV energies should reveal the high momentum components of the nuclear wave function. In quantum fluids, neutron scattering at hundreds of MeV energies should measure the Bose condensate in superfluid /sup 4/He and the Fermi surface discontinuity and depletion of the Fermi sea in /sup 3/He. In molecular and condensed matter systems, X-ray Compton scattering at keV energies reveals electronic n/sub k/. Such experiments test many-body wave functions calculated by methods such as Green Function and Path Integral Monte Carlo, and Fermi Hypernetted Chain. However, an outstanding issue has been the corrections to the IA due to the scattering of the recoiling particle from neighboring particles, which are termed ''final state effects'' (FSE). The FSE should be especially important in nuclei and quantum fluids where the potentials have steeply repulsive cores. While there have been a variety of theories proposed for FSE, until now none has been adequately tested by experiment. Recently, the ''hard core perturbation theory'' (HCPT) for FSE in quantum fluids by Silver has been successfully compared to new neutron scattering measurements on /sup 4/He by P. E. Sokol and colleagues. In this paper, we shall discuss the lessons of this success for the extraction of n/sub k/ in nuclei by inclusive ''quasielastic electron-nucleus scattering'' (QENS). 19 refs., 12 figs.
Grazing-incidence small-angle X-ray scattering: application to the study of quantum dot lattices
Buljan, Maja Radić, Nikola; Bernstorff, Sigrid; Dražić, Goran; Bogdanović-Radović, Iva; Holý, Václav
2012-01-01
The modelling of grazing-incidence small-angle X-ray scattering (GISAXS) from three-dimensional quantum dot lattices is described. The ordering of quantum dots in three-dimensional quantum dot lattices is investigated by grazing-incidence small-angle X-ray scattering (GISAXS). Theoretical models describing GISAXS intensity distributions for three general classes of lattices of quantum dots are proposed. The classes differ in the type of disorder of the positions of the quantum dots. The models enable full structure determination, including lattice type, lattice parameters, the type and degree of disorder in the quantum dot positions and the distributions of the quantum dot sizes. Applications of the developed models are demonstrated using experimentally measured data from several types of quantum dot lattices formed by a self-assembly process.
Temporal mode sorting using dual-stage quantum frequency conversion by asymmetric Bragg scattering.
Christensen, Jesper B; Reddy, Dileep V; McKinstrie, C J; Rottwitt, K; Raymer, M G
2015-09-01
The temporal shape of single photons provides a high-dimensional basis of temporal modes, and can therefore support quantum computing schemes that go beyond the qubit. However, the lack of linear optical components to act as quantum gates has made it challenging to efficiently address specific temporal-mode components from an arbitrary superposition. Recent progress towards realizing such a "quantum pulse gate," has been proposed using nonlinear optical signal processing to add coherently the effect of multiple stages of quantum frequency conversion. This scheme, called temporal-mode interferometry [D. V. Reddy, Phys. Rev. A 91, 012323 (2015)], has been shown in the case of three-wave mixing to promise near-unity mode-sorting efficiency. Here we demonstrate that it is also possible to achieve high mode-sorting efficiency using four-wave mixing, if one pump pulse is long and the other short - a configuration we call asymmetrically-pumped Bragg scattering. PMID:26368430
Fast GPU-based calculations in few-body quantum scattering
NASA Astrophysics Data System (ADS)
Pomerantsev, V. N.; Kukulin, V. I.; Rubtsova, O. A.; Sakhiev, S. K.
2016-07-01
A principally novel approach towards solving the few-particle (many-dimensional) quantum scattering problems is described. The approach is based on a complete discretization of few-particle continuum and usage of massively parallel computations of integral kernels for scattering equations by means of GPU. The discretization for continuous spectrum of few-particle Hamiltonian is realized with a projection of all scattering operators and wave functions onto the stationary wave-packet basis. Such projection procedure leads to a replacement of singular multidimensional integral equations with linear matrix ones having finite matrix elements. Different aspects of the employment of multithread GPU computing for fast calculation of the matrix kernel of the equation are studied in detail. As a result, the fully realistic three-body scattering problem above the break-up threshold is solved on an ordinary desktop PC with GPU for a rather small computational time.
Correlating scattering times with the strength of the ν=5/2 fractional quantum Hall state
NASA Astrophysics Data System (ADS)
Mondal, Sumit; Watson, John; Gardner, Geoffrey; Samkharadze, Nodar; Csathy, Gabor; Manfra, Michael
2012-02-01
There is widespread interest in the fractional quantum Hall effect at ν=5/2. Theory predicts that the state at ν=5/2 may possess non-Abelian braiding statistics. Experimental interrogation remains difficult due to the fragility of the excitation gaps requiring both high quality samples and examination at low temperatures. Mounting evidence suggests that the strength of the most fragile fractional quantum Hall states in the 2^nd Landau level including ν=5/2 are poorly correlated with the scattering time extracted from zero-field mobility measurements at higher temperatures. It is also unclear if the quantum scattering time derived from analysis of the low-field Shubnikov de-Haas oscillations provides any additional information relevant to prediction of the strengths of the observed fractional states. We report on a systematic attempt to correlate the T=0.3K behavior of the mobility lifetime, quantum scattering time, and an effective high field mobility lifetime evaluated at ν=5/2 with the measured activation gap. We will present results from a number of heterostructure designs over a wide span of zero-field mobility ranging from ˜10x10^6cm^2/Vs to greater than 20x10^6cm^2/Vs.
A simple method for finding the scattering coefficients of quantum graphs
Cottrell, Seth S.
2015-09-15
Quantum walks are roughly analogous to classical random walks, and similar to classical walks they have been used to find new (quantum) algorithms. When studying the behavior of large graphs or combinations of graphs, it is useful to find the response of a subgraph to signals of different frequencies. In doing so, we can replace an entire subgraph with a single vertex with variable scattering coefficients. In this paper, a simple technique for quickly finding the scattering coefficients of any discrete-time quantum graph will be presented. These scattering coefficients can be expressed entirely in terms of the characteristic polynomial of the graph’s time step operator. This is a marked improvement over previous techniques which have traditionally required finding eigenstates for a given eigenvalue, which is far more computationally costly. With the scattering coefficients we can easily derive the “impulse response” which is the key to predicting the response of a graph to any signal. This gives us a powerful set of tools for rapidly understanding the behavior of graphs or for reducing a large graph into its constituent subgraphs regardless of how they are connected.
Vibronic Raman Scattering at the Quantum Limit of Plasmons
El-Khoury, Patrick Z.; Hess, Wayne P.
2014-07-09
We record sequences of Raman spectra at a plasmonic junction formed by a gold AFM tip in contact with a silver surface coated with 4,4’-dimercaptostilbene (DMS). A 2D correlation analysis of the recorded trajectories reveals that the observable vibrational states can be divided into sub-sets. The first set comprises the totally symmetric vibrations of DMS (ag) that are neither correlated with each other nor to the fluctuating background, which is assigned to the signature of charge transfer plasmons tunneling through DMS. The second set consists of bu vibrations, which are correlated both with each other and with the continuum. Our findings are rationalized on the basis of the charge-transfer theory of Raman scattering, and illustrate how the tunneling plasmons modulate the vibronic coupling term from which the intensities of the bu states are derived.
Ranzani, Leonardo; Spietz, Lafe; Aumentado, Jose
2013-07-08
In this work, we characterize the 2-port scattering parameters of a superconducting quantum interference device amplifier at {approx}20 mK over several gigahertz of bandwidth. The measurement reference plane is positioned on a 6.25 {Omega} microstrip line situated directly at the input and output of the device by means of a thru-reflect-line cryogenic calibration procedure. From the scattering parameters, we derive the device available power gain, isolation, and input impedance over the 2-8 GHz range. This measurement methodology provides a path towards designing wide-band matching circuits for low impedance superconducting amplifiers operating at dilution refrigerator temperatures.
NASA Astrophysics Data System (ADS)
Punegov, V. I.; Sivkov, D. V.
2015-03-01
Two independent approaches to calculate the angular distribution of X-ray diffusion scattering from a crystalline medium with spheroidal quantum dots (QDs) have been proposed. The first method is based on the analytical solution involving the multipole expansion of elastic strain fields beyond QDs. The second approach is based on calculations of atomic displacements near QDs by the Green's function method. An analysis of the diffuse scattering intensity distribution in the reciprocal space within these two approaches shows that both methods yield similar results for the chosen models of QD spatial distribution.
Punegov, V. I. Sivkov, D. V.
2015-03-15
Two independent approaches to calculate the angular distribution of X-ray diffusion scattering from a crystalline medium with spheroidal quantum dots (QDs) have been proposed. The first method is based on the analytical solution involving the multipole expansion of elastic strain fields beyond QDs. The second approach is based on calculations of atomic displacements near QDs by the Green’s function method. An analysis of the diffuse scattering intensity distribution in the reciprocal space within these two approaches shows that both methods yield similar results for the chosen models of QD spatial distribution.
Two-dimensional Coulomb scattering of a quantum particle: Wave functions and Green's functions
NASA Astrophysics Data System (ADS)
Pupyshev, V. V.
2016-02-01
We solve the problem of the propagation of a charged quantum particle in a two-dimensional plane embedded in the three-dimensional coordinate space. We consider scattering of this particle by a stable Coulomb center situated in the same plane. We study the wave function of this particle, its Green's function, and all radial components of these functions. We derive uniform majorant bounds on absolute values of these functions and find the wave function representation in terms of regular radial Coulomb functions and the scattering amplitude representation via partial phases. We obtain integral representations of the Greens's function and all its radial components.
Quantum Mechanical Description of Raman Scattering from Molecules in Plasmonic Cavities.
Schmidt, Mikolaj K; Esteban, Ruben; González-Tudela, Alejandro; Giedke, Geza; Aizpurua, Javier
2016-06-28
Plasmon-enhanced Raman scattering can push single-molecule vibrational spectroscopy beyond a regime addressable by classical electrodynamics. We employ a quantum electrodynamics (QED) description of the coherent interaction of plasmons and molecular vibrations that reveal the emergence of nonlinearities in the inelastic response of the system. For realistic situations, we predict the onset of phonon-stimulated Raman scattering and a counterintuitive dependence of the anti-Stokes emission on the frequency of excitation. We further show that this QED framework opens a venue to analyze the correlations of photons emitted from a plasmonic cavity. PMID:27203727
Quantum effects in the scattering of argon from 2H-W(100)
Schweizer, E. K.; Rettner, C. T.
1989-06-26
Diffraction has been observed in the scattering of Ar from a 2H-W(100) surface. Results are found to be consistent with an effective surface corrugation amplitude of about 0.05 A, which is similar to values obtained for He and Ne diffraction from this surface. The temperature dependence yields a surface Debye temperature of /similar to/400 K. We also find that the shape and behavior of surface scattering rainbows observed in this system are best accounted for by a quantum mechanical treatment of the Ar-surface interaction.
Dong, Jianping
2014-03-15
The 2D space-fractional Schrödinger equation in the time-independent and time-dependent cases for the scattering problems in the fractional quantum mechanics is studied. We define the Green's functions for the two cases and give the mathematical expression of them in infinite series form and in terms of some special functions. The asymptotic formulas of the Green's functions are also given, and applied to get the approximate wave functions for the fractional quantum scattering problems. These results contain those in the standard (integer) quantum mechanics as special cases, and can be applied to study the complex quantum systems.
Grebogi, C.; Yorke, J.A.
1991-12-01
This report discusses the following topics: controlling chaotic dynamical systems; embedding of experimental data; effect of noise on critical exponents of crises; transition to chaotic scattering; and distribution of floaters on a fluid surface. (LSP)
NASA Astrophysics Data System (ADS)
Laroche, C.; Labbé, R.; Pétrélis, F.; Fauve, S.
2012-02-01
We show that electric motors and dynamos can be used to illustrate most elementary instabilities or bifurcations discussed in courses on nonlinear oscillators and dynamical systems. These examples are easier to understand and display a richer behavior than the ones commonly used from mechanics, electronics, hydrodynamics, lasers, chemical reactions, and population dynamics. In particular, an electric motor driven by a dynamo can display stationary, Hopf, and codimension-two bifurcations by tuning the driving speed of the dynamo and the electric current in the stator of the electric motor. When the dynamo is driven at constant torque instead of constant rotation rate, chaotic reversals of the generated current and of the angular rotation of the motor are observed. Simple deterministic models are presented which capture the observed dynamical regimes.
Rowland, Brad A; Wyatt, Robert E
2007-10-28
One of the major obstacles in employing complex-valued trajectory methods for quantum barrier scattering calculations is the search for isochrones. In this study, complex-valued derivative propagation method trajectories in the arbitrary Lagrangian-Eulerian frame are employed to solve the complex Hamilton-Jacobi equation for quantum barrier scattering problems employing constant velocity trajectories moving along rectilinear paths whose initial points can be in the complex plane or even along the real axis. It is shown that this effectively removes the need for isochrones for barrier transmission problems. Model problems tested include the Eckart, Gaussian, and metastable quadratic+cubic potentials over a variety of wave packet energies. For comparison, the "exact" solution is computed from the time-dependent Schrodinger equation via pseudospectral methods. PMID:17979316
NASA Astrophysics Data System (ADS)
Bauke, Heiko; Klaiber, Michael; Yakaboylu, Enderalp; Hatsagortsyan, Karen Z.; Ahrens, Sven; Müller, Carsten; Keitel, Christoph H.
2013-05-01
Computational methods are indispensable to study the quantum dynamics of relativistic light-matter interactions in parameter regimes where analytical methods become inapplicable. We present numerical methods for solving the time-dependent Dirac equation and the time-dependent Klein-Gordon equation and their implementation on high performance graphics cards. These methods allow us to study tunneling from hydrogen-like highly charged ions in strong laser fields and Kapitza-Dirac scattering in the relativistic regime.
NASA Astrophysics Data System (ADS)
Anders, Frithjof B.; Schmitt, Sebastian
2010-04-01
Scattering states fulfill the correct boundary conditions of a current carrying open quantum system. Discretizing the energy continuum of these states allows for employing Wilson's numerical renormalization group approach without violating the boundary conditions by using a finite size system. We evolve the analytically known steady-state density operator for a non-interacting quantum-system at finite bias to the full interacting problem by the time-dependent numerical renormalization group after switching on the local charging energy. Using a newly developed algorithm for steady-state nonequilibrium Green functions, we can calculate the current I as function of bias voltage V for arbitrary temperature and magnetic field. A comparison with second-order and GW Kadanoff-Baym-Keldysh results shows excellent agreement for weak interaction strength U.
Spectra in the chaotic region: A quantum analysis of the photodissociation of H/sup +//sub 3/
Gomez Llorente, J.M.; Zakrzewski, J.; Taylor, H.S.; Kulander, K.C.
1988-11-01
A quantum theory of periodic orbit based resonances is presented and applied to the photodissociation of highly excited H/sup +//sub 3/. Ab initio stabilization computations are performed to show that periodic orbits are the origin of stable roots producing scars along the orbits in the system's wave functions. Spacings and widths of the resonances are in satisfactory agreement with the experiment and verify the mechanism proposed by Gomez and Pollak. The validity and utility of the PO based resonance theory to study the dynamics of highly excited systems is demonstrated.
Bouten, Luc; Stockton, John; Sarma, Gopal; Mabuchi, Hideo
2007-05-15
We propose a model, based on a quantum stochastic differential equation (QSDE), to describe the scattering of polarized laser light by an atomic gas. The gauge terms in the QSDE account for the direct scattering of the laser light into different field channels. Once the model has been set, we can rigorously derive quantum filtering equations for balanced polarimetry and homodyne detection experiments, study the statistics of output processes, and investigate a strong driving, weak coupling limit.
Babikov, Dmitri; Semenov, Alexander
2016-01-28
A mixed quantum/classical approach to inelastic scattering (MQCT) is developed in which the relative motion of two collision partners is treated classically, and the rotational and vibrational motion of each molecule is treated quantum mechanically. The cases of molecule + atom and molecule + molecule are considered including diatomics, symmetric-top rotors, and asymmetric-top rotor molecules. Phase information is taken into consideration, permitting calculations of elastic and inelastic, total and differential cross sections for excitation and quenching. The method is numerically efficient and intrinsically parallel. The scaling law of MQCT is favorable, which enables calculations at high collision energies and for complicated molecules. Benchmark studies are carried out for several quite different molecular systems (N2 + Na, H2 + He, CO + He, CH3 + He, H2O + He, HCOOCH3 + He, and H2 + N2) in a broad range of collision energies, which demonstrates that MQCT is a viable approach to inelastic scattering. At higher collision energies it can confidently replace the computationally expensive full-quantum calculations. At low collision energies and for low-mass systems results of MQCT are less accurate but are still reasonable. A proposal is made for blending MQCT calculations at higher energies with full-quantum calculations at low energies. PMID:26618533
Quantum Critical Quasiparticle Scattering within the Superconducting State of CeCoIn5
NASA Astrophysics Data System (ADS)
Paglione, Johnpierre; Tanatar, M. A.; Reid, J.-Ph.; Shakeripour, H.; Petrovic, C.; Taillefer, Louis
2016-07-01
The thermal conductivity κ of the heavy-fermion metal CeCoIn5 was measured in the normal and superconducting states as a function of temperature T and magnetic field H , for a current and field parallel to the [100] direction. Inside the superconducting state, when the field is lower than the upper critical field Hc 2, κ /T is found to increase as T →0 , just as in a metal and in contrast to the behavior of all known superconductors. This is due to unpaired electrons on part of the Fermi surface, which dominate the transport above a certain field. The evolution of κ /T with field reveals that the electron-electron scattering (or transport mass m⋆) of those unpaired electrons diverges as H →Hc 2 from below, in the same way that it does in the normal state as H →Hc 2 from above. This shows that the unpaired electrons sense the proximity of the field-tuned quantum critical point of CeCoIn5 at H⋆=Hc 2 even from inside the superconducting state. The fact that the quantum critical scattering of the unpaired electrons is much weaker than the average scattering of all electrons in the normal state reveals a k -space correlation between the strength of pairing and the strength of scattering, pointing to a common mechanism, presumably antiferromagnetic fluctuations.
Scattering-induced quantum correlation in electronic waveguides with static magnetic impurities
NASA Astrophysics Data System (ADS)
Ghanbari-Adivi, E.; Soltani, M.; Alami, Z.; Sheikhali, M.
2016-07-01
Entanglement generation due to low-energy scattering of the transporting electrons in an electronic waveguide by a quantum dot magnetic impurity is theoretically investigated. The transverse confining potential of the waveguide is considered as a two-dimensional harmonic potential, and the interaction of the electron with the impurity is described by a zero-range pseudopotential modulated by an Ising or a Heisenberg spin interaction. Our calculation shows that the scattering process leads to creation of a considerable amount of entanglement in the state of the reflected and transmitted electrons. The situation is extended to the scattering of the electrons by two well-separated magnetic impurities localized on the nanowire axis. It is shown that the scattering process causes the magnetic impurities embedded in the nanowire to share their quantum information; subsequently, they can be entangled by spin interaction with the injected electron. The created entanglement between the impurities is calculated and discussed. It is shown that the exact three-dimensional problem can be approximated as a one-dimensional problem under certain circumstances. The approximate results are compared to exact calculations and discussed.
Quantum Critical Quasiparticle Scattering within the Superconducting State of CeCoIn_{5}.
Paglione, Johnpierre; Tanatar, M A; Reid, J-Ph; Shakeripour, H; Petrovic, C; Taillefer, Louis
2016-07-01
The thermal conductivity κ of the heavy-fermion metal CeCoIn_{5} was measured in the normal and superconducting states as a function of temperature T and magnetic field H, for a current and field parallel to the [100] direction. Inside the superconducting state, when the field is lower than the upper critical field H_{c2}, κ/T is found to increase as T→0, just as in a metal and in contrast to the behavior of all known superconductors. This is due to unpaired electrons on part of the Fermi surface, which dominate the transport above a certain field. The evolution of κ/T with field reveals that the electron-electron scattering (or transport mass m^{⋆}) of those unpaired electrons diverges as H→H_{c2} from below, in the same way that it does in the normal state as H→H_{c2} from above. This shows that the unpaired electrons sense the proximity of the field-tuned quantum critical point of CeCoIn_{5} at H^{⋆}=H_{c2} even from inside the superconducting state. The fact that the quantum critical scattering of the unpaired electrons is much weaker than the average scattering of all electrons in the normal state reveals a k-space correlation between the strength of pairing and the strength of scattering, pointing to a common mechanism, presumably antiferromagnetic fluctuations. PMID:27419578
Electron Raman scattering in semiconductor quantum well wire of cylindrical ring geometry
NASA Astrophysics Data System (ADS)
Re., Betancourt-Riera; Ri., Betancourt-Riera; M. Nieto Jalil, J.; Riera, R.
2015-11-01
We study the electron states and the differential cross section for an electron Raman scattering process in a semiconductor quantum well wire of cylindrical ring geometry. The electron Raman scattering developed here can be used to provide direct information about the electron band structures of these confinement systems. We assume that the system grows in a GaAs/Al0.35Ga0.65As matrix. The system is modeled by considering T = 0 K and also a single parabolic conduction band, which is split into a sub-band system due to the confinement. The emission spectra are discussed for different scattering configurations, and the selection rules for the processes are also studied. Singularities in the spectra are found and interpreted.
Manakov, N.L.; Nekipelov, A.A.; Fai-brevenshtei-breven, A.G.
1987-04-01
The method of the Sturm expansion of the relativistic Coulomb Green function G(E) is extended to the continuum range chemically bondEchemically bond>mc/sup 2/. The cross section for elastic and inelastic scattering of a ..gamma.. quantum by a hydrogenlike ion is calculated. Asymmetry effects in the polarization dependence of the scattering cross section are considered.
NASA Astrophysics Data System (ADS)
Song, Guo-Zhu; Wu, Fang-Zhou; Zhang, Mei; Yang, Guo-Jian
2016-06-01
Quantum repeater is the key element in quantum communication and quantum information processing. Here, we investigate the possibility of achieving a heralded quantum repeater based on the scattering of photons off single emitters in one-dimensional waveguides. We design the compact quantum circuits for nonlocal entanglement generation, entanglement swapping, and entanglement purification, and discuss the feasibility of our protocols with current experimental technology. In our scheme, we use a parametric down-conversion source instead of ideal single-photon sources to realize the heralded quantum repeater. Moreover, our protocols can turn faulty events into the detection of photon polarization, and the fidelity can reach 100% in principle. Our scheme is attractive and scalable, since it can be realized with artificial solid-state quantum systems. With developed experimental technique on controlling emitter-waveguide systems, the repeater may be very useful in long-distance quantum communication.
Song, Guo-Zhu; Wu, Fang-Zhou; Zhang, Mei; Yang, Guo-Jian
2016-01-01
Quantum repeater is the key element in quantum communication and quantum information processing. Here, we investigate the possibility of achieving a heralded quantum repeater based on the scattering of photons off single emitters in one-dimensional waveguides. We design the compact quantum circuits for nonlocal entanglement generation, entanglement swapping, and entanglement purification, and discuss the feasibility of our protocols with current experimental technology. In our scheme, we use a parametric down-conversion source instead of ideal single-photon sources to realize the heralded quantum repeater. Moreover, our protocols can turn faulty events into the detection of photon polarization, and the fidelity can reach 100% in principle. Our scheme is attractive and scalable, since it can be realized with artificial solid-state quantum systems. With developed experimental technique on controlling emitter-waveguide systems, the repeater may be very useful in long-distance quantum communication. PMID:27350159
Song, Guo-Zhu; Wu, Fang-Zhou; Zhang, Mei; Yang, Guo-Jian
2016-01-01
Quantum repeater is the key element in quantum communication and quantum information processing. Here, we investigate the possibility of achieving a heralded quantum repeater based on the scattering of photons off single emitters in one-dimensional waveguides. We design the compact quantum circuits for nonlocal entanglement generation, entanglement swapping, and entanglement purification, and discuss the feasibility of our protocols with current experimental technology. In our scheme, we use a parametric down-conversion source instead of ideal single-photon sources to realize the heralded quantum repeater. Moreover, our protocols can turn faulty events into the detection of photon polarization, and the fidelity can reach 100% in principle. Our scheme is attractive and scalable, since it can be realized with artificial solid-state quantum systems. With developed experimental technique on controlling emitter-waveguide systems, the repeater may be very useful in long-distance quantum communication. PMID:27350159
NASA Astrophysics Data System (ADS)
Dong, Jianping
2014-12-01
Integral form of the space-time-fractional Schrödinger equation for the scattering problem in the fractional quantum mechanics is studied in this paper. We define the fractional Green's function for the space-time fractional Schrödinger equation and express it in terms of Fox's H-function and in a computable series form. The asymptotic formula of the Green's function for large argument is also obtained, and applied to study the fractional quantum scattering problem. We get the approximate scattering wave function with correction of every order.
Scattering mechanisms in shallow undoped Si/SiGe quantum wells
Laroche, Dominique; Huang, S. -H.; Nielsen, Erik; Chuang, Y.; Li, J. -Y.; Liu, C. W.; Lu, Tzu -Ming
2015-10-07
We report the magneto-transport study and scattering mechanism analysis of a series of increasingly shallow Si/SiGe quantum wells with depth ranging from ~ 100 nm to ~ 10 nm away from the heterostructure surface. The peak mobility increases with depth, suggesting that charge centers near the oxide/semiconductor interface are the dominant scattering source. The power-law exponent of the electron mobility versus density curve, μ ∝ nα, is extracted as a function of the depth of the Si quantum well. At intermediate densities, the power-law dependence is characterized by α ~ 2.3. At the highest achievable densities in the quantum wellsmore » buried at intermediate depth, an exponent α ~ 5 is observed. Lastly, we propose and show by simulations that this increase in the mobility dependence on the density can be explained by a non-equilibrium model where trapped electrons smooth out the potential landscape seen by the two-dimensional electron gas.« less
Scattering mechanisms in shallow undoped Si/SiGe quantum wells
Laroche, D.; Nielsen, E.; Lu, T. M.; Huang, S.-H.; Chuang, Y.; Li, J.-Y. Liu, C. W.
2015-10-15
We report the magneto-transport study and scattering mechanism analysis of a series of increasingly shallow Si/SiGe quantum wells with depth ranging from ∼ 100 nm to ∼ 10 nm away from the heterostructure surface. The peak mobility increases with depth, suggesting that charge centers near the oxide/semiconductor interface are the dominant scattering source. The power-law exponent of the electron mobility versus density curve, μ ∝ n{sup α}, is extracted as a function of the depth of the Si quantum well. At intermediate densities, the power-law dependence is characterized by α ∼ 2.3. At the highest achievable densities in the quantum wells buried at intermediate depth, an exponent α ∼ 5 is observed. We propose and show by simulations that this increase in the mobility dependence on the density can be explained by a non-equilibrium model where trapped electrons smooth out the potential landscape seen by the two-dimensional electron gas.
Scattering of a vortex pair by a single quantum vortex in a Bose-Einstein condensate
NASA Astrophysics Data System (ADS)
Smirnov, L. A.; Smirnov, A. I.; Mironov, V. A.
2016-01-01
We analyze the scattering of vortex pairs (the particular case of 2D dark solitons) by a single quantum vortex in a Bose-Einstein condensate with repulsive interaction between atoms. For this purpose, an asymptotic theory describing the dynamics of such 2D soliton-like formations in an arbitrary smoothly nonuniform flow of a ultracold Bose gas is developed. Disregarding the radiation loss associated with acoustic wave emission, we demonstrate that vortex-antivortex pairs can be put in correspondence with quasiparticles, and their behavior can be described by canonical Hamilton equations. For these equations, we determine the integrals of motion that can be used to classify various regimes of scattering of vortex pairs by a single quantum vortex. Theoretical constructions are confirmed by numerical calculations performed directly in terms of the Gross-Pitaevskii equation. We propose a method for estimating the radiation loss in a collision of a soliton-like formation with a phase singularity. It is shown by direct numerical simulation that under certain conditions, the interaction of vortex pairs with a core of a single quantum vortex is accompanied by quite intense acoustic wave emission; as a result, the conditions for applicability of the asymptotic theory developed here are violated. In particular, it is visually demonstrated by a specific example how radiation losses lead to a transformation of a vortex-antivortex pair into a vortex-free 2D dark soliton (i.e., to the annihilation of phase singularities).
Scattering mechanisms in shallow undoped Si/SiGe quantum wells
Laroche, Dominique; Huang, S. -H.; Nielsen, Erik; Chuang, Y.; Li, J. -Y.; Liu, C. W.; Lu, Tzu -Ming
2015-10-07
We report the magneto-transport study and scattering mechanism analysis of a series of increasingly shallow Si/SiGe quantum wells with depth ranging from ~ 100 nm to ~ 10 nm away from the heterostructure surface. The peak mobility increases with depth, suggesting that charge centers near the oxide/semiconductor interface are the dominant scattering source. The power-law exponent of the electron mobility versus density curve, μ ∝ n^{α}, is extracted as a function of the depth of the Si quantum well. At intermediate densities, the power-law dependence is characterized by α ~ 2.3. At the highest achievable densities in the quantum wells buried at intermediate depth, an exponent α ~ 5 is observed. Lastly, we propose and show by simulations that this increase in the mobility dependence on the density can be explained by a non-equilibrium model where trapped electrons smooth out the potential landscape seen by the two-dimensional electron gas.
Würth, Christian; Resch-Genger, Ute
2015-06-01
The ever-increasing use of fluorescent nanomaterials and micrometer-sized beads in the life and material sciences requires reliable procedures for the measurement of the key performance parameter fluorescence quantum yield (Φf) of scattering particle dispersions and reference systems to evaluate the performance of such measurements. This encouraged us to systematically study, both theoretically and experimentally, the optical determination of photoluminescent quantum yield as a function of the scattering and absorption properties of the sample and the illumination geometry with an integrating sphere method. The latter included measurements with a direct and an indirect illumination. As a representative and easy-to-prepare reference system, we used ethanolic dispersions of 250 nm sized silica particles and the dye rhodamine 101 and systematically varied the concentration of the dye and particles within the typical ranges of spectroscopic and (bio)analytical applications of fluorescent nanomaterials. Based on our measurements, we recommend indirect sample illumination geometry for the accurate measurement of Φf of samples with low or unknown absorption and high scattering coefficients such as dispersions of luminescent particles or fluorescent reporters in biological matrices. This finding is of utmost relevance for all (bio)analytical applications of fluorescent nanomaterials ranging from particle labels and probes over assay platforms to safety barcodes. PMID:25955619
Brouard, M; Chadwick, H; Gordon, S D S; Hornung, B; Nichols, B; Kłos, J; Aoiz, F J; Stolte, S
2014-10-28
Fully quantum state selected and resolved inelastic scattering of NO(X) by krypton has been investigated. Initial Λ-doublet state selection is achieved using an inhomogeneous hexapole electric field. Differential cross sections and even-moment polarization dependent differential cross sections have been obtained at a collision energy of 514 cm(-1) for both spin-orbit and parity conserving and changing collisions. Experimental results are compared with those obtained from quantum scattering calculations and are shown to be in very good agreement. Hard shell quantum scattering calculations are also performed to determine the effects of the different parts of the potential on the scattering dynamics. Comparisons are also made with the NO(X) + Ar system. PMID:25362298
Brouard, M. Chadwick, H.; Gordon, S. D. S.; Hornung, B.; Nichols, B.; Kłos, J.; Aoiz, F. J.; Stolte, S.
2014-10-28
Fully quantum state selected and resolved inelastic scattering of NO(X) by krypton has been investigated. Initial Λ-doublet state selection is achieved using an inhomogeneous hexapole electric field. Differential cross sections and even-moment polarization dependent differential cross sections have been obtained at a collision energy of 514 cm{sup −1} for both spin-orbit and parity conserving and changing collisions. Experimental results are compared with those obtained from quantum scattering calculations and are shown to be in very good agreement. Hard shell quantum scattering calculations are also performed to determine the effects of the different parts of the potential on the scattering dynamics. Comparisons are also made with the NO(X) + Ar system.
Quantum chaos inside space-temporal Sinai billiards
NASA Astrophysics Data System (ADS)
Addazi, Andrea
2016-04-01
We discuss general aspects of non-relativistic quantum chaos theory of scattering of a quantum particle on a system of a large number of naked singularities. We define such a system space-temporal Sinai billiard. We discuss the problem in semiclassical approach. We show that in semiclassical regime the formation of trapped periodic semiclassical orbits inside the system is unavoidable. This leads to general expression of survival probabilities and scattering time delays, expanded to the chaotic Pollicott-Ruelle resonances. Finally, we comment on possible generalizations of these aspects to relativistic quantum field theory.
Grazing-incidence small-angle X-ray scattering: application to the study of quantum dot lattices
Buljan, Maja; Radić, Nikola; Bernstorff, Sigrid; Dražić, Goran; Bogdanović-Radović, Iva; Holý, Václav
2012-01-01
The ordering of quantum dots in three-dimensional quantum dot lattices is investigated by grazing-incidence small-angle X-ray scattering (GISAXS). Theoretical models describing GISAXS intensity distributions for three general classes of lattices of quantum dots are proposed. The classes differ in the type of disorder of the positions of the quantum dots. The models enable full structure determination, including lattice type, lattice parameters, the type and degree of disorder in the quantum dot positions and the distributions of the quantum dot sizes. Applications of the developed models are demonstrated using experimentally measured data from several types of quantum dot lattices formed by a self-assembly process. PMID:22186289
Applications of Quantum Theory of Atomic and Molecular Scattering to Problems in Hypersonic Flow
NASA Technical Reports Server (NTRS)
Malik, F. Bary
1995-01-01
The general status of a grant to investigate the applications of quantum theory in atomic and molecular scattering problems in hypersonic flow is summarized. Abstracts of five articles and eleven full-length articles published or submitted for publication are included as attachments. The following topics are addressed in these articles: fragmentation of heavy ions (HZE particles); parameterization of absorption cross sections; light ion transport; emission of light fragments as an indicator of equilibrated populations; quantum mechanical, optical model methods for calculating cross sections for particle fragmentation by hydrogen; evaluation of NUCFRG2, the semi-empirical nuclear fragmentation database; investigation of the single- and double-ionization of He by proton and anti-proton collisions; Bose-Einstein condensation of nuclei; and a liquid drop model in HZE particle fragmentation by hydrogen.
Barrier scattering with complex-valued quantum trajectories: Taxonomy and analysis of isochrones
David, Julianne K.; Wyatt, Robert E.
2008-03-07
To facilitate the search for isochrones when using complex-valued trajectory methods for quantum barrier scattering calculations, the structure and shape of isochrones in the complex plane were studied. Isochrone segments were categorized based on their distinguishing features, which are shared by each situation studied: High and low energy wave packets, scattering from both thick and thin Gaussian and Eckart barriers of varying height. The characteristic shape of the isochrone is a trifurcated system: Trajectories that transmit the barrier are launched from the lower branch (T), while the middle and upper branches form the segments for reflected trajectories (F and B). In addition, a model is presented for the curved section of the lower branch (from which transmitted trajectories are launched), and important features of the complex extension of the initial wave packet are identified.
Resonant light scattering of a laser frequency comb by a quantum dot
NASA Astrophysics Data System (ADS)
Konthasinghe, K.; Peiris, M.; Muller, A.
2014-08-01
We investigate the spectral and temporal properties of light scattered near resonantly by a single quantum dot when the incident laser field is a frequency comb consisting of a superposition of monochromatic waves equidistant in frequency. Such fields encompass those generated by, e.g., a periodically pulsed laser. A general theoretical treatment for the calculation of first- and second-order correlation functions is given which takes account of spectral diffusion through a slowly varying detuning from resonance, permitting accurate comparison with experiments. We explore the two distinct regimes in which the frequency-comb separation is either larger or smaller than the radiative decay rate. We verify the validity of our calculations by a comparison with experimental data for the case of a bichromatic field and discuss the manifestation of phase coherence between the incoming field and the scattered single-photon wave packet.
Single quantum dot controls a plasmonic cavity’s scattering and anisotropy
Hartsfield, Thomas; Chang, Wei-Shun; Yang, Seung-Cheol; Ma, Tzuhsuan; Shi, Jinwei; Sun, Liuyang; Shvets, Gennady; Link, Stephan; Li, Xiaoqin
2015-01-01
Plasmonic cavities represent a promising platform for controlling light–matter interaction due to their exceptionally small mode volume and high density of photonic states. Using plasmonic cavities for enhancing light’s coupling to individual two-level systems, such as single semiconductor quantum dots (QD), is particularly desirable for exploring cavity quantum electrodynamic (QED) effects and using them in quantum information applications. The lack of experimental progress in this area is in part due to the difficulty of precisely placing a QD within nanometers of the plasmonic cavity. Here, we study the simplest plasmonic cavity in the form of a spherical metallic nanoparticle (MNP). By controllably positioning a semiconductor QD in the close proximity of the MNP cavity via atomic force microscope (AFM) manipulation, the scattering spectrum of the MNP is dramatically modified due to Fano interference between the classical plasmonic resonance of the MNP and the quantized exciton resonance in the QD. Moreover, our experiment demonstrates that a single two-level system can render a spherical MNP strongly anisotropic. These findings represent an important step toward realizing quantum plasmonic devices. PMID:26372957
Effect of spin-flip scattering on the electron transport through double quantum dots
NASA Astrophysics Data System (ADS)
Yang, Fu-Bin; Huang, Rui; Cheng, Yan
2015-05-01
We systematically investigate the electron transport through double quantum dots (DQD) with particular emphasis on the spin-flip scattering of an electron in the DQD. By means of the slave-boson mean-field approximation, we calculate the linear conductance and the transmission in the Kondo regime at zero temperature. The obtained results show that both the linear conductance and transmission probability are quite sensitive to the spin-flip strength when the DQD structure is changed among the serial, parallel and T-shaped. It is suggested that such a theoretical model can be used to study the physical phenomenon related to the spin manipulation transport.
Dynamical basis sets for algebraic variational calculations in quantum-mechanical scattering theory
NASA Technical Reports Server (NTRS)
Sun, Yan; Kouri, Donald J.; Truhlar, Donald G.; Schwenke, David W.
1990-01-01
New basis sets are proposed for linear algebraic variational calculations of transition amplitudes in quantum-mechanical scattering problems. These basis sets are hybrids of those that yield the Kohn variational principle (KVP) and those that yield the generalized Newton variational principle (GNVP) when substituted in Schlessinger's stationary expression for the T operator. Trial calculations show that efficiencies almost as great as that of the GNVP and much greater than the KVP can be obtained, even for basis sets with the majority of the members independent of energy.
Topological quantum scattering under the influence of a nontrivial boundary condition
NASA Astrophysics Data System (ADS)
Mota, Herondy
2016-04-01
We consider the quantum scattering problem of a relativistic particle in (2 + 1)-dimensional cosmic string spacetime under the influence of a nontrivial boundary condition imposed on the solution of the Klein-Gordon equation. The solution is then shifted as consequence of the nontrivial boundary condition and the role of the phase shift is to produce an Aharonov-Bohm-like effect. We examine the connection between this phase shift and the electromagnetic and gravitational analogous of the Aharonov-Bohm effect and compare the present results with previous ones obtained in the literature, also considering non-relativistic cases.
Finite element basis for the expansion of radial wavefunction in quantum scattering calculations
NASA Astrophysics Data System (ADS)
Hwang, Woonglin; Sup Lee, Yoon; Park, Seung C.
1991-11-01
Radial wavefunctions in quantum scattering calculations are expanded in terms of two shape functions for each finite element. This approach is the R matrix version of Kohn's variational method and also directly applicable to S matrix in the log-derivative version. The linear algebra involved amounts to solving definite banded systems. In this basis set method, R matrix or log-derivative matrix is greatly simplified and the computational effort is linearly proportional to the number of radial basis functions, promising computational efficiencies for large scale calculations. Convergences for test vases are also reasonably rapid.
NASA Technical Reports Server (NTRS)
Sharafeddin, Omar A.; Judson, Richard S.; Kouri, Donald J.; Hoffman, David K.
1990-01-01
The novel wave-packet propagation scheme presented is based on the time-dependent form of the Lippman-Schwinger integral equation and does not require extensive matrix inversions, thereby facilitating application to systems in which some degrees of freedom express the potential in a basis expansion. The matrix to be inverted is a function of the kinetic energy operator, and is accordingly diagonal in a Bessel function basis set. Transition amplitudes for various orbital angular momentum quantum numbers are obtainable via either Fourier transform of the amplitude density from the time to the energy domain, or the direct analysis of the scattered wave packet.
NASA Astrophysics Data System (ADS)
Altmann, Eduardo G.; Portela, Jefferson S. E.; Tél, Tamás
2013-04-01
There are numerous physical situations in which a hole or leak is introduced in an otherwise closed chaotic system. The leak can have a natural origin, it can mimic measurement devices, and it can also be used to reveal dynamical properties of the closed system. A unified treatment of leaking systems is provided and applications to different physical problems, in both the classical and quantum pictures, are reviewed. The treatment is based on the transient chaos theory of open systems, which is essential because real leaks have finite size and therefore estimations based on the closed system differ essentially from observations. The field of applications reviewed is very broad, ranging from planetary astronomy and hydrodynamical flows to plasma physics and quantum fidelity. The theory is expanded and adapted to the case of partial leaks (partial absorption and/or transmission) with applications to room acoustics and optical microcavities in mind. Simulations in the limaçon family of billiards illustrate the main text. Regarding billiard dynamics, it is emphasized that a correct discrete-time representation can be given only in terms of the so-called true-time maps, while traditional Poincaré maps lead to erroneous results. Perron-Frobenius-type operators are generalized so that they describe true-time maps with partial leaks.
Casimir force between integrable and chaotic pistons
Alvarez, Ezequiel; Mazzitelli, Francisco D.; Wisniacki, Diego A.; Monastra, Alejandro G.
2010-11-15
We have computed numerically the Casimir force between two identical pistons inside a very long cylinder, considering different shapes for the pistons. The pistons can be considered quantum billiards, whose spectrum determines the vacuum force. The smooth part of the spectrum fixes the force at short distances and depends only on geometric quantities like the area or perimeter of the piston. However, correcting terms to the force, coming from the oscillating part of the spectrum which is related to the classical dynamics of the billiard, could be qualitatively different for classically integrable or chaotic systems. We have performed a detailed numerical analysis of the corresponding Casimir force for pistons with regular and chaotic classical dynamics. For a family of stadium billiards, we have found that the correcting part of the Casimir force presents a sudden change in the transition from regular to chaotic geometries. This suggests that there could be signatures of quantum chaos in the Casimir effect.
Image encryption with chaotically coupled chaotic maps
NASA Astrophysics Data System (ADS)
Pisarchik, A. N.; Zanin, M.
2008-10-01
We present a novel secure cryptosystem for direct encryption of color images, based on chaotically coupled chaotic maps. The proposed cipher provides good confusion and diffusion properties that ensures extremely high security because of the chaotic mixing of pixels’ colors. Information is mixed and distributed over a complete image using a complex strategy that makes known plaintext attack unfeasible. The encryption algorithm guarantees the three main goals of cryptography: strong cryptographic security, short encryption/decryption time, and robustness against noise and other external disturbances. Due to the high speed, the proposed cryptosystem is suitable for application in real-time communication systems.
Ławniczak, Michał; Białous, Małgorzata; Yunko, Vitalii; Bauch, Szymon; Sirko, Leszek
2015-03-01
We present the results of an experimental study of the elastic enhancement factor W for a microwave rectangular cavity simulating a two-dimensional quantum billiard in a transient region between regular and chaotic dynamics. The cavity was coupled to a vector network analyzer via two microwave antennas. The departure of the system from an integrable one due to the presence of antennas acting as scatterers is characterized by the parameter of chaoticity κ=2.8. The experimental results for the rectangular cavity are compared with those obtained for a microwave rough cavity simulating a chaotic quantum billiard. The experimental results were obtained for the frequency range ν=16-18.5 GHz and moderate absorption strength γ=5.2-7.4. We show that the elastic enhancement factor for the rectangular cavity lies below the theoretical value W=3 predicted for integrable systems, and it is significantly higher than that obtained for the rough cavity. The results obtained for the microwave rough cavity are smaller than those obtained within the framework of random matrix theory, and they lie between them and those predicted within a recently introduced model of the two-channel coupling [V. V. Sokolov and O. V. Zhirov, arXiv:1411.6211 [nucl-th
Cerkic, A.; Milosevic, D. B.
2006-03-15
Using the example of electron-atom scattering in a strong laser field, it is shown that the oscillatory structure of the scattered electron spectrum can be explained as a consequence of the interference of the real electron trajectories in terms of Feynman's path integral. While in previous work on quantum-orbit theory the complex solutions of the saddle-point equations were considered, we show here that for the electron-atom scattering with much simpler real solutions a satisfactory agreement with the strong-field-approximation results can be achieved. Real solutions are applicable both for the direct (low-energy) and the rescattering (high-energy) plateau in the scattered electron spectrum. In between the plateaus and beyond the rescattering cutoff good results can be obtained using the complex (quantum) solutions and the uniform approximation. The interference of real solutions is related to the recent attosecond double-slit experiment in time.
Angle-resolved scattering spectroscopy of explosives using an external cavity quantum cascade laser
NASA Astrophysics Data System (ADS)
Suter, Jonathan D.; Bernacki, Bruce E.; Phillips, Mark C.
2012-01-01
We present a study of the spectral and angular dependence of the diffuse scatter of mid-infrared (MIR) laser light from explosives residues on surfaces. Experiments were performed using an external cavity quantum cascade laser (ECQCL) tunable between 7 and 8 μm (1270 to 1400 cm-1) for surface illumination. A mercury cadmium telluride (MCT) detector was used to detect backscattered spectra as a function of surface angle at a 2 meter standoff. A ferroelectric focal plane array was used to build hyperspectral images at a 0.5 meter standoff. Residues of RDX, tetryl, and TNT were investigated on surfaces including a painted car door for angles between zero (specular) and 50 degrees. We observe spectral signatures of the explosives in the diffuse scattering geometry which differ significantly from those observed in transmission geometries. Characterization of the scattered light spectra of explosives on surfaces will be essential for understanding the performance of standoff explosives detection instruments and developing robust spectral analysis techniques.
NASA Astrophysics Data System (ADS)
Goray, L. I.; Chkhalo, N. I.; Tsyrlin, G. E.
2009-04-01
Scattering of X rays by structures with multilayer ensembles of quantum dots MBE-grown in the In(Ga)As-GaAs system is studied by high-resolution grazing X-ray reflectometry. The peaks of the diffuse scattering intensity are discovered for the first time in structures with both vertically uncorrelated and vertically correlated quantum dots. It is shown that the position of the peak is totally determined by angle of inclination of the quantum dot pyramidal faces (the so-called blaze condition for diffraction gratings), which was theoretically predicted earlier. Comparison with the results of scattering simulation carried out by the technique of boundary integral equations indicates that a simple geometrical condition allows one to exactly determine the value of from the position of the intensity peak, the shape of which depends on many parameters. As follows from the theory and experiment, the width and height of the peaks for samples with vertically correlated quantum dots are larger than for those with uncorrelated dots. The roughness and interdiffusion of interfaces and the height of quantum dots are found from the position and amplitude of Bragg peaks. Thus, the conventional application of high-resolution grazing X-ray reflectometry is extended in this work to determination of the quantum dot geometry.
NASA Astrophysics Data System (ADS)
Kushwaha, Manvir S.
2013-04-01
The nanofabrication technology has taught us that an m-dimensional confining potential imposed upon an n-dimensional electron gas paves the way to a quasi-(n-m)-dimensional electron gas, with m ⩽ n and 1 ⩽ n, m ⩽ 3. This is the road to the (semiconducting) quasi-n dimensional electron gas systems we have been happily traversing on now for almost two decades. Achieving quasi-one dimensional electron gas (Q-1DEG) [or quantum wire(s) for more practical purposes] led us to some mixed moments in this journey: while the reduced phase space for the scattering led us believe in the route to the faster electron devices, the proximity to the 1D systems left us in the dilemma of describing it as a Fermi liquid or as a Luttinger liquid. No one had ever suspected the potential of the former, but it took quite a while for some to convince the others on the latter. A realistic Q-1DEG system at the low temperatures is best describable as a Fermi liquid rather than as a Luttinger liquid. In the language of condensed matter physics, a critical scrutiny of Q-1DEG systems has provided us with a host of exotic (electronic, optical, and transport) phenomena unseen in their higher- or lower-dimensional counterparts. This has motivated us to undertake a systematic investigation of the inelastic electron scattering (IES) and the inelastic light scattering (ILS) from the elementary electronic excitations in quantum wires. We begin with the Kubo's correlation functions to derive the generalized dielectric function, the inverse dielectric function, and the Dyson equation for the dynamic screened potential in the framework of Bohm-Pines' random-phase approximation. These fundamental tools then lead us to develop methodically the theory of IES and ILS for the Q-1DEG systems. As an application of the general formal results, which know no bounds regarding the subband occupancy, we compute the density of states, the Fermi energy, the full excitation spectrum [comprised of intrasubband and
NASA Astrophysics Data System (ADS)
Buhmann, H.; Predel, H.; Molenkamp, L. W.; Gurzhi, R. N.; Kalinenko, A. N.; Kopeliovich, A. I.; Yanovsky, A. V.
2001-10-01
Experimentally electron-beam injection and detection via quantum point-contacts is used to investigate the scattering of a non-equilibrium electron distribution in a two-dimensional electron gas (2DEG) of a GaAs/(Ga,Al)As heterostructure. The energy dependence of electron-electron scattering processes has been studied in a weak magnetic field by investigating the detector signal. Assuming electron beams with a narrow opening angle a magnetic field B perpendicular to the 2DEG plane causes only electrons which are scattered in a point O at an angle α to reach the detector. Thus, it is possible to measure directly the energy dependence of the angular electron distribution after scattering. The experimental data give a clear evidence for the importance of small angle scattering processes in two-dimensional systems, as predicted theoretically.
Neutron scattering signatures of the 3D hyperhoneycomb Kitaev quantum spin liquid
NASA Astrophysics Data System (ADS)
Smith, A.; Knolle, J.; Kovrizhin, D. L.; Chalker, J. T.; Moessner, R.
2015-11-01
Motivated by recent synthesis of the hyperhoneycomb material β -Li2IrO3 , we study the dynamical structure factor (DSF) of the corresponding 3D Kitaev quantum spin-liquid (QSL), whose fractionalized degrees of freedom are Majorana fermions and emergent flux loops. The properties of this 3D model are known to differ in important ways from those of its 2D counterpart—it has a finite-temperature phase transition, as well as distinct features in the Raman response. We show, however, that the qualitative behavior of the DSF is broadly dimension-independent. Characteristics of the 3D DSF include a response gap even in the gapless QSL phase and an energy dependence deriving from the Majorana fermion density of states. Since the majority of the response is from states containing a single Majorana excitation, our results suggest inelastic neutron scattering as the spectroscopy of choice to illuminate the physics of Majorana fermions in Kitaev QSLs.
Spin-flip relaxation via optical phonon scattering in quantum dots
Wang, Zi-Wu; Liu, Lei; Li, Shu-Shen
2013-12-14
Based on the spin-orbit coupling admixture mechanism, we theoretically investigate the spin-flip relaxation via optical phonon scattering in quantum dots by considering the effect of lattice relaxation due to the electron-acoustic phonon deformation potential coupling. The relaxation rate displays a cusp-like structure (or a spin hot spot) that becomes more clearly with increasing temperature. We also calculate the relaxation rate of the spin-conserving process, which follows a Gaussian form and is several orders of magnitude larger than that of spin-flip process. Moreover, we find that the relaxation rate displays the oscillatory behavior due to the interplay effects between the magnetic and spatial confinement for the spin-flip process not for the spin-conserving process. The trends of increasing and decreasing temperature dependence of the relaxation rates for two relaxation processes are obtained in the present model.
NASA Astrophysics Data System (ADS)
Szyczewski, A.; Hołderna-Natkaniec, K.; Natkaniec, I.
2004-05-01
Inelastic incoherent neutron scattering spectra of progesterone and testosterone measured at 20 and 290 K were compared with the IR spectra measured at 290 K. The Phonon Density of States spectra display well resolved peaks of low frequency internal vibration modes up to 1200 cm -1. The quantum chemistry calculations were performed by semiempirical PM3 method and by the density functional theory method with different basic sets for isolated molecule, as well as for the dimer system of testosterone. The proposed assignment of internal vibrations of normal modes enable us to conclude about the sequence of the onset of the torsion movements of the CH 3 groups. These conclusions were correlated with the results of proton molecular dynamics studies performed by NMR method. The GAUSSIAN program had been used for calculations.
Yoxall, Edward Rahmani, Mohsen; Maier, Stefan A.; Phillips, Chris C.; Navarro-Cía, Miguel
2013-11-18
We demonstrate the use of a pulsed quantum cascade laser, wavelength tuneable between 6 and 10 μm, with a scattering-type scanning near-field optical microscope (s-SNOM). A simple method for calculating the signal-to-noise ratio (SNR) of the s-SNOM measurement is presented. For pulsed lasers, the SNR is shown to be highly dependent on the degree of synchronization between the laser pulse and the sampling circuitry; in measurements on a gold sample, the SNR is 26 with good synchronization and less than 1 without. Simulations and experimental s-SNOM images, with a resolution of 100 nm, corresponding to λ/80, and an acquisition time of less than 90 s, are presented as proof of concept. They show the change in the field profile of plasmon-resonant broadband antennas when they are excited with wavelengths of 7.9 and 9.5 μm.
Analysis of temporal evolution of quantum dot surface chemistry by surface-enhanced Raman scattering
Doğan, İlker; Gresback, Ryan; Nozaki, Tomohiro; van de Sanden, Mauritius C. M.
2016-01-01
Temporal evolution of surface chemistry during oxidation of silicon quantum dot (Si-QD) surfaces were probed using surface-enhanced Raman scattering (SERS). A monolayer of hydrogen and chlorine terminated plasma-synthesized Si-QDs were spin-coated on silver oxide thin films. A clearly enhanced signal of surface modes, including Si-Clx and Si-Hx modes were observed from as-synthesized Si-QDs as a result of the plasmonic enhancement of the Raman signal at Si-QD/silver oxide interface. Upon oxidation, a gradual decrease of Si-Clx and Si-Hx modes, and an emergence of Si-Ox and Si-O-Hx modes have been observed. In addition, first, second and third transverse optical modes of Si-QDs were also observed in the SERS spectra, revealing information on the crystalline morphology of Si-QDs. An absence of any of the abovementioned spectral features, but only the first transverse optical mode of Si-QDs from thick Si-QD films validated that the spectral features observed from Si-QDs on silver oxide thin films are originated from the SERS effect. These results indicate that real-time SERS is a powerful diagnostic tool and a novel approach to probe the dynamic surface/interface chemistry of quantum dots, especially when they involve in oxidative, catalytic, and electrochemical surface/interface reactions. PMID:27389331
Analysis of temporal evolution of quantum dot surface chemistry by surface-enhanced Raman scattering
NASA Astrophysics Data System (ADS)
Doğan, Ilker; Gresback, Ryan; Nozaki, Tomohiro; van de Sanden, Mauritius C. M.
2016-07-01
Temporal evolution of surface chemistry during oxidation of silicon quantum dot (Si-QD) surfaces were probed using surface-enhanced Raman scattering (SERS). A monolayer of hydrogen and chlorine terminated plasma-synthesized Si-QDs were spin-coated on silver oxide thin films. A clearly enhanced signal of surface modes, including Si-Clx and Si-Hx modes were observed from as-synthesized Si-QDs as a result of the plasmonic enhancement of the Raman signal at Si-QD/silver oxide interface. Upon oxidation, a gradual decrease of Si-Clx and Si-Hx modes, and an emergence of Si-Ox and Si-O-Hx modes have been observed. In addition, first, second and third transverse optical modes of Si-QDs were also observed in the SERS spectra, revealing information on the crystalline morphology of Si-QDs. An absence of any of the abovementioned spectral features, but only the first transverse optical mode of Si-QDs from thick Si-QD films validated that the spectral features observed from Si-QDs on silver oxide thin films are originated from the SERS effect. These results indicate that real-time SERS is a powerful diagnostic tool and a novel approach to probe the dynamic surface/interface chemistry of quantum dots, especially when they involve in oxidative, catalytic, and electrochemical surface/interface reactions.
NASA Astrophysics Data System (ADS)
Mahmoud, Samadpour; Azam Iraji, zad; Mehdi, Molaei
2014-04-01
TiO2 nanorod layers are synthesized by simple chemical oxidation of Ti substrates. Diffuse reflectance spectroscopy measurements show effective light scattering properties originating from nanorods with length scales on the order of one micron. The films are sensitized with CdSe quantum dots (QDs) by successive ionic layer adsorption and reaction (SILAR) and integrated as a photoanode in quantum dot sensitized solar cells (QDSCs). Incorporating nanorods in photoanode structures provided 4- to 8-fold enhancement in light scattering, which leads to a high power conversion efficiency, 3.03% (Voc = 497 mV, Jsc = 11.32 mA/cm2, FF = 0.54), in optimized structures. High efficiency can be obtained just by tuning the photoanode structure without further treatments, which will make this system a promising nanostructure for efficient quantum dot sensitized solar cells.
Quantum scattering calculations for ro-vibrational de-excitation of CO by hydrogen atoms
Song, Lei; Avoird, Ad van der; Karman, Tijs; Groenenboom, Gerrit C.; Balakrishnan, N.
2015-05-28
We present quantum-mechanical scattering calculations for ro-vibrational relaxation of carbon monoxide (CO) in collision with hydrogen atoms. Collisional cross sections of CO ro-vibrational transitions from v = 1, j = 0 − 30 to v′ = 0, j′ are calculated using the close coupling method for collision energies between 0.1 and 15 000 cm{sup −1} based on the three-dimensional potential energy surface of Song et al. [J. Phys. Chem. A 117, 7571 (2013)]. Cross sections of transitions from v = 1, j ≥ 3 to v′ = 0, j′ are reported for the first time at this level of theory. Also calculations by the more approximate coupled states and infinite order sudden (IOS) methods are performed in order to test the applicability of these methods to H–CO ro-vibrational inelastic scattering. Vibrational de-excitation rate coefficients of CO (v = 1) are presented for the temperature range from 100 K to 3000 K and are compared with the available experimental and theoretical data. All of these results and additional rate coefficients reported in a forthcoming paper are important for including the effects of H–CO collisions in astrophysical models.
NASA Astrophysics Data System (ADS)
Holderna-Natkaniec, K.; Szyczewski, A.; Natkaniec, I.; Khavryutchenko, V. D.; Pawlukojc, A.
Inelastic incoherent neutron scattering (IINS) and neutron diffraction spectra of progesterone and testosterone were measured simultaneously on the NERA spectrometer at the IBR-2 pulsed reactor in Dubna. Both studied samples do not indicate any phase transition in the temperature range from 20 to 290K. The IINS spectra have been transformed to the phonon density of states (PDS) in the one-phonon scattering approximation. The PDS spectra display well-resolved peaks of low-frequency internal vibration modes up to 600cm-1. The assignment of these modes was proposed taking into account the results of calculations of the structure and dynamics of isolated molecules of the investigated substances. The quantum chemistry calculations were performed by the semi-empirical PM3 method and at the restricted Hartree-Fock level with the 6-31* basis set. The lower internal modes assigned to torsional vibration of the androstane skeleton mix with the lattice vibrations. The intense bands in the PDS spectra in the frequency range from 150 to 300cm-1 are related to librations of structurally inequivalent methyl groups.
Inelastic electron and Raman scattering from the collective excitations in quantum wires
NASA Astrophysics Data System (ADS)
Kushwaha, Manvir
2014-03-01
The nanofabrication technology has taught us that an m-dimensional confining potential imposed upon an n-dimensional electron gas paves the way to a quasi-(n- m)-dimensional electron gas, with m <= n and 1 <= n , m <= 3 . This is the road to the (semiconducting) quasi- n dimensional electron gas systems we have been happily traversing on now for almost two decades. Achieving quasi-one dimensional electron gas (Q-1DEG) led us to some mixed moments in this journey: while the reduced phase space for the scattering led us believe in the route to the faster electron devices, the proximity to the 1D systems left us in the dilemma of describing it as a Fermi liquid or as a Luttinger liquid. No one had ever suspected the potential of the former, but it took quite a while for some to convince the others on the latter. A realistic Q-1DEG system at the low temperatures is best describable as a Fermi liquid rather than as a Luttinger liquid. This has motivated us to employ the Bohm-Pines' full RPA to develop a systematic methodology for the inelastic electron and light scattering from the collective (plasmon) excitations in Q-1DEG [or quantum wires]. We will discuss in detail the results published in AIP Advances 3, 042103 (2013).
Quantum scattering calculations for ro-vibrational de-excitation of CO by hydrogen atoms
NASA Astrophysics Data System (ADS)
Song, Lei; Balakrishnan, N.; van der Avoird, Ad; Karman, Tijs; Groenenboom, Gerrit C.
2015-05-01
We present quantum-mechanical scattering calculations for ro-vibrational relaxation of carbon monoxide (CO) in collision with hydrogen atoms. Collisional cross sections of CO ro-vibrational transitions from v = 1, j = 0 - 30 to v' = 0, j' are calculated using the close coupling method for collision energies between 0.1 and 15 000 cm-1 based on the three-dimensional potential energy surface of Song et al. [J. Phys. Chem. A 117, 7571 (2013)]. Cross sections of transitions from v = 1, j ≥ 3 to v' = 0, j' are reported for the first time at this level of theory. Also calculations by the more approximate coupled states and infinite order sudden (IOS) methods are performed in order to test the applicability of these methods to H-CO ro-vibrational inelastic scattering. Vibrational de-excitation rate coefficients of CO (v = 1) are presented for the temperature range from 100 K to 3000 K and are compared with the available experimental and theoretical data. All of these results and additional rate coefficients reported in a forthcoming paper are important for including the effects of H-CO collisions in astrophysical models.
Synchronization of chaotic systems
Pecora, Louis M.; Carroll, Thomas L.
2015-09-15
We review some of the history and early work in the area of synchronization in chaotic systems. We start with our own discovery of the phenomenon, but go on to establish the historical timeline of this topic back to the earliest known paper. The topic of synchronization of chaotic systems has always been intriguing, since chaotic systems are known to resist synchronization because of their positive Lyapunov exponents. The convergence of the two systems to identical trajectories is a surprise. We show how people originally thought about this process and how the concept of synchronization changed over the years to a more geometric view using synchronization manifolds. We also show that building synchronizing systems leads naturally to engineering more complex systems whose constituents are chaotic, but which can be tuned to output various chaotic signals. We finally end up at a topic that is still in very active exploration today and that is synchronization of dynamical systems in networks of oscillators.
Synchronization of chaotic systems
NASA Astrophysics Data System (ADS)
Pecora, Louis M.; Carroll, Thomas L.
2015-09-01
We review some of the history and early work in the area of synchronization in chaotic systems. We start with our own discovery of the phenomenon, but go on to establish the historical timeline of this topic back to the earliest known paper. The topic of synchronization of chaotic systems has always been intriguing, since chaotic systems are known to resist synchronization because of their positive Lyapunov exponents. The convergence of the two systems to identical trajectories is a surprise. We show how people originally thought about this process and how the concept of synchronization changed over the years to a more geometric view using synchronization manifolds. We also show that building synchronizing systems leads naturally to engineering more complex systems whose constituents are chaotic, but which can be tuned to output various chaotic signals. We finally end up at a topic that is still in very active exploration today and that is synchronization of dynamical systems in networks of oscillators.
Quantum and classical dynamics of reactive scattering of H2 from metal surfaces.
Kroes, Geert-Jan; Díaz, Cristina
2016-06-27
We review the state-of-the art in dynamics calculations on the reactive scattering of H2 from metal surfaces, which is an important model system of an elementary reaction that is relevant to heterogeneous catalysis. In many applications, quantum dynamics and classical trajectory calculations are performed within the Born-Oppenheimer static surface model. However, ab initio molecular dynamics (AIMD) is finding increased use in applications aimed at modeling the effect of surface phonons on the dynamics. Molecular dynamics with electronic friction has been used to model the effect of electron-hole pair excitation. Most applications are still based on potential energy surfaces (PESs) or forces computed with density functional theory (DFT), using a density functional within the generalized gradient approximation to the exchange-correlation energy. A new development is the use of a semi-empirical version of DFT (the specific reaction parameter (SRP) approach to DFT). We also discuss the accurate methods that have become available to represent electronic structure data for the molecule-surface interaction in global PESs. It has now become possible to describe highly activated H2 + metal surface reactions with chemical accuracy using the SRP-DFT approach, as has been shown for H2 + Cu(111) and Cu(100). However, chemical accuracy with SRP-DFT has yet to be demonstrated for weakly activated systems like H2 + Ru(0001) and non-activated systems like H2 + Pd(111), for which SRP DFs are not yet available. There is now considerable evidence that electron-hole pair (ehp) excitation does not need to be modeled to achieve the (chemically) accurate calculation of dissociative chemisorption and scattering probabilities. Dynamics calculations show that phonons can be safely neglected in the chemically accurate calculation of sticking probabilities on cold metal surfaces for activated systems, and in the calculation of a number of other observables. However, there is now sufficient
NASA Astrophysics Data System (ADS)
Zavaritskaya, T. N.; Kucherenko, I. V.; Mel'nik, N. N.; Karczewski, G.; Skorikov, M. L.
2013-11-01
Photoluminescence and Raman scattering spectra in CdTe/ZnTe heterostructures and superlattices with narrow quantum wells (4.8-9.2 Å) in a temperature range of 5-300 K have been measured. The temperature dependences of the intensity of exciton luminescence in isolated quantum wells have been studied, and the thermal activation energies associated with the effective barriers for electrons and holes have been determined. In CdTe/ZnTe heterostructures, the binding energies of an exciton with a heavy hole have been determined as functions of the quantum well width. The multiphonon Raman spectra that exhibit distinctive features, such as the weak intensity of nLO phonon lines of ZnTe ( n < 8), the absence of their dependence on the number n ( n > 2), and the multiple participation in scattering of acoustic LA phonons with large wave vector, have been investigated. The results have been explained based on the concept of the relaxation of hot excitons over the exciton band.
NASA Astrophysics Data System (ADS)
Urbina, Juan-Diego; Kuipers, Jack; Matsumoto, Sho; Hummel, Quirin; Richter, Klaus
2016-03-01
The interplay between single-particle interference and quantum indistinguishability leads to signature correlations in many-body scattering. We uncover these with a semiclassical calculation of the transmission probabilities through mesoscopic cavities for systems of noninteracting particles. For chaotic cavities we provide the universal form of the first two moments of the transmission probabilities over ensembles of random unitary matrices, including weak localization and dephasing effects. If the incoming many-body state consists of two macroscopically occupied wave packets, their time delay drives a quantum-classical transition along a boundary determined by the bosonic birthday paradox. Mesoscopic chaotic scattering of Bose-Einstein condensates is, then, a realistic candidate to build a boson sampler and to observe the macroscopic Hong-Ou-Mandel effect.
Suzuki, Hideyuki; Imura, Jun-ichi; Horio, Yoshihiko; Aihara, Kazuyuki
2013-01-01
The chaotic Boltzmann machine proposed in this paper is a chaotic pseudo-billiard system that works as a Boltzmann machine. Chaotic Boltzmann machines are shown numerically to have computing abilities comparable to conventional (stochastic) Boltzmann machines. Since no randomness is required, efficient hardware implementation is expected. Moreover, the ferromagnetic phase transition of the Ising model is shown to be characterised by the largest Lyapunov exponent of the proposed system. In general, a method to relate probabilistic models to nonlinear dynamics by derandomising Gibbs sampling is presented. PMID:23558425
NASA Astrophysics Data System (ADS)
Kotulski, Zbigniew; Szczepaski, Janusz
In the paper we propose a new method of constructing cryptosystems utilising a nonpredictability property of discrete chaotic systems. We formulate the requirements for such systems to assure their safety. We also give examples of practical realisation of chaotic cryptosystems, using a generalisation of the method presented in [7]. The proposed algorithm of encryption and decryption is based on multiple iteration of a certain dynamical chaotic system. We assume that some part of the initial condition is a plain message. As the secret key we assume the system parameter(s) and additionally another part of the initial condition.
Gamberg, Leonard; Milton, Kimball A.
2000-04-01
We develop the quantum field theory of electron-point magnetic monopole interactions and, more generally, dyon-dyon interactions, based on the original string-dependent ''nonlocal'' action of Dirac and Schwinger. We demonstrate that a viable nonperturbative quantum field theoretic formulation can be constructed that results in a string independent cross section for monopole-electron and dyon-dyon scattering. Such calculations can be done only by using nonperturbative approximations such as the eikonal approximation and not by some mutilation of lowest-order perturbation theory. (c) 2000 The American Physical Society.
NASA Astrophysics Data System (ADS)
Gamberg, Leonard; Milton, Kimball A.
2000-04-01
We develop the quantum field theory of electron-point magnetic monopole interactions and, more generally, dyon-dyon interactions, based on the original string-dependent ``nonlocal'' action of Dirac and Schwinger. We demonstrate that a viable nonperturbative quantum field theoretic formulation can be constructed that results in a string independent cross section for monopole-electron and dyon-dyon scattering. Such calculations can be done only by using nonperturbative approximations such as the eikonal approximation and not by some mutilation of lowest-order perturbation theory.
2011-01-01
A direct insulator-quantum Hall (I-QH) transition corresponds to a crossover/transition from the insulating regime to a high Landau level filling factor ν > 2 QH state. Such a transition has been attracting a great deal of both experimental and theoretical interests. In this study, we present three different two-dimensional electron systems (2DESs) which are in the vicinity of nanoscaled scatterers. All these three devices exhibit a direct I-QH transition, and the transport properties under different nanaoscaled scatterers are discussed. PMID:21711637
Mutual stabilization of chaotic systems through entangled cupolets
NASA Astrophysics Data System (ADS)
Morena, Matthew Allan
Recent experimental and theoretical work has detected signatures of chaotic behavior in nearly every physical science, including quantum entanglement. In some instances, chaos either plays a significant role or, as an underlying presence, explains perplexing observations. There are certain properties of chaotic systems which are consistently encountered and become focal points of the investigations. For instance, chaotic systems typically admit a dense set of unstable periodic orbits around an attractor. These orbits collectively provide a rich source of qualitative information about the associated system and their abundance has been utilized in a variety of applications. We begin this thesis by describing a control scheme that stabilizes the unstable periodic orbits of chaotic systems and we go on to discuss several properties of these orbits. This technique allows for the creation of thousands of periodic orbits, known as cupolets ( Chaotic Unstable Periodic Orbit-lets ). We then present several applications of cupolets for investigating chaotic systems. First, we demonstrate an effective technique that combines cupolets with algebraic graph theory in order to transition between their orbits. This also induces certainty into the control of nonlinear systems and effectively provides an efficient algorithm for the steering and targeting of chaotic systems. Next, we establish that many higher-order cupolets are amalgamations of simpler cupolets, possibly through bifurcations. From a sufficiently large set of cupolets, we obtain a hierarchal subset of fundamental cupolets from which other cupolets may be assembled and dynamical invariants approximated. We then construct an independent coordinate system aligned to the local dynamical geometry and that reveals the local stretching and folding dynamics which characterize chaotic behavior. This partitions the dynamical landscape into regions of high or low chaoticity, thereby supporting prediction capabilities. Finally
NASA Astrophysics Data System (ADS)
Olivares-Amaya, Roberto
The understanding of molecular effects in nanoscale environments is becoming increasingly relevant for various emerging fields. These include spectroscopy for molecular identification as well as in finding molecules for energy harvesting. Theoretical quantum chemistry has been increasingly useful to address these phenomena to yield an understanding of these effects. In the first part of this dissertation, we study the chemical effect of surface-enhanced Raman scattering (SERS). We use quantum chemistry simulations to study the metal-molecule interactions present in these systems. We find that the excitations that provide a chemical enhancement contain a mixed contribution from the metal and the molecule. Moreover, using atomistic studies we propose an additional source of enhancement, where a transition metal dopant surface could provide an additional enhancement. We also develop methods to study the electrostatic effects of molecules in metallic environments. We study the importance of image-charge effects, as well as field-bias to molecules interacting with perfect conductors. The atomistic modeling and the electrostatic approximation enable us to study the effects of the metal interacting with the molecule in a complementary fashion, which provides a better understanding of the complex effects present in SERS. In the second part of this dissertation, we present the Harvard Clean Energy Project, a high-throughput approach for a large-scale computational screening and design of organic photovoltaic materials. We create molecular libraries to search for candidates structures and use quantum chemistry, machine learning and cheminformatics methods to characterize these systems and find structure-property relations. The scale of this study requires an equally large computational resource. We rely on distributed volunteer computing to obtain these properties. In the third part of this dissertation we present our work related to the acceleration of electronic structure
Zero-strain GaAs quantum dot molecules as investigated by x-ray diffuse scattering
Hanke, M.; Schmidbauer, M.; Grigoriev, D.; Schaefer, P.; Koehler, R.; Metzger, T. H.; Wang, Zh. M.; Mazur, Yu. I.; Salamo, G. J.
2006-07-31
The authors report on x-ray diffuse scattering at nominally strain-free GaAs(001) quantum dot molecules (QDMs). Al{sub 0.3}Ga{sub 0.7}As deposited by molecular beam epitaxy on GaAs(001) acts as barrier layer between the GaAs(001) substrate and subsequently grown QDMs; the adjusted thickness of 50 nm preserves the in-plane lattice parameter. Pairs of lenselike quantum dots are created with preferential orientation along [110] placed on shallow hills. Grazing incidence diffraction along with kinematical scattering simulations indicate completely strain-free QDs which prove a strongly suppressed intermixing between QDMs and the underlying AlGaAs barrier layer.
Full dimension Rb2He ground triplet potential energy surface and quantum scattering calculations.
Guillon, Grégoire; Viel, Alexandra; Launay, Jean-Michel
2012-05-01
We have developed a three-dimensional potential energy surface for the lowest triplet state of the Rb(2)He complex. A global analytic fit is provided as in the supplementary material [see supplementary material at http://dx.doi.org/10.1063/1.4709433 for the corresponding Fortran code]. This surface is used to perform quantum scattering calculations of (4)He and (3)He colliding with (87)Rb(2) in the partial wave J = 0 at low and ultralow energies. For the heavier helium isotope, the computed vibrational relaxation probabilities show a broad and strong shape resonance for a collisional energy of 0.15 K and a narrow Feshbach resonance at about 17 K for all initial Rb(2) vibrational states studied. The broad resonance corresponds to an efficient relaxation mechanism that does not occur when (3)He is the colliding partner. The Feshbach resonance observed at higher collisional energy is robust with respect to the isotopic substitution. However, its effect on the vibrational relaxation mechanism is faint for both isotopes. PMID:22583230
Full dimension Rb2He ground triplet potential energy surface and quantum scattering calculations
NASA Astrophysics Data System (ADS)
Guillon, Grégoire; Viel, Alexandra; Launay, Jean-Michel
2012-05-01
We have developed a three-dimensional potential energy surface for the lowest triplet state of the Rb2He complex. A global analytic fit is provided as in the supplementary material [see supplementary material at http://dx.doi.org/10.1063/1.4709433E-JCPSA6-136-034218 for the corresponding Fortran code]. This surface is used to perform quantum scattering calculations of 4He and 3He colliding with 87Rb2 in the partial wave J = 0 at low and ultralow energies. For the heavier helium isotope, the computed vibrational relaxation probabilities show a broad and strong shape resonance for a collisional energy of 0.15 K and a narrow Feshbach resonance at about 17 K for all initial Rb2 vibrational states studied. The broad resonance corresponds to an efficient relaxation mechanism that does not occur when 3He is the colliding partner. The Feshbach resonance observed at higher collisional energy is robust with respect to the isotopic substitution. However, its effect on the vibrational relaxation mechanism is faint for both isotopes.
Discrete states and carrier-phonon scattering in quantum dot population dynamics
Man, Minh Tan; Lee, Hong Seok
2015-01-01
The influence of the growth conditions of multilayer CdTe/ZnTe quantum dots (QDs) on Si substrate upon their carrier dynamics is studied using intensity integration and broadening photoluminescence. The unusual temperature dependence of the line broadening is explained using a model for interband transitions that involves a lowest discrete electronic state (1Se) with different discrete hole states (1S3/2 and 2S3/2) and a 1P transition. These transitions are expected to play a critical role in both the thermally activated energy and the line broadening of the QDs. We also demonstrate that a thermally activated transition between two different states occurs with band low-temperature quenching, with values separated by 5.8–16 meV. The main nonradiative process is thermal escape assisted by carrier scattering via emission of longitudinal phonons through the hole states at high temperature, with an average energy of 19.3–20.2 meV. PMID:25652600
Celli, Milva; Powers, Anna; Colognesi, Daniele; Xu, Minzhong; Bačić, Zlatko; Ulivi, Lorenzo
2013-10-28
We have performed high-resolution inelastic neutron scattering (INS) measurements on binary hydrogen clathrate hydrates exhibiting the hexagonal structure (sH). Two samples, differing only in the ortho/para fraction of hydrogen, were prepared using heavy water and methyl tert-butyl ether as the promoter in its perdeuterated form. The INS spectrum of the translation-rotation (TR) excitations of the guest H2 molecule was obtained by subtracting the very weak signal due to the D2O lattice modes. By means of a subtraction procedure, it has been possible to obtain separately the spectra of caged p-H2 and o-H2. sH clathrates are comprised of three distinct types of cages, two of which, differing in shape and size, are each occupied by one H2 molecule only. Both contribute to the measured INS spectrum which is, therefore, rather complex and challenging to assign unambiguously. To assist with the interpretation, the INS spectra are calculated accurately utilizing the quantum methodology which incorporates the coupled five-dimensional TR energy levels and wave functions of the H2 molecule confined in each type of nanocage. The computed INS spectra are highly realistic and reflect the complexity of the coupled TR dynamics of the guest H2 in the anisotropic confining environment. The simulated INS spectra of p-H2 and o-H2 in the small and medium cages are compared with the experimental data, and are indispensable for their interpretation. PMID:24182049
Manthe, Uwe; Ellerbrock, Roman
2016-05-28
A new approach for the quantum-state resolved analysis of polyatomic reactions is introduced. Based on the singular value decomposition of the S-matrix, energy-dependent natural reaction channels and natural reaction probabilities are defined. It is shown that the natural reaction probabilities are equal to the eigenvalues of the reaction probability operator [U. Manthe and W. H. Miller, J. Chem. Phys. 99, 3411 (1993)]. Consequently, the natural reaction channels can be interpreted as uniquely defined pathways through the transition state of the reaction. The analysis can efficiently be combined with reactive scattering calculations based on the propagation of thermal flux eigenstates. In contrast to a decomposition based straightforwardly on thermal flux eigenstates, it does not depend on the choice of the dividing surface separating reactants from products. The new approach is illustrated studying a prototypical example, the H + CH4 → H2 + CH3 reaction. The natural reaction probabilities and the contributions of the different vibrational states of the methyl product to the natural reaction channels are calculated and discussed. The relation between the thermal flux eigenstates and the natural reaction channels is studied in detail. PMID:27250291
NASA Astrophysics Data System (ADS)
Manthe, Uwe; Ellerbrock, Roman
2016-05-01
A new approach for the quantum-state resolved analysis of polyatomic reactions is introduced. Based on the singular value decomposition of the S-matrix, energy-dependent natural reaction channels and natural reaction probabilities are defined. It is shown that the natural reaction probabilities are equal to the eigenvalues of the reaction probability operator [U. Manthe and W. H. Miller, J. Chem. Phys. 99, 3411 (1993)]. Consequently, the natural reaction channels can be interpreted as uniquely defined pathways through the transition state of the reaction. The analysis can efficiently be combined with reactive scattering calculations based on the propagation of thermal flux eigenstates. In contrast to a decomposition based straightforwardly on thermal flux eigenstates, it does not depend on the choice of the dividing surface separating reactants from products. The new approach is illustrated studying a prototypical example, the H + CH4 → H2 + CH3 reaction. The natural reaction probabilities and the contributions of the different vibrational states of the methyl product to the natural reaction channels are calculated and discussed. The relation between the thermal flux eigenstates and the natural reaction channels is studied in detail.
Scattering mechanisms in shallow undoped Si/SiGe quantum wells
NASA Astrophysics Data System (ADS)
Laroche, Dominique; Huang, Shih-Hsien; Nielsen, Erik; Chuang, Yen; Li, Jiun-Yun; Liu, Chih-Wen; Lu, Tzu-Ming
We report the magneto-transport and scattering mechanism analysis of a series of increasingly shallow Si/SiGe quantum wells with the shallowest 2DEG located only ~ 10 nm away from the surface. The peak mobility increases with increasing depth, suggesting that charge centers near the oxide/semiconductor interface is the main source of disorder. The power-law exponent of the mobility versus density curve, μ ~nα , is extracted as a function of the depth. At intermediate densities, the power-law dependence is characterized by α ~ 2 . 3 while at the highest achievable densities for devices with intermediate depth, an exponent α ~ 5 is observed. We propose, and show by simulations, that this increase in α is explained by a non-equilibrium model where electrons migrating to the surface smooth out the potential landscape seen by the 2DEG. This work has been supported by the Division of Materials Sciences and Engineering, Office of Basic Energy Sciences, U.S. Department of Energy (DOE). Sandia National Laboratories is a multi program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. DOE's National Nuclear Security Administration under contract DE-AC04-94AL
NASA Astrophysics Data System (ADS)
Celli, Milva; Powers, Anna; Colognesi, Daniele; Xu, Minzhong; Bačić, Zlatko; Ulivi, Lorenzo
2013-10-01
We have performed high-resolution inelastic neutron scattering (INS) measurements on binary hydrogen clathrate hydrates exhibiting the hexagonal structure (sH). Two samples, differing only in the ortho/para fraction of hydrogen, were prepared using heavy water and methyl tert-butyl ether as the promoter in its perdeuterated form. The INS spectrum of the translation-rotation (TR) excitations of the guest H2 molecule was obtained by subtracting the very weak signal due to the D2O lattice modes. By means of a subtraction procedure, it has been possible to obtain separately the spectra of caged p-H2 and o-H2. sH clathrates are comprised of three distinct types of cages, two of which, differing in shape and size, are each occupied by one H2 molecule only. Both contribute to the measured INS spectrum which is, therefore, rather complex and challenging to assign unambiguously. To assist with the interpretation, the INS spectra are calculated accurately utilizing the quantum methodology which incorporates the coupled five-dimensional TR energy levels and wave functions of the H2 molecule confined in each type of nanocage. The computed INS spectra are highly realistic and reflect the complexity of the coupled TR dynamics of the guest H2 in the anisotropic confining environment. The simulated INS spectra of p-H2 and o-H2 in the small and medium cages are compared with the experimental data, and are indispensable for their interpretation.
Jarlov, C; Wodey, É; Lyasota, A; Calic, M; Gallo, P; Dwir, B; Rudra, A; Kapon, E
2016-08-12
Using site-controlled semiconductor quantum dots (QDs) free of multiexcitonic continuum states, integrated with photonic crystal membrane cavities, we clarify the effects of pure dephasing and phonon scattering on exciton-cavity coupling in the weak-coupling regime. In particular, the observed QD-cavity copolarization and cavity mode feeding versus QD-cavity detuning are explained quantitatively by a model of a two-level system embedded in a solid-state environment. PMID:27563983
NASA Astrophysics Data System (ADS)
Jarlov, C.; Wodey, É.; Lyasota, A.; Calic, M.; Gallo, P.; Dwir, B.; Rudra, A.; Kapon, E.
2016-08-01
Using site-controlled semiconductor quantum dots (QDs) free of multiexcitonic continuum states, integrated with photonic crystal membrane cavities, we clarify the effects of pure dephasing and phonon scattering on exciton-cavity coupling in the weak-coupling regime. In particular, the observed QD-cavity copolarization and cavity mode feeding versus QD-cavity detuning are explained quantitatively by a model of a two-level system embedded in a solid-state environment.
2012-01-01
The excitation energy-dependent nature of Raman scattering spectrum, vibration, electronic or both, has been studied using different excitation sources on as-grown and annealed n- and p-type modulation-doped Ga1 − xInxNyAs1 − y/GaAs quantum well structures. The samples were grown by molecular beam technique with different N concentrations (y = 0%, 0.9%, 1.2%, 1.7%) at the same In concentration of 32%. Micro-Raman measurements have been carried out using 532 and 758 nm lines of diode lasers, and the 1064 nm line of the Nd-YAG laser has been used for Fourier transform-Raman scattering measurements. Raman scattering measurements with different excitation sources have revealed that the excitation energy is the decisive mechanism on the nature of the Raman scattering spectrum. When the excitation energy is close to the electronic band gap energy of any constituent semiconductor materials in the sample, electronic transition dominates the spectrum, leading to a very broad peak. In the condition that the excitation energy is much higher than the band gap energy, only vibrational modes contribute to the Raman scattering spectrum of the samples. Line shapes of the Raman scattering spectrum with the 785 and 1064 nm lines of lasers have been observed to be very broad peaks, whose absolute peak energy values are in good agreement with the ones obtained from photoluminescence measurements. On the other hand, Raman scattering spectrum with the 532 nm line has exhibited only vibrational modes. As a complementary tool of Raman scattering measurements with the excitation source of 532 nm, which shows weak vibrational transitions, attenuated total reflectance infrared spectroscopy has been also carried out. The results exhibited that the nature of the Raman scattering spectrum is strongly excitation energy-dependent, and with suitable excitation energy, electronic and/or vibrational transitions can be investigated. PMID:23190628
Bialek, J.M.
1988-01-01
Chaotic behavior may be observed in deterministic Hamiltonian Systems with as few as three dimensions, i.e, X, P, and t. The amount of chaotic behavior depends on the relative influence of the integrable and non-integrable parts of the Hamiltonian. The Standard Map is such a system and the amount of chaotic behavior may be varied by adjusting a single parameter. The global phase space portrait is a complicated mixture of quiescent and chaotic regions. First a new calculational method, characterized by a Fractual Diagram, is presented. This allows the quantitative prediction of the boundaries between regular and chaotic regions in phase space. Where these barriers are located gives qualitative insight into diffusion in phase space. The method is illustrated with the Standard Map but may be applied to any Hamiltonian System. The second phenomenon is the Universal Behavior predicted to occur for all area preserving maps. As a parameter is varied causing the mapping to become more chaotic a pattern is observed in the location and stability of the fixed points of the maps. The fixed points undergo an infinite sequence of period doubling bifurcations in a finite range of the parameter. The relative locations of the fixed point bifurcation and the parameter intervals between bifurcations both asymptotically approach constants which are Universal in that the same constants keep appearing in different problems.
Azuri, Asaf; Pollak, Eli
2015-07-07
In-plane two and three dimensional diffraction patterns are computed for the vertical scattering of an Ar atom from a frozen LiF(100) surface. Suitable collimation of the incoming wavepacket serves to reveal the quantum mechanical diffraction. The interaction potential is based on a fit to an ab initio potential calculated using density functional theory with dispersion corrections. Due to the potential coupling found between the two horizontal surface directions, there are noticeable differences between the quantum angular distributions computed for two and three dimensional scattering. The quantum results are compared to analogous classical Wigner computations on the same surface and with the same conditions. The classical dynamics largely provides the envelope for the quantum diffractive scattering. The classical results also show that the corrugation along the [110] direction of the surface is smaller than along the [100] direction, in qualitative agreement with experimental observations of unimodal and bimodal scattering for the [110] and [100] directions, respectively.
NASA Astrophysics Data System (ADS)
Repin, E. V.; Burmistrov, I. S.
2016-04-01
We explore the inelastic electron-scattering cross section off a metallic quantum dot close to the Stoner instability. We focus on the regime of strong Coulomb blockade in which the scattering cross section is dominated by the cotunneling processes. For large enough exchange interaction, the quantum dot acquires a finite total spin in the ground state. In this so-called mesoscopic Stoner instability regime, we find that at low enough temperatures, the inelastic scattering cross section (including the contribution due to an elastic electron spin flip) for an electron with an energy close to the chemical potential is different from the case of a magnetic impurity with the same spin. This difference stems from (i) the presence of low-lying many-body states of a quantum dot and (ii) the correlations of the tunneling amplitudes. Our results provide a possible explanation for the absence of the dephasing rate saturation at low temperatures in a recent experiment [N. Teneh, A. Yu. Kuntsevich, V. M. Pudalov, and M. Reznikov, Phys. Rev. Lett. 109, 226403 (2012), 10.1103/PhysRevLett.109.226403] in which the existence of local spin droplets in disordered electron liquid has been unraveled.
Cascade Chaotic System With Applications.
Zhou, Yicong; Hua, Zhongyun; Pun, Chi-Man; Chen, C L Philip
2015-09-01
Chaotic maps are widely used in different applications. Motivated by the cascade structure in electronic circuits, this paper introduces a general chaotic framework called the cascade chaotic system (CCS). Using two 1-D chaotic maps as seed maps, CCS is able to generate a huge number of new chaotic maps. Examples and evaluations show the CCS's robustness. Compared with corresponding seed maps, newly generated chaotic maps are more unpredictable and have better chaotic performance, more parameters, and complex chaotic properties. To investigate applications of CCS, we introduce a pseudo-random number generator (PRNG) and a data encryption system using a chaotic map generated by CCS. Simulation and analysis demonstrate that the proposed PRNG has high quality of randomness and that the data encryption system is able to protect different types of data with a high-security level. PMID:25373135
Non-resonant elastic scattering of low-energy photons by atomic sodium confined in quantum plasmas
Ghosh, Avijit Ray, Debasis
2015-03-15
The non-resonant elastic scattering of low-energy photons by the bound valence electron in the ground state 3s of atomic sodium confined in quantum plasmas is investigated theoretically. The incident photon energy is assumed to be much smaller than the 3s-3p excitation energy. The alkali atom sodium is first formulated as an effective one-electron problem in which the attractive interaction between the valence electron and the atomic ion core is simulated by a spherically symmetric model potential. The Shukla-Eliasson oscillatory exponential cosine screened-Coulomb potential model is then used to mimic the effective two-body (valence-core) interaction within quantum plasmas. Non-relativistic calculations performed within the electric dipole approximation indicate that the non-resonant elastic photon scattering cross-section undergoes a dramatic growth by several orders of magnitude as the quantum wave number increases. A qualitative explanation of this phenomenon is presented. In the absence of the oscillatory cosine screening term, a similar growth is observed at larger values of the quantum wave number. Our computed relevant atomic data are in very good agreement with the experimental as well as the previous theoretical data for the zero-screening (free atom) case, and with the very limited, accurate theoretical results available for the case of exponential screened-Coulomb two-body interaction, without the cosine screening term.
NASA Astrophysics Data System (ADS)
Burova, T. G.; Shcherbakov, R. S.
2016-05-01
Quantum-mechanical calculations of the intensity distribution in the resonant Raman scattering spectra of aqueous solutions of tyrosine excited by laser radiation with wavelengths of 244, 229, 218, 200, and 193 nm, as well as in the nonresonant Raman scattering spectrum excited at a wavelength of 488 nm, are performed. Satisfactory agreement is achieved between the calculation results and the experimental data. It is shown that the changes in the intensity distribution observed in the spectra with a change in the excitation wavelength from 244 to 193 nm correlate with the determined changes in the contribution made by excited electronic states into the scattering tensor components. It is noted that it is necessary to take into account the Herzberg-Teller effect and that the number of excited electronic states taken into account considerably affects the calculated relative intensities of lines. The possibility of existence of several tyrosine conformers in aqueous solution at room temperature is shown.
Warehime, Mick; Alexander, Millard H.
2014-07-14
We restate the application of the finite element method to collinear triatomic reactive scattering dynamics with a novel treatment of the scattering boundary conditions. The method provides directly the reactive scattering wave function and, subsequently, the probability current density field. Visualizing these quantities provides additional insight into the quantum dynamics of simple chemical reactions beyond simplistic one-dimensional models. Application is made here to a symmetric reaction (H+H{sub 2}), a heavy-light-light reaction (F+H{sub 2}), and a heavy-light-heavy reaction (F+HCl). To accompany this article, we have written a MATLAB code which is fast, simple enough to be accessible to a wide audience, as well as generally applicable to any problem that can be mapped onto a collinear atom-diatom reaction. The code and user's manual are available for download from http://www2.chem.umd.edu/groups/alexander/FEM.
NASA Astrophysics Data System (ADS)
Warehime, Mick; Alexander, Millard H.
2014-07-01
We restate the application of the finite element method to collinear triatomic reactive scattering dynamics with a novel treatment of the scattering boundary conditions. The method provides directly the reactive scattering wave function and, subsequently, the probability current density field. Visualizing these quantities provides additional insight into the quantum dynamics of simple chemical reactions beyond simplistic one-dimensional models. Application is made here to a symmetric reaction (H+H2), a heavy-light-light reaction (F+H2), and a heavy-light-heavy reaction (F+HCl). To accompany this article, we have written a MATLAB code which is fast, simple enough to be accessible to a wide audience, as well as generally applicable to any problem that can be mapped onto a collinear atom-diatom reaction. The code and user's manual are available for download from http://www2.chem.umd.edu/groups/alexander/FEM.
NASA Astrophysics Data System (ADS)
Potapov, A.; Ali, M. K.
2001-04-01
We consider the problem of stabilizing unstable equilibria by discrete controls (the controls take discrete values at discrete moments of time). We prove that discrete control typically creates a chaotic attractor in the vicinity of an equilibrium. Artificial neural networks with reinforcement learning are known to be able to learn such a control scheme. We consider examples of such systems, discuss some details of implementing the reinforcement learning to controlling unstable equilibria, and show that the arising dynamics is characterized by positive Lyapunov exponents, and hence is chaotic. This chaos can be observed both in the controlled system and in the activity patterns of the controller.
Experiments in chaotic dynamics
NASA Astrophysics Data System (ADS)
Moon, F. C.
Mathematical tools for the description of chaotic phenomena in physical systems are described and demonstrated, summarizing in part the principles presented in the author's book-length treatise on chaotic vibrations (Moon, 1987). Consideration is given to phase-plane and pseudo-phase-plane techniques, bifurcation diagrams, FFTs, autocorrelation functions, single and double Poincare maps, reduction to one-dimensional maps, Liapunov exponents, fractal dimensions, invariant distributions, chaos diagrams, and basin-boundary diagrams. The results obtained by application of these methods to data from typical mechanical and electronic oscillation experiments are presented graphically and discussed in detail.
Chaotic Hierarchy in High Dimensions
NASA Astrophysics Data System (ADS)
Postnov, D. E.; Balanov, A. G.; Sosnovtseva, O. V.; Mosekilde, E.
The paper suggests a new mechanism for the development of higher-order chaos in accordance with the concept of a chaotic hierarchy. A discrete-time model is proposed which demonstrates how the creation of coexisting chaotic attractors combined with boundary crises can produce a continued growth of the Lyapunov dimension of the resulting chaotic behavior.
Quantum Image Encryption Algorithm Based on Quantum Image XOR Operations
NASA Astrophysics Data System (ADS)
Gong, Li-Hua; He, Xiang-Tao; Cheng, Shan; Hua, Tian-Xiang; Zhou, Nan-Run
2016-03-01
A novel encryption algorithm for quantum images based on quantum image XOR operations is designed. The quantum image XOR operations are designed by using the hyper-chaotic sequences generated with the Chen's hyper-chaotic system to control the control-NOT operation, which is used to encode gray-level information. The initial conditions of the Chen's hyper-chaotic system are the keys, which guarantee the security of the proposed quantum image encryption algorithm. Numerical simulations and theoretical analyses demonstrate that the proposed quantum image encryption algorithm has larger key space, higher key sensitivity, stronger resistance of statistical analysis and lower computational complexity than its classical counterparts.
Quantum Image Encryption Algorithm Based on Quantum Image XOR Operations
NASA Astrophysics Data System (ADS)
Gong, Li-Hua; He, Xiang-Tao; Cheng, Shan; Hua, Tian-Xiang; Zhou, Nan-Run
2016-07-01
A novel encryption algorithm for quantum images based on quantum image XOR operations is designed. The quantum image XOR operations are designed by using the hyper-chaotic sequences generated with the Chen's hyper-chaotic system to control the control-NOT operation, which is used to encode gray-level information. The initial conditions of the Chen's hyper-chaotic system are the keys, which guarantee the security of the proposed quantum image encryption algorithm. Numerical simulations and theoretical analyses demonstrate that the proposed quantum image encryption algorithm has larger key space, higher key sensitivity, stronger resistance of statistical analysis and lower computational complexity than its classical counterparts.
Semenov, Alexander; Babikov, Dmitri
2016-06-01
Theoretical foundation is laid out for description of permutation symmetry in the inelastic scattering processes that involve collisions of two identical molecules, within the framework of the mixed quantum/classical theory (MQCT). In this approach, the rotational (and vibrational) states of two molecules are treated quantum-mechanically, whereas their translational motion (responsible for scattering) is treated classically. This theory is applied to H2 + H2 system, and the state-to-state transition cross sections are compared versus those obtained from the full-quantum calculations and experimental results from the literature. Good agreement is found in all cases. It is also found that results of MQCT, where the Coriolis coupling is included classically, are somewhat closer to exact full-quantum results than results of the other approximate quantum methods, where those coupling terms are neglected. These new developments allow applications of MQCT to a broad variety of molecular systems and processes. PMID:27187769
Chaotic Scattering In Magnetic Current Sheets
NASA Astrophysics Data System (ADS)
Martin, R.; Holland, D.; Matsuoka, H.; Rappa, R.
We revisit the subject of nonlinear charged particle dynamics and chaos in current sheet magnetic fields using the modified Harris magnetic field. While much has been written on this subject in the last decade we feel there are some as-yet-unanswered fundamental questions as well as some "folklore" which is in need of clarification. We begin by demonstrating that the general behavior of the average exponential di- vergence rate (AEDR) of individual orbits is strongly correlated with the phase space partitions, i.e. the AEDR for integrable orbits goes to zero for long times, the AEDR of stochastic orbits approaches an asymptotic value for long times, and the AEDR of transient orbits (and short lived stochastic orbits) is not well defined. Furthermore, we show that the Lyapunov exponent for a distribution of particles only has well de- fined values at the resonant energy surfaces defined by Burkhart and Chen. Next it is shown that the "chaos" of the system is maximum at = 1 only in the sense that a lot of particles enter the stochastic region of phase space for this energy. The average Lyapunov exponent at = 1 actually approaches zero, and for those energies where the Lyapunov exponent is defined, it increases as the ratio of normal component of the field to the asymptotic field strength increases. Finally, we present particle escape rate and fractal invariant set results corroborating these conclusions and consider the consequences for anomalous transport in these fields.
NASA Technical Reports Server (NTRS)
Wang, Dunyou; Stallcop, James R.; Dateo, Christopher E.; Schwenke, David W.; Huo, Winifred M.
2004-01-01
A three-dimensional time-dependent quantum dynamics approach using a recently developed ab initio potential energy surface is applied to study ro-vibrational excitation in N+N2 exchange scattering for collision energies in the range 2.1- 3.2 eV. State-to-state integral exchange cross sections are examined to determine the distribution of excited rotational states of N(sub 2). The results demonstrate that highly-excited rotational states are produced by exchange scattering and furthermore, that the maximum value of (Delta)j increases rapidly with increasing collision energies. Integral exchange cross sections and exchange rate constants for excitation to the lower (upsilon = 0-3) vibrational energy levels are presented as a function of the collision energy. Excited-vibrational-state distributions for temperatures at 2,000 K and 10,000 K are included.
NASA Astrophysics Data System (ADS)
Zhang, Xu
This paper introduces a class of polynomial maps in Euclidean spaces, investigates the conditions under which there exist Smale horseshoes and uniformly hyperbolic invariant sets, studies the chaotic dynamical behavior and strange attractors, and shows that some maps are chaotic in the sense of Li-Yorke or Devaney. This type of maps includes both the Logistic map and the Hénon map. For some diffeomorphisms with the expansion dimension equal to one or two in three-dimensional spaces, the conditions under which there exist Smale horseshoes and uniformly hyperbolic invariant sets on which the systems are topologically conjugate to the two-sided fullshift on finite alphabet are obtained; for some expanding maps, the chaotic region is analyzed by using the coupled-expansion theory and the Brouwer degree theory. For three types of higher-dimensional polynomial maps with degree two, the conditions under which there are Smale horseshoes and uniformly hyperbolic invariant sets are given, and the topological conjugacy between the maps on the invariant sets and the two-sided fullshift on finite alphabet is obtained. Some interesting maps with chaotic attractors and positive Lyapunov exponents in three-dimensional spaces are found by using computer simulations. In the end, two examples are provided to illustrate the theoretical results.
NASA Astrophysics Data System (ADS)
Anders, Frithjof B.
2008-08-01
We propose a numerical renormalization group (NRG) approach to steady-state currents through nanodevices. A discretization of the scattering-states continuum ensures the correct boundary condition for an open quantum system. We introduce two degenerate Wilson chains for current carrying left- and right-moving electrons reflecting time-reversal symmetry in the absence of a finite bias V. We employ the time-dependent NRG to evolve the known steady-state density operator for a noninteracting junction into the density operator of the fully interacting nanodevice at finite bias. We calculate the differential conductance as function of V, T, and the external magnetic field.
Chaotic motion in a primordial comet disk beyond Neptune and comet influx to the solar system
NASA Astrophysics Data System (ADS)
Torbett, M. V.; Smoluchowski, R.
1990-05-01
Previous calculations using a heliocentric frame have shown that a scattered disk of cometesimals beyond Neptune develops chaotic motions with divergence timescales less than 1 Myr. Here, improved numerical simulations using a baryocentric system and thus including the additional frequencies associated with motions of the sun are described. Because the onset of chaotic motion is characterized by the appearance of broadband noise, the inclusion of these additional perturbations should increase the likelihood of stochastic behavior and thus the chaotic zone should be larger. The results indicate that comets in a low-eccentricity primordial disk beyond Neptune can exhibit chaotic motions which lead to interesting consequences for the dynamics of comets.
Photonic Rutherford scattering: A classical and quantum mechanical analogy in ray and wave optics
NASA Astrophysics Data System (ADS)
Selmke, Markus; Cichos, Frank
2013-06-01
Using Fermat's least-optical-path principle, the family of ray trajectories through a special (but common) type of a gradient refractive index lens n(r)=n0+ΔnR /r is solved analytically. The solution gives a ray equation r(ϕ) that is closely related to Rutherford scattering trajectories; we therefore refer to this refraction process as "photonic Rutherford scattering." It is shown that not only do the classical limits correspond but also the wave-mechanical pictures coincide—the time-independent Schrödingier equation and the Helmholtz equation permit the same mapping between the scattering of massive particles and optical scalar waves. Scattering of narrow beams of light finally recovers the classical trajectories. The analysis suggests that photothermal single-particle microscopy measures photonic Rutherford scattering in specific limits and allows for an individual single-scatterer probing. A macroscopic experiment is demonstrated to directly measure the scattering angle to impact parameter relation, which is otherwise accessible only indirectly in Rutherford-scattering experiments.
Dynamic interpretation of atomic and molecular spectra in the chaotic regime
Taylor, H.S.; Zakrzewski, J.
1988-10-01
A quantum partitioning theory is given for extracting dynamic information from the high-resolution spectra of highly excited atoms and molecules that is relatively simple to apply. The presented approach is applicable whenever the classical counterpart of the system studied is chaotic. The theory allows a picture of the underlying non-statistically-describable part of the dynamics to be obtained from the spectra. The theory presented effectively uses and unifies many aspects of classical trajectory approaches, Feshbach resonant-scattering partitioning theory, semiclassical periodic-orbit theory, ''scars'' theory, bright- and dark-state concepts, and Fourier transforms of the spectra. The power of the theory is demonstrated quantitatively by interpreting the dynamics underlying the absorption spectra of the hydrogen atom in a strong uniform magnetic field.
Choi, B.H.; Poe, R.T.
1985-08-01
We present a systematic formulation of the atom--surface scattering dynamics which includes the vibrational states of the atoms in the solid (phonons). The properties of the total scattering wave function of the system, a representation of the interaction potential matrix, and the characteristics of the independent physical solutions are all derived from the translational invariance of the full Hamiltonian. The scattering equations in the integral forms as well as the related Green functions were also obtained. The configurational representations of the Green functions, in particular, are quite different from those of the conventional scattering theory where the collision partners are spatially localized. Various versions of the integral expression of scattering, transition, and reactance matrices were also obtained. They are useful for introducing approximation schemes. From the present formulation, some specific theoretical schemes which are more realistic compared to those that have been employed so far and at the same time capable of yielding effective ab initio computation are derived in the following paper. The time reversal invariance and the microscopic reversibility of the atom--surface scattering were discussed. The relations between the in and outgoing scattering wave functions which are satisfied in the atom--surface system and important in the transition matrix methods were presented. The phonon annihilation and creation, and the adsorption and desorption of the atom are related through the time reversal invariance, and thus the microscopic reversibility can be tested by the experiment.
Coherent Scattering of a Multiphoton Quantum Superposition by a Mirror BEC
De Martini, Francesco; Sciarrino, Fabio; Vitelli, Chiara; Cataliotti, Francesco S.
2010-02-05
We present the proposition of an experiment in which the multiphoton quantum superposition consisting of Napprox =10{sup 5} particles generated by a quantum-injected optical parametric amplifier, seeded by a single-photon belonging to an Einstein-Podolsky-Rosen entangled pair, is made to interact with a mirror-Bose-Einstein condensate (BEC) shaped as a Bragg interference structure. The overall process will realize a macroscopic quantum superposition involving a microscopic single-photon state of polarization entangled with the coherent macroscopic transfer of momentum to the BEC structure, acting in spacelike separated distant places.
NASA Astrophysics Data System (ADS)
Zadoyan, R.; Kohen, D.; Lidar, D. A.; Apkarian, V. A.
2001-05-01
Molecular ro-vibronic coherences, joint energy-time distributions of quantum amplitudes, are selectively prepared, manipulated, and imaged in time-frequency-resolved coherent anti-Stokes Raman scattering (TFRCARS) measurements using femtosecond laser pulses. The studies are implemented in iodine vapor, with its thermally occupied statistical ro-vibrational density serving as initial state. The evolution of the massive ro-vibronic superpositions, consisting of 10 3 eigenstates, is followed through two-dimensional images. The first- and second-order coherences are captured using time-integrated frequency-resolved CARS, while the third-order coherence is captured using time-gated frequency-resolved CARS. The Fourier filtering provided by time-integrated detection projects out single ro-vibronic transitions, while time-gated detection allows the projection of arbitrary ro-vibronic superpositions from the coherent third-order polarization. A detailed analysis of the data is provided to highlight the salient features of this four-wave mixing process. The richly patterned images of the ro-vibrational coherences can be understood in terms of phase evolution in rotation-vibration-electronic Hilbert space, using time-circuit diagrams. Beside the control and imaging of chemistry, the controlled manipulation of massive quantum coherences suggests the possibility of quantum computing. We argue that the universal logic gates necessary for arbitrary quantum computing - all single qubit operations and the two-qubit controlled-NOT (CNOT) gate - are available in time-resolved four-wave mixing in a molecule. The molecular rotational manifold is naturally "wired" for carrying out all single qubit operations efficiently, and in parallel. We identify vibronic coherences as one example of a naturally available two-qubit CNOT gate, wherein the vibrational qubit controls the switching of the targeted electronic qubit.
Scattering Problem and Resonances for Three-Body Coulomb Quantum Systems: Parallel Calculations
NASA Astrophysics Data System (ADS)
Yarevsky, E.
2016-02-01
An approach to the solution of scattering and resonance problems based on splitting the potential into a finite range part and a long range tail part is proposed. The explicit solution to the Schrödinger equation for the long range tail Hamiltonian is used as an incoming wave. This reformulation of the scattering problem makes it suitable for treatment by the exterior complex scaling. The same technique is used to determine resonances of the system. Calculations are performed with the finite element method which allows efficient parallel computations. The approach is illustrated with calculations of the electron resonant scattering on the hydrogen and the helium ion.
Statistics of chaotic resonances in an optical microcavity
NASA Astrophysics Data System (ADS)
Wang, Li; Lippolis, Domenico; Li, Ze-Yang; Jiang, Xue-Feng; Gong, Qihuang; Xiao, Yun-Feng
2016-04-01
Distributions of eigenmodes are widely concerned in both bounded and open systems. In the realm of chaos, counting resonances can characterize the underlying dynamics (regular vs chaotic), and is often instrumental to identify classical-to-quantum correspondence. Here, we study, both theoretically and experimentally, the statistics of chaotic resonances in an optical microcavity with a mixed phase space of both regular and chaotic dynamics. Information on the number of chaotic modes is extracted by counting regular modes, which couple to the former via dynamical tunneling. The experimental data are in agreement with a known semiclassical prediction for the dependence of the number of chaotic resonances on the number of open channels, while they deviate significantly from a purely random-matrix-theory-based treatment, in general. We ascribe this result to the ballistic decay of the rays, which occurs within Ehrenfest time, and importantly, within the time scale of transient chaos. The present approach may provide a general tool for the statistical analysis of chaotic resonances in open systems.
Quantum Multimode Model of Elastic Scattering from Bose-Einstein Condensates
Zin, P.; Chwedenczuk, J.; Trippenbach, M.; Veitia, A.; Rzazewski, K.
2005-05-27
Mean field approximation treats only coherent aspects of the evolution of a Bose-Einstein condensate. However, in many experiments some atoms scatter out of the condensate. We study a semianalytic model of two counterpropagating atomic Gaussian wave packets incorporating the dynamics of incoherent scattering processes. Within the model we can treat processes of the elastic collision of atoms into the initially empty modes, and observe how, with growing occupation, the bosonic enhancement is slowly kicking in. A condition for the bosonic enhancement effect is found in terms of relevant parameters. Scattered atoms form a squeezed state. Not only are we able to calculate the dynamics of mode occupation, but also the full statistics of scattered atoms.
NASA Astrophysics Data System (ADS)
Abdurakhmanov, I. B.; Kadyrov, A. S.; Avazbaev, S. K.; Bray, I.
2016-06-01
Details of the recently developed quantum-mechanical two-center convergent close-coupling approach (Abdurakhmanov et al 2016 J. Phys. B: At. Mol. Phys. 49 03LT01) to proton-hydrogen scattering are presented. The formulation is based on the exact (fully quantum-mechanical) three-body Schrödinger equation. The total scattering wavefunction is expanded using a two-center pseudostate basis. This allows one to include all underlying processes, namely, direct scattering and ionization, electron capture into bound and continuum states of the projectile. The off-shell integration in the coupled-channel Lippmann–Schwinger integral equations emerging from the three-body Schrödinger equation for the scattering wavefunction is taken analytically which greatly reduces computational effort. While the calculated electron capture cross sections are in a good agreement with experiment, some discrepancy exists for the ionization cross sections.
Hypogenetic chaotic jerk flows
NASA Astrophysics Data System (ADS)
Li, Chunbiao; Sprott, Julien Clinton; Xing, Hongyan
2016-03-01
Removing the amplitude or polarity information in the feedback loop of a jerk structure shows that special nonlinearities with partial information in the variable can also lead to chaos. Some striking properties are found for this kind of hypogenetic chaotic jerk flow, including multistability of symmetric coexisting attractors from an asymmetric structure, hidden attractors with respect to equilibria but with global attraction, easy amplitude control, and phase reversal which is convenient for chaos applications.
NASA Astrophysics Data System (ADS)
Tiutiunnyk, Anton; Akimov, Volodymyr; Tulupenko, Viktor; Mora-Ramos, Miguel E.; Kasapoglu, Esin; Morales, Alvaro L.; Duque, Carlos Alberto
2016-04-01
The differential cross-section of electron Raman scattering and the Raman gain are calculated and analysed in the case of prismatic quantum dots with equilateral triangle base shape. The study takes into account their dependencies on the size of the triangle, the influence of externally applied electric field as well as the presence of an ionized donor center located at the triangle's orthocenter. The calculations are made within the effective mass and parabolic band approximations, with a diagonalization scheme being applied to obtain the eigenfunctions and eigenvalues of the x- y Hamiltonian. The incident and secondary (scattered) radiation have been considered linearly-polarized along the y-direction, coinciding with the direction of the applied electric field. For the case with an impurity center, Raman scattering with the intermediate state energy below the initial state one has been found to show maximum differential cross-section more than by an order of magnitude bigger than that resulting from the scheme with lower intermediate state energy. The Raman gain has maximum magnitude around 35 nm dot size and electric field of 40 kV/cm for the case without impurity and at maximum considered values of the input parameters for the case with impurity. Values of Raman gain of the order of up to 104cm-1 are predicted in both cases.
Resonances in Coupled $\pi K\text{-}\eta K$ Scattering from Quantum Chromodynamics
Dudek, Jozef J.; Edwards, Robert G.; Thomas, Christopher E.; Wilson, David J.
2014-10-01
Using first-principles calculation within Quantum Chromodynamics, we are able to reproduce the pattern of experimental strange resonances which appear as complex singularities within coupled πK, ηK scattering amplitudes. We make use of numerical computation within the lattice discretized approach to QCD, extracting the energy dependence of scattering amplitudes through their relation- ship to the discrete spectrum of the theory in a finite-volume, which we map out in unprecedented detail.
Chaotic spectra: How to extract dynamic information
Taylor, H.S.; Gomez Llorente, J.M.; Zakrzewski, J.; Kulander, K.C.
1988-10-01
Nonlinear dynamics is applied to chaotic unassignable atomic and molecular spectra with the aim of extracting detailed information about regular dynamic motions that exist over short intervals of time. It is shown how this motion can be extracted from high resolution spectra by doing low resolution studies or by Fourier transforming limited regions of the spectrum. These motions mimic those of periodic orbits (PO) and are inserts into the dominant chaotic motion. Considering these inserts and the PO as a dynamically decoupled region of space, resonant scattering theory and stabilization methods enable us to compute ladders of resonant states which interact with the chaotic quasi-continuum computed in principle from basis sets placed off the PO. The interaction of the resonances with the quasicontinuum explains the low resolution spectra seen in such experiments. It also allows one to associate low resolution features with a particular PO. The motion on the PO thereby supplies the molecular movements whose quantization causes the low resolution spectra. Characteristic properties of the periodic orbit based resonances are discussed. The method is illustrated on the photoabsorption spectrum of the hydrogen atom in a strong magnetic field and on the photodissociation spectrum of H/sub 3//sup +/. Other molecular systems which are currently under investigation using this formalism are also mentioned. 53 refs., 10 figs., 2 tabs.
Semenov, Alexander; Babikov, Dmitri
2015-12-17
The mixed quantum classical theory, MQCT, for inelastic scattering of two molecules is developed, in which the internal (rotational, vibrational) motion of both collision partners is treated with quantum mechanics, and the molecule-molecule scattering (translational motion) is described by classical trajectories. The resultant MQCT formalism includes a system of coupled differential equations for quantum probability amplitudes, and the classical equations of motion in the mean-field potential. Numerical tests of this theory are carried out for several most important rotational state-to-state transitions in the N2 + H2 system, in a broad range of collision energies. Besides scattering resonances (at low collision energies) excellent agreement with full-quantum results is obtained, including the excitation thresholds, the maxima of cross sections, and even some smaller features, such as slight oscillations of energy dependencies. Most importantly, at higher energies the results of MQCT are nearly identical to the full quantum results, which makes this approach a good alternative to the full-quantum calculations that become computationally expensive at higher collision energies and for heavier collision partners. Extensions of this theory to include vibrational transitions or general asymmetric-top rotor (polyatomic) molecules are relatively straightforward. PMID:26323089
NASA Astrophysics Data System (ADS)
Touma, J.; Wisdom, J.
1993-02-01
The discovery (by Laskar, 1989, 1990) that the evolution of the solar system is chaotic, made in a numerical integration of the averaged secular approximation of the equations of motions for the planets, was confirmed by Sussman and Wisdom (1992) by direct numerical integration of the whole solar system. This paper presents results of direct integrations of the rotation of Mars in the chaotically evolved planetary system, made using the same model as that used by Sussman and Wisdom. The numerical integration shows that the obliquity of Mars undergoes large chaotic variations, which occur as the system evolves in the chaotic zone associated with a secular spin-orbit resonance.
Using Chaotic System in Encryption
NASA Astrophysics Data System (ADS)
Findik, Oğuz; Kahramanli, Şirzat
In this paper chaotic systems and RSA encryption algorithm are combined in order to develop an encryption algorithm which accomplishes the modern standards. E.Lorenz's weather forecast' equations which are used to simulate non-linear systems are utilized to create chaotic map. This equation can be used to generate random numbers. In order to achieve up-to-date standards and use online and offline status, a new encryption technique that combines chaotic systems and RSA encryption algorithm has been developed. The combination of RSA algorithm and chaotic systems makes encryption system.
The chaotic atom model via a fractal approximation of motion
NASA Astrophysics Data System (ADS)
Agop, M.; Nica, P.; Gurlui, S.; Focsa, C.; Magop, D.; Borsos, Z.
2011-10-01
A new model of the atom is built based on a complete and detailed nonlinear dynamics analysis (complete time series, Poincaré sections, complete phase space, Lyapunov exponents, bifurcation diagrams and fractal analysis), through the correlation of the chaotic-stochastic model with a fractal one. Some specific mechanisms that ensure the atom functionality are proposed: gun, chaotic gun and multi-gun effects for the excited states (the classical analogue of quantum absorption) and the fractalization of the trajectories for the stationary states (a natural way of introducing the quantification).
NASA Astrophysics Data System (ADS)
Gostein, Michael
The effects of molecular rotation and vibration in the dynamics of H2 scattering from Pd(111) and Cu(110) were studied using molecular beam and laser spectroscopy techniques. These studies test state-of-the- art theoretical simulations of molecule-surface interactions, a fundamental understanding of which is relevant to diverse fields in science and technology. Experiments on the rotational state dependence of H2 dissociation on Pd(111) were motivated by recent theoretical results concerning the concept of dynamical steering. This concept has been invoked to explain the enhancement of sticking at low translational energy for H2 incident on certain metals. It suggests that sticking should also be enhanced for low rotational energy in these systems. The experiments presented here qualitatively confirm this prediction. For incident translational energies from 31- 95 meV, the H2/Pd(111) sticking coefficient goes down as the rotational quantum number J is raised from 0 to 3. It then increases for J = 4 and 5, which is consistent with rotational energy also helping directly overcome the activation barrier. A fraction of the scattered H2 molecules are also rotationally excited. This occurs directly upon scattering but is activated by the surface temperature, not the incident translational energy. This behavior is not explained by current theoretical treatments and requires further exploration. Experiments on the vibrational state dependence of H2 scattering from Cu(110) and Pd(111) were motivated by continued considerations of activation barriers to dissociative adsorption, since vibrational energy assists in surmounting barriers which occur 'late' along the reaction path. The survival probability of H2 in the rovibrational state (v = 1, J = 1), prepared by stimulated Raman scattering, was measured for scattering from each surface. In both cases the (v = 1, J = 1) survival probability is smaller than that of the ground vibrational state, in accord with expectations for a
Wu Chunbai; Raymer, M. G.; Wang, Y. Y.; Benabid, F.
2010-11-15
We explore theoretically the phase correlation between multiple generated sidebands in a Raman optical frequency comb under conditions of spontaneous initiation from quantum zero-point noise. We show that there is a near-deterministic correlation between sideband phases in each laser shot which may lead to synthesis of attosecond pulse trains.
NASA Astrophysics Data System (ADS)
Kurlov, S. S.; Flores, Y. V.; Elagin, M.; Semtsiv, M. P.; Schrottke, L.; Grahn, H. T.; Tarasov, G. G.; Masselink, W. T.
2016-04-01
A phenomenological scattering-rate model introduced for terahertz quantum cascade lasers (QCLs) [Schrottke et al., Semicond. Sci. Technol. 25, 045025 (2010)] is extended to mid-infrared (MIR) QCLs by including the energy dependence of the intersubband scattering rates for energies higher than the longitudinal optical phonon energy. This energy dependence is obtained from a phenomenological fit of the intersubband scattering rates based on published lifetimes of a number of MIR QCLs. In our approach, the total intersubband scattering rate is written as the product of the exchange integral for the squared moduli of the envelope functions and a phenomenological factor that depends only on the transition energy. Using the model to calculate scattering rates and imposing periodical boundary conditions on the current density, we find a good agreement with low-temperature data for current-voltage, power-current, and energy-photon flux characteristics for a QCL emitting at 5.2 μm.
Attosecond quantum entanglement in neutron Compton scattering from water in the keV range
NASA Astrophysics Data System (ADS)
Chatzidimitriou-Dreismann, C. A.
2006-11-01
Scattering of neutrons in the 24- 150 keV incident energy range from H2O relative to that of D2O and H2O- D2O mixtures was reported very recently. Studying time-of-flight integrated intensities, the applied experimental procedure appears to be transparent and may open up a novel class of neutron experiments regarding the “anomalous” scattering from protons, firstly observed in our experiment at ISIS in the 5- 100 eV range. The keV-results were analyzed within standard theory, also including (1) multiple scattering and (2) the strong incident-energy dependence of the neutron-proton cross-section σH(E0) in this energy range. The analysis reveals a striking anomalous ratio of scattering intensity of H2O relative to that of D2O of about 20%, thus being in surprisingly good agreement with the earlier results of the original experiment at ISIS.
Exact quantum scattering calculations of transport properties for the H{sub 2}O–H system
Dagdigian, Paul J.; Alexander, Millard H.
2013-11-21
Transport properties for collisions of water with hydrogen atoms are computed by means of exact quantum scattering calculations. For this purpose, a potential energy surface (PES) was computed for the interaction of rigid H{sub 2}O, frozen at its equilibrium geometry, with a hydrogen atom, using a coupled-cluster method that includes all singles and doubles excitations, as well as perturbative contributions of connected triple excitations. To investigate the importance of the anisotropy of the PES on transport properties, calculations were performed with the full potential and with the spherical average of the PES. We also explored the determination of the spherical average of the PES from radial cuts in six directions parallel and perpendicular to the C{sub 2} axis of the molecule. Finally, the computed transport properties were compared with those computed with a Lennard-Jones 12-6 potential.
NASA Astrophysics Data System (ADS)
Zamoum, R.; Lavagna, M.; Crépieux, A.
2016-06-01
We calculate the nonsymmetrized current noise in a quantum dot connected to two reservoirs by using the nonequilibrium Green function technique. We show that both the current autocorrelator (inside a single reservoir) and the current cross-correlator (between the two reservoirs) are expressed in terms of transmission amplitude and coefficient through the barriers. We identify the different energy-transfer processes involved in each contribution to the autocorrelator, and we highlight the fact that when there are several physical processes, the contribution results from a coherent superposition of scattering paths. Varying the gate and bias voltages, we discuss the profile of the differential Fano factor in light of recent experiments, and we identify the conditions for having a distinct value for the autocorrelator in the left and right reservoirs.
Colognesi, Daniele; Celli, Milva; Ulivi, Lorenzo; Powers, Anna; Xu, Minzhong; Bačić, Zlatko
2014-10-07
We report inelastic neutron scattering (INS) measurements on molecular hydrogen deuteride (HD) trapped in binary cubic (sII) and hexagonal (sH) clathrate hydrates, performed at low temperature using two different neutron spectrometers in order to probe both energy and momentum transfer. The INS spectra of binary clathrate samples exhibit a rich structure containing sharp bands arising from both the rotational transitions and the rattling modes of the guest molecule. For the clathrates with sII structure, there is a very good agreement with the rigorous fully quantum simulations which account for the subtle effects of the anisotropy, angular and radial, of the host cage on the HD microscopic dynamics. The sH clathrate sample presents a much greater challenge, due to the uncertainties regarding the crystal structure, which is known only for similar crystals with different promoter, but nor for HD (or H{sub 2}) plus methyl tert-butyl ether (MTBE-d12)
Chaotic Systems with Absorption
NASA Astrophysics Data System (ADS)
Altmann, Eduardo G.; Portela, Jefferson S. E.; Tél, Tamás
2013-10-01
Motivated by applications in optics and acoustics we develop a dynamical-system approach to describe absorption in chaotic systems. We introduce an operator formalism from which we obtain (i) a general formula for the escape rate κ in terms of the natural conditionally invariant measure of the system, (ii) an increased multifractality when compared to the spectrum of dimensions Dq obtained without taking absorption and return times into account, and (iii) a generalization of the Kantz-Grassberger formula that expresses D1 in terms of κ, the positive Lyapunov exponent, the average return time, and a new quantity, the reflection rate. Simulations in the cardioid billiard confirm these results.
NASA Technical Reports Server (NTRS)
Binzel, R. P.; Green, J. R.; Opal, C. B.
1986-01-01
Thomas et al. (1984) analyzed 14 Voyager 2 images of Saturn's satellite Hyperion and interpreted them to be consistent with a coherent (nonchaotic) rotation period of 13.1 days. This interpretation was criticized by Peale and Wisdom (1984), who argued that the low sampling frequency of Voyager data does not allow chaotic or nonchaotic rotation to be distinguished. New observations obtained with a higher sampling frequency are reported here which conclusively show that the 13.1 day period found by Thomas et al. was not due to coherent rotation.
Learning, Exploration and Chaotic Policies
NASA Astrophysics Data System (ADS)
Potapov, Alexei B.; Ali, M. K.
We consider different versions of exploration in reinforcement learning. For the test problem, we use navigation in a shortcut maze. It is shown that chaotic ɛ-greedy policy may be as efficient as a random one. The best results were obtained with a model chaotic neuron. Therefore, exploration strategy can be implemented in a deterministic learning system such as a neural network.
Wave-Chaotic Optical Resonators and Lasers
NASA Astrophysics Data System (ADS)
Stone, A. Douglas
2001-10-01
Deformed cylindrical and spherical dielectric optical resonators and lasers are analyzed from the perspective of non-linear dynamics and quantum chaos theory. In the short-wavelength limit such resonators behave like billiard systems with non-zero escape probability due to refraction. A ray model is introduced to predict the resonance lifetimes and emission patterns from such a cavity. A universal wavelength-independent broadening is predicted and found for large deformations of the cavity. However there are significant wave-chaotic corrections to the model which arise from chaos-assisted tunneling and dynamical localization effects. Highly directional emission from lasers based on these resonators is predicted from chaotic "whispering gallery" modes for index of refraction less than two. The detailed nature of the emission pattern can be understood from the nature of the phase-space flow in the billiard, and a dramatic variation of this pattern with index of refraction is found due to an effect we term "dynamical eclipsing". Semiconductor lasers of this type also show highly directional emission and high output power but from different modes associated with periodic orbits, both stable and unstable. A semiclassical approach to these modes is briefly reviewed. These asymmetric resonant cavities (ARCs) show promise as components in future integrated optical devices, providing perhaps the first application of quantum chaos theory.
NASA Astrophysics Data System (ADS)
Englund, John C.; Bowden, Charles M.
1992-07-01
The formalism of Englund and Bowden [Phys. Rev. A 42, 2870 (1990)] is used to conduct a detailed investigation into the statistics of spontaneously generated Raman solitons and their origin in phase waves. Two approaches are adopted. In one, a Monte Carlo simulation of the stochastic differential equations describing stimulated Raman scattering is carried out, with quantum noise entering through the Stokes vacuum. The other involves determining analytically the field statistics in the quantum-initiation regime, finding the corresponding phase-wave statistics, and determining numerically the class of phase waves that appear in the nonlinear regime as solitons. Computations involving quasi-Gaussian and rectangular pump-pulse profiles consistently indicate soliton yields of roughly 10% and 4%, respectively; differences in the distributions of soliton delay times and peak intensities are also indicated. The Monte Carlo method is adapted to the experimental parameter values of MacPherson et al. [Phys. Rev. A 40, 6745 (1989)], and gives yields and distribution in good accord with the experiment.
Raman scattering of InAs/AlAs quantum dot superlattices grown on (001) and (311)B GaAs surfaces
2012-01-01
We present a comparative analysis of Raman scattering by acoustic and optical phonons in InAs/AlAs quantum dot superlattices grown on (001) and (311)B GaAs surfaces. Doublets of folded longitudinal acoustic phonons up to the fifth order were observed in the Raman spectra of (001)- and (311)B-oriented quantum dot superlattices measured in polarized scattering geometries. The energy positions of the folded acoustic phonons are well described by the elastic continuum model. Besides the acoustic phonons, the spectra display features related to confined transverse and longitudinal optical as well as interface phonons in quantum dots and spacer layers. Their frequency positions are discussed in terms of phonon confinement, elastic stress, and atomic intermixing. PMID:22916827
Chaotic Nonlinear Prime Number Function
NASA Astrophysics Data System (ADS)
Mateos, Luis A.
2011-06-01
Dynamical systems in nature, such as heartbeat patterns, DNA sequence pattern, prime number distribution, etc., exhibit nonlinear (chaotic) space-time fluctuations and exact quantification of the fluctuation pattern for predictability purposes has not yet been achieved [1]. In this paper a chaotic-nonlinear prime number function P(s) is developed, from which prime numbers are generated and decoded while composite numbers are encoded over time following the Euler product methodology, which works on sequences progressively culled from multiples of the preceding primes. By relating this P(s) to a virtually closed 2D number line manifold, it is possible to represent the evolving in time of nonlinear (chaotic) systems to a final value where the system becomes stable, becomes linear. This nonlinear prime number function is proposed as a chaotic model system able to describe chaotic systems.
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.
Fully quantum state-resolved inelastic scattering between He and NO(X 2Π)
NASA Astrophysics Data System (ADS)
Kłos, J.; Aoiz, F. J.; Verdasco, J. E.; Brouard, M.; Marinakis, S.; Stolte, S.
2007-07-01
Quantum mechanical close-coupling calculations have been used to obtain fully quantum state-resolved differential cross sections and opacity functions for the rotationally inelastic collisions of NO(XΠ2) with He at collision energies of 63 and 147meV using the most recent ab initio potential energy surfaces of Kłos et al. [J. Chem. Phys. 112, 2195 (2000)]. Double peaks observed in the Λ-doublet resolved differential cross sections are shown to be related to the presence of analogous peaks in the corresponding opacity functions. These structures can be linked directly to a specific expansion term in the potential, and reflect the fact that NO is not quite homonuclear.
Resonant inelastic light scattering and photoluminescence in isolated nc-Si/SiO{sub 2} quantum dots
Bairamov, F. B. Toporov, V. V.; Poloskin, E. D.; Bairamov, H.; Roeder, C.; Sprung, C.; Bohmhammel, K.; Seidel, J.; Irmer, G.; Lashkul, A.; Laehderanta, E.; Song, Y. W.
2013-05-15
Observation at the room temperature the spectra of the resonant inelastic light scattering by the spatially confined optical phonons as well as the excitonic luminescence caused by confinement effects in the ensemble of isolated quantum dots (QDs) nc-Si/SiO{sub 2} is reported. It is shown that the samples investigated are high purity and high crystalline perfection quality nc-Si/SiO{sub 2} QDs without amorphous phase {alpha}-Si and contaminants. Comparison between the experimental data obtained and phenomenological model of the strong space confinement of optical phonons revealed the need of the more accurate form of the weighted function for the confinement of optical phonons. It is shown that simultaneous detection of the inelastic light scattering by the confinement of phonons and the excitonic luminescence spectra by the confined electron-hole pairs in the nc-Si/SiO{sub 2} QDs allows selfconsistently to determine more accurate values of the diameter of the nc-Si/SiO{sub 2} QDs.
21 THz quantum-cascade laser operating up to 144 K based on a scattering-assisted injection design
Khanal, Sudeep; Reno, John L.; Kumar, Sushil
2015-07-22
A 2.1 THz quantum cascade laser (QCL) based on a scattering-assisted injection and resonant-phonon depopulation design scheme is demonstrated. The QCL is based on a four-well period implemented in the GaAs/Al0.15Ga0.85As material system. The QCL operates up to a heat-sink temperature of 144 K in pulsed-mode, which is considerably higher than that achieved for previously reported THz QCLs operating around the frequency of 2 THz. At 46 K, the threshold current-density was measured as ~745 A/cm2 with a peak-power output of ~10 mW. Electrically stable operation in a positive differential-resistance regime is achieved by a careful choice of design parameters.more » The results validate the robustness of scattering-assisted injection schemes for development of low-frequency (ν < 2.5 THz) QCLs.« less
NASA Astrophysics Data System (ADS)
Berning, Andreas; Werner, Hans-Joachim
1994-02-01
The potential energy surfaces (PESs) of the three lowest electronic states of the system N+2+He have been computed using accurate multiconfiguration-reference configuration (MRCI) wave functions and a large basis set. The approach of the He atom leads to nonadiabatic mixing of the A 2Πu(A') and X 2Σ+g(A') states of N+2. The three adiabatic interaction potentials have been transformed into a set of four diabatic potentials, one of which describes the collision-induced nonadiabatic coupling between the two A' states. The computed potentials have been fitted to analytical functions and used in quantum scattering calculations for electronically inelastic transitions between individual rovibrational levels of the A 2Πu and the X 2Σ+g states of N+2. Our results are compared to transitions observed experimentally by Katayama and co-workers between the rotational levels of the A,v=3 and 4 and X,v=6, 7, and 8 vibrational manifolds. In general, good agreement is found for transitions between nearly isoenergetic vibrational states. However, for transitions which traverse large energy gaps, we obtained cross sections which are several orders of magnitude smaller than experimentally observed. Inclusion of the vibrational degree of freedom of the N+2 molecule in the scattering calculations was found to have only an insignificant effect on the transition probabilities.
21 THz quantum-cascade laser operating up to 144 K based on a scattering-assisted injection design
Khanal, Sudeep; Reno, John L.; Kumar, Sushil
2015-07-22
A 2.1 THz quantum cascade laser (QCL) based on a scattering-assisted injection and resonant-phonon depopulation design scheme is demonstrated. The QCL is based on a four-well period implemented in the GaAs/Al_{0.15}Ga_{0.85}As material system. The QCL operates up to a heat-sink temperature of 144 K in pulsed-mode, which is considerably higher than that achieved for previously reported THz QCLs operating around the frequency of 2 THz. At 46 K, the threshold current-density was measured as ~745 A/cm^{2} with a peak-power output of ~10 mW. Electrically stable operation in a positive differential-resistance regime is achieved by a careful choice of design parameters. The results validate the robustness of scattering-assisted injection schemes for development of low-frequency (ν < 2.5 THz) QCLs.
Huang, Danhong; Lyo, S.K.
1999-08-09
The effect of higher-order corrections to the Born approximation is studied for the previously obtained giant conductance enhancement in tunnel-coupled double quantum wires in a parallel magnetic field. The relative correction is found to be significant and depends on various effects such as the magnetic field, electron and impurity densities, impurity positions, symmetric and asymmetric doping profiles, and center barrier thickness.
Effect of incoherent scattering on three-terminal quantum Hall thermoelectrics
NASA Astrophysics Data System (ADS)
Sánchez, Rafael; Sothmann, Björn; Jordan, Andrew N.
2016-01-01
A three-terminal conductor presents peculiar thermoelectric and thermal properties in the quantum Hall regime: it can behave as a symmetric rectifier and as an ideal thermal diode. These properties rely on the coherent propagation along chiral edge channels. We investigate the effect of breaking the coherent propagation by the introduction of a probe terminal. It is shown that chiral effects not only survive the presence of incoherence but they can even improve the thermoelectric performance in the totally incoherent regime.
Reprint of : Effect of incoherent scattering on three-terminal quantum Hall thermoelectrics
NASA Astrophysics Data System (ADS)
Sánchez, Rafael; Sothmann, Björn; Jordan, Andrew N.
2016-08-01
A three-terminal conductor presents peculiar thermoelectric and thermal properties in the quantum Hall regime: it can behave as a symmetric rectifier and as an ideal thermal diode. These properties rely on the coherent propagation along chiral edge channels. We investigate the effect of breaking the coherent propagation by the introduction of a probe terminal. It is shown that chiral effects not only survive the presence of incoherence but they can even improve the thermoelectric performance in the totally incoherent regime.
Quantum dwell-correlation times in the scattering of two nonrelativistic particles
NASA Astrophysics Data System (ADS)
Hahne, G. E.
2009-12-01
In a previous paper [G. E. Hahne, J. Phys. A 36, 7149 (2003)] the author studied a nontraditional boundary value problem associated with Schrödinger’s partial differential equation for the wave function of a structureless particle moving in four-dimensional spacetime: in this boundary value problem, instead of the conventional specification of initial wave-function values on a time=constant surface, suitable time-dependent boundary and normal-derivative values are given on a three-dimensional space-time surface surrounding a slablike region of interaction in four-dimensional spacetime. The particle’s time coordinate plays a natural role as an operator and observable in the modified formalism. In the present paper, the formalism is extended to describe a system of two nonrelativistic particles—each with its own time coordinate—scattering from background potentials and from one another in four-dimensional spacetime. The two-body interaction is taken as a generic noninstantaneous action-at-a-distance, which depends independently on the space-time positions of the two particles. The dynamics is expressed in terms of an integral equation for the wave function, that is, a nonrelativistic version of the Bethe-Salpeter equation. An optical theorem is derived for the transition operator associated with scattering processes; when the theorem holds, the pointwise probability current density derivable from the wave function is conserved globally, that is, in a region covering the space-time domain of significant interparticle interaction. A general formula for the expected dwell-correlation time for the two particles in the space-time region in terms of the scattering matrices is worked out.
NASA Astrophysics Data System (ADS)
Fishman, S.; Soffer, A.
2016-07-01
We employ the recently developed multi-time scale averaging method to study the large time behavior of slowly changing (in time) Hamiltonians. We treat some known cases in a new way, such as the Zener problem, and we give another proof of the adiabatic theorem in the gapless case. We prove a new uniform ergodic theorem for slowly changing unitary operators. This theorem is then used to derive the adiabatic theorem, do the scattering theory for such Hamiltonians, and prove some classical propagation estimates and asymptotic completeness.
PLANETARY CHAOTIC ZONE CLEARING: DESTINATIONS AND TIMESCALES
Morrison, Sarah; Malhotra, Renu
2015-01-20
We investigate the orbital evolution of particles in a planet's chaotic zone to determine their final destinations and their timescales of clearing. There are four possible final states of chaotic particles: collision with the planet, collision with the star, escape, or bounded but non-collision orbits. In our investigations, within the framework of the planar circular restricted three body problem for planet-star mass ratio μ in the range 10{sup –9} to 10{sup –1.5}, we find no particles hitting the star. The relative frequencies of escape and collision with the planet are not scale-free, as they depend upon the size of the planet. For planet radius R{sub p} ≥ 0.001 R{sub H} where R{sub H} is the planet's Hill radius, we find that most chaotic zone particles collide with the planet for μ ≲ 10{sup –5}; particle scattering to large distances is significant only for higher mass planets. For fixed ratio R{sub p} /R{sub H} , the particle clearing timescale, T {sub cl}, has a broken power-law dependence on μ. A shallower power law, T {sub cl} ∼ μ{sup –1/3}, prevails at small μ where particles are cleared primarily by collisions with the planet; a steeper power law, T {sub cl} ∼ μ{sup –3/2}, prevails at larger μ where scattering dominates the particle loss. In the limit of vanishing planet radius, we find T {sub cl} ≈ 0.024 μ{sup –3/2}. The interior and exterior boundaries of the annular zone in which chaotic particles are cleared are increasingly asymmetric about the planet's orbit for larger planet masses; the inner boundary coincides well with the classical first order resonance overlap zone, Δa {sub cl,} {sub int} ≅ 1.2 μ{sup 0.28} a{sub p} ; the outer boundary is better described by Δa {sub cl,} {sub ext} ≅ 1.7 μ{sup 0.31} a{sub p} , where a{sub p} is the planet-star separation.
Surface defects characterization in a quantum wire by coherent phonons scattering
Rabia, M. S.
2015-03-30
The influence of surface defects on the scattering properties of elastic waves in a quasi-planar crystallographic waveguide is studied in the harmonic approximation using the matching method formalism. The structural model is based on three infinite atomic chains forming a perfect lattice surmounted by an atomic surface defect. Following the Landauer approach, we solve directly the Newton dynamical equation with scattering boundary conditions and taking into account the next nearest neighbour’s interaction. A detailed study of the defect-induced fluctuations in the transmission spectra is presented for different adatom masses. As in the electronic case, the presence of localized defect-induced states leads to Fano-like resonances. In the language of mechanical vibrations, these are called continuum resonances. Numerical results reveal the intimate relation between transmission spectra and localized defect states and provide a basis for the understanding of conductance spectroscopy experiments in disordered mesoscopic systems. The results could be useful for the design of phononic devices.
Chaotic systems with absorption.
Altmann, Eduardo G; Portela, Jefferson S E; Tél, Tamás
2013-10-01
Motivated by applications in optics and acoustics we develop a dynamical-system approach to describe absorption in chaotic systems. We introduce an operator formalism from which we obtain (i) a general formula for the escape rate κ in terms of the natural conditionally invariant measure of the system, (ii) an increased multifractality when compared to the spectrum of dimensions D(q) obtained without taking absorption and return times into account, and (iii) a generalization of the Kantz-Grassberger formula that expresses D(1) in terms of κ, the positive Lyapunov exponent, the average return time, and a new quantity, the reflection rate. Simulations in the cardioid billiard confirm these results. PMID:24138240
Chaotic advection in blood flow.
Schelin, A B; Károlyi, Gy; de Moura, A P S; Booth, N A; Grebogi, C
2009-07-01
In this paper we argue that the effects of irregular chaotic motion of particles transported by blood can play a major role in the development of serious circulatory diseases. Vessel wall irregularities modify the flow field, changing in a nontrivial way the transport and activation of biochemically active particles. We argue that blood particle transport is often chaotic in realistic physiological conditions. We also argue that this chaotic behavior of the flow has crucial consequences for the dynamics of important processes in the blood, such as the activation of platelets which are involved in the thrombus formation. PMID:19658798
Krauss, R.H. Jr.; Flynn, E.; Ruminer, P.
1997-10-01
This is the final report of a one-year, Laboratory Directed Research and Development (LDRD) project at Los Alamos National Laboratory (LANL). This project has supported the collaborative development with Sandia National Laboratories (SNL) and the University of New Mexico (UNM) of two critical components for a hand-held low-field magnetic sensor based on superconducting quantum interference device (SQUID) sensor technology. The two components are a digital signal processing (DSP) algorithm for background noise rejection and a small hand-held dewar cooled by a cryocooler. A hand-held sensor has been designed and fabricated for detection of extremely weak magnetic fields in unshielded environments. The sensor is capable of measuring weak magnetic fields in unshielded environments and has multiple applications. We have chosen to pursue battlefield medicine as the highest probability near-term application because of stated needs of several agencies.
NASA Astrophysics Data System (ADS)
Chou, Chia-Chun
2015-08-01
The complex quantum Hamilton-Jacobi equation for the complex action is approximately solved by propagating individual Bohmian trajectories in real space. Equations of motion for the complex action and its spatial derivatives are derived through use of the derivative propagation method. We transform these equations into the arbitrary Lagrangian-Eulerian version with the grid velocity matching the flow velocity of the probability fluid. Setting higher-order derivatives equal to zero, we obtain a truncated system of equations of motion describing the rate of change in the complex action and its spatial derivatives transported along approximate Bohmian trajectories. A set of test trajectories is propagated to determine appropriate initial positions for transmitted trajectories. Computational results for transmitted wave packets and transmission probabilities are presented and analyzed for a one-dimensional Eckart barrier and a two-dimensional system involving either a thick or thin Eckart barrier along the reaction coordinate coupled to a harmonic oscillator.
Hybrid theory and calculation of e-N2 scattering. [quantum mechanics - nuclei (nuclear physics)
NASA Technical Reports Server (NTRS)
Chandra, N.; Temkin, A.
1975-01-01
A theory of electron-molecule scattering was developed which was a synthesis of close coupling and adiabatic-nuclei theories. The theory is shown to be a close coupling theory with respect to vibrational degrees of freedom but is a adiabatic-nuclei theory with respect to rotation. It can be applied to any number of partial waves required, and the remaining ones can be calculated purely in one or the other approximation. A theoretical criterion based on fixed-nuclei calculations and not on experiment can be given as to which partial waves and energy domains require the various approximations. The theory allows all cross sections (i.e., pure rotational, vibrational, simultaneous vibration-rotation, differential and total) to be calculated. Explicit formulae for all the cross sections are presented.
Carmichael, Justin R; Omar Diallo, Souleymane
2013-01-01
We present our new development of a high pressure cell for inelastic neutron scattering measurements of helium at ultra-low temperatures. The cell has a large sample volume of ~140 cm3, and a working pressure of ~70 bar, with a relatively thin wall-thickness (1.1 mm) - thanks to the high yield strength aluminum used in the design. Two variants of this cell have been developed; one with permanently joined components using electron-beam welding and explosion welding, methods that have little or no impact on the global heat treatment of the cell, and another with modular and interchangeable components, which include a capacitance pressure gauge, that can be sealed using traditional indium wire technique. The performance of the cell has been tested in recent measurements on superfluid liquid helium near the solidification line.
Converged variational quantum scattering results for the three-dimensional F+HD reaction
NASA Astrophysics Data System (ADS)
Manolopoulos, David E.; D'Mello, Michael; Wyatt, Robert E.; Walker, Robert B.
1990-06-01
The log derivative version of the Kohn variational principle is used to calculate J=0 reaction probabilities and state-to-state time delays for the F+HD reaction, on the T5A potential energy surface, in the total energy range Etot=0.236 to 0.350 eV. While the computed reaction probabilities to H+DF are comparatively bland, those to D+HF show considerable resonant structure as a function of the scattering energy. For example, the computed state-to-state time delays for the predominant HF( v'=2) resonance et Etot=0.2575 eV imply the existence of a metastable collision complex with a half-life of about 0.1 ps. These results are discussed in the light of the high-resolution molecular beam experiments of Lee and coworkers and the bending corrected rotating linear model calculations of Hayes and Walker.
Carmichael, J R; Diallo, S O
2013-01-01
We present our new development of a high pressure cell for inelastic neutron scattering measurements of helium at ultra-low temperatures. The cell has a large sample volume of ~140 cm(3) and a working pressure of ~7 MPa, with a relatively thin wall-thickness (1.1 mm)--thanks to the high yield strength aluminum used in the design. Two variants of this cell have been developed. The first cell is permanently joined components using electron-beam welding and explosion welding, methods that have little or no impact on the global heat treatment of the cell. The second cell discussed has modular and interchangeable components, which includes a capacitance pressure gauge, that can be sealed using the traditional indium wire technique. The performance of the cells have been tested in recent measurements on superfluid liquid helium near the solidification line. PMID:23387689
NASA Astrophysics Data System (ADS)
Suter, Jonathan D.; Bernacki, Bruce; Phillips, Mark C.
2012-09-01
We present a study of the spectral and angular dependence of scattered mid-infrared light from surfaces coated with explosives residues (TNT, RDX, and tetryl) detected at a 2 m standoff distance. An external cavity quantum cascade laser provided tunable illumination between 7 and 8 μm. Important differences were identified in the spectral features between specular reflection and diffuse scattering which will impact most practical testing scenarios and complicate material identification. We discuss some of the factors influencing the dependence of observed spectra on the experimental geometry.
NASA Astrophysics Data System (ADS)
Hashemi, G.; Rezaei, G.
2015-09-01
In this paper, we have investigated the electron Raman scattering associated with a donor impurity in a two-dimensional parabolic quantum dot under the influence of external electric and magnetic fields, the hydrostatic pressure and temperature. To this end, energy eigenvalues and corresponding eigenvectors are calculated using the direct matrix diagonalization method and the differential cross-section is obtained via the Fermi‧s golden rule. Our results indicate that the differential cross-section of the system is strongly affected by the external fields, the hydrostatic pressure, temperature, the confinement potential, and the polarization vectors of incident and scattered lights.
Suter, Jonathan D.; Bernacki, Bruce E.; Phillips, Mark C.
2012-09-01
We present a study of the spectral and angular dependence of scattered mid-infrared light from surfaces coated with explosives residues (TNT, RDX, and tetryl) detected at a 2 meter standoff distance. An external cavity quantum cascade laser provided tunable illumination between 7 and 8 µm. Important differences were identified in the spectral features between specular reflection and diffuse scattering which will impact most practical testing scenarios and complicate material identification. We discuss some of the factors influencing the dependence of observed spectra on the experimental geometry.
Huang, Liang; Lai Yingcheng; Ferry, David K.; Goodnick, Stephen M.; Akis, Richard
2009-07-31
The concentrations of wave functions about classical periodic orbits, or quantum scars, are a fundamental phenomenon in physics. An open question is whether scarring can occur in relativistic quantum systems. To address this question, we investigate confinements made of graphene whose classical dynamics are chaotic and find unequivocal evidence of relativistic quantum scars. The scarred states can lead to strong conductance fluctuations in the corresponding open quantum dots via the mechanism of resonant transmission.
Cryptosystems based on chaotic dynamics
McNees, R.A.; Protopopescu, V.; Santoro, R.T.; Tolliver, J.S.
1993-08-01
An encryption scheme based on chaotic dynamics is presented. This scheme makes use of the efficient and reproducible generation of cryptographically secure pseudo random numbers from chaotic maps. The result is a system which encrypts quickly and possesses a large keyspace, even in small precision implementations. This system offers an excellent solution to several problems including the dissemination of key material, over the air rekeying, and other situations requiring the secure management of information.
Fermi resonance in dynamical tunneling in a chaotic billiard
NASA Astrophysics Data System (ADS)
Yi, Chang-Hwan; Kim, Ji-Hwan; Yu, Hyeon-Hye; Lee, Ji-Won; Kim, Chil-Min
2015-08-01
We elucidate that Fermi resonance ever plays a decisive role in dynamical tunneling in a chaotic billiard. Interacting with each other through an avoided crossing, a pair of eigenfunctions are coupled through tunneling channels for dynamical tunneling. In this case, the tunneling channels are an islands chain and its pair unstable periodic orbit, which equals the quantum number difference of the eigenfunctions. This phenomenon of dynamical tunneling is confirmed in a quadrupole billiard in relation with Fermi resonance.
Blackburn, Jeffrey L.; Chappell, Helen; Luther, Joseph M.; Nozik, Arthur J.; Johnson, Justin C.
2011-02-28
In this report, we carefully study the effects of photooxidation on the Raman spectra of lead chalcogenide (PbX) quantum dots (QDs). Photoexcitation of PbS, PbSe, and PbTe QD films at 488 nm with power densities as low as 30 W/cm^{2} gives rise to several peaks related to both lead(II) oxide and the group VI chalcogenates (PbXO_{4}). The amplitudes of these peaks are shown to increase with continuous laser illumination in air, but are completely absent for samples illuminated under rigorously air-free conditions. These results suggest that the ~135 cm^{-1} Raman peak often assigned to an intrinsic PbX LO phonon is more likely an artifact arising from photooxidation. The myriad of potential photooxidation products formed quickly in laser-illuminated, air-exposed PbX QDs suggest that caution should be used in the assignment and interpretation of phonon spectra and phonon-mediated exciton relaxation pathways of these materials, unless the processing and experiments are conducted under air-free conditions.
Quantum state resolved scattering dynamics of F +HCl→HF(v,J)+Cl
NASA Astrophysics Data System (ADS)
Zolot, A. M.; Nesbitt, D. J.
2007-09-01
State-to-state reaction dynamics of the reaction F +HCl→HF(v,J)+Cl have been studied under single-collision conditions using an intense discharge F atom source in crossed supersonic molecular beams at Ecom=4.3(1.3)kcal/mol. Nascent HF product is monitored by shot-noise limited direct infrared laser absorption, providing quantum state distributions as well as additional information on kinetic energy release from high resolution Dopplerimetry. The vibrational distributions are highly inverted, with 34(4)%, 44(2)%, and 8(1)% of the total population in vHF=1, 2, and 3, respectively, consistent with predominant energy release into the newly formed bond. However, there is a small [14(1)%] but significant formation channel into the vHF=0 ground state, which is directly detectable for the first time via direct absorption methods. Of particular dynamical interest, both the HF(v =2,J) and HF(v =1,J) populations exhibit strongly bimodal J distributions. These results differ significantly from previous flow and arrested-relaxation studies and may signal the presence of microscopic branching in the reaction dynamics.
NASA Astrophysics Data System (ADS)
Li, Xingmin; Wei, L. F.
2016-05-01
Weak dipolar interactions exist widely in various atomic, nuclear and molecular systems, and could be utilized to implement the desired quantum information processings. However, these interactions are relatively weak and hard to be measured precisely. Here, we propose an approach to detect such a weak interaction by probing the transport of a single waveguide-photon scattered by two aside qubits with a single dipolar exchange-interaction. By a full quantum theory of photon transports in optical waveguide, we show that the dipolar interaction between the aside two qubits significantly influence the transmitted spectra of the photon traveling along the one-dimensional waveguide. Thus, probing the relevant changes in the transmitted spectra and the transmission probability distribution specifically for the resonant photons, compared with those scattered by the two individual qubits, the information of the single dipolar interaction between the qubits could be extracted. The feasibility of the proposal is also discussed.
Franz, J.; Gianturco, F. A.
2013-11-28
In this paper we report new quantum calculations of the dynamics for low-energy positrons interacting with gaseous molecules of tetrahydrofuran. The new quantum scattering cross sections are differential and integral cross sections at collision energies between 1.0 and 25.0 eV and include a careful treatment of the additional effects on the scattering process brought about by the permanent dipole moment of the target molecule. The present results are compared with an extensive range of measured data, both for the angular distributions and for the elastic integral cross sections and agree remarkably well with all findings. The new calculated quantities reported here also show the importance of correcting the experimental integral cross sections for the angular discrimination in the forward direction.
Chaotic Pattern Dynamics in Spatially Ramped Turbulence
NASA Astrophysics Data System (ADS)
Wiener, R. J.; Ashbaker, E.; Olsen, T.; Bodenschatz, E.
2003-11-01
In previous experiments(Richard J. Wiener et al), Phys. Rev. E 55, 5489 (1997)., Taylor vortex flow in an hourglass geometry has demonstrated a period-doubling cascade to chaotic pattern dynamics. A spatial ramp exists in the Reynolds number. For low reduced Reynolds numbesr \\varepsilon, supercritical vortex flow occurs between regions of subcritical structureless flow with soft boundaries that allow for pattern dynamics. At \\varepsilon ≈ 0.5, the pattern exhibits phase slips that occur irregularly in time. At \\varepsilon ≈ 1.0 the entire system is supercritical, and the pattern is stabilized against phase slips. At \\varepsilon > 15, shear flow creates a spatial ramp in turbulence. Remarkably, the phase slip instability reoccurs. Vortex pairs are created chaotically, possibly due to the spatial variation of the turbulence. The variance and Fourier spectra of time series of light scattered off Kalliroscope tracer were measured. These indicate that a region of turbulence exists, within which phase slips occur, bounded by regions of laminar flow which may provide soft boundaries that allow for the phase dynamics. Despite the presence of turbulence, the dynamics might be describable by a phase equation.
Sun, Ruiling; Wang, Yong; Ni, Yongnian; Kokot, Serge
2014-07-01
A novel, highly selective resonance light scattering (RLS) method was researched and developed for the analysis of phenol in different types of industrial water. An important aspect of the method involved the use of graphene quantum dots (GQDs), which were initially obtained from the pyrolysis of citric acid dissolved in aqueous solutions. The GQDs in the presence of horseradish peroxidase (HRP) and H2O2 were found to react quantitatively with phenol such that the RLS spectral band (310 nm) was quantitatively enhanced as a consequence of the interaction between the GQDs and the quinone formed in the above reaction. It was demonstrated that the novel analytical method had better selectivity and sensitivity for the determination of phenol in water as compared to other analytical methods found in the literature. Thus, trace amounts of phenol were detected over the linear ranges of 6.00×10(-8)-2.16×10(-6)M and 2.40×10(-6)-2.88×10(-5)M with a detection limit of 2.20×10(-8)M. In addition, three different spiked waste water samples and two untreated lake water samples were analysed for phenol. Satisfactory results were obtained with the use of the novel, sensitive and rapid RLS method. PMID:24840454
Exact quantum scattering calculation of transport properties for free radicals: OH(X2Π)-helium
NASA Astrophysics Data System (ADS)
Dagdigian, Paul J.; Alexander, Millard H.
2012-09-01
Transport properties for OH-He are computed through quantum scattering calculations using the ab initio potential energy surfaces determined by Lee et al. [J. Chem. Phys. 113, 5736 (2000), 10.1063/1.1290605]. To gauge the importance of the open-shell character of OH and the anisotropy of the potential on the transport properties, including the collision integrals Ω(1,1) and Ω(2,2), as well as the diffusion coefficient, calculations were performed with the full potential, with the difference potential Vdif set to zero, and with only the spherical average of the potential. Slight differences (3%-5%) in the computed diffusion coefficient were found between the values obtained using the full potential and the truncated potentials. The computed diffusion coefficients were compared to recent experimental measurements and those computed with a Lennard-Jones (LJ) 12-6 potential. The values obtained with the full potential were slightly higher than the experimental values. The LJ 12-6 potential was found to underestimate the variation in temperature as compared to that obtained using the full OH-He ab initio potential.
NASA Astrophysics Data System (ADS)
Ernest, Alllan David; Collins, Matthew P.
2015-08-01
Analysis of astrophysical phenomena relies on knowledge of cross sections. These cross sections are measured in scattering experiments, or calculated using theoretical techniques such as partial wave analysis. It has been recently shown [1,2,3] however that photon scattering cross sections depend also on the degree of localization of the target particle, and that particles in large-scale, deep-gravity wells can exhibit lower cross sections than those measured in lab-based experiments where particles are implicitly localized. This purely quantum effect arises as a consequence of differences in the gravitational eigenspectral distribution of a particle’s wavefunction in different situations, and is in addition to the obvious notion that delocalized particle scattering is less likely simply because the target particles are ‘in a bigger box’.In this presentation we consider the quantum equilibrium statistics of particles in gravitational potentials corresponding to dark matter density profiles. We show that as galactic halos approach equilibrium, the dark eigenstates of the eigenspectral ensemble are favoured and baryons exhibit lower photon scattering cross sections, rendering halos less visible than expected from currently accepted cross sections. Traditional quantum theory thus predicts that baryons that have not coalesced into self-bound macroscopic structures such as stars, can essentially behave as dark matter simply by equilibrating within a deep gravity well. We will discuss this effect and the consequences for microwave anisotropy analysis and primordial nucleosynthesis.[1] Ernest, A. D., and Collins, M. P., 2014, Australian Institute of Physics, AIP Congress, Canberra, December, 2014.[2] Ernest, A. D., 2009, J. Phys. A: Math. Theor., 42, 115207, 115208.[3] Ernest, A. D., 2012, In Prof. Ion Cotaescu (Ed) Advances in Quantum Theory (pp 221-248). Rijeka: InTech. ISBN 978-953-51-0087-4
NASA Astrophysics Data System (ADS)
Freeman, Walter J.
2013-01-01
The first step of the sensory systems is to construct the meaning of the information they receive from the senses. They do this by generating random noise and then filtering the noise with adaptive filters. We simulate the operation with the solutions of matrices of ordinary differential equations that predict subcritical Hopf bifurcations between point and limit cycle attractors. The second step is integration of the outputs from the several sensory systems into a multisensory percept, called a gestalt, which in the third step is consolidated and stored as knowledge. Simulation of the second step requires use of landscapes of nonconvergent chaotic attractors. This is not deterministic chaos, which is much too brittle owing to the infinite sensitivity to initial conditions. It is a hybrid form we call stochastic chaos, which is stabilized by additive noise modeled on noise sources in the sensory systems. Thus bifurcation and chaos theory provides tools for succinct empirical models of cortical dynamics performing the most basic cognitive operations: generalization, abstraction, and categorization in constructing knowledge. The descriptions are in a form that is suitable for more advanced modeling using analog VLSI, neuropercolation from random graph theory, non-equilibrium dissipative thermodynamics, and macroscopic many-body physics. This review concludes with a summary of the applications of stochastic chaos in pattern classification and some prescriptions for neurobiologists on what to look for in large-scale anatomical formations.
Dimension of chaotic attractors
Farmer, J.D.; Ott, E.; Yorke, J.A.
1982-09-01
Dimension is perhaps the most basic property of an attractor. In this paper we discuss a variety of different definitions of dimension, compute their values for a typical example, and review previous work on the dimension of chaotic attractors. The relevant definitions of dimension are of two general types, those that depend only on metric properties, and those that depend on probabilistic properties (that is, they depend on the frequency with which a typical trajectory visits different regions of the attractor). Both our example and the previous work that we review support the conclusion that all of the probabilistic dimensions take on the same value, which we call the dimension of the natural measure, and all of the metric dimensions take on a common value, which we call the fractal dimension. Furthermore, the dimension of the natural measure is typically equal to the Lyapunov dimension, which is defined in terms of Lyapunov numbers, and thus is usually far easier to calculate than any other definition. Because it is computable and more physically relevant, we feel that the dimension of the natural measure is more important than the fractal dimension.
Studies in Chaotic adiabatic dynamics
Jarzynski, C.
1994-01-01
Chaotic adiabatic dynamics refers to the study of systems exhibiting chaotic evolution under slowly time-dependent equations of motion. In this dissertation the author restricts his attention to Hamiltonian chaotic adiabatic systems. The results presented are organized around a central theme, namely, that the energies of such systems evolve diffusively. He begins with a general analysis, in which he motivates and derives a Fokker-Planck equation governing this process of energy diffusion. He applies this equation to study the {open_quotes}goodness{close_quotes} of an adiabatic invariant associated with chaotic motion. This formalism is then applied to two specific examples. The first is that of a gas of noninteracting point particles inside a hard container that deforms slowly with time. Both the two- and three-dimensional cases are considered. The results are discussed in the context of the Wall Formula for one-body dissipation in nuclear physics, and it is shown that such a gas approaches, asymptotically with time, an exponential velocity distribution. The second example involves the Fermi mechanism for the acceleration of cosmic rays. Explicit evolution equations are obtained for the distribution of cosmic ray energies within this model, and the steady-state energy distribution that arises when this equation is modified to account for the injection and removal of cosmic rays is discussed. Finally, the author re-examines the multiple-time-scale approach as applied to the study of phase space evolution under a chaotic adiabatic Hamiltonian. This leads to a more rigorous derivation of the above-mentioned Fokker-Planck equation, and also to a new term which has relevance to the problem of chaotic adiabatic reaction forces (the forces acting on slow, heavy degrees of freedom due to their coupling to light, fast chaotic degrees).
Flights in a pseudo-chaotic system
NASA Astrophysics Data System (ADS)
Lowenstein, J. H.; Vivaldi, F.
2011-09-01
We consider the problem of transport in a one-parameter family of piecewise rotations of the torus, for rotation number approaching 1/4. This is a zero-entropy system which in this limit exhibits a divided phase space, with island chains immersed in a "pseudo-chaotic" region. We identify a novel mechanism for long-range transport, namely the adiabatic destruction of accelerator-mode islands. This process originates from the approximate translational invariance of the phase space and leads to long flights of linear motion, for a significant measure of initial conditions. We show that the asymptotic probability distribution of the flight lengths is determined by the geometric properties of a partition of the accelerator-mode island associated with the flight. We establish the existence of flights travelling distances of order O(1) in phase space. We provide evidence for the existence of a scattering process that connects flights travelling in opposite directions.
Nonlinear Dynamics, Chaotic and Complex Systems
NASA Astrophysics Data System (ADS)
Infeld, E.; Zelazny, R.; Galkowski, A.
2011-04-01
Part I. Dynamic Systems Bifurcation Theory and Chaos: 1. Chaos in random dynamical systems V. M. Gunldach; 2. Controlling chaos using embedded unstable periodic orbits: the problem of optimal periodic orbits B. R. Hunt and E. Ott; 3. Chaotic tracer dynamics in open hydrodynamical flows G. Karolyi, A. Pentek, T. Tel and Z. Toroczkai; 4. Homoclinic chaos L. P. Shilnikov; Part II. Spatially Extended Systems: 5. Hydrodynamics of relativistic probability flows I. Bialynicki-Birula; 6. Waves in ionic reaction-diffusion-migration systems P. Hasal, V. Nevoral, I. Schreiber, H. Sevcikova, D. Snita, and M. Marek; 7. Anomalous scaling in turbulence: a field theoretical approach V. Lvov and I. Procaccia; 8. Abelian sandpile cellular automata M. Markosova; 9. Transport in an incompletely chaotic magnetic field F. Spineanu; Part III. Dynamical Chaos Quantum Physics and Foundations Of Statistical Mechanics: 10. Non-equilibrium statistical mechanics and ergodic theory L. A. Bunimovich; 11. Pseudochaos in statistical physics B. Chirikov; 12. Foundations of non-equilibrium statistical mechanics J. P. Dougherty; 13. Thermomechanical particle simulations W. G. Hoover, H. A. Posch, C. H. Dellago, O. Kum, C. G. Hoover, A. J. De Groot and B. L. Holian; 14. Quantum dynamics on a Markov background and irreversibility B. Pavlov; 15. Time chaos and the laws of nature I. Prigogine and D. J. Driebe; 16. Evolutionary Q and cognitive systems: dynamic entropies and predictability of evolutionary processes W. Ebeling; 17. Spatiotemporal chaos information processing in neural networks H. Szu; 18. Phase transitions and learning in neural networks C. Van den Broeck; 19. Synthesis of chaos A. Vanecek and S. Celikovsky; 20. Computational complexity of continuous problems H. Wozniakowski; Part IV. Complex Systems As An Interface Between Natural Sciences and Environmental Social and Economic Sciences: 21. Stochastic differential geometry in finance studies V. G. Makhankov; Part V. Conference Banquet
Chaotic Mixing around a Quasigeostrophic Ellipsoidal Vortex
NASA Astrophysics Data System (ADS)
Miyazaki, T.; Yamamoto, M.
2002-05-01
Melnikov functions computed along the heteroclinic and homoclinic orbits intersect zero transversely in any cases, suggesting the occurrence of chaotic mixing of fluid particles. In fact, numerically computed stroboscopic Poincare plots scatter along the heteroclinic and homoclinic orbits even when the perturbations are very weak. It is found that the chaotic region is wider on the plane z>0 and that the vertical shear induces the mixing most efficiently. The chaotic regions expand wider and wider as the perturbations become stronger. 1)S. P. Meacham, et al.: Dyn. Atmos. Oceans 21 (1994) 167. 2)S. P. Meacham, et al: Phys. Fluids 9 (1997) 2310. 3)L.M.Polvani & J.Wisdom: Phys. Fluids A2 (1990) 123. 4)M.D.Dahleh: Phys. Fluids A4 (1992) 1979. 5)A.Kawakami & M.Funakoshi: Fluid Dynamics Research 25 (1999) 167.
NASA Technical Reports Server (NTRS)
2006-01-01
[figure removed for brevity, see original site] Poster Version Large Magellanic Cloud
This vibrant image from NASA's Spitzer Space Telescope shows the Large Magellanic Cloud, a satellite galaxy to our own Milky Way galaxy.
The infrared image, a mosaic of more than 100,000 individual tiles, offers astronomers a unique chance to study the lifecycle of stars and dust in a single galaxy. Nearly one million objects are revealed for the first time in this Spitzer view, which represents about a 1,000-fold improvement in sensitivity over previous space-based missions. Most of the new objects are dusty stars of various ages populating the Large Magellanic Cloud; the rest are thought to be background galaxies.
The blue color in the picture, seen most prominently in the central bar, represents starlight from older stars. The chaotic, bright regions outside this bar are filled with hot, massive stars buried in thick blankets of dust. The red clouds contain cooler interstellar gas and molecular-sized dust grains illuminated by ambient starlight.
The Large Magellanic Cloud, located 160,000 light-years from Earth, is one of a handful of dwarf galaxies that orbit our own Milky Way. It is approximately one-third as wide as the Milky Way, and, if it could be seen in its entirety, would cover the same amount of sky as a grid of about 480 full moons. About one-third of the whole galaxy can be seen in the Spitzer image.
This picture is a composite of infrared light captured by Spitzer's infrared array camera. Light with wavelengths of 8 and 5.8 microns is red and orange: 4.5-micron light is green; and 3.6-micron light is blue.
Chaotic synchronization system and electrocardiogram
NASA Astrophysics Data System (ADS)
Pei, Liuqing; Dai, Xinlai; Li, Baodong
1997-01-01
A mathematical model of chaotic synchronization of the heart-blood flow coupling dynamics is proposed, which is based on a seven dimension nonlinear dynamical system constructed by three subsystems of the sinoatrial node natural pacemaker, the cardiac relaxation oscillator and the dynamics of blood-fluid in heart chambers. The existence and robustness of the self-chaotic synchronization of the system are demonstrated by both methods of theoretical analysis and numerical simulation. The spectrum of Lyapunov exponent, the Lyapunov dimension and the Kolmogorov entropy are estimated when the system was undergoing the state of self-chaotic synchronization evolution. The time waveform of the dynamical variable, which represents the membrane potential of the cardiac integrative cell, shows a shape which is similar to that of the normal electrocardiogram (ECG) of human, thus implies that the model possesses physiological significance functionally.
Analysis of Rattleback Chaotic Oscillations
Stavrinides, Stavros G.; Banerjee, Santo
2014-01-01
Rattleback is a canoe-shaped object, already known from ancient times, exhibiting a nontrivial rotational behaviour. Although its shape looks symmetric, its kinematic behaviour seems to be asymmetric. When spun in one direction it normally rotates, but when it is spun in the other direction it stops rotating and oscillates until it finally starts rotating in the other direction. It has already been reported that those oscillations demonstrate chaotic characteristics. In this paper, rattleback's chaotic dynamics are studied by applying Kane's model for different sets of (experimentally decided) parameters, which correspond to three different experimental prototypes made of wax, gypsum, and lead-solder. The emerging chaotic behaviour in all three cases has been studied and evaluated by the related time-series analysis and the calculation of the strange attractors' invariant parameters. PMID:24511290
CHAOTIC ZONES AROUND GRAVITATING BINARIES
Shevchenko, Ivan I.
2015-01-20
The extent of the continuous zone of chaotic orbits of a small-mass tertiary around a system of two gravitationally bound primaries of comparable masses (a binary star, a binary black hole, a binary asteroid, etc.) is estimated analytically, as a function of the tertiary's orbital eccentricity. The separatrix map theory is used to demonstrate that the central continuous chaos zone emerges (above a threshold in the primaries' mass ratio) due to overlapping of the orbital resonances corresponding to the integer ratios p:1 between the tertiary and the central binary periods. In this zone, the unlimited chaotic orbital diffusion of the tertiary takes place, up to its ejection from the system. The primaries' mass ratio, above which such a chaotic zone is universally present at all initial eccentricities of the tertiary, is estimated. The diversity of the observed orbital configurations of biplanetary and circumbinary exosystems is shown to be in accord with the existence of the primaries' mass parameter threshold.
Analysis of rattleback chaotic oscillations.
Hanias, Michael; Stavrinides, Stavros G; Banerjee, Santo
2014-01-01
Rattleback is a canoe-shaped object, already known from ancient times, exhibiting a nontrivial rotational behaviour. Although its shape looks symmetric, its kinematic behaviour seems to be asymmetric. When spun in one direction it normally rotates, but when it is spun in the other direction it stops rotating and oscillates until it finally starts rotating in the other direction. It has already been reported that those oscillations demonstrate chaotic characteristics. In this paper, rattleback's chaotic dynamics are studied by applying Kane's model for different sets of (experimentally decided) parameters, which correspond to three different experimental prototypes made of wax, gypsum, and lead-solder. The emerging chaotic behaviour in all three cases has been studied and evaluated by the related time-series analysis and the calculation of the strange attractors' invariant parameters. PMID:24511290
von Horsten, H F; Banks, S T; Clary, D C
2011-09-01
We present an efficient approach to the determination of two-dimensional potential energy surfaces for use in quantum reactive scattering simulations. Our method involves first determining the minimum energy path (MEP) for the reaction by means of an ab initio intrinsic reaction coordinate calculation. This one-dimensional potential is then corrected to take into account the zero point energies of the spectator modes. These are determined from Hessians in curvilinear coordinates after projecting out the modes to be explicitly treated in quantum scattering calculations. The final (1+1)-dimensional potential is constructed by harmonic expansion about each point along the MEP before transforming the whole surface to hyperspherical coordinates for use in the two-dimensional scattering simulations. This new method is applied to H-atom abstraction from methane, ethane and propane. For the latter, both reactive channels (producing i-C(3)H(7) or n-C(3)H(7)) are investigated. For all reactions, electronic structure calculations are performed using an efficient, explicitly correlated, coupled cluster methodology (CCSD(T)-F12). Calculated thermal rate constants are compared to experimental and previous theoretical results. PMID:21913767
Maji, Kaushik; Kouri, Donald J
2011-03-28
We have developed a new method for solving quantum dynamical scattering problems, using the time-independent Schrödinger equation (TISE), based on a novel method to generalize a "one-way" quantum mechanical wave equation, impose correct boundary conditions, and eliminate exponentially growing closed channel solutions. The approach is readily parallelized to achieve approximate N(2) scaling, where N is the number of coupled equations. The full two-way nature of the TISE is included while propagating the wave function in the scattering variable and the full S-matrix is obtained. The new algorithm is based on a "Modified Cayley" operator splitting approach, generalizing earlier work where the method was applied to the time-dependent Schrödinger equation. All scattering variable propagation approaches to solving the TISE involve solving a Helmholtz-type equation, and for more than one degree of freedom, these are notoriously ill-behaved, due to the unavoidable presence of exponentially growing contributions to the numerical solution. Traditionally, the method used to eliminate exponential growth has posed a major obstacle to the full parallelization of such propagation algorithms. We stabilize by using the Feshbach projection operator technique to remove all the nonphysical exponentially growing closed channels, while retaining all of the propagating open channel components, as well as exponentially decaying closed channel components. PMID:21456641
NASA Astrophysics Data System (ADS)
von Horsten, H. F.; Banks, S. T.; Clary, D. C.
2011-09-01
We present an efficient approach to the determination of two-dimensional potential energy surfaces for use in quantum reactive scattering simulations. Our method involves first determining the minimum energy path (MEP) for the reaction by means of an ab initio intrinsic reaction coordinate calculation. This one-dimensional potential is then corrected to take into account the zero point energies of the spectator modes. These are determined from Hessians in curvilinear coordinates after projecting out the modes to be explicitly treated in quantum scattering calculations. The final (1 + 1)-dimensional potential is constructed by harmonic expansion about each point along the MEP before transforming the whole surface to hyperspherical coordinates for use in the two-dimensional scattering simulations. This new method is applied to H-atom abstraction from methane, ethane and propane. For the latter, both reactive channels (producing i-C3H7 or n-C3H7) are investigated. For all reactions, electronic structure calculations are performed using an efficient, explicitly correlated, coupled cluster methodology (CCSD(T)-F12). Calculated thermal rate constants are compared to experimental and previous theoretical results.
A semiclassical reversibility paradox in simple chaotic systems.
Tomsovic, Steven
2016-06-13
Using semiclassical methods, it is possible to construct very accurate approximations in the short-wavelength limit of quantum dynamics that rely exclusively on classical dynamical input. For systems whose classical realization is strongly chaotic, there is an exceedingly short logarithmic Ehrenfest time scale, beyond which the quantum and classical dynamics of a system necessarily diverge, and yet the semiclassical construction remains valid far beyond that time. This fact leads to a paradox if one ponders the reversibility and predictability properties of quantum and classical mechanics. They behave very differently relative to each other, with classical dynamics being essentially irreversible/unpredictable, whereas quantum dynamics is reversible/stable. This begs the question: 'How can an accurate approximation to a reversible/stable dynamics be constructed from an irreversible/unpredictable one?' The resolution of this incongruity depends on a couple of key ingredients: a well-known, inherent, one-way structural stability of chaotic systems; and an overlap integral not being amenable to the saddle point method. PMID:27140974
The chaotic regime of D-term inflation
NASA Astrophysics Data System (ADS)
Buchmüller, W.; Domcke, V.; Schmitz, K.
2014-11-01
We consider D-term inflation for small couplings of the inflaton to matter fields. Standard hybrid inflation then ends at a critical value of the inflaton field that exceeds the Planck mass. During the subsequent waterfall transition the inflaton continues its slow-roll motion, whereas the waterfall field rapidly grows by quantum fluctuations. Beyond the decoherence time, the waterfall field becomes classical and approaches a time-dependent minimum, which is determined by the value of the inflaton field and the self-interaction of the waterfall field. During the final stage of inflation, the effective inflaton potential is essentially quadratic, which leads to the standard predictions of chaotic inflation. The model illustrates how the decay of a false vacuum of GUT-scale energy density can end in a period of `chaotic inflation'.
The chaotic regime of D-term inflation
Buchmüller, W.; Domcke, V.
2014-11-01
We consider D-term inflation for small couplings of the inflaton to matter fields. Standard hybrid inflation then ends at a critical value of the inflaton field that exceeds the Planck mass. During the subsequent waterfall transition the inflaton continues its slow-roll motion, whereas the waterfall field rapidly grows by quantum fluctuations. Beyond the decoherence time, the waterfall field becomes classical and approaches a time-dependent minimum, which is determined by the value of the inflaton field and the self-interaction of the waterfall field. During the final stage of inflation, the effective inflaton potential is essentially quadratic, which leads to the standard predictions of chaotic inflation. The model illustrates how the decay of a false vacuum of GUT-scale energy density can end in a period of 'chaotic inflation'.
AGN flickering and chaotic accretion
NASA Astrophysics Data System (ADS)
King, Andrew; Nixon, Chris
2015-10-01
Observational arguments suggest that the growth phases of the supermassive black holes in active galactic nuclei have a characteristic time-scale ˜105 yr. We show that this is the time-scale expected in the chaotic accretion picture of black hole feeding, because of the effect of self-gravity in limiting the mass of any accretion-disc feeding event.
Learning in a Chaotic Environment
ERIC Educational Resources Information Center
Goldman, Ellen; Plack, Margaret; Roche, Colleen; Smith, Jeffrey; Turley, Catherine
2009-01-01
Purpose: The purpose of this study is to understand how, when, and why emergency medicine residents learn while working in the chaotic environment of a hospital emergency room. Design/methodology/approach: This research used a qualitative interview methodology with thematic data analysis that was verified with the entire population of learners.…
A Chaos-based Arbitrated Quantum Signature Scheme in Quantum Crypotosystem
NASA Astrophysics Data System (ADS)
Wang, Yijun; Xu, Ke; Guo, Ying
2014-01-01
An arbitrated quantum signature (AQS) scheme is demonstrated on a basis of an improved quantum chaotic encryption algorithm using the quantum one-time pad with a chaotic operation string. In this scheme, the signatory signs the message while the receiver verifies the signature's validity with the aid of the trusty arbitrator who plays a crucial role when a possible dispute arises. Analysis shows that the signature can neither be forged nor disavowed by any malicious attackers.
NASA Astrophysics Data System (ADS)
Makshantsev, B. I.; Makshantsev, V. B.
2001-09-01
A problem of scattering of an ensemble of photons by material particles is solved. The vector potential of each of the incident photons scattered by particles is described by a nonspreading wave packet. The expressions for cross sections for elastic and inelastic scattering of electromagnetic radiation are derived taking the space — time localisation of photons into account. The possible experiments for verifying these theoretical results are discussed.
Quantum reactive scattering of O({sup 3}P)+H{sub 2} at collision energies up to 4.4 eV
Gacesa, Marko; Kharchenko, Vasili
2014-10-28
We report the results of quantum scattering calculations for the O({sup 3}P)+H{sub 2} reaction for a range of collision energies from 0.4 to 4.4 eV, important for astrophysical and atmospheric processes. The total and state-to-state reactive cross sections are calculated using a fully quantum time-independent coupled-channel approach on recent potential energy surfaces of {sup 3}A{sup ′} and {sup 3}A{sup ″} symmetry. A larger basis set than in the previous studies was used to ensure single-surface convergence at higher energies. Our results agree well with the published data at lower energies and indicate the breakdown of reduced dimensionality approach at collision energies higher than 1.5 eV. Differential cross sections and momentum transfer cross sections are also reported.
2.1 THz quantum-cascade laser operating up to 144 K based on a scattering-assisted injection design.
Khanal, Sudeep; Reno, John L; Kumar, Sushil
2015-07-27
A 2.1 THz quantum cascade laser (QCL) based on a scattering-assisted injection and resonant-phonon depopulation design scheme is demonstrated. The QCL is based on a four-well period implemented in the GaAs/Al0.15Ga0.85As material system. The QCL operates up to a heat-sink temperature of 144 K in pulsed-mode, which is considerably higher than that achieved for previously reported THz QCLs operating around the frequency of 2 THz. At 46 K, the threshold current-density was measured as ∼ 745 A/cm2 with a peak-power output of ∼10 mW. Electrically stable operation in a positive differential-resistance regime is achieved by a careful choice of design parameters. The results validate the robustness of scattering-assisted injection schemes for development of low-frequency (ν < 2.5 THz) QCLs. PMID:26367626
Kurzmann, A. Beckel, A.; Lorke, A.; Geller, M.; Ludwig, A.; Wieck, A. D.
2015-02-07
We have investigated the influence of a layer of charged self-assembled quantum dots (QDs) on the mobility of a nearby two-dimensional electron gas (2DEG). Time-resolved transconductance spectroscopy was used to separate the two contributions of the change in mobility, which are: (i) The electrons in the QDs act as Coulomb scatterers for the electrons in the 2DEG. (ii) The screening ability and, hence, the mobility of the 2DEG decreases when the charge carrier density is reduced by the charged QDs, i.e., the mobility itself depends on the charge carrier concentration. Surprisingly, we find a negligible influence of the Coulomb scattering on the mobility for a 2DEG, separated by a 30 nm tunneling barrier to the layer of QDs. This means that the mobility change is completely caused by depletion, i.e., reduction of the charge carrier density in the 2DEG, which indirectly influences the mobility.
Quantum size effect as evidenced by small-angle X-ray scattering of In{sub 2}O{sub 3} nanoparticles
Souza, E. C. C.; Rey, J. F. Q.; Muccillo, E. N. S.
2009-01-29
Indium oxide nanoparticles were synthesized by a surfactant-free room-temperature soft chemistry route. The medium particle size of the thermally treated gel was evaluated by X-ray diffraction experiments, nitrogen adsorption measurements, transmission electron microscopy observations and small-angle X-ray scattering using synchrotron radiation. The main results show the single-crystalline nature of the prepared nanoparticles with 8 nm in diameter. The photoluminescence emission spectrum at room-temperature shows a broad peak with onset at, approximately, 315 nm as a result of quantum size effect produced by a small population of nanoparticles with average size of about 2.8 nm as revealed by small-angle X-ray scattering.
NASA Astrophysics Data System (ADS)
Yung, Y. Y.; Choi, B. H.; Tang, K. T.
1980-01-01
Three dimensional quantum mechanical calculations are carried out for the reactive scattering of D+H2→DH+H on the ab initio potential energy surface calculated by Liu and Siegbahn and fitted by Truhlar and Horowitz. The differential and total cross sections as well as the S matrix elements are obtained from the adiabatic distorted wave method. Threshold energy, cross sections and product distributions over final states are all in good agreement with experimental measurements. Results are also compared with the corresponding ones obtained on the Porter-Karplus and the Yates-Lester semi-empirical surfaces.
Coldea, Radu; Tennant, D. A.; Tyleczynski, Z.
2003-01-01
The magnetic excitations of the quasi-2D spin-1/2 frustrated Heisenberg antiferromagnet Cs{sub 2}CuCl{sub 4} are explored throughout the 2D Brillouin zone using high-resolution time-of-flight inelastic neutron scattering. Measurements are made both in the magnetically ordered phase, stabilized at low temperatures by the weak interlayer couplings, as well as in the spin liquid phase above the ordering temperature T{sub N}, when the 2D magnetic layers are decoupled. In the spin liquid phase the dynamical correlations are dominated by highly dispersive excitation continua, a characteristic signature of fractionalization of S = 1 spin waves into pairs of deconfined S = 1/2 spinons and the hallmark of a resonating-valence-bond (RVB) state. The boundaries of the excitation continua have strong 2D-modulated incommensurate dispersion relations. Upon cooling below T{sub N} magnetic order in an incommensurate spiral forms due to the 2D frustrated couplings. In this phase sharp magnons carrying a small part of the total scattering weight are observed at low energies, but the dominant continuum scattering which occurs at medium to high energies is essentially unchanged compared to the spin liquid phase. Linear spin-wave theory including one- and two-magnon processes can describe the sharp magnon excitation, but not the dominant continuum scattering, which instead is well described by a parametrized two-spinon cross section. Those results suggest a crossover in the nature of the excitations from S = 1 spin waves at low energies to deconfined S = 1/2 spinons at medium to high energies, which could be understood if Cs{sub 2}CuCl{sub 4} was in the close proximity of transition between a fractional RVB spin liquid and a magnetically ordered state. A large renormalization factor of the excitation energies [R = 1.63(5)], indicating strong quantum fluctuations in the ground state, is obtained using the exchange couplings determined from saturation-field measurements. We provide an
Qualtum cosmics-and-chaotics--the ultimate tortoise in physics and modern medicine.
Kothari, M V; Mehta, L A
1997-01-01
Qualtum cosmics is the qualitative opposite of quantum mechanics. The flip-side of qualtum cosmics is qualtum chaotics, the two governing much of what is seen as inscrutable in medicine. The Ultimate (Last) Tortoise is close to Einsteinean idea of a Unified Theory, a single concept that can explain whatsoever there is in physics, (and in medicine, or what have you). PMID:10740733
NASA Astrophysics Data System (ADS)
Tereshchenko, Sergei A.; Podgaetskii, Vitalii M.; Vorob'ev, Nikolai S.; Smirnov, A. V.
1996-03-01
A transient two-flux model of the interaction of light with a strongly scattering medium is developed on the basis of the concept of the paraxial photon propagating along the direction of thin pulsed laser beam incident on such a medium. An analitic expression for the radiation flux transmitted by a scattering medium is derived. Calculations are made of the dependences of the parameters of the temporal distributions of the transmitted radiation on the characteristics of the scattering medium. It is swown that the absorption and scattering coefficients of such a medium con be determined from the profile of the temporal distributions of the transmitted radiation. An experimental determination of the temporal distributions is reported for the radiation from a picosecond neodymium laser transmitted by a model scattering medium (a solution of dried milk in water). The experimental results are described well by the theoretical model.
Recovering chaotic properties from small data.
Shao, Chenxi; Fang, Fang; Liu, Qingqing; Wang, Tingting; Wang, Binghong; Yin, Peifeng
2014-12-01
Physical properties are obviously essential to study a chaotic system that generates discrete-time signals, but recovering chaotic properties of a signal source from small data is a very troublesome work. Existing chaotic models are weak in dealing with such case in that most of them need big data to exploit those properties. In this paper, geometric theory is considered to solve this problem. We build a smooth trajectory from series to implicitly exhibit the chaotic properties with series-nonuniform rational B-spline (S-NURBS) modeling method, which is presented by our team to model slow-changing chaotic time series. As for the part of validation, we reveal how well our model recovers the properties from both the statistical and the chaotic aspects to confirm the effectiveness of the model. Finally a practical chaotic model is built up to recover the chaotic properties contained in the Musa standard dataset, which is used in analyzing software reliability, thereby further proves the high credibility of this model in practical time series. The effectiveness of the S-NURBS modeling leads us to believe that it is really a feasible and worthy research area to study chaotic systems from geometric perspective. For this reason, we reckon that we have opened up a new horizon for chaotic system research. PMID:24686313
NASA Astrophysics Data System (ADS)
Schieve, William C.; Horwitz, Lawrence P.
2009-04-01
1. Foundations of quantum statistical mechanics; 2. Elementary examples; 3. Quantum statistical master equation; 4. Quantum kinetic equations; 5. Quantum irreversibility; 6. Entropy and dissipation: the microscopic theory; 7. Global equilibrium: thermostatics and the microcanonical ensemble; 8. Bose-Einstein ideal gas condensation; 9. Scaling, renormalization and the Ising model; 10. Relativistic covariant statistical mechanics of many particles; 11. Quantum optics and damping; 12. Entanglements; 13. Quantum measurement and irreversibility; 14. Quantum Langevin equation: quantum Brownian motion; 15. Linear response: fluctuation and dissipation theorems; 16. Time dependent quantum Green's functions; 17. Decay scattering; 18. Quantum statistical mechanics, extended; 19. Quantum transport with tunneling and reservoir ballistic transport; 20. Black hole thermodynamics; Appendix; Index.
NASA Astrophysics Data System (ADS)
Xu, Minzhong; Bačić, Zlatko
2011-11-01
We present an in-depth description of the methodology for accurate quantum calculation of the inelastic neutron scattering (INS) spectra of an H2 molecule confined inside a nanosize cavity of an arbitrary shape. This methodology was introduced in a recent work [M. Xu, L. Ulivi, M. Celli, D. Colognesi, and Z. Bačić, Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.83.241403 83, 241403(R) (2011)], where the INS spectra of para- and ortho-H2 in the small cage of the structure II clathrate hydrate were simulated and compared with the measured spectra. The key distinctive feature of our approach, and its main strength and advantage, is the use of the coupled quantum 5D translation-rotation (TR) energy levels and wave functions of the entrapped H2 molecule, rigorously calculated on the 5D intermolecular potential energy surface (PES), as the initial and the final states of the INS transitions. In this work, we describe the implementation of the 5D TR wave functions within the quantum INS formalism, and obtain the working expressions for the matrix elements required to compute the INS spectra of the nanoconfined H2 molecule. The computational approach devised for efficient calculation of the 5D TR eigenstates in the compact contracted basis, indispensable for our quantum simulation of the INS spectra, is presented as well. Since the TR coupling is fully taken into account, the computed INS spectra exhibit a uniquely high degree of realism and faithfully reflect the quantum dynamics of H2 on the PES of the host environment.
Chaotic attractors with separated scrolls
Bouallegue, Kais
2015-07-15
This paper proposes a new behavior of chaotic attractors with separated scrolls while combining Julia's process with Chua's attractor and Lorenz's attractor. The main motivation of this work is the ability to generate a set of separated scrolls with different behaviors, which in turn allows us to choose one or many scrolls combined with modulation (amplitude and frequency) for secure communication or synchronization. This set seems a new class of hyperchaos because each element of this set looks like a simple chaotic attractor with one positive Lyapunov exponent, so the cardinal of this set is greater than one. This new approach could be used to generate more general higher-dimensional hyperchaotic attractor for more potential application. Numerical simulations are given to show the effectiveness of the proposed theoretical results.
Illusion optics in chaotic light
Zhang Suheng; Gan Shu; Xiong Jun; Zhang Xiangdong; Wang Kaige
2010-08-15
The time-reversal process provides the possibility to counteract the time evolution of a physical system. Recent research has shown that such a process can occur in the first-order field correlation of chaotic light and result in the spatial interference and phase-reversal diffraction in an unbalanced interferometer. Here we report experimental investigations on the invisibility cloak and illusion phenomena in chaotic light. In an unbalanced interferometer illuminated by thermal light, we have observed the cloak effect and the optical transformation of one object into another object. The experimental results can be understood by the phase-reversal diffraction, and they demonstrate the theoretical proposal of similar effects in complementary media.
Chaotic attractors with separated scrolls
NASA Astrophysics Data System (ADS)
Bouallegue, Kais
2015-07-01
This paper proposes a new behavior of chaotic attractors with separated scrolls while combining Julia's process with Chua's attractor and Lorenz's attractor. The main motivation of this work is the ability to generate a set of separated scrolls with different behaviors, which in turn allows us to choose one or many scrolls combined with modulation (amplitude and frequency) for secure communication or synchronization. This set seems a new class of hyperchaos because each element of this set looks like a simple chaotic attractor with one positive Lyapunov exponent, so the cardinal of this set is greater than one. This new approach could be used to generate more general higher-dimensional hyperchaotic attractor for more potential application. Numerical simulations are given to show the effectiveness of the proposed theoretical results.
Chaotic desynchronization of multistrain diseases
NASA Astrophysics Data System (ADS)
Schwartz, Ira B.; Shaw, Leah B.; Cummings, Derek A. T.; Billings, Lora; McCrary, Marie; Burke, Donald S.
2005-12-01
Multistrain diseases are diseases that consist of several strains, or serotypes. The serotypes may interact by antibody-dependent enhancement (ADE), in which infection with a single serotype is asymptomatic, but infection with a second serotype leads to serious illness accompanied by greater infectivity. It has been observed from serotype data of dengue hemorrhagic fever that outbreaks of the four serotypes occur asynchronously. Both autonomous and seasonally driven outbreaks were studied in a model containing ADE. For sufficiently small ADE, the number of infectives of each serotype synchronizes, with outbreaks occurring in phase. When the ADE increases past a threshold, the system becomes chaotic, and infectives of each serotype desynchronize. However, certain groupings of the primary and secondary infectives remain synchronized even in the chaotic regime.
Chaotic pulsations in stellar models
Buchler, J.R. )
1990-12-01
The irregular behavior of large-amplitude pulsating stars undergoing radial oscillations is examined theoretically, with a focus on hydrodynamic simulations of the W Virginis population II Cepheids (stars which show both regular and RV Tau characteristics). Sequences of models are constructed as one-parameter families (with luminosity, mass, and composition fixed and Teff as the control parameter) and analyzed to derive a systematic map of the bifurcation set; i.e., of the possible types of pulsations. The results are presented graphically, and it is shown that both cascades of period doubling (via destabilization of an overtone through a half-integer-type resonance) and tangent bifurcation are possible routes to chaos in these systems, depending on the stellar parameters. The general robustness of the chaotic behavior and the existence of a 'chaotic blue edge' in stellar-parameter space are demonstrated. 55 refs.
Xu, Shanshan; Rephaeli, Eden; Fan, Shanhui
2013-11-27
We consider a general class of integrated quantum systems where photon-photon interaction occurs in a quantum device that is localized in space. Using techniques that are closely related to cluster decomposition principles in quantum field theory, we provide a general constraint on the analytic properties of a two-photon S matrix in this class of systems. We also show that the photon-photon interaction in these systems inevitably leads to frequency mixing and entanglement and that frequencies of the single photons cannot be preserved in these systems. PMID:24329447
Chaotic inflation and supersymmetry breaking
Kallosh, Renata; Linde, Andrei; Rube, Tomas; Olive, Keith A.
2011-10-15
We investigate the recently proposed class of chaotic inflation models in supergravity with an arbitrary inflaton potential V({phi}). These models are extended to include matter fields in the visible sector and we employ a mechanism of supersymmetry breaking based on a particular phenomenological version of the KKLT mechanism (the KL model). We describe specific features of reheating in this class of models and show how one can solve the cosmological moduli and gravitino problems in this context.
Determinism in synthesized chaotic waveforms.
Corron, Ned J; Blakely, Jonathan N; Hayes, Scott T; Pethel, Shawn D
2008-03-01
The output of a linear filter driven by a randomly polarized square wave, when viewed backward in time, is shown to exhibit determinism at all times when embedded in a three-dimensional state space. Combined with previous results establishing exponential divergence equivalent to a positive Lyapunov exponent, this result rigorously shows that such reverse-time synthesized waveforms appear equally to have been produced by a deterministic chaotic system. PMID:18517561
Modelling chaotic vibrations using NASTRAN
NASA Technical Reports Server (NTRS)
Sheerer, T. J.
1993-01-01
Due to the unavailability and, later, prohibitive cost of the computational power required, many phenomena in nonlinear dynamic systems have in the past been addressed in terms of linear systems. Linear systems respond to periodic inputs with periodic outputs, and may be characterized in the time domain or in the frequency domain as convenient. Reduction to the frequency domain is frequently desireable to reduce the amount of computation required for solution. Nonlinear systems are only soluble in the time domain, and may exhibit a time history which is extremely sensitive to initial conditions. Such systems are termed chaotic. Dynamic buckling, aeroelasticity, fatigue analysis, control systems and electromechanical actuators are among the areas where chaotic vibrations have been observed. Direct transient analysis over a long time period presents a ready means of simulating the behavior of self-excited or externally excited nonlinear systems for a range of experimental parameters, either to characterize chaotic behavior for development of load spectra, or to define its envelope and preclude its occurrence.
Modelling chaotic vibrations using NASTRAN
NASA Astrophysics Data System (ADS)
Sheerer, T. J.
1993-09-01
Due to the unavailability and, later, prohibitive cost of the computational power required, many phenomena in nonlinear dynamic systems have in the past been addressed in terms of linear systems. Linear systems respond to periodic inputs with periodic outputs, and may be characterized in the time domain or in the frequency domain as convenient. Reduction to the frequency domain is frequently desireable to reduce the amount of computation required for solution. Nonlinear systems are only soluble in the time domain, and may exhibit a time history which is extremely sensitive to initial conditions. Such systems are termed chaotic. Dynamic buckling, aeroelasticity, fatigue analysis, control systems and electromechanical actuators are among the areas where chaotic vibrations have been observed. Direct transient analysis over a long time period presents a ready means of simulating the behavior of self-excited or externally excited nonlinear systems for a range of experimental parameters, either to characterize chaotic behavior for development of load spectra, or to define its envelope and preclude its occurrence.
Chaotic pendulum: The complete attractor
NASA Astrophysics Data System (ADS)
DeSerio, Robert
2003-03-01
A commercial chaotic pendulum is modified to study nonlinear dynamics, including the determination of Poincaré sections, fractal dimensions, and Lyapunov exponents. The apparatus is driven by a simple oscillating mechanism powered by a 200 pulse per revolution stepper motor running at constant angular velocity. A computer interface generates the uniform pulse train needed to run the stepper motor and, with each pulse, reads a rotary encoder attached to the pendulum axle. Ten million readings from overnight runs of 50 000 drive cycles were smoothed and differentiated to obtain the pendulum angle θ and the angular velocity ω at each pulse of the drive. A plot of the 50 000 (θ,ω) phase points corresponding to one phase of the drive system produces a single Poincaré section. Thus, 200 Poincaré sections are experimentally available, one at each step of the drive. Viewed separately, any one of them strikingly illustrates the fractal geometry of the underlying chaotic attractor. Viewed sequentially in a repeating loop, they demonstrate the stretching and folding of phase point density typical of chaotic dynamics. Results for four pendulum damping conditions are presented and compared.
CHAOTIC CAPTURE OF NEPTUNE TROJANS
Nesvorny, David; Vokrouhlicky, David
2009-06-15
Neptune Trojans (NTs) are swarms of outer solar system objects that lead/trail planet Neptune during its revolutions around the Sun. Observations indicate that NTs form a thick cloud of objects with a population perhaps {approx}10 times more numerous than that of Jupiter Trojans and orbital inclinations reaching {approx}25 deg. The high inclinations of NTs are indicative of capture instead of in situ formation. Here we study a model in which NTs were captured by Neptune during planetary migration when secondary resonances associated with the mean-motion commensurabilities between Uranus and Neptune swept over Neptune's Lagrangian points. This process, known as chaotic capture, is similar to that previously proposed to explain the origin of Jupiter's Trojans. We show that chaotic capture of planetesimals from an {approx}35 Earth-mass planetesimal disk can produce a population of NTs that is at least comparable in number to that inferred from current observations. The large orbital inclinations of NTs are a natural outcome of chaotic capture. To obtain the {approx}4:1 ratio between high- and low-inclination populations suggested by observations, planetary migration into a dynamically excited planetesimal disk may be required. The required stirring could have been induced by Pluto-sized and larger objects that have formed in the disk.
Non-scale-invariant density perturbations from chaotic extended inflation
Mollerach, S. ); Matarrese, S. )
1992-03-15
Chaotic inflation is analyzed in the frame of scalar-tensor theories of gravity. Fluctuations in the energy density arise from quantum fluctuations of the Brans-Dicke field and of the inflaton field. The spectrum of perturbations is studied for a class of models: it is non-scale-invariant and, for certain values of the parameters, it has a peak. If the peak appears at astrophysically interesting scales it may help to reconcile the cold-dark-matter scenario for structure formation with large-scale observations.
Non scale-invariant density perturbations from chaotic extended inflation
NASA Technical Reports Server (NTRS)
Mollerach, Silvia; Matarrese, Sabino
1991-01-01
Chaotic inflation is analyzed in the frame of scalar-tensor theories of gravity. Fluctuations in the energy density arise from quantum fluctuations of the Brans-Dicke field and of the inflation field. The spectrum of perturbations is studied for a class of models: it is non scale-invarient and, for certain values of the parameters, it has a peak. If the peak appears at astrophysically interesting scales, it may help to reconcile the Cold Dark Matter scenario for structure formation with large scale observations.
Characterizing chaotic melodies in automatic music composition
NASA Astrophysics Data System (ADS)
Coca, Andrés E.; Tost, Gerard O.; Zhao, Liang
2010-09-01
In this paper, we initially present an algorithm for automatic composition of melodies using chaotic dynamical systems. Afterward, we characterize chaotic music in a comprehensive way as comprising three perspectives: musical discrimination, dynamical influence on musical features, and musical perception. With respect to the first perspective, the coherence between generated chaotic melodies (continuous as well as discrete chaotic melodies) and a set of classical reference melodies is characterized by statistical descriptors and melodic measures. The significant differences among the three types of melodies are determined by discriminant analysis. Regarding the second perspective, the influence of dynamical features of chaotic attractors, e.g., Lyapunov exponent, Hurst coefficient, and correlation dimension, on melodic features is determined by canonical correlation analysis. The last perspective is related to perception of originality, complexity, and degree of melodiousness (Euler's gradus suavitatis) of chaotic and classical melodies by nonparametric statistical tests.
Intermittent chaotic chimeras for coupled rotators
NASA Astrophysics Data System (ADS)
Olmi, Simona; Martens, Erik A.; Thutupalli, Shashi; Torcini, Alessandro
2015-09-01
Two symmetrically coupled populations of N oscillators with inertia m display chaotic solutions with broken symmetry similar to experimental observations with mechanical pendulums. In particular, we report evidence of intermittent chaotic chimeras, where one population is synchronized and the other jumps erratically between laminar and turbulent phases. These states have finite lifetimes diverging as a power law with N and m . Lyapunov analyses reveal chaotic properties in quantitative agreement with theoretical predictions for globally coupled dissipative systems.
NASA Astrophysics Data System (ADS)
Svec, Miloslav
2015-04-01
Unitary evolution law describes isolated particle scattering processes in an empty Minkowski spacetime. We put forward a hypothesis that the physical Universe includes a quantum environment that interacts with some particle scattering and decay processes. While the scattering process is governed by the S -matrix dynamics and its conservation laws and unitarity, the interaction with the environment evolves the produced final state ρf(S ) to the observed state ρf(O ). To be consistent with the Standard Model this new interaction must be a pure dephasing interaction. Governed by a nonunitary evolution law, it modifies the phases of the S -matrix amplitudes and can give rise to mixing of such amplitudes to form observed amplitudes. We present the first test of unitary evolution law in particle scattering. Conservation of P -parity in strong interactions imposes constraints on partial wave helicity and nucleon transversity amplitudes in π N →π π N processes. An independent set of constraints on these amplitudes is imposed by the S -matrix unitary evolution law. The unitary evolution evolves pure initial states into pure final states leading to 9 independent constraints on 16 components of angular intensities in π N →π π N processes. When expressed in terms of parity conserving transversity amplitudes, all 9 constraints are identities provided a single constraint on the transversity amplitudes holds true. The constraint implies that relative phases between transversity amplitudes of the same naturality and transversity must be 0 or ±π . Assuming a self-consistent set of these unitary phases we use the CERN data on spin observables Ru0 and Ry0 to determine a unique solution for the S - and P -wave moduli below 1080 MeV. The data require ρ0(770 )-f0(980 ) mixing in the S -wave but this unitary solution is excluded by data on observables Rx0 within at least 5 standard deviations. All previous amplitude analyses of π N →π π N processes found nonunitary
NASA Astrophysics Data System (ADS)
Jang, H.; Nojiri, H.; Gerber, S.; Lee, W.-S.; Zhu, D.; Lee, J.-S.; Kao, C.-C.
X-ray scattering under high magnetic fields provides unique opportunities for solving many scientific puzzles in quantum materials, such as strongly correlated electron systems. Incorporating high magnetic field capability presents serious challenges at an x-ray facility, including the limitation on the maximum magnetic field even with a DC magnet (up to ~20 Tesla), expensive cost in development, radiation damage, and limited flexibility in the experimental configuration. These challenges are especially important when studying the symmetry broken state induced by the high magnetic field are necessary, for example, exploring intertwined orders between charge density wave (CDW) and high Tc superconductivity. Moreover, a gap in magnetic field strengths has led to many discrepancies and puzzling issues for understanding strongly correlated systems - is a CDW competing or more intimately intertwined with high-temperature superconductivity. To bridge this gap and resolve these experimental discrepancies, one needs an innovative experimental approach. Here, we will present a new approach to x-ray scattering under high magnetic field up to 28 Teals by taking advantage of brilliant x-ray free electron laser (FEL). The FEL generates sufficiently high photon flux for single shot x-ray scattering experiment. In this talk, we will also present the first demonstration about the field induced CDW order in YBCO Ortho-VIII with 28 Tesla, which show the totally unexpected three-dimensional behavior.
Xia, H. Patterson, R.; Feng, Y.; Shrestha, S.; Conibeer, G.
2014-08-11
The rates of charge carrier relaxation by phonon emission are of substantial importance in the field of hot carrier solar cell, primarily in investigation of mechanisms to slow down hot carrier cooling. In this work, energy and momentum resolved deformation potentials relevant to electron-phonon scattering are computed for wurtzite InN and GaN as well as an InN/GaN multiple quantum well (MQW) superlattice using ab-initio methods. These deformation potentials reveal important features such as discontinuities across the electronic bandgap of the materials and variations over tens of eV. The energy dependence of the deformation potential is found to be very similar for wurtzite nitrides despite differences between the In and Ga pseudopotentials and their corresponding electronic band structures. Charge carrier relaxation by this mechanism is expected to be minimal for electrons within a few eV of the conduction band edge. However, hole scattering at energies more accessible to excitation by solar radiation is possible between heavy and light hole states. Moderate reductions in overall scattering rates are observed in MQW relative to the bulk nitride materials.
NASA Astrophysics Data System (ADS)
Xia, H.; Patterson, R.; Feng, Y.; Shrestha, S.; Conibeer, G.
2014-08-01
The rates of charge carrier relaxation by phonon emission are of substantial importance in the field of hot carrier solar cell, primarily in investigation of mechanisms to slow down hot carrier cooling. In this work, energy and momentum resolved deformation potentials relevant to electron-phonon scattering are computed for wurtzite InN and GaN as well as an InN/GaN multiple quantum well (MQW) superlattice using ab-initio methods. These deformation potentials reveal important features such as discontinuities across the electronic bandgap of the materials and variations over tens of eV. The energy dependence of the deformation potential is found to be very similar for wurtzite nitrides despite differences between the In and Ga pseudopotentials and their corresponding electronic band structures. Charge carrier relaxation by this mechanism is expected to be minimal for electrons within a few eV of the conduction band edge. However, hole scattering at energies more accessible to excitation by solar radiation is possible between heavy and light hole states. Moderate reductions in overall scattering rates are observed in MQW relative to the bulk nitride materials.
NASA Astrophysics Data System (ADS)
Gu, Huaguang
2013-06-01
The transition from chaotic bursting to chaotic spiking has been simulated and analyzed in theoretical neuronal models. In the present study, we report experimental observations in a neural pacemaker of a transition from chaotic bursting to chaotic spiking within a bifurcation scenario from period-1 bursting to period-1 spiking. This was induced by adjusting extracellular calcium or potassium concentrations. The bifurcation scenario began from period-doubling bifurcations or period-adding sequences of bursting pattern. This chaotic bursting is characterized by alternations between multiple continuous spikes and a long duration of quiescence, whereas chaotic spiking is comprised of fast, continuous spikes without periods of quiescence. Chaotic bursting changed to chaotic spiking as long interspike intervals (ISIs) of quiescence disappeared within bursting patterns, drastically decreasing both ISIs and the magnitude of the chaotic attractors. Deterministic structures of the chaotic bursting and spiking patterns are also identified by a short-term prediction. The experimental observations, which agree with published findings in theoretical neuronal models, demonstrate the existence and reveal the dynamics of a neuronal transition from chaotic bursting to chaotic spiking in the nervous system.
Information encoder/decoder using chaotic systems
Miller, Samuel Lee; Miller, William Michael; McWhorter, Paul Jackson
1997-01-01
The present invention discloses a chaotic system-based information encoder and decoder that operates according to a relationship defining a chaotic system. Encoder input signals modify the dynamics of the chaotic system comprising the encoder. The modifications result in chaotic, encoder output signals that contain the encoder input signals encoded within them. The encoder output signals are then capable of secure transmissions using conventional transmission techniques. A decoder receives the encoder output signals (i.e., decoder input signals) and inverts the dynamics of the encoding system to directly reconstruct the original encoder input signals.
Information encoder/decoder using chaotic systems
Miller, S.L.; Miller, W.M.; McWhorter, P.J.
1997-10-21
The present invention discloses a chaotic system-based information encoder and decoder that operates according to a relationship defining a chaotic system. Encoder input signals modify the dynamics of the chaotic system comprising the encoder. The modifications result in chaotic, encoder output signals that contain the encoder input signals encoded within them. The encoder output signals are then capable of secure transmissions using conventional transmission techniques. A decoder receives the encoder output signals (i.e., decoder input signals) and inverts the dynamics of the encoding system to directly reconstruct the original encoder input signals. 32 figs.
Multiple Sequence Alignment Based on Chaotic PSO
NASA Astrophysics Data System (ADS)
Lei, Xiu-Juan; Sun, Jing-Jing; Ma, Qian-Zhi
This paper introduces a new improved algorithm called chaotic PSO (CPSO) based on the thought of chaos optimization to solve multiple sequence alignment. For one thing, the chaotic variables are generated between 0 and 1 when initializing the population so that the particles are distributed uniformly in the solution space. For another thing, the chaotic sequences are generated using the Logistic mapping function in order to make chaotic search and strengthen the diversity of the population. The simulation results of several benchmark data sets of BAliBase show that the improved algorithm is effective and has good performances for the data sets with different similarity.
NASA Astrophysics Data System (ADS)
Semenov, Alexander; Dubernet, Marie-Lise; Babikov, Dmitri
2014-09-01
The mixed quantum/classical theory (MQCT) for inelastic molecule-atom scattering developed recently [A. Semenov and D. Babikov, J. Chem. Phys. 139, 174108 (2013)] is extended to treat a general case of an asymmetric-top-rotor molecule in the body-fixed reference frame. This complements a similar theory formulated in the space-fixed reference-frame [M. Ivanov, M.-L. Dubernet, and D. Babikov, J. Chem. Phys. 140, 134301 (2014)]. Here, the goal was to develop an approximate computationally affordable treatment of the rotationally inelastic scattering and apply it to H2O + He. We found that MQCT is somewhat less accurate at lower scattering energies. For example, below E = 1000 cm-1 the typical errors in the values of inelastic scattering cross sections are on the order of 10%. However, at higher scattering energies MQCT method appears to be rather accurate. Thus, at scattering energies above 2000 cm-1 the errors are consistently in the range of 1%-2%, which is basically our convergence criterion with respect to the number of trajectories. At these conditions our MQCT method remains computationally affordable. We found that computational cost of the fully-coupled MQCT calculations scales as n2, where n is the number of channels. This is more favorable than the full-quantum inelastic scattering calculations that scale as n3. Our conclusion is that for complex systems (heavy collision partners with many internal states) and at higher scattering energies MQCT may offer significant computational advantages.
Ontic and epistemic descriptions of chaotic systems
NASA Astrophysics Data System (ADS)
Atmanspacher, Harald
2000-05-01
Traditional philosophical discourse draws a distinction between ontology and epistemology and generally enforces this distinction by keeping the two subject areas separated and unrelated. In addition, the relationship between the two areas is of central importance to physics and philosophy of physics. For instance, all kinds of measurement-related problems force us to consider both our knowledge of the states and observables of a system (epistemic perspective) and its states and observables independent of such knowledge (ontic perspective). This applies to quantum systems in particular. In this contribution we present an example which shows the importance of distinguishing between ontic and epistemic levels of description even for classical systems. Corresponding conceptions of ontic and epistemic states and their evolution will be introduced and discussed with respect to aspects of stability and information flow. These aspects show why the ontic/epistemic distinction is particularly important for systems exhibiting deterministic chaos. Moreover, this distinction provides some understanding of the relationships between determinism, causation, predictability, randomness, and stochasticity in chaotic systems.
NASA Astrophysics Data System (ADS)
Kushwaha, Manvir S.
2016-03-01
We investigate a one-component, quasi-zero-dimensional, quantum plasma exposed to a parabolic potential and an applied magnetic field in the symmetric gauge. If the size of such a system as can be realized in the semiconducting quantum dots is on the order of the de Broglie wavelength, the electronic and optical properties become highly tunable. Then the quantum size effects challenge the observation of many-particle phenomena such as the magneto-optical absorption, Raman intensity, and electron energy loss spectrum. An exact analytical solution of the problem leads us to infer that these many-particle phenomena are, in fact, dictated by the generalized Kohn's theorem in the long-wavelength limit. Maneuvering the confinement and/or the magnetic field furnishes the resonance energy capable of being explored with the FIR, Raman, or electron energy loss spectroscopy. This implies that either of these probes should be competent in observing the localized magnetoplasmons in the system. A deeper insight into the physics of quantum dots is paving the way for their implementation in diverse fields such as quantum computing and medical imaging.
A Chaotic System with Different Shapes of Equilibria
NASA Astrophysics Data System (ADS)
Pham, Viet-Thanh; Jafari, Sajad; Wang, Xiong; Ma, Jun
Although many chaotic systems have been introduced in the literature, a few of them possess uncountably infinite equilibrium points. The aim of our short work is to widen the current knowledge of the chaotic systems with an infinite number of equilibria. A three-dimensional system with special properties, for example, exhibiting chaotic attractor with circular equilibrium, chaotic attractor with ellipse equilibrium, chaotic attractor with square-shaped equilibrium, and chaotic attractor with rectangle-shaped equilibrium, is proposed.
Chaotic neurochips for fuzzy computing
NASA Astrophysics Data System (ADS)
Szu, Harold H.; Zadeh, Lotfi A.; Hsu, Charles C.; DeWitte, Joseph T., Jr.; Moon, Gyu; Gobovic, Desa; Zaghloul, Mona E.
1994-03-01
A massive chaotic neural network (CNN) is demonstrated with a fixed-point Hebbian synaptic weight dynamic: an instantaneous input, and a piecewise negative logic output. The variable slope of the output versus the input becomes a software control of the collective chaos hardware. Two applications are given. The mean synaptic weight field plays an important role for fast pattern recognition capability in examples of both the habituation and the novelty detections. Another novel usage of CNN is to be a bridge between neural learning and learnable fuzzy logic.
Enhanced predictability in chaotic geophysical systems
Brindley, J.; Kapitaniak, T.
1996-06-01
Using the Lorenz equations as an example we show that one chaotic system can be controlled by synchronizing its behavior with the chaotic behavior of another system. We particularly discuss the implications of this phenomenon in geophysical systems. {copyright} {ital 1996 American Institute of Physics.}
Forecasting catastrophe by exploiting chaotic dynamics
Stewart, H.B.; Lansbury, A.N.
1990-01-01
Our purpose here is to introduce a variation on the theme of short term forecasting from a chaotic time series. We show that for the lowest-dimensional chaotic attractors, it is possible to predict incipient catastrophes, or crises, by examining time series data taken near the catastrophic bifurcation threshold, but always remaining on the safe side of the threshold.
NASA Astrophysics Data System (ADS)
Shebeko, A.
2013-12-01
The clothing procedure, put forward in quantum field theory by Greenberg and Schweber, is applied for the description of nucleon-nucleon ( N- N) scattering below the pion production threshold and deuteron properties. We consider pseudoscalar ( π and η), vector ( ρ and ω) and scalar ( δ and σ) meson fields interacting with N and ones via the Yukawa-type couplings to introduce trial interactions between "bare" particles. The subsequent unitary clothing transformations (UCTs) are found to express the total Hamiltonian through new interaction operators that refer to particles with physical (observable) properties, the so-called clothed particles. The corresponding analytic expressions in momentum space are compared with the separate meson contributions to the one-boson-exchange potentials in the meson theory of nuclear forces. We will also show a worked example where the UCTs method is used in the framework of a gauge-independent field-theoretical treatment of electromagnetic interactions of deuterons (bound systems).
Hennig, Carsten; Schmatz, Stefan
2016-07-20
Employing dimensionality-reduced time-independent quantum scattering theory and summation over all possible total angular momentum states, initial-state selected reaction cross sections for the exothermic gas-phase bimolecular nucleophilic substitution (SN2) reaction Cl(-) + CH3Br → ClCH3 + Br(-) have been calculated. The carbon-halogen bonds and the rotation of the methyl halides are taken into account. In agreement with previous calculations for J = 0, initial rotational motion of CH3Br decreases the reaction probability and consequently the cross sections. The experimentally obtained thermal rate constant for 300 K is reproduced within the experimental error. For lower temperatures, it is calculated to be below the experimental values but shows the same strong increase for T → 0. PMID:27381461
NASA Astrophysics Data System (ADS)
Goble, Nicholas J.; Watson, John D.; Manfra, Michael J.; Gao, Xuan P. A.
2014-07-01
Understanding the nonmonotonic behavior in the temperature dependent resistance R(T) of strongly correlated two-dimensional (2D) carriers in clean semiconductors has been a central issue in the studies of 2D metallic states and metal-insulator transitions. We have studied the transport of high mobility 2D holes in 20-nm-wide GaAs quantum wells with varying short-range disorder strength by changing the Al fraction x in the AlxGa1-xAs barrier. Via varying the short-range interface roughness and alloy scattering, it is observed that increasing x suppresses both the strength and characteristic temperature scale of the 2D metallicity, pointing to the distinct role of short-range vs long-range disorder in the 2D metallic transport in this correlated 2D hole system with interaction parameter rs˜20.
NASA Astrophysics Data System (ADS)
Bačić, Z.; Kress, J. D.; Parker, G. A.; Pack, R. T.
1990-02-01
Accurate 3D coupled channel calculations for total angular momentum J=0 for the reaction F+H2→HF+H using a realistic potential energy surface are analyzed. The reactive scattering is formulated using the hyperspherical (APH) coordinates of Pack and Parker. The adiabatic basis functions are generated quite efficiently using the discrete variable representation method. Reaction probabilities for relative collision energies of up to 17.4 kcal/mol are presented. To aid in the interpretation of the resonances and quantum structure observed in the calculated reaction probabilities, we analyze the phases of the S matrix transition elements, Argand diagrams, time delays and eigenlifetimes of the collision lifetime matrix. Collinear (1D) and reduced dimensional 3D bending corrected rotating linear model (BCRLM) calculations are presented and compared with the accurate 3D calculations.
NASA Technical Reports Server (NTRS)
Schwenke, David W.; Truhlar, Donald G.
1990-01-01
The Generalized Newton Variational Principle for 3D quantum mechanical reactive scattering is briefly reviewed. Then three techniques are described which improve the efficiency of the computations. First, the fact that the Hamiltonian is Hermitian is used to reduce the number of integrals computed, and then the properties of localized basis functions are exploited in order to eliminate redundant work in the integral evaluation. A new type of localized basis function with desirable properties is suggested. It is shown how partitioned matrices can be used with localized basis functions to reduce the amount of work required to handle the complex boundary conditions. The new techniques do not introduce any approximations into the calculations, so they may be used to obtain converged solutions of the Schroedinger equation.
Werfelli, Ghofran; Halvick, Philippe; Honvault, Pascal; Kerkeni, Boutheïna; Stoecklin, Thierry
2015-09-21
The observed abundances of the methylidyne cation, CH(+), in diffuse molecular clouds can be two orders of magnitude higher than the prediction of the standard gas-phase models which, in turn, predict rather well the abundances of neutral CH. It is therefore necessary to investigate all the possible formation and destruction processes of CH(+) in the interstellar medium with the most abundant species H, H2, and e(-). In this work, we address the destruction process of CH(+) by hydrogen abstraction. We report a new calculation of the low temperature rate coefficients for the abstraction reaction, using accurate time-independent quantum scattering and a new high-level ab initio global potential energy surface including a realistic model of the long-range interaction between the reactants H and CH(+). The calculated thermal rate coefficient is in good agreement with the experimental data in the range 50 K-800 K. However, at lower temperatures, the experimental rate coefficient takes exceedingly small values which are not reproduced by the calculated rate coefficient. Instead, the latter rate coefficient is close to the one given by the Langevin capture model, as expected for a reaction involving an ion and a neutral species. Several recent theoretical works have reported a seemingly good agreement with the experiment below 50 K, but an analysis of these works show that they are based on potential energy surfaces with incorrect long-range behavior. The experimental results were explained by a loss of reactivity of the lowest rotational states of the reactant; however, the quantum scattering calculations show the opposite, namely, a reactivity enhancement with rotational excitation. PMID:26395702
Semenov, Alexander; Babikov, Dmitri
2014-01-28
The mixed quantum/classical theory (MQCT) for rotationally inelastic scattering developed recently [A. Semenov and D. Babikov, J. Chem. Phys. 139, 174108 (2013)] is benchmarked against the full quantum calculations for two molecular systems: He + H{sub 2} and Na + N{sub 2}. This allows testing new method in the cases of light and reasonably heavy reduced masses, for small and large rotational quanta, in a broad range of collision energies and rotational excitations. The resultant collision cross sections vary through ten-orders of magnitude range of values. Both inelastic and elastic channels are considered, as well as differential (over scattering angle) cross sections. In many cases results of the mixed quantum/classical method are hard to distinguish from the full quantum results. In less favorable cases (light masses, larger quanta, and small collision energies) some deviations are observed but, even in the worst cases, they are within 25% or so. The method is computationally cheap and particularly accurate at higher energies, heavier masses, and larger densities of states. At these conditions MQCT represents a useful alternative to the standard full-quantum scattering theory.
NASA Astrophysics Data System (ADS)
Semenov, Alexander; Babikov, Dmitri
2014-01-01
The mixed quantum/classical theory (MQCT) for rotationally inelastic scattering developed recently [A. Semenov and D. Babikov, J. Chem. Phys. 139, 174108 (2013)] is benchmarked against the full quantum calculations for two molecular systems: He + H2 and Na + N2. This allows testing new method in the cases of light and reasonably heavy reduced masses, for small and large rotational quanta, in a broad range of collision energies and rotational excitations. The resultant collision cross sections vary through ten-orders of magnitude range of values. Both inelastic and elastic channels are considered, as well as differential (over scattering angle) cross sections. In many cases results of the mixed quantum/classical method are hard to distinguish from the full quantum results. In less favorable cases (light masses, larger quanta, and small collision energies) some deviations are observed but, even in the worst cases, they are within 25% or so. The method is computationally cheap and particularly accurate at higher energies, heavier masses, and larger densities of states. At these conditions MQCT represents a useful alternative to the standard full-quantum scattering theory.
Ganguly, A. E-mail: aganguly@maths.iitkgp.ernet.in; Das, A.
2014-11-15
We consider one-dimensional stationary position-dependent effective mass quantum model and derive a generalized Korteweg-de Vries (KdV) equation in (1+1) dimension through Lax pair formulation, one being the effective mass Schrödinger operator and the other being the time-evolution of wave functions. We obtain an infinite number of conserved quantities for the generated nonlinear equation and explicitly show that the new generalized KdV equation is an integrable system. Inverse scattering transform method is applied to obtain general solution of the nonlinear equation, and then N-soliton solution is derived for reflectionless potentials. Finally, a special choice has been made for the variable mass function to get mass-deformed soliton solution. The influence of position and time-dependence of mass and also of the different representations of kinetic energy operator on the nature of such solitons is investigated in detail. The remarkable features of such solitons are demonstrated in several interesting figures and are contrasted with the conventional KdV-soliton associated with constant-mass quantum model.
Colognesi, Daniele; Celli, Milva; Ulivi, Lorenzo; Xu, Minzhong; Bačić, Zlatko
2013-08-15
We report inelastic neutron scattering (INS) measurements on molecular hydrogen trapped in simple (D2O) and binary (D2O plus perdeuterated tetrahydrofuran) clathrate hydrates, performed at a low temperature using two different neutron spectrometers to probe both energy and momentum transfer. The INS spectra of binary clathrate samples exhibit a rich structure containing sharp bands arising from both the rotational transitions and the rattling modes of the guest H2 molecule. They agree well with the rigorous fully quantum simulations, which account for the subtle effects of the anisotropy, angular and radial, of the host cage on the H2 microscopic dynamics and the resulting spectra. The simple clathrate samples present a much greater challenge, due to the multiple H2 occupancy of the large cages, which makes the quantum calculations an extremely difficult task. In addition, we discuss in detail various physical aspects of the experimental and simulated INS spectra, such as their temperature dependence, the effects of the cage geometry, and the different features associated with the ortho-hydrogen and para-hydrogen species. PMID:23514207
NASA Astrophysics Data System (ADS)
Bossé, G.; Pan, LiDong; Li, Yize S.; Greene, L. H.; Eckstein, J.; Armitage, N. P.
2016-02-01
We present THz range optical conductivity data of a thin film of the near quantum critical heavy-fermion compound CeFe2Ge2 . Our complex conductivity measurements find a deviation from conventional Drude-like transport in a temperature range previously reported to exhibit unconventional behavior. We calculate the frequency-dependent effective mass and scattering rate using an extended Drude model analysis. We find the inelastic scattering rate can be described by a temperature-dependent power law ωn (T ), where n (T ) approaches ˜1.0 ±0.2 at 1.5 K. This is compared to the ρ ˜T1.5 behavior claimed in dc resistivity data and the ρ ˜T2 expected from Fermi-liquid theory. In addition to a low-temperature mass renormalization, we find an anomalous mass renormalization that persists to high temperature. We attribute this to a Hund's coupling in the Fe states in a manner similar to that recently proposed in the ferropnictides. CeFe2Ge2 appears to be a very interesting system where one may study the interplay between the usual 4 f lattice Kondo effect and this Hund's enhanced Kondo effect in the 3 d states.
Alexander, M.H.
1991-06-15
The authors report the results of fully quantum close coupled studies of collisions of nitrogen oxide with a silver surface. The recent corrected effective medium potential energy surfaces (PES) of DePristo and Alexander were used. The final state rotational distributions show evidence of at least four rotational rainbows, corresponding to scattering on (and interference between) the two PES which arise when the degeneracy of the NO molecule is lifted upon approach to the surface. A strong tendency is seen to populate the lower spin-orbit manifold at low to moderate final J, which disappears as J rises beyond 30.5 and the final states are better described in Hund`s case (b). Simultaneously, there exists a propensity to populate those A-doublet levels in which the electronic-rotational wave function is antisymmetric with respect to reflection of the electronic coordinates in the plane of rotation of the scattered NO molecule. This feature is opposite to what has been seen experimentally. An approximate averaging over the lateral position of the NO molecule above the surface that although the rainbow oscillations are strongly sensitive to surface corrugation, the fine-structure propensities are not.
NASA Astrophysics Data System (ADS)
Cho, Yong Jai; Choi, Sang Don
1996-03-01
Utilizing state-independent projection operators, we obtain a Lorentzian form of cyclotron-transition absorption spectra in the quantum limit. The linewidth formula is applied to determine the dilation and uniaxial deformation-potential constants (Ξd, Ξu) for anisotropic materials. By fitting the theoretical values to the experimental data, we obtain Ξu=18.0+/-0.6 eV and Ξd=-12.2+/-0.68 eV for Ge.
Multiple channel secure communication using chaotic system encoding
Miller, S.L.
1996-12-31
fA new method to encrypt signals using chaotic systems has been developed that offers benefits over conventional chaotic encryption methods. The method simultaneously encodes multiple plaintext streams using a chaotic system; a key is required to extract the plaintext from the chaotic cipertext. A working prototype demonstrates feasibility of the method by simultaneously encoding and decoding multiple audio signals using electrical circuits.
NASA Astrophysics Data System (ADS)
Marciani, M.; Schomerus, H.; Beenakker, C. W. J.
2016-08-01
We calculate the joint distribution P(S , Q) of the scattering matrix S and time-delay matrix Q = - iℏS† dS / dE of a chaotic quantum dot coupled by point contacts to metal electrodes. While S and Q are statistically independent for ballistic coupling, they become correlated for tunnel coupling. We relate the ensemble averages of Q and S and thereby obtain the average density of states at the Fermi level. We apply this to a calculation of the effect of a tunnel barrier on the Majorana resonance in a topological superconductor. We find that the presence of a Majorana bound state is hidden in the density of states and in the thermal conductance if even a single scattering channel has unit tunnel probability. The electrical conductance remains sensitive to the appearance of a Majorana bound state, and we calculate the variation of the average conductance through a topological phase transition.
Effect of a tunnel barrier on the scattering from a Majorana bound state in an Andreev billiard
NASA Astrophysics Data System (ADS)
Marciani, M.; Schomerus, H.; Beenakker, C. W. J.
2016-03-01
We calculate the joint distribution P(S, Q) of the scattering matrix S and time-delay matrix Q = - iℏ S† dS / dE of a chaotic quantum dot coupled by point contacts to metal electrodes. While S and Q are statistically independent for ballistic coupling, they become correlated for tunnel coupling. We relate the ensemble averages of Q and S and thereby obtain the average density of states at the Fermi level. We apply this to a calculation of the effect of a tunnel barrier on the Majorana resonance in a topological superconductor. We find that the presence of a Majorana bound state is hidden in the density of states and in the thermal conductance if even a single scattering channel has unit tunnel probability. The electrical conductance remains sensitive to the appearance of a Majorana bound state, and we calculate the variation of the average conductance through a topological phase transition.
Urey Prize Lecture - Chaotic dynamics in the solar system
NASA Technical Reports Server (NTRS)
Wisdom, Jack
1987-01-01
Attention is given to solar system cases in which chaotic solutions of Newton's equations are important, as in chaotic rotation and orbital evolution. Hyperion is noted to be tumbling chaotically; chaotic orbital evolution is suggested to be of fundamental importance to an accounting for the Kirkwood gaps in asteroid distribution and for the phase space boundary of the chaotic zone at the 3/1 mean-motion commensurability with Jupiter. In addition, chaotic trajectories in the 2/1 chaotic zone reach very high eccentricities by a route that carries them to high inclinations temporarily.
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
Chaotic eigenfunctions in momentum space
NASA Astrophysics Data System (ADS)
Bäcker, A.; Schubert, R.
1999-07-01
We study eigenstates of chaotic billiards in the momentum representation and propose the radially integrated momentum distribution as a useful measure to detect localization effects. For the momentum distribution, the radially integrated momentum distribution, and the angular integrated momentum distribution explicit formulae in terms of the normal derivative along the billiard boundary are derived. We present a detailed numerical study for the stadium and the cardioid billiard, which shows in several cases that the radially integrated momentum distribution is a good indicator of localized eigenstates, such as scars, or bouncing ball modes. We also find examples, where the localization is more strongly pronounced in position space than in momentum space, which we discuss in detail. Finally, applications and generalizations are discussed.
Kinetically modified nonminimal chaotic inflation
NASA Astrophysics Data System (ADS)
Pallis, Constantinos
2015-06-01
We consider supersymmetric (SUSY) and non-SUSY models of chaotic inflation based on the ϕn potential with 2 ≤n ≤6 . We show that the coexistence of a nonminimal coupling to gravity fR=1 +cRϕn /2 with a kinetic mixing of the form fK=cKfRm can accommodate inflationary observables favored by the Bicep2/Keck Array and Planck results for 0 ≤m ≤4 and 2.5 ×10-4≤rR K=cR/cKn /4≤1 , where the upper limit is not imposed for n =2 . Inflation can be attained for sub-Planckian inflaton values with the corresponding effective theories retaining the perturbative unitarity up to the Planck scale.
Polynomial chaotic inflation in supergravity
Nakayama, Kazunori; Takahashi, Fuminobu; Yanagida, Tsutomu T. E-mail: fumi@tuhep.phys.tohoku.ac.jp
2013-08-01
We present a general polynomial chaotic inflation model in supergravity, for which the predicted spectral index and tensor-to-scalar ratio can lie within the 1σ region allowed by the Planck results. Most importantly, the predicted tensor-to-scalar ratio is large enough to be probed in the on-going and future B-mode experiments. We study the inflaton dynamics and the subsequent reheating process in a couple of specific examples. The non-thermal gravitino production from the inflaton decay can be suppressed in a case with a discrete Z{sub 2} symmetry. We find that the reheating temperature can be naturally as high as O(10{sup 9−10}) GeV, sufficient for baryon asymmetry generation through (non-)thermal leptogenesis.
Chaotic desynchronization of multistrain diseases
NASA Astrophysics Data System (ADS)
Shaw, Leah; Billings, Lora; McCrary, Marie; Schwartz, Ira
2005-03-01
Dengue fever, a multi-strain disease, has four distinct co-existing serotypes (strains). The serotypes interact by antibody-dependent enhancement (ADE), in which infection with a single serotype is asymptomatic, but contact with a second serotype leads to serious illness accompanied by greater infectivity. It has been observed from serotype data that outbreaks of the four serotypes occur asynchronously (Nisalak et al., Am. J. Trop. Med. Hyg. 68: 192). We developed a compartmental model and did bifurcation analysis for multiple serotypes with ADE. Both autonomous and seasonally driven versions were studied. For sufficiently small ADE, we find that the number of infectives of each serotype synchronizes, with outbreaks occurring in phase. However, when the ADE increases past a threshold, the system becomes chaotic, and infectives of each serotype desynchronize.
Regular transport dynamics produce chaotic travel times.
Villalobos, Jorge; Muñoz, Víctor; Rogan, José; Zarama, Roberto; Johnson, Neil F; Toledo, Benjamín; Valdivia, Juan Alejandro
2014-06-01
In the hope of making passenger travel times shorter and more reliable, many cities are introducing dedicated bus lanes (e.g., Bogota, London, Miami). Here we show that chaotic travel times are actually a natural consequence of individual bus function, and hence of public transport systems more generally, i.e., chaotic dynamics emerge even when the route is empty and straight, stops and lights are equidistant and regular, and loading times are negligible. More generally, our findings provide a novel example of chaotic dynamics emerging from a single object following Newton's laws of motion in a regularized one-dimensional system. PMID:25019866
a Competitive Searching-Based Chaotic Cipher
NASA Astrophysics Data System (ADS)
Formolo, Daniel; de Oliveira, Luiz P. L.; Sobottka, Marcelo
In this paper we propose a high performance searching-based chaotic cipher. Experiments shows that its efficiency is comparable to the efficiencies of some widely used and known ciphers, namely, AES, RC4 and Sosemanuk. Also, its performance is better than some recently proposed chaotic ciphers of the same kind. The proposed cryptosystem shows independence with respect to the statistical characteristics of the plain texts, which prevents statistical attacks. The results of the tests suggest that this chaotic cipher can be competitive for practical usage.
Controlling chaotic robots with kinematical redundancy.
Li, Li; Liu, Zhaohui; Zhang, Dengcai; Zhang, H
2006-03-01
Robots with kinematical redundancy under the pseudoinverse control exhibit undesirable chaotic joint motion, which leads to erratic behaviors. In this study, we used the delayed feedback method to control chaotic motions of a planar 3R rigid and a planar 3R flexible redundant robot under the pseudoinverse control when the end-effector traces a closed-path repeatedly in the work space. It was demonstrated that chaotic motions of robots with kinematical redundancy can be turned into regular motion when the delayed feedback method was applied with some appropriate parameters. This study provides a new insight helpful to solve the repeatability problem of redundant manipulators. PMID:16599763
Chaotic Response of the Pacemaker Neuron
NASA Astrophysics Data System (ADS)
Hayashi, Hatsuo; Ishizuka, Satoru; Hirakawa, Kazuyoshi
1985-06-01
Excitable membranes respond irregularly to a periodic stimulation with proper stimulus parameters. Because irregular firing is macroscopic, it seems that irregularity is caused by other factors besides microscopic membrane noise. The responses of the repetitively firing Onchidium pacemaker neuron to a sinusoidal current stimulation were investigated. The irregular responses are classified into three kinds of chaotic oscillation: chaos, intermittency and random alternation. 1/2- and 1/1-harmonic responses bifurcate to chaos via intermittency and random alternation respectively. Harmonic and chaotic responses alternate with each other with increasing frequency of stimulation and with smaller amplitude. Nonlinear factors, threshold and refractory period, are concerned with hyperbolicity of chaotic responses.
Reinventing the wheel: The chaotic sandwheel
NASA Astrophysics Data System (ADS)
Tongen, Anthony; Thelwell, Roger J.; Becerra-Alonso, David
2013-02-01
The Malkus chaotic waterwheel, a tool to mechanically demonstrate Lorenzian dynamics, motivates the study of a chaotic sandwheel. We model the sandwheel in parallel with the waterwheel when possible, noting where methods may be extended and where no further analysis seems feasible. Numerical simulations are used to compare and contrast the behavior of the sandwheel with the waterwheel. Simulations confirm that the sandwheel retains many of the elements of chaotic Lorenzian dynamics. However, bifurcation diagrams show dramatic differences in where the order-chaos-order transitions occur.
Cai, W.; Zheng, T.F.; Lax, M.
1988-05-15
We study the transport of a quasi-two-dimensional electron-hole gas in a semiconductor quantum well. The screening in the presence of the electron-hole interaction is carefully considered. The method of nonequilibrium phonon wave packet, developed by us, is generalized to include the simultaneous presence of two-dimensional electrons and holes. The occurrence of negative absolute mobility for electrons is discussed. The mobility of minority electrons and majority holes are calculated by use of a drifted temperature model for both types of carriers. The mobilities of minority electrons (from negative to positive) as functions of lattice temperature and electric field are shown. Comparison is made with experiment.
Chaotic Scattering and Escape Times of Marginally Trapped Ultracold Neutrons
Coakley, K. J.; Doyle, J. M.; Dzhosyuk, S. N.; Yang, L.; Huffman, P. R.
2005-01-01
We compute classical trajectories of Ultracold neutrons (UCNs) in a superconducting Ioffe-type magnetic trap using a symplectic integration method. We find that the computed escape time for a particular set of initial conditions (momentum and position) does not generally stabilize as the time step parameter is reduced unless the escape time is short (less than approximately 10 s). For energy intervals where more than half of the escape times computed for UCN realizations are numerically well determined, we predict the median escape time as a function of the midpoint of the interval. PMID:27308152
Sabavath, Gopi Kishan; Banerjee, I.; Mahapatra, S. K.; Shaw, Pankaj Kumar; Sekar Iyengar, A. N.
2015-08-15
Floating potential fluctuations from a direct current magnetron sputtering plasma have been analysed using time series analysis techniques like phase space plots, power spectra, frequency bifurcation plot, etc. The system exhibits quasiperiodic-chaotic-quasiperiodic-chaotic transitions as the discharge voltage was increased. The transitions of the fluctuations, quantified using the largest Lyapunov exponent, have been corroborated by Hurst exponent and the Shannon entropy. The Shannon entropy is high for quasiperiodic and low for chaotic oscillations.
A four-wing chaotic attractor and its circuit implementation
NASA Astrophysics Data System (ADS)
van Wyk, M. A.; Qi, G.; van Wyk, B. J.
2008-02-01
By introducing a state feedback control to a proposed four dimensional chaotic system, an extremely complex four-wing chaotic attractor is derived having larger positive Lyapunov Exponent (LE) than other chaotic systems. Spectral analysis shows that the system in the four-wing chaotic mode has very broad frequency bandwidth, verifying its random nature, and indicating the prospect for engineering applications such as secure communications. Finally, an analog circuit, implementing the new four-wing chaotic system, is presented.
Cvitas, Marko T; Althorpe, Stuart C
2009-04-23
We describe a quantum wave packet method for computing the state-to-state quantum dynamics of 4-atom AB + CD --> ABC + D reactions. The approach is an extension to 4-atom reactions of a version of the reactant-product decoupling (RPD) approach, applied previously to 3-atom reactions ( J. Chem. Phys. 2001, 114 , 1601 ). The approach partitions the coordinate space of the reaction into separate reagent, strong-interaction, and product regions, using a system of artificial absorbing and reflecting potentials. It employs a partitioned version of the split-operator propagator, which is more efficient than partitioning the (exact) time-dependent Schrodinger equation. The wave packet bounces off a reflecting potential in the entrance channel, which generates a source term; this is transformed efficiently from reagent to product Jacobi coordinates by exploiting some simple angular momentum properties. The efficiency and accuracy of the method is demonstrated by numerical tests on the benchmark OH + H(2) --> H(2)O + H reaction. PMID:19298045
Neutron, Electron and X-ray Scattering Investigation of Cr1-xVx Near Quantum Criticality
Sokolov, D A; Aronson, Meigan C.; Wu, Lijun; Zhu, Yimei; Nelson, C.; Mansfield, J. F.; Sun, K.; Erwin, R.; Lynn, J. W.; Lumsden, Mark D; Nagler, Stephen E
2014-01-01
The weakness of electron-electron correlations in the itinerant antiferromagnet Cr doped with V has long been considered the reason that neither new collective electronic states or even non Fermi liquid behaviour are observed when antiferromagnetism in Cr1 xVx is suppressed to zero temperature. We present the results of neutron and electron diffraction measurements of several lightly doped single crystals of Cr1 xVx in which the archtypal spin density wave instability is progressively suppressed as the V content increases, freeing the nesting-prone Fermi surface for a new striped charge instability that occurs at xc=0.037. This novel nesting driven instability relieves the entropy accumulation associated with the suppression of the spin density wave and avoids the formation of a quantum critical point by stabilising a new type of charge order at temperatures in excess of 400 K. Restructuring of the Fermi surface near quantum critical points is a feature found in materials as diverse as heavy fermions, high temperature copper oxide superconductors and now even elemental metals such as Cr.
Electron transport and dephasing in semiconductor quantum dots
NASA Astrophysics Data System (ADS)
Huibers, Andrew Gerrit A.
At low temperatures, electrons in semiconductors can be phase coherent over distances exceeding tens of microns and are sufficiently monochromatic that a variety of interesting quantum interference phenomena can be observed and manipulated. This work discusses electron transport measurements through cavities (quantum dots) formed by laterally confining electrons in the two-dimensional sub-band of a GaAs/AlGaAs heterojunction. Metal gates fabricated using e-beam lithography enable fine control of the cavity shape as well as the leads which connect the dot cavity to source and drain reservoirs. Quantum dots can be modeled by treating the devices as chaotic scatterers. Predictions of this theoretical description are found to be in good quantitative agreement with experimental measurements of full conductance distributions at different temperatures. Weak localization, the suppression of conductance due to phase-coherent backscattering at zero magnetic field, is used to measure dephasing times in the system. Mechanisms responsible for dephasing, including electron-electron scattering and Nyquist phase relaxation, are investigated by studying the loss of phase coherence as a function of temperature. Coupling of external microwave fields to the device is also studied to shed light on the unexpected saturation of dephasing that is observed below an electron temperature of 100 mK. The effect of external fields in the present experiment is explained in terms of Joule heating from an ac bias.
Distributions of off-diagonal scattering matrix elements: Exact results
Nock, A. Kumar, S. Sommers, H.-J. Guhr, T.
2014-03-15
Scattering is a ubiquitous phenomenon which is observed in a variety of physical systems which span a wide range of length scales. The scattering matrix is the key quantity which provides a complete description of the scattering process. The universal features of scattering in chaotic systems is most generally modeled by the Heidelberg approach which introduces stochasticity to the scattering matrix at the level of the Hamiltonian describing the scattering center. The statistics of the scattering matrix is obtained by averaging over the ensemble of random Hamiltonians of appropriate symmetry. We derive exact results for the distributions of the real and imaginary parts of the off-diagonal scattering matrix elements applicable to orthogonally-invariant and unitarily-invariant Hamiltonians, thereby solving a long standing problem. -- Highlights: •Scattering problem in complex or chaotic systems. •Heidelberg approach to model the chaotic nature of the scattering center. •A novel route to the nonlinear sigma model based on the characteristic function. •Exact results for the distributions of off-diagonal scattering-matrix elements. •Universal aspects of the scattering-matrix fluctuations.
Semenov, Alexander; Dubernet, Marie-Lise; Babikov, Dmitri
2014-09-21
The mixed quantum/classical theory (MQCT) for inelastic molecule-atom scattering developed recently [A. Semenov and D. Babikov, J. Chem. Phys. 139, 174108 (2013)] is extended to treat a general case of an asymmetric-top-rotor molecule in the body-fixed reference frame. This complements a similar theory formulated in the space-fixed reference-frame [M. Ivanov, M.-L. Dubernet, and D. Babikov, J. Chem. Phys. 140, 134301 (2014)]. Here, the goal was to develop an approximate computationally affordable treatment of the rotationally inelastic scattering and apply it to H{sub 2}O + He. We found that MQCT is somewhat less accurate at lower scattering energies. For example, below E = 1000 cm{sup −1} the typical errors in the values of inelastic scattering cross sections are on the order of 10%. However, at higher scattering energies MQCT method appears to be rather accurate. Thus, at scattering energies above 2000 cm{sup −1} the errors are consistently in the range of 1%–2%, which is basically our convergence criterion with respect to the number of trajectories. At these conditions our MQCT method remains computationally affordable. We found that computational cost of the fully-coupled MQCT calculations scales as n{sup 2}, where n is the number of channels. This is more favorable than the full-quantum inelastic scattering calculations that scale as n{sup 3}. Our conclusion is that for complex systems (heavy collision partners with many internal states) and at higher scattering energies MQCT may offer significant computational advantages.
A practical test for noisy chaotic dynamics
NASA Astrophysics Data System (ADS)
BenSaïda, Ahmed
2015-12-01
This code computes the largest Lyapunov exponent and tests for the presence of a chaotic dynamics, as opposed to stochastic dynamics, in a noisy scalar series. The program runs under MATLAB® programming language.
Literalism, perspectivism, chaotic fragmentalism and psychotherapy techniques.
Leitner, L M
1982-12-01
Literalism and chaotic fragmentalism have been advanced as two concepts to explain psychopathology while perspectivism has been used to explain psychological health (Landfield, 1980 a). It is hypothesized that, to the extent that they are therapeutic, all therapies move clients toward perspectivism and away from literalism and chaotic fragmentalism. Eight major schools of psychotherapy are discussed in terms of the principles of technique which enable them to change literalism and chaotic fragmentalism. The advantages of a unifying theory permitting diversity of techniques are discussed in relation to the ability of the clinician to be flexible yet not confused. Further, the unifying concepts of literalism, perspectivism, and chaotic fragmentalism are used to understand systematically the strengths and weaknesses of many therapeutic techniques. Finally, the implications of the differences in therapeutic techniques for changing different types of literalisms are discussed. PMID:7150515
Nonreciprocal wave scattering on nonlinear string-coupled oscillators
Lepri, Stefano; Pikovsky, Arkady
2014-12-01
We study scattering of a periodic wave in a string on two lumped oscillators attached to it. The equations can be represented as a driven (by the incident wave) dissipative (due to radiation losses) system of delay differential equations of neutral type. Nonlinearity of oscillators makes the scattering non-reciprocal: The same wave is transmitted differently in two directions. Periodic regimes of scattering are analyzed approximately, using amplitude equation approach. We show that this setup can act as a nonreciprocal modulator via Hopf bifurcations of the steady solutions. Numerical simulations of the full system reveal nontrivial regimes of quasiperiodic and chaotic scattering. Moreover, a regime of a “chaotic diode,” where transmission is periodic in one direction and chaotic in the opposite one, is reported.
An improved chaotic cryptosystem with external key
NASA Astrophysics Data System (ADS)
Xiang, Tao; Wong, Kwok-wo; Liao, Xiaofeng
2008-11-01
In recent years, external key was introduced to chaotic cryptography by Pareek et al. and find its application in several discrete chaotic cryptosystems. The first part of this paper is devoted to the analysis of their essential weaknesses as well as some redundancies that contribute little to the security of those cryptosystems. Then, an improved scheme with all existing deficiencies and redundancies eliminated, is proposed. Theoretic analysis and numerical simulation both verify its superiority and security.
A new butterfly-shaped chaotic attractor
NASA Astrophysics Data System (ADS)
Kim, Dongwon; Chang, Pyung Hun
In this paper, a new chaotic system is proposed that consists of six terms including one multiplier and one quadratic term. The characteristics of this system are examined by theoretical and numerical analysis, such as equilibria, their stabilities, Lyapunov exponents and Lyapunov dimension, dissipativity, as well as, Poincaré maps, bifurcations, waveforms, power spectrums are performed. In addition, the forming mechanisms of compound structures of the new chaotic attractor are investigated.
Chaotic dynamics of weakly nonlinear systems
Vavriv, D.M.
1996-06-01
A review is given on the recent results in studying chaotic phenomena in weakly nonlinear systems. We are concerned with the class of chaotic states that can arise in physical systems with any degree of nonlinearity however small. The conditions for, and the mechanisms of, the transitions to chaos are discussed. These findings are illustrated by the results of the stability analysis of practical microwave and optical devices. {copyright} {ital 1996 American Institute of Physics.}
Tao, Liang; McCurdy, C.W.; Rescigno, T.N.
2008-11-25
We show how to combine finite elements and the discrete variable representation in prolate spheroidal coordinates to develop a grid-based approach for quantum mechanical studies involving diatomic molecular targets. Prolate spheroidal coordinates are a natural choice for diatomic systems and have been used previously in a variety of bound-state applications. The use of exterior complex scaling in the present implementation allows for a transparently simple way of enforcing Coulomb boundary conditions and therefore straightforward application to electronic continuum problems. Illustrative examples involving the bound and continuum states of H2+, as well as the calculation of photoionization cross sections, show that the speed and accuracy of the present approach offer distinct advantages over methods based on single-center expansions.
NASA Astrophysics Data System (ADS)
Reiter, G. F.; Deb, Aniruddha
2014-12-01
Neutron Compton scattering(NCS) measurements of the momentum distribution of light ions using the Vesuvio instrument at ISIS provide a sensitive local probe of the environment of those ions. NCS measurements of the proton momentum distribution in bulk water show only small deviations from the usual picture of water as a collection of molecules, with the protons covalently bonded to an oxygen and interacting weakly, primarily electrostatically, with nearby molecules. However, a series of measurements of the proton momentum distribution in carbon nanotubes, xerogel, and Nafion show that the proton delocalizes over distances of 0.2-0.3Å when water is confined on the scale of 20Å. This delocalization must be the result of changes in the Born-Oppenheimer surface for the protons, which would imply that there are large deviations in the electron distribution from that of a collection of weakly interacting molecules. This has been observed at Spring-8 using x-ray Compton scattering. The observed deviation in the valence electron momentum distribution from that of bulk water is more than an order of magnitude larger than the change observed in bulk water as the water is heated from just above melting to just below boiling. We conclude that the protons and electrons in nano-confined water are in a qualitatively different ground state from that of bulk water. Since the properties of this state persist at room temperature, and the confinement distance necessary to observe it is comparable to the distance between the elements of biological cells, this state presumably plays a role in the functioning of those cells.
Chaotic magnetic fields: Particle motion and energization
Dasgupta, Brahmananda; Ram, Abhay K.; Li, Gang; Li, Xiaocan
2014-02-11
Magnetic field line equations correspond to a Hamiltonian dynamical system, so the features of a Hamiltonian systems can easily be adopted for discussing some essential features of magnetic field lines. The integrability of the magnetic field line equations are discussed by various authors and it can be shown that these equations are, in general, not integrable. We demonstrate several examples of realistic chaotic magnetic fields, produced by asymmetric current configurations. Particular examples of chaotic force-free field and non force-free fields are shown. We have studied, for the first time, the motion of a charged particle in chaotic magnetic fields. It is found that the motion of a charged particle in a chaotic magnetic field is not necessarily chaotic. We also showed that charged particles moving in a time-dependent chaotic magnetic field are energized. Such energization processes could play a dominant role in particle energization in several astrophysical environments including solar corona, solar flares and cosmic ray propagation in space.
Urey Prize Lecture - Chaotic dynamics in the solar system
NASA Astrophysics Data System (ADS)
Wisdom, J.
1987-11-01
Newton's equations have chaotic solutions as well as regular solutions. There are several physical situations in the solar system where chaotic solutions of Newton's equations play an important role. There are examples of both chaotic rotation and chaotic orbital evolution. Hyperion is currently tumbling chaotically. Many of the other irregularly shaped satellites in the solar system have had chaotic rotations in the past. This episode of chaotic tumbling could have had a significant effect on the orbital histories of these satellites. Chaotic orbital evolution seems to be an essential ingredient in the explanation of the Kirkwood gaps in the distribution of asteroids. Chaotic trajectories at the 3/1 commensurability have the correct properties to provide a dynamical route for the transport of meteoritic material from the asteroid belt to Earth.
NASA Astrophysics Data System (ADS)
Robertson, J.; Metcalfe, G.; Wang, S.; Barnes, S. J.
2014-12-01
The concentration of bubbles, crystals or droplets into small volumes of magma is a key trigger for many interesting magmatic processes. For example, gas slugs driving Strombolian eruptions form from the coalesence of exsolved bubbles within a volcanic conduit, while Ni-Cu-PGE magmatic sulfide deposits require a concentration of dense sulfide droplets from a large volume of magma to form a massive ore body. However the physical mechanism for this clustering remains unresolved - especially since small particles in active magma flows are expected to mostly track flow streamlines rather than clustering. We have uncovered a previously unreported clustering mechanism which is applicable to magmatic flows. This mechanism involves the interaction of particles with two kinds of chaotic flow structure: (a) high-strain regions within the well-mixed chaotic zones of the flow, and (b) unmixed islands of stability within the chaotic flow, known as Kolmogorov-Arnold-Moser (KAM) regions. The first figure shows the difference between chaotic and KAM regions in a chaotic laminar pipe flow. Trapping occurs when particles are scattered from high-strain regions in the chaotic zones and become trapped in the KAM regions, leading to a rapid concentration of particles relative to their original distribution (shown in the second series of figures). Using a combination of these analogue experiments and theoretical analysis we outline the conditions under which this clustering process can occur. We examine the onset of secondary density-related instabilities and the effects of increased particle-particle interaction within the clustered particles, and highlight the impact of particle clustering on the dynamics of magma ascent and emplacement.
Are earthquakes deterministic or chaotic?
NASA Astrophysics Data System (ADS)
Rundle, John B.; Julian, Bruce R.; Turcotte, Donald L.
During the last decade, physicists and applied mathematicians have made substantial headway in understanding the dynamics of complex nonlinear systems. Progress has been possible due to the development of several new tools, including the renormalization group approach, phase portraits, and scaling methods (fractals). At the same time, mathematical geophysicists interested in earthquakes have begun to utilize these same concepts to generate models of faults and fractures.In order to bring these scientific communities together, it was decided to convene the workshop, Physics of Earthquake Faults: Deterministic or Chaotic?, held February 12-15, at the Asilomar conference center near Monterey, Calif. Thirty-six Earth scientists met with 15 physicists and applied mathematicians to discuss how recent advances in nonlinear systems might be applied to better understand earthquakes. Funding was provided by the Geodynamics Branch of the National Aeronautics and Space Administration, the National Science Foundation, and the Office of Basic Energy Sciences of the U.S. Department of Energy. Organizational and logistical support were provided by the U.S. Geological Survey.
Applied mathematics of chaotic systems
Jen, E.; Alber, M.; Camassa, R.; Choi, W.; Crutchfield, J.; Holm, D.; Kovacic, G.; Marsden, J.
1996-07-01
This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The objectives of the project were to develop new mathematical techniques for describing chaotic systems and for reexpressing them in forms that can be solved analytically and computationally. The authors focused on global bifurcation analysis of rigid body motion in an ideal incompressible fluid and on an analytical technique for the exact solution of nonlinear cellular automata. For rigid-body motion, they investigated a new completely integrable partial differential equation (PDE) representing model motion of fronts in nematic crystals and studied perturbations of the integrable PDE. For cellular automata with multiple domain structures, the work has included: (1) identification of the associated set of conserved quantities for each type of domain; (2) use of the conserved quantities to construct isomorphism between the nonlinear system and a linear template; and (3) use of exact solvability methods to characterize detailed structure of equilibrium states and to derive bounds for maximal transience times.
Chaotic mixing across oceanic jets
Miller, P.; Jones, C.K.; Haller, G.; Pratt, L. |
1996-06-01
The perspective of geometric dynamical systems is used to study the transport of fluid across oceanic jets. We study the mixing associated with the simplest analytical models for jets, namely, neutral modes superimposed on a base mean flow, where the base flow and the neutral modes are approximately potential vorticity conserving. The base jet plus a single neutral mode is an integrable flow in the appropriate moving frame, and heteroclinic orbits act as impenetrable boundaries separating different regions of phase space. Superimposing more than one neutral mode results in the breakup of these heteroclinic orbits and associated chaotic mixing. Using a cusped jet model we study the case where the perturbation is periodic in time. We present numerical simulations of the Poincar{acute e} map along with calculations of the Melnikov integral which characterizes the exchange rate across such boundaries. The analytical and numerical results show that these models explain mixing along the edges of the jet, but do not appear to explain mixing across the body of the jet. {copyright} {ital 1996 American Institute of Physics.}
NASA Astrophysics Data System (ADS)
Wang, Xing-Yuan; Bao, Xue-Mei
2013-05-01
In this paper, we propose a novel block cryptographic scheme based on a spatiotemporal chaotic system and a chaotic neural network (CNN). The employed CNN comprises a 4-neuron layer called a chaotic neuron layer (CNL), where the spatiotemporal chaotic system participates in generating its weight matrix and other parameters. The spatiotemporal chaotic system used in our scheme is the typical coupled map lattice (CML), which can be easily implemented in parallel by hardware. A 160-bit-long binary sequence is used to generate the initial conditions of the CML. The decryption process is symmetric relative to the encryption process. Theoretical analysis and experimental results prove that the block cryptosystem is secure and practical, and suitable for image encryption.
Craig, Ian M.; Phillips, Mark C.; Taubman, Matthew S.; Josberger, Erik E.; Raschke, Markus Bernd
2013-02-04
Infrared scattering scanning near-field optical microscopy (s-SNOM) is an apertureless superfocusing technique that uses the antenna properties of a conducting atomic force microscope (AFM) tip to achieve infrared spatial resolution below the diffraction limit. The instrument can be used either in imaging mode, where a fixed wavelength light source is tuned to a molecular resonance and the AFM raster scans an image, or in spectroscopy mode where the AFM is held stationary over a feature of interest and the light frequency is varied to obtain a spectrum. In either case, a strong, stable, coherent infrared source is required. Here we demonstrate the integration of a broadly tunable external cavity quantum cascade laser (ECQCL) into an s-SNOM and use it to obtain infrared spectra of microcrystals of chemicals adsorbed onto gold substrates. Residues of the explosive compound tetryl was deposited onto gold substrates. s-SNOM experiments were performed in the 1260-1400 cm-1 tuning range of the ECQCL, corresponding to the NO2 symmetric stretch vibrational fingerprint region. Vibrational infrared spectra were collected on individual chemical domains with a collection area of *500nm2 and compared to ensemble averaged far-field reflection-absorption infrared spectroscopy (RAIRS) results.
NASA Astrophysics Data System (ADS)
Craig, Ian M.; Phillips, Mark C.; Taubman, Matthew S.; Josberger, Erik E.; Raschke, Markus B.
2013-01-01
Infrared scattering scanning near-field optical microscopy (s-SNOM) is an apertureless superfocusing technique that uses the antenna properties of a conducting atomic force microscope (AFM) tip to achieve infrared spatial resolution below the diffraction limit. The instrument can be used either in imaging mode, where a fixed wavelength light source is tuned to a molecular resonance and the AFM raster scans an image, or in spectroscopy mode where the AFM is held stationary over a feature of interest and the light frequency is varied to obtain a spectrum. In either case, a strong, stable, coherent infrared source is required. Here we demonstrate the integration of a broadly tunable external cavity quantum cascade laser (ECQCL) into an s-SNOM and use it to obtain infrared spectra of microcrystals of chemicals adsorbed onto gold substrates. Residues of the explosive compound tetryl was deposited onto gold substrates. s-SNOM experiments were performed in the 1260-1400cm-1 tuning range of the ECQCL, corresponding to the N02 symmetric stretch vibrational fingerprint region. Vibrational infrared spectra were collected on individual chemical domains with a collection area of ~500 nm2 and compared to ensemble averaged far-field reflection-absorption infrared spectroscopy (RAIRS) results.
Zheludev, Andrey I; Garlea, Vasile O; Masuda, T.; Manaka, H.; Regnault, L.-P.; Ressouche, E.; Grenier, B.; Chung, J.-H.; Qiu, Y.; Habicht, Klaus; Kiefer, K.; Boehm, Martin
2007-01-01
Inelastic and elastic neutron scattering is used to study spin correlations in the quasi-one-dimensional quantum antiferromagnet IPA-CuCl3 in strong applied magnetic fields. A condensation of magnons and commensurate transverse long-range ordering is observe at a critical field Hc=9.5 T. The field dependencies of the energies and polarizations of all magnon branches are investigated both below and above the transition point. Their dispersion is measured across the entire one-dimensional Brillouin zone in magnetic fields up to 14 T. The critical wave vector of magnon spectrum truncation Masuda et al., Phys. Rev. Lett. 96, 047210 2006 is found to shift from hc0,35 at HHC to hc=0.25 for HHC. A drastic reduction of magnon bandwidths in the ordered phase Garlea et al., Phys. Rev. Lett. 98, 167202 2007 is observed and studied in detail. New features of the spectrum, presumably related to this bandwidth collapse, are observed just above the transition field.
Dissipative discrete breathers: periodic, quasiperiodic, chaotic, and mobile.
Martínez, P J; Meister, M; Floría, L M; Falo, F
2003-06-01
The properties of discrete breathers in dissipative one-dimensional lattices of nonlinear oscillators subject to periodic driving forces are reviewed. We focus on oscillobreathers in the Frenkel-Kontorova chain and rotobreathers in a ladder of Josephson junctions. Both types of exponentially localized solutions are easily obtained numerically using adiabatic continuation from the anticontinuous limit. Linear stability (Floquet) analysis allows the characterization of different types of bifurcations experienced by periodic discrete breathers. Some of these bifurcations produce nonperiodic localized solutions, namely, quasiperiodic and chaotic discrete breathers, which are generally impossible as exact solutions in Hamiltonian systems. Within a certain range of parameters, propagating breathers occur as attractors of the dissipative dynamics. General features of these excitations are discussed and the Peierls-Nabarro barrier is addressed. Numerical scattering experiments with mobile breathers reveal the existence of two-breather bound states and allow a first glimpse at the intricate phenomenology of these special multibreather configurations. PMID:12777126
Chaotic Transport in Semiconductor, Optical, and Cold-Atom Systems
NASA Astrophysics Data System (ADS)
Judd, T.; Henning, A.; Hardwick, D.; Scott, R.; Balanov, A.; Wilkinson, P.; Fowler, D.; Martin, A.; Fromhold, T.
We show that the reflection of quantum-mechanical waves from semiconductor surfaces creates new regimes of nonlinear dynamics, which offer sensitive control of electrons and ultra-cold atoms. For electrons in superlattices, comprising alternating layers of different semiconductor materials, multiple reflections of electron waves from the layer interfaces induce a unique type of chaotic electron motion when a bias voltage and tilted magnetic field are applied. Changing the field parameters switches the chaos on and off abruptly, thus producing a sharp increase in the measured current flow by creating unbounded electron orbits. These orbits correspond to either intricate web patterns or attractors in phase space depending on the electron decoherence rate. We show that related dynamics provide a mechanism for controlling the transmission of electromagnetic waves through spatially-modulated photonic crystals. Finally, we consider the quantum dynamics of a Bose-Einstein condensate, comprising 120,000 rubidium atoms cooled to 10 nK, incident on a stadium billiard etched in a room-temperature silicon surface. Despite the huge temperature difference between the condensate and the billiard, quantum-mechanical reflection can shield the cold atoms from the disruptive influence of the surface, thus enabling the billiard to imprint signatures of single-particle classical trajectories in the collective motion of the reflected atom cloud.
NASA Astrophysics Data System (ADS)
Le Gouët, Jean-Louis; Moiseev, Sergey
2012-06-01
Interaction of quantum radiation with multi-particle ensembles has sparked off intense research efforts during the past decade. Emblematic of this field is the quantum memory scheme, where a quantum state of light is mapped onto an ensemble of atoms and then recovered in its original shape. While opening new access to the basics of light-atom interaction, quantum memory also appears as a key element for information processing applications, such as linear optics quantum computation and long-distance quantum communication via quantum repeaters. Not surprisingly, it is far from trivial to practically recover a stored quantum state of light and, although impressive progress has already been accomplished, researchers are still struggling to reach this ambitious objective. This special issue provides an account of the state-of-the-art in a fast-moving research area that makes physicists, engineers and chemists work together at the forefront of their discipline, involving quantum fields and atoms in different media, magnetic resonance techniques and material science. Various strategies have been considered to store and retrieve quantum light. The explored designs belong to three main—while still overlapping—classes. In architectures derived from photon echo, information is mapped over the spectral components of inhomogeneously broadened absorption bands, such as those encountered in rare earth ion doped crystals and atomic gases in external gradient magnetic field. Protocols based on electromagnetic induced transparency also rely on resonant excitation and are ideally suited to the homogeneous absorption lines offered by laser cooled atomic clouds or ion Coulomb crystals. Finally off-resonance approaches are illustrated by Faraday and Raman processes. Coupling with an optical cavity may enhance the storage process, even for negligibly small atom number. Multiple scattering is also proposed as a way to enlarge the quantum interaction distance of light with matter. The
NASA Astrophysics Data System (ADS)
Meyers, Ronald E.; Deacon, Keith S.; Tunick, Arnold
2013-09-01
We report on an experimental demonstration of quantum imaging where the images are stored in both space and time. Quantum images of remote objects are produced with rotating ground glass induced chaotic laser light and two sensors measuring at different space-time points. Quantum images are observed to move depending on the time delay between the sensor measurements. The experiments provide a new testbed for exploring the time and space scale fundamental physics of quantum imaging and suggest new pathways for quantum information storage and processing. The moved quantum images are in fact new images that are stored in a space-time virtual memory process. The images are stored within the same quantum imaging data sets and thus quantum imaging can produce more information per photon measured than was previously realized.
Nakayama, Masaaki Ohno, Tatsuya; Furukawa, Yoshiaki
2015-04-07
We have systematically investigated the photoluminescence (PL) dynamics of free excitons in GaAs/Al{sub 0.3}Ga{sub 0.7}As single quantum wells, focusing on the energy relaxation process due to exciton–acoustic-phonon scattering under non-resonant and weak excitation conditions as a function of GaAs-layer thickness from 3.6 to 12.0 nm and temperature from 30 to 50 K. The free exciton characteristics were confirmed by observation that the PL decay time has a linear dependence with temperature. We found that the free exciton PL rise rate, which is the reciprocal of the rise time, is inversely linear with the GaAs-layer thickness and linear with temperature. This is consistent with a reported theoretical study of the exciton–acoustic-phonon scattering rate in the energy relaxation process in quantum wells. Consequently, it is conclusively verified that the PL rise rate is dominated by the exciton–acoustic-phonon scattering rate. In addition, from quantitative analysis of the GaAs-layer thickness and temperature dependences, we suggest that the PL rise rate reflects the number of exciton–acoustic-phonon scattering events.
2015-01-01
We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE) algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE) algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC) algorithm, interactive chaotic evolution (ICE) that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed. PMID:25879067
Desktop chaotic systems: Intuition and visualization
NASA Technical Reports Server (NTRS)
Bright, Michelle M.; Melcher, Kevin J.; Qammar, Helen K.; Hartley, Tom T.
1993-01-01
This paper presents a dynamic study of the Wildwood Pendulum, a commercially available desktop system which exhibits a strange attractor. The purpose of studying this chaotic pendulum is twofold: to gain insight in the paradigmatic approach of modeling, simulating, and determining chaos in nonlinear systems; and to provide a desktop model of chaos as a visual tool. For this study, the nonlinear behavior of this chaotic pendulum is modeled, a computer simulation is performed, and an experimental performance is measured. An assessment of the pendulum in the phase plane shows the strange attractor. Through the use of a box-assisted correlation dimension methodology, the attractor dimension is determined for both the model and the experimental pendulum systems. Correlation dimension results indicate that the pendulum and the model are chaotic and their fractal dimensions are similar.
An investigation of chaotic Kolmogorov flows
NASA Technical Reports Server (NTRS)
Platt, N.; Sirovich, L.; Fitzmaurice, N.
1990-01-01
A two dimensional flow governed by the incompressible Navier-Stokes equations with a steady spatially periodic forcing (known as the Kolmogorov flow) is numerically simulated. The behavior of the flow and its transition states as the Reynolds number (Re) varies is investigated in detail, as well as a number of the flow features. A sequence of bifurcations is shown to take place in the flow as Re varied. Two main regimes of the flow were observed: small and large scale structure regimes corresponding to different ranges of Re. Each of the regimes includes a number of quasiperiodic, chaotic, and relaminarization windows. In addition, each range contains a chaotic window with non-ergodic chaotic attractors. Spatially disordered, but temporally steady states were discovered in large scale structure regime. Features of the diverse cases are displayed in terms of the temporal power spectrum, Poincare sections and, where possible, Lyapunov exponents and Kaplan-Yorke dimension.
Controlled transitions between cupolets of chaotic systems
Morena, Matthew A. Short, Kevin M.; Cooke, Erica E.
2014-03-15
We present an efficient control scheme that stabilizes the unstable periodic orbits of a chaotic system. The resulting orbits are known as cupolets and collectively provide an important skeleton for the dynamical system. Cupolets exhibit the interesting property that a given sequence of controls will uniquely identify a cupolet, regardless of the system's initial state. This makes it possible to transition between cupolets, and thus unstable periodic orbits, simply by switching control sequences. We demonstrate that although these transitions require minimal controls, they may also involve significant chaotic transients unless carefully controlled. As a result, we present an effective technique that relies on Dijkstra's shortest path algorithm from algebraic graph theory to minimize the transients and also to induce certainty into the control of nonlinear systems, effectively providing an efficient algorithm for the steering and targeting of chaotic systems.
Controlled transitions between cupolets of chaotic systems
NASA Astrophysics Data System (ADS)
Morena, Matthew A.; Short, Kevin M.; Cooke, Erica E.
2014-03-01
We present an efficient control scheme that stabilizes the unstable periodic orbits of a chaotic system. The resulting orbits are known as cupolets and collectively provide an important skeleton for the dynamical system. Cupolets exhibit the interesting property that a given sequence of controls will uniquely identify a cupolet, regardless of the system's initial state. This makes it possible to transition between cupolets, and thus unstable periodic orbits, simply by switching control sequences. We demonstrate that although these transitions require minimal controls, they may also involve significant chaotic transients unless carefully controlled. As a result, we present an effective technique that relies on Dijkstra's shortest path algorithm from algebraic graph theory to minimize the transients and also to induce certainty into the control of nonlinear systems, effectively providing an efficient algorithm for the steering and targeting of chaotic systems.
Controlled transitions between cupolets of chaotic systems.
Morena, Matthew A; Short, Kevin M; Cooke, Erica E
2014-03-01
We present an efficient control scheme that stabilizes the unstable periodic orbits of a chaotic system. The resulting orbits are known as cupolets and collectively provide an important skeleton for the dynamical system. Cupolets exhibit the interesting property that a given sequence of controls will uniquely identify a cupolet, regardless of the system's initial state. This makes it possible to transition between cupolets, and thus unstable periodic orbits, simply by switching control sequences. We demonstrate that although these transitions require minimal controls, they may also involve significant chaotic transients unless carefully controlled. As a result, we present an effective technique that relies on Dijkstra's shortest path algorithm from algebraic graph theory to minimize the transients and also to induce certainty into the control of nonlinear systems, effectively providing an efficient algorithm for the steering and targeting of chaotic systems. PMID:24697373
Controlled transitions between cupolets of chaotic systems
Morena, Matthew A.; Short, Kevin M.; Cooke, Erica E.
2014-01-01
We present an efficient control scheme that stabilizes the unstable periodic orbits of a chaotic system. The resulting orbits are known as cupolets and collectively provide an important skeleton for the dynamical system. Cupolets exhibit the interesting property that a given sequence of controls will uniquely identify a cupolet, regardless of the system's initial state. This makes it possible to transition between cupolets, and thus unstable periodic orbits, simply by switching control sequences. We demonstrate that although these transitions require minimal controls, they may also involve significant chaotic transients unless carefully controlled. As a result, we present an effective technique that relies on Dijkstra's shortest path algorithm from algebraic graph theory to minimize the transients and also to induce certainty into the control of nonlinear systems, effectively providing an efficient algorithm for the steering and targeting of chaotic systems. PMID:24697373
Dynamic visual cryptography based on chaotic oscillations
NASA Astrophysics Data System (ADS)
Petrauskiene, Vilma; Palivonaite, Rita; Aleksa, Algiment; Ragulskis, Minvydas
2014-01-01
Dynamic visual cryptography scheme based on chaotic oscillations is proposed in this paper. Special computational algorithms are required for hiding the secret image in the cover moiré grating, but the decryption of the secret is completely visual. The secret image is leaked in the form of time-averaged geometric moiré fringes when the cover image is oscillated by a chaotic law. The relationship among the standard deviation of the stochastic time variable, the pitch of the moiré grating and the pixel size ensuring visual decryption of the secret is derived. The parameters of these chaotic oscillations must be carefully preselected before the secret image is leaked from the cover image. Several computational experiments are used to illustrate the functionality and the applicability of the proposed image hiding technique.
NASA Astrophysics Data System (ADS)
Dietz, B.; Richter, A.; Samajdar, R.
2015-08-01
The fluctuations exhibited by the cross sections generated in a compound-nucleus reaction or, more generally, in a quantum-chaotic scattering process, when varying the excitation energy or another external parameter, are characterized by the width Γcorr of the cross-section correlation function. Brink and Stephen [Phys. Lett. 5, 77 (1963), 10.1016/S0375-9601(63)80037-7] proposed a method for its determination by simply counting the number of maxima featured by the cross sections as a function of the parameter under consideration. They stated that the product of the average number of maxima per unit energy range and Γcorr is constant in the Ercison region of strongly overlapping resonances. We use the analogy between the scattering formalism for compound-nucleus reactions and for microwave resonators to test this method experimentally with unprecedented accuracy using large data sets and propose an analytical description for the regions of isolated and overlapping resonances.
Transient chaotic transport in dissipative drift motion
NASA Astrophysics Data System (ADS)
Oyarzabal, R. S.; Szezech, J. D.; Batista, A. M.; de Souza, S. L. T.; Caldas, I. L.; Viana, R. L.; Sanjuán, M. A. F.
2016-04-01
We investigate chaotic particle transport in magnetised plasmas with two electrostatic drift waves. Considering dissipation in the drift motion, we verify that the removed KAM surfaces originate periodic attractors with their corresponding basins of attraction. We show that the properties of the basins depend on the dissipation and the space-averaged escape time decays exponentially when the dissipation increases. We find positive finite time Lyapunov exponents in dissipative drift motion, consequently the trajectories exhibit transient chaotic transport. These features indicate how the transient plasma transport depends on the dissipation.
Denoising signals corrupted by chaotic noise
NASA Astrophysics Data System (ADS)
Manjunath, G.; Sivaji Ganesh, S.; Anand, G. V.
2010-12-01
We consider the problem of signal estimation where the observed time series is modeled as yi=xi+si with {xi} being an orbit of a chaotic self-map on a compact subset of Rd and {si} a sequence in Rd converging to zero. This model is motivated by experimental results in the literature where the ocean ambient noise and the ocean clutter are found to be chaotic. Making use of observations up to time n, we propose an estimate of si for i
Inhibition of quantum transport due to 'scars' of unstable periodic orbits
NASA Technical Reports Server (NTRS)
Jensen, R. V.; Sanders, M. M.; Saraceno, M.; Sundaram, B.
1989-01-01
A new quantum mechanism for the suppression of chaotic ionization of highly excited hydrogen atoms explains the appearance of anomalously stable states in the microwave ionization experiments of Koch et al. A novel phase-space representation of the perturbed wave functions reveals that the inhibition of quantum transport is due to the selective excitation of wave functions that are highly localized near unstable periodic orbits in the chaotic classical phase space. The 'scarred' wave functions provide a new basis for the quantum description of a variety of classically chaotic systems.
Chaotic correlations in barrier billiards with arbitrary barriers
NASA Astrophysics Data System (ADS)
Osbaldestin, A. H.; Adamson, L. N. C.
2013-06-01
We study autocorrelation functions in symmetric barrier billiards for golden mean trajectories with arbitrary barriers. Renormalization analysis reveals the presence of a chaotic invariant set and thus that, for a typical barrier, there are chaotic correlations. The chaotic renormalization set is the analogue of the so-called orchid that arises in a generalized Harper equation.
Bifurcation Structures in a Bimodal Piecewise Linear Map: Chaotic Dynamics
NASA Astrophysics Data System (ADS)
Panchuk, Anastasiia; Sushko, Iryna; Avrutin, Viktor
In this work, we investigate the bifurcation structure of the parameter space of a generic 1D continuous piecewise linear bimodal map focusing on the regions associated with chaotic attractors (cyclic chaotic intervals). The boundaries of these regions corresponding to chaotic attractors with different number of intervals are identified. The results are obtained analytically using the skew tent map and the map replacement technique.
Lee, Sang-Bong
1993-09-01
Quantum manifestation of classical chaos has been one of the extensively studied subjects for more than a decade. Yet clear understanding of its nature still remains to be an open question partly due to the lack of a canonical definition of quantum chaos. The classical definition seems to be unsuitable in quantum mechanics partly because of the Heisenberg quantum uncertainty. In this regard, quantum chaos is somewhat misleading and needs to be clarified at the very fundamental level of physics. Since it is well known that quantum mechanics is more fundamental than classical mechanics, the quantum description of classically chaotic nature should be attainable in the limit of large quantum numbers. The focus of my research, therefore, lies on the correspondence principle for classically chaotic systems. The chaotic damped driven pendulum is mainly studied numerically using the split operator method that solves the time-dependent Schroedinger equation. For classically dissipative chaotic systems in which (multi)fractal strange attractors often emerge, several quantum dissipative mechanisms are also considered. For instance, Hoover`s and Kubo-Fox-Keizer`s approaches are studied with some computational analyses. But the notion of complex energy with non-Hermiticity is extensively applied. Moreover, the Wigner and Husimi distribution functions are examined with an equivalent classical distribution in phase-space, and dynamical properties of the wave packet in configuration and momentum spaces are also explored. The results indicate that quantum dynamics embraces classical dynamics although the classicalquantum correspondence fails to be observed in the classically chaotic regime. Even in the semi-classical limits, classically chaotic phenomena would eventually be suppressed by the quantum uncertainty.
Tunneling through a quantum dot in a quantum waveguide
NASA Astrophysics Data System (ADS)
Arsen'ev, A. A.
2010-07-01
The problem is considered of scattering in a system consisting of a quantum waveguide and a quantum dot weakly coupled to the waveguide. It is assumed that the quantum waveguide is described by the Pauli equations, and the Rashba spin-orbit interaction is taken into account. The possibility of tunneling through the quantum dot is proved.