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].
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.
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.
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
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.
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
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.
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
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.
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.
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.
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
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.
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.
Quantum algorithms for quantum field theories.
Jordan, Stephen P; Lee, Keith S M; Preskill, John
2012-06-01
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We developed a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions (φ(4) theory) in spacetime of four and fewer dimensions. Its run time is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. In the strong-coupling and high-precision regimes, our quantum algorithm achieves exponential speedup over the fastest known classical algorithm. PMID:22654052
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.
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
Introducing Scattering Theory with a Computer
ERIC Educational Resources Information Center
Merrill, John R.
1973-01-01
Discusses a new method of presenting the scattering theory, including classical explanation of cross sections, quantum mechanical expressions for phase shifts, and use of a computer to solve problems. (CC)
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
Electromagnetic scattering theory
NASA Technical Reports Server (NTRS)
Bird, J. F.; Farrell, R. A.
1986-01-01
Electromagnetic scattering theory is discussed with emphasis on the general stochastic variational principle (SVP) and its applications. The stochastic version of the Schwinger-type variational principle is presented, and explicit expressions for its integrals are considered. Results are summarized for scalar wave scattering from a classic rough-surface model and for vector wave scattering from a random dielectric-body model. Also considered are the selection of trial functions and the variational improvement of the Kirchhoff short-wave approximation appropriate to large size-parameters. Other applications of vector field theory discussed include a general vision theory and the analysis of hydromagnetism induced by ocean motion across the geomagnetic field. Levitational force-torque in the magnetic suspension of the disturbance compensation system (DISCOS), now deployed in NOVA satellites, is also analyzed using the developed theory.
NASA Astrophysics Data System (ADS)
Murdin, P.
2000-11-01
A theory based on the premise that, on the microscopic scale, physical quantities have discrete, rather than a continuous range of, values. The theory was devised in the early part of the twentieth century to account for certain phenomena that could not be explained by classical physics. In 1900, the German physicist, Max Planck (1858-1947), was able precisely to describe the previously unexplaine...
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.
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.
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.
Experimental confirmation of neoclassical Compton scattering theory
Aristov, V. V.; Yakunin, S. N.; Despotuli, A. A.
2013-12-15
Incoherent X-ray scattering spectra of diamond and silicon crystals recorded on the BESSY-2 electron storage ring have been analyzed. All spectral features are described well in terms of the neoclassical scattering theory without consideration for the hypotheses accepted in quantum electrodynamics. It is noted that the accepted tabular data on the intensity ratio between the Compton and Rayleigh spectral components may significantly differ from the experimental values. It is concluded that the development of the general theory (considering coherent scattering, incoherent scattering, and Bragg diffraction) must be continued.
Theory of Graphene Raman Scattering.
Heller, Eric J; Yang, Yuan; Kocia, Lucas; Chen, Wei; Fang, Shiang; Borunda, Mario; Kaxiras, Efthimios
2016-02-23
Raman scattering plays a key role in unraveling the quantum dynamics of graphene, perhaps the most promising material of recent times. It is crucial to correctly interpret the meaning of the spectra. It is therefore very surprising that the widely accepted understanding of Raman scattering, i.e., Kramers-Heisenberg-Dirac theory, has never been applied to graphene. Doing so here, a remarkable mechanism we term"transition sliding" is uncovered, explaining the uncommon brightness of overtones in graphene. Graphene's dispersive and fixed Raman bands, missing bands, defect density and laser frequency dependence of band intensities, widths of overtone bands, Stokes, anti-Stokes anomalies, and other known properties emerge simply and directly. PMID:26799915
NASA Astrophysics Data System (ADS)
Bastin, Ted
2009-07-01
List of participants; Preface; Part I. Introduction: 1. The function of the colloquium - editorial; 2. The conceptual problem of quantum theory from the experimentalist's point of view O. R. Frisch; Part II. Niels Bohr and Complementarity: The Place of the Classical Language: 3. The Copenhagen interpretation C. F. von Weizsäcker; 4. On Bohr's views concerning the quantum theory D. Bohm; Part III. The Measurement Problem: 5. Quantal observation in statistical interpretation H. J. Groenewold; 6. Macroscopic physics, quantum mechanics and quantum theory of measurement G. M. Prosperi; 7. Comment on the Daneri-Loinger-Prosperi quantum theory of measurement Jeffrey Bub; 8. The phenomenology of observation and explanation in quantum theory J. H. M. Whiteman; 9. Measurement theory and complex systems M. A. Garstens; Part IV. New Directions within Quantum Theory: What does the Quantum Theoretical Formalism Really Tell Us?: 10. On the role of hidden variables in the fundamental structure of physics D. Bohm; 11. Beyond what? Discussion: space-time order within existing quantum theory C. W. Kilmister; 12. Definability and measurability in quantum theory Yakir Aharonov and Aage Petersen; 13. The bootstrap idea and the foundations of quantum theory Geoffrey F. Chew; Part V. A Fresh Start?: 14. Angular momentum: an approach to combinatorial space-time Roger Penrose; 15. A note on discreteness, phase space and cohomology theory B. J. Hiley; 16. Cohomology of observations R. H. Atkin; 17. The origin of half-integral spin in a discrete physical space Ted Bastin; Part VI. Philosophical Papers: 18. The unity of physics C. F. von Weizsäcker; 19. A philosophical obstacle to the rise of new theories in microphysics Mario Bunge; 20. The incompleteness of quantum mechanics or the emperor's missing clothes H. R. Post; 21. How does a particle get from A to B?; Ted Bastin; 22. Informational generalization of entropy in physics Jerome Rothstein; 23. Can life explain quantum mechanics? H. H
Scattering processes in lattice gauge theories
NASA Astrophysics Data System (ADS)
Alessandrini, V.; Krzywicki, A.
1980-06-01
Scattering between gauge invariant lattice excitations is studied in the framework of a 2+1 dimensional lattice theory with U(1) gauge symmetry. We put the theory in a form analogous to theories of conventional large quantum systems (spin waves in a solid, for example) and we calculate explicitly the cross section for boxiton scattering. The general strategy we have developed goes beyond the simple example of compact QED. Laboratoire associé au CNRS. Postal address: LPTHE, Bâtiment 211, Université Paris-Sud, 91405 Orsay, France.
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.
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).
Quaternionic quantum field theory
Adler, S.L.
1985-08-19
We show that a quaternionic quantum field theory can be formulated when the numbers of bosonic and fermionic degrees of freedom are equal and the fermions, as well as the bosons, obey a second-order wave equation. The theory is initially defined in terms of a quaternion-imaginary Lagrangian using the Feynman sum over histories. A Schroedinger equation can be derived from the functional integral, which identifies the quaternion-imaginary quantum Hamiltonian. Conversely, the transformation theory based on this Hamiltonian can be used to rederive the functional-integral formulation.
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).
Scattering theory for arbitrary potentials
Kadyrov, A.S.; Bray, I.; Stelbovics, A.T.; Mukhamedzhanov, A.M.
2005-09-15
The fundamental quantities of potential scattering theory are generalized to accommodate long-range interactions. Definitions for the scattering amplitude and wave operators valid for arbitrary interactions including potentials with a Coulomb tail are presented. It is shown that for the Coulomb potential the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure.
Supersymmetric Quantum Field Theories
NASA Astrophysics Data System (ADS)
Grigore, D. R.
2005-03-01
We consider some supersymmetric multiplets in a purely quantum framework. A crucial point is to ensure the positivity of the scalar product in the Hilbert space of the quantum system. For the vector multiplet we obtain some discrepancies with respect to the literature in the expression of the super-propagator and we prove that the model is consistent only for positive mass. The gauge structure is constructed purely deductive and leads to the necessity of introducing scalar ghost superfields, in analogy to the usual gauge theories. Then we consider a supersymmetric extension of quantum gauge theory based on a vector multiplet containing supersymmetric partners of spin 3/2 for the vector fields. As an application we consider the supersymmetric electroweak theory. The resulting self-couplings of the gauge bosons agree with the standard model up to a divergence.
NASA Astrophysics Data System (ADS)
Griffiths, Robert B.
2001-11-01
Quantum mechanics is one of the most fundamental yet difficult subjects in physics. Nonrelativistic quantum theory is presented here in a clear and systematic fashion, integrating Born's probabilistic interpretation with Schrödinger dynamics. Basic quantum principles are illustrated with simple examples requiring no mathematics beyond linear algebra and elementary probability theory. The quantum measurement process is consistently analyzed using fundamental quantum principles without referring to measurement. These same principles are used to resolve several of the paradoxes that have long perplexed physicists, including the double slit and Schrödinger's cat. The consistent histories formalism used here was first introduced by the author, and extended by M. Gell-Mann, J. Hartle and R. Omnès. Essential for researchers yet accessible to advanced undergraduate students in physics, chemistry, mathematics, and computer science, this book is supplementary to standard textbooks. It will also be of interest to physicists and philosophers working on the foundations of quantum mechanics. Comprehensive account Written by one of the main figures in the field Paperback edition of successful work on philosophy of quantum mechanics
NASA Astrophysics Data System (ADS)
Akhmeteli, Andrey
2013-03-01
Is it possible to offer a ``no drama'' quantum theory? Something as simple (in principle) as classical electrodynamics - a theory described by a system of partial differential equations (PDE) in 3+1 dimensions, but reproducing unitary evolution of a quantum field theory in the Fock space? The following results suggest an affirmative answer: 1. The scalar field can be algebraically eliminated from scalar electrodynamics; the resulting equations describe independent evolution of the electromagnetic field (EMF). 2. After introduction of a complex 4-potential (producing the same EMF as the standard real 4-potential), the spinor field can be algebraically eliminated from spinor electrodynamics; the resulting equations describe independent evolution of EMF. 3. The resulting theories for EMF can be embedded into quantum field theories. Another fundamental result: in a general case, the Dirac equation is equivalent to a 4th order PDE for just one component, which can be made real by a gauge transform. Issues related to the Bell theorem are discussed. A. Akhmeteli, Int'l Journal of Quantum Information, Vol. 9, Suppl., 17-26 (2011) A. Akhmeteli, Journal of Mathematical Physics, Vol. 52, 082303 (2011) A. Akhmeteli, quant-ph/1111.4630 A. Akhmeteli, J. Phys.: Conf. Ser., Vol. 361, 012037 (2012)
NASA Astrophysics Data System (ADS)
Akhmeteli, Andrey
2012-02-01
Is it possible to offer a ``no drama'' quantum theory? Something as simple (in principle) as classical electrodynamics - a theory described by a system of partial differential equations (PDE) in 3+1 dimensions, but reproducing unitary evolution of a quantum field theory in the configuration space? The following results suggest an affirmative answer: 1. The scalar field can be algebraically eliminated from scalar electrodynamics; the resulting equations describe independent evolution of the electromagnetic field (EMF). 2. After introduction of a complex 4-potential (producing the same EMF as the standard real 4-potential), the spinor field can be algebraically eliminated from spinor electrodynamics; the resulting equations describe independent evolution of EMF. 3. The resulting theories for EMF can be embedded into quantum field theories. Another fundamental result: in a general case, the Dirac equation is equivalent to a 4th order PDE for just one component, which can be made real by a gauge transform. Issues related to the Bell theorem are discussed. A. Akhmeteli, Int'l Journal of Quantum Information, Vol. 9, Suppl., 17-26 (2011) A. Akhmeteli, Journal of Mathematical Physics, Vol. 52, 082303 (2011) A. Akhmeteli, quant-ph/1108.1588
Quantum set theory and applications
Rodriguez, E.
1984-01-01
The work of von Neumann tells us that the logic of quantum mechanics is not Boolenan. This suggests the formulation of a quantum theory of sets based on quantum logic much as modern set theory is based on Boolean logic. In the first part of this dissertation such a quantum set theory is developed. In the second part, quantum set theory is proposed as a universal language for physics. A quantum topology and the beginnings of a quantum geometry are developed in this language. Finally, a toy model is studied. It gives indications of possible lines for progress in this program.
Barnett, Stephen M.; Cresser, James D.
2005-08-15
We present a Markovian quantum theory of friction. Our approach is based on the idea that collisions between a Brownian particle and single molecules of the surrounding medium constitute, as far as the particle is concerned, instantaneous simultaneous measurements of its position and momentum.
NASA Astrophysics Data System (ADS)
Akhmeteli, Andrey
2012-05-01
Is it possible to offer a "no drama" quantum theory? Something as simple (in principle) as classical electrodynamics - a theory described by a system of partial differential equations in 3+1 dimensions, but reproducing unitary evolution of a quantum field theory in the configuration space? The following results suggest an affirmative answer: 1. The scalar field can be algebraically eliminated from scalar electrodynamics; the resulting equations describe independent evolution of the electromagnetic field. 2. After introduction of a complex 4-potential (producing the same electromagnetic field as the standard real 4-potential), the spinor field can be algebraically eliminated from spinor electrodynamics; the resulting equations describe independent evolution of the electromagnetic field. 3. The resulting theories for the electromagnetic field can be embedded into quantum field theories. Another fundamental result: in a general case, the Dirac equation is equivalent to a 4th order partial differential equations for just one component, which can be made real by a gauge transform. Issues related to the Bell theorem are discussed.
The Quantum Underground: Early quantum theory textbooks
NASA Astrophysics Data System (ADS)
Gearhart, Clayton
2011-04-01
Quantum theory had its beginnings in 1900, when Max Planck derived his famous formula for the energy density of black-body radiation. But the early quantum theory textbooks we remember today--for example, those of Arnold Summerfeld (1919), Fritz Reiche (1921), and a shorter Report by James Jeans (1914), did not appear until some years later, and all were written by physicists who were themselves active participants in early quantum theory. Surprisingly, not all early texts fit this pattern. Reiche himself had written a review article on quantum theory for general readers in Die Naturwissenschaften in 1913, long before his research had shifted to quantum topics. And a year later, textbooks by Hermann Sieveking and Sigfried Valentiner treated quantum theory for students and non-specialists, although neither was active in quantum theoretical research. A third and better known author, Owen Richardson, also treated quantum theory in a 1914 book on electromagnetism. I will describe these early and little-known treatments of quantum theory, all of which were written by physicists whose primary research and professional interests lay elsewhere.
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.
Quantum algorithms for quantum field theories
NASA Astrophysics Data System (ADS)
Jordan, Stephen
2015-03-01
Ever since Feynman's original proposal for quantum computers, one of the primary applications envisioned has been efficient simulation of other quantum systems. In fact, it has been conjectured that quantum computers would be universal simulators, which can simulate all physical systems using computational resources that scale polynomially with the system's number of degrees of freedom. Quantum field theories have posed a challenge in that the set of degrees of freedom is formally infinite. We show how quantum computers, if built, could nevertheless efficiently simulate certain quantum field theories at bounded energy scales. Our algorithm includes a new state preparation technique which we believe may find additional applications in quantum algorithms. Joint work with Keith Lee and John Preskill.
Informational derivation of quantum theory
NASA Astrophysics Data System (ADS)
Chiribella, Giulio; D'Ariano, Giacomo Mauro; Perinotti, Paolo
2011-07-01
We derive quantum theory from purely informational principles. Five elementary axioms—causality, perfect distinguishability, ideal compression, local distinguishability, and pure conditioning—define a broad class of theories of information processing that can be regarded as standard. One postulate—purification—singles out quantum theory within this class.
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.
Effective methods for quantum theories
NASA Astrophysics Data System (ADS)
Brahma, Suddhasattwa
Whenever a full theory is unavailable, effective frameworks serve as powerful tools for examining physical phenomena below some energy scale. However, standard quantum field theory techniques are not always applicable in various exotic, yet physically relevant, systems. This thesis presents a new effective method for quantum theories, which is particularly tailored towards background independent theories such as gravity. Our main motivation is to utilize these techniques to extract the semi-classical dynamics from canonical quantum gravity theories. Application to field theoretic toy models of loop quantum gravity and non-associative quantum mechanics is elaborated in detail. We also extend this framework to fully constrained systems, as is required for gravity, and discuss several consequences for quantum gravity.
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 simulation of quantum field theory using continuous variables
Marshall, Kevin; Pooser, Raphael C.; Siopsis, George; Weedbrook, Christian
2015-12-14
Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault tolerant architecture. This has lead to the point that continuous-variable quantum computing can indeed be thought of as a viable alternative for universal quantum computing. With that in mind, we present a new algorithm for continuous-variable quantum computers which gives an exponential speedup over the best known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonic quantum field theory, a problem that is known to be hard using a classical computer. Thus, we give an experimental implementation based on cluster states that is feasible with today's technology.
Quantum simulation of quantum field theory using continuous variables
NASA Astrophysics Data System (ADS)
Marshall, Kevin; Pooser, Raphael; Siopsis, George; Weedbrook, Christian
2015-12-01
The year 1982 is often credited as the year that theoretical quantum computing was started with a keynote speech by Richard Feynman, who proposed a universal quantum simulator, the idea being that if you had such a machine you could in principle "imitate any quantum system, including the physical world." With that in mind, we present an algorithm for a continuous-variable quantum computing architecture which gives an exponential speedup over the best-known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonic quantum field theory, a problem that is believed to be hard using a classical computer. Building on this, we give an experimental implementation based on continuous-variable states that is feasible with today's technology.
Quantum simulation of quantum field theory using continuous variables
Marshall, Kevin; Pooser, Raphael C.; Siopsis, George; Weedbrook, Christian
2015-12-14
Much progress has been made in the field of quantum computing using continuous variables over the last couple of years. This includes the generation of extremely large entangled cluster states (10,000 modes, in fact) as well as a fault tolerant architecture. This has lead to the point that continuous-variable quantum computing can indeed be thought of as a viable alternative for universal quantum computing. With that in mind, we present a new algorithm for continuous-variable quantum computers which gives an exponential speedup over the best known classical methods. Specifically, this relates to efficiently calculating the scattering amplitudes in scalar bosonicmore » quantum field theory, a problem that is known to be hard using a classical computer. Thus, we give an experimental implementation based on cluster states that is feasible with today's technology.« less
Integrable structures in quantum field theory
NASA Astrophysics Data System (ADS)
Negro, Stefano
2016-08-01
This review was born as notes for a lecture given at the Young Researchers Integrability School (YRIS) school on integrability in Durham, in the summer of 2015. It deals with a beautiful method, developed in the mid-nineties by Bazhanov, Lukyanov and Zamolodchikov and, as such, called BLZ. This method can be interpreted as a field theory version of the quantum inverse scattering, also known as the algebraic Bethe ansatz. Starting with the case of conformal field theories (CFTs) we show how to build the field theory analogues of commuting transfer T matrices and Baxter Q-operators of integrable lattice models. These objects contain the complete information of the integrable structure of the theory, viz. the integrals of motion, and can be used, as we will show, to derive the thermodynamic Bethe ansatz and nonlinear integral equations. This same method can be easily extended to the description of integrable structures of certain particular massive deformations of CFTs; these, in turn, can be described as quantum group reductions of the quantum sine-Gordon model and it is an easy step to include this last theory in the framework of BLZ approach. Finally we show an interesting and surprising connection of the BLZ structures with classical objects emerging from the study of classical integrable models via the inverse scattering transform method. This connection goes under the name of ODE/IM correspondence and we will present it for the specific case of quantum sine-Gordon model only.
NASA Astrophysics Data System (ADS)
Salam, Abdus; Wigner, E. P.
2010-03-01
Preface; List of contributors; Bibliography of P. A. M. Dirac; 1. Dirac in Cambridge R. J. Eden and J. C. Polkinghorne; 2. Travels with Dirac in the Rockies J. H. Van Vleck; 3. 'The golden age of theoretical physics': P. A. M. Dirac's scientific work from 1924 to 1933 Jagdish Mehra; 4. Foundation of quantum field theory Res Jost; 5. The early history of the theory of electron: 1897-1947 A. Pais; 6. The Dirac equation A. S. Wightman; 7. Fermi-Dirac statistics Rudolph Peierls; 8. Indefinite metric in state space W. Heisenberg; 9. On bras and kets J. M. Jauch; 10. The Poisson bracket C. Lanczos; 11. La 'fonction' et les noyaux L. Schwartz; 12. On the Dirac magnetic poles Edoardo Amadli and Nicola Cabibbo; 13. The fundamental constants and their time variation Freeman J. Dyson; 14. On the time-energy uncertainty relation Eugene P. Wigner; 15. The path-integral quantisation of gravity Abdus Salam and J. Strathdee; Index; Plates.
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 theory of measurements as quantum decision theory
NASA Astrophysics Data System (ADS)
Yukalov, V. I.; Sornette, D.
2015-03-01
Theory of quantum measurements is often classified as decision theory. An event in decision theory corresponds to the measurement of an observable. This analogy looks clear for operationally testable simple events. However, the situation is essentially more complicated in the case of composite events. The most difficult point is the relation between decisions under uncertainty and measurements under uncertainty. We suggest a unified language for describing the processes of quantum decision making and quantum measurements. The notion of quantum measurements under uncertainty is introduced. We show that the correct mathematical foundation for the theory of measurements under uncertainty, as well as for quantum decision theory dealing with uncertain events, requires the use of positive operator-valued measure that is a generalization of projection-valued measure. The latter is appropriate for operationally testable events, while the former is necessary for characterizing operationally uncertain events. In both decision making and quantum measurements, one has to distinguish composite nonentangled events from composite entangled events. Quantum probability can be essentially different from classical probability only for entangled events. The necessary condition for the appearance of an interference term in the quantum probability is the occurrence of entangled prospects and the existence of an entangled strategic state of a decision maker or of an entangled statistical state of a measuring device.
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.
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.
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.
Studies in quantum field theory
NASA Astrophysics Data System (ADS)
Polmar, S. K.
The theoretical physics group at Washington University has been devoted to the solution of problems in theoretical and mathematical physics. All of the personnel on this task have a similar approach to their research in that they apply sophisticated analytical and numerical techniques to problems primarily in quantum field theory. Specifically, this group has worked on quantum chromodynamics, classical Yang-Mills fields, chiral symmetry breaking condensates, lattice field theory, strong-coupling approximations, perturbation theory in large order, nonlinear waves, 1/N expansions, quantum solitons, phase transitions, nuclear potentials, and early universe calculations.
Unification of quantum information theory
NASA Astrophysics Data System (ADS)
Abeyesinghe, Anura
We present the unification of many previously disparate results in noisy quantum Shannon theory and the unification of all of noiseless quantum Shannon theory. More specifically we deal here with bipartite, unidirectional, and memoryless quantum Shannon theory. We find all the optimal protocols and quantify the relationship between the resources used, both for the one-shot and for the ensemble case, for what is arguably the most fundamental task in quantum information theory: sharing entangled states between a sender and a receiver. We find that all of these protocols are derived from our one-shot superdense coding protocol and relate nicely to each other. We then move on to noisy quantum information theory and give a simple, direct proof of the "mother" protocol, or rather her generalization to the Fully Quantum Slepian-Wolf protocol (FQSW). FQSW simultaneously accomplishes two goals: quantum communication-assisted entanglement distillation, and state transfer from the sender to the receiver. As a result, in addition to her other "children," the mother protocol generates the state merging primitive of Horodecki, Oppenheim, and Winter as well as a new class of distributed compression protocols for correlated quantum sources, which are optimal for sources described by separable density operators. Moreover, the mother protocol described here is easily transformed into the so-called "father" protocol, demonstrating that the division of single-sender/single-receiver protocols into two families was unnecessary: all protocols in the family are children of the mother.
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.
Quantum Theory is an Information Theory
NASA Astrophysics Data System (ADS)
D'Ariano, Giacomo M.; Perinotti, Paolo
2016-03-01
In this paper we review the general framework of operational probabilistic theories (OPT), along with the six axioms from which quantum theory can be derived. We argue that the OPT framework along with a relaxed version of five of the axioms, define a general information theory. We close the paper with considerations about the role of the observer in an OPT, and the interpretation of the von Neumann postulate and the Schrödinger-cat paradox.
Elementary Concepts of Quantum Theory
ERIC Educational Resources Information Center
Warren, J. W.
1974-01-01
Discusses the importance and difficulties of teaching basic quantum theory. Presents a discussion of wave-particle duality, indeterminacy, the nature of a quantized state of a system, and the exclusion principle. (MLH)
Quantum Field Theory in (0 + 1) Dimensions
ERIC Educational Resources Information Center
Boozer, A. D.
2007-01-01
We show that many of the key ideas of quantum field theory can be illustrated simply and straightforwardly by using toy models in (0 + 1) dimensions. Because quantum field theory in (0 + 1) dimensions is equivalent to quantum mechanics, these models allow us to use techniques from quantum mechanics to gain insight into quantum field theory. In…
NASA Astrophysics Data System (ADS)
Kaasbjerg, Kristen; Nitzan, Abraham
2015-03-01
We develop a theoretical framework for the description of light emission from plasmonic contacts based on the nonequilibrium Green function formalism. Our theory establishes a fundamental link between the finite-frequency quantum noise and ac conductance of the contact and the light emission. Calculating the quantum noise to higher orders in the electron-plasmon interaction, we identify a plasmon-induced electron-electron interaction as the source of experimentally observed above-threshold light emission from biased STM contacts. Our findings provide important insight into the effect of interactions on the light emission from atomic-scale contacts.
Vukmirovic, Nenad; Wang, Lin-Wang
2009-11-10
This review covers the description of the methodologies typically used for the calculation of the electronic structure of self-assembled and colloidal quantum dots. These are illustrated by the results of their application to a selected set of physical effects in quantum dots.
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.
Colloquium: Theory of quantum corrals and quantum mirages
NASA Astrophysics Data System (ADS)
Fiete, Gregory A.; Heller, Eric J.
2003-07-01
Quantum corrals are two-dimensional structures built atom by atom on an atomically clean metallic surface using a scanning tunneling microscope (STM). These two-dimensional structures “corral” electrons in the surface states of noble metals, leading to standing-wave patterns in the electron density inside the quantum corral. The authors review the physics of quantum corrals and relate the signal of the STM to the scattering properties of substrate electrons from atomic impurities supported on the surface. The theory includes the effects of incoherent surface-state electron scattering at the impurities and quantitively describes nearly all of the current STM data on quantum corrals, including the recent quantum mirage experiments with Kondo effect. The physics underlying the recent mirage experiments is discussed, as are some of the outstanding questions regarding the Kondo effect from impurities in nanoscale structures on metallic surfaces. The authors also summarize recent work on variations of “quantum” corrals: Optical corrals and acoustical corrals.
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.
QUANTUM MODE-COUPLING THEORY: Formulation and Applications to Normal and Supercooled Quantum Liquids
NASA Astrophysics Data System (ADS)
Rabani, Eran; Reichman, David R.
2005-05-01
We review our recent efforts to formulate and study a mode-coupling approach to real-time dynamic fluctuations in quantum liquids. Comparison is made between the theory and recent neutron scattering experiments performed on liquid ortho-deuterium and para-hydrogen. We discuss extensions of the theory to supercooled and glassy states where quantum fluctuations compete with thermal fluctuations. Experimental scenarios for quantum glassy liquids are briefly discussed.
Quantum Hamilton-Jacobi theory.
Roncadelli, Marco; Schulman, L S
2007-10-26
Quantum canonical transformations have attracted interest since the beginning of quantum theory. Based on their classical analogues, one would expect them to provide a powerful quantum tool. However, the difficulty of solving a nonlinear operator partial differential equation such as the quantum Hamilton-Jacobi equation (QHJE) has hindered progress along this otherwise promising avenue. We overcome this difficulty. We show that solutions to the QHJE can be constructed by a simple prescription starting from the propagator of the associated Schrödinger equation. Our result opens the possibility of practical use of quantum Hamilton-Jacobi theory. As an application, we develop a surprising relation between operator ordering and the density of paths around a semiclassical trajectory. PMID:17995307
Quantum spectral dimension in quantum field theory
NASA Astrophysics Data System (ADS)
Calcagni, Gianluca; Modesto, Leonardo; Nardelli, Giuseppe
2016-03-01
We reinterpret the spectral dimension of spacetimes as the scaling of an effective self-energy transition amplitude in quantum field theory (QFT), when the system is probed at a given resolution. This picture has four main advantages: (a) it dispenses with the usual interpretation (unsatisfactory in covariant approaches) where, instead of a transition amplitude, one has a probability density solving a nonrelativistic diffusion equation in an abstract diffusion time; (b) it solves the problem of negative probabilities known for higher-order and nonlocal dispersion relations in classical and quantum gravity; (c) it clarifies the concept of quantum spectral dimension as opposed to the classical one. We then consider a class of logarithmic dispersion relations associated with quantum particles and show that the spectral dimension dS of spacetime as felt by these quantum probes can deviate from its classical value, equal to the topological dimension D. In particular, in the presence of higher momentum powers it changes with the scale, dropping from D in the infrared (IR) to a value dSUV ≤ D in the ultraviolet (UV). We apply this general result to Stelle theory of renormalizable gravity, which attains the universal value dSUV = 2 for any dimension D.
Multiphoton-scattering theory and generalized master equations
NASA Astrophysics Data System (ADS)
Shi, Tao; Chang, Darrick E.; Cirac, J. Ignacio
2015-11-01
We develop a scattering theory to investigate the multiphoton transmission in a one-dimensional waveguide in the presence of quantum emitters. It is based on a path integral formalism, uses displacement transformations, and does not require the Markov approximation. We obtain the full time evolution of the global system, including the emitters and the photonic field. Our theory allows us to compute the transition amplitude between arbitrary initial and final states, as well as the S matrix of the asymptotic in and out states. For the case of few incident photons in the waveguide, we also rederive a generalized master equation in the Markov limit. We compare the predictions of the developed scattering theory and that with the Markov approximation. We illustrate our methods with five examples of few-photon scattering: (i) by a two-level emitter, (ii) in the Jaynes-Cummings model; (iii) by an array of two-level emitters; (iv) by a two-level emitter in the half-end waveguide; and (v) by an array of atoms coupled to Rydberg levels. In the first two, we show the application of the scattering theory in the photon scattering by a single emitter, and examine the correctness of our theory with the well-known results. In the third example, we analyze the condition of the Markov approximation for the photon scattering in the array of emitters. In the fourth one, we show how a quantum emitter can generate entanglement of outgoing photons. Finally, we highlight the interplay between the phenomenon of electromagnetic-induced transparency and the Rydberg interaction, and show how this results in a rich variety of possibilities in the quantum statistics of the scattering photons.
Metric quantum field theory: A preliminary look
Watson, W.N.
1988-01-01
Spacetime coordinates are involved in uncertainty relations; spacetime itself appears to exhibit curvature. Could the continua associated with field variables exhibit curvature This question, as well as the ideas that (a) difficulties with quantum theories of gravitation may be due to their formulation in an incorrect analogy with other quantum field theories, (b) spacetime variables should not be any more basic than others for describing physical phenomena, and (c) if field continua do not exhibit curvature, the reasons would be of interest, motivated the formulation of a theory of variable curvature and torsion in the electromagnetic four-potential's reciprocal space. Curvature and torsion equation completely analogous to those for a gauge theory of gravitation (the Einstein-Cartan-Sciama-Kibble theory) are assumed for this continuum. The interaction-Hamiltonian density of this theory, to a first approximation, implies that in addition to the Maxwell-Dirac field interaction of ordinary quantum electrodynamics, there should also be an interaction between Dirac-field vector and pseudovector currents unmediated by photons, as well as other interactions involving two or three Dirac-field currents interacting with the Maxwell field at single spacetime events. Calculations expressing Bhabha-scattering cross sections for incident beams with parallel spins differ from those of unmodified quantum electrodynamics by terms of first order in the gravitational constant of the theory, but the corresponding cross section for unpolarized incident beams differs from that of the unmodified theory only by terms of higher order in that constant. Undesirable features of the present theory include its nonrenormalizability, the obscurity of the meaning of its inverse field operator, and its being based on electrodynamics rather than electroweak dynamics.
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
(Studies in quantum field theory)
Not Available
1990-01-01
During the period 4/1/89--3/31/90 the theoretical physics group supported by Department of Energy Contract No. AC02-78ER04915.A015 and consisting of Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Senior Research Associate Visser has made progress in many areas of theoretical and mathematical physics. Professors Bender and Shrauner, Associate Professor Papanicolaou, Assistant Professor Ogilvie, and Research Associate Visser are currently conducting research in many areas of high energy theoretical and mathematical physics. These areas include: strong-coupling approximation; classical solutions of non-Abelian gauge theories; mean-field approximation in quantum field theory; path integral and coherent state representations in quantum field theory; lattice gauge calculations; the nature of perturbation theory in large order; quark condensation in QCD; chiral symmetry breaking; the 1/N expansion in quantum field theory; effective potential and action in quantum field theories, including OCD; studies of the early universe and inflation, and quantum gravity.
NASA Astrophysics Data System (ADS)
Bender, Carl M.
2015-07-01
The average quantum physicist on the street would say that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under combined matrix transposition and complex conjugation) in order to guarantee that the energy eigenvalues are real and that time evolution is unitary. However, the Hamiltonian H = p2 + ix3, which is obviously not Dirac Hermitian, has a positive real discrete spectrum and generates unitary time evolution, and thus it defines a fully consistent and physical quantum theory. Evidently, the axiom of Dirac Hermiticity is too restrictive. While H = p2 + ix3 is not Dirac Hermitian, it is PT symmetric; that is, invariant under combined parity P (space reflection) and time reversal T. The quantum mechanics defined by a PT-symmetric Hamiltonian is a complex generalization of ordinary quantum mechanics. When quantum mechanics is extended into the complex domain, new kinds of theories having strange and remarkable properties emerge. In the past few years, some of these properties have been verified in laboratory experiments. A particularly interesting PT-symmetric Hamiltonian is H = p2 - x4, which contains an upside-down potential. This potential is discussed in detail, and it is explained in intuitive as well as in rigorous terms why the energy levels of this potential are real, positive, and discrete. Applications of PT-symmetry in quantum field theory are also discussed.
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.
"Phonon" scattering beyond perturbation theory
NASA Astrophysics Data System (ADS)
Qiu, WuJie; Ke, XueZhi; Xi, LiLi; Wu, LiHua; Yang, Jiong; Zhang, WenQing
2016-02-01
Searching and designing materials with intrinsically low lattice thermal conductivity (LTC) have attracted extensive consideration in thermoelectrics and thermal management community. The concept of part-crystalline part-liquid state, or even part-crystalline part-amorphous state, has recently been proposed to describe the exotic structure of materials with chemical- bond hierarchy, in which a set of atoms is weakly bonded to the rest species while the other sublattices retain relatively strong rigidity. The whole system inherently manifests the coexistence of rigid crystalline sublattices and fluctuating noncrystalline substructures. Representative materials in the unusual state can be classified into two categories, i.e., caged and non-caged ones. LTCs in both systems deviate from the traditional T -1 relationship ( T, the absolute temperature), which can hardly be described by small-parameter-based perturbation approaches. Beyond the classical perturbation theory, an extra rattling-like scattering should be considered to interpret the liquid-like and sublattice-amorphization-induced heat transport. Such a kind of compounds could be promising high-performance thermoelectric materials, due to the extremely low LTCs. Other physical properties for these part-crystalline substances should also exhibit certain novelty and deserve further exploration.
Recoverability in quantum information theory
NASA Astrophysics Data System (ADS)
Wilde, Mark
The fact that the quantum relative entropy is non-increasing with respect to quantum physical evolutions lies at the core of many optimality theorems in quantum information theory and has applications in other areas of physics. In this work, we establish improvements of this entropy inequality in the form of physically meaningful remainder terms. One of the main results can be summarized informally as follows: if the decrease in quantum relative entropy between two quantum states after a quantum physical evolution is relatively small, then it is possible to perform a recovery operation, such that one can perfectly recover one state while approximately recovering the other. This can be interpreted as quantifying how well one can reverse a quantum physical evolution. Our proof method is elementary, relying on the method of complex interpolation, basic linear algebra, and the recently introduced Renyi generalization of a relative entropy difference. The theorem has a number of applications in quantum information theory, which have to do with providing physically meaningful improvements to many known entropy inequalities. This is based on arXiv:1505.04661, now accepted for publication in Proceedings of the Royal Society A. I acknowledge support from startup funds from the Department of Physics and Astronomy at LSU, the NSF under Award No. CCF-1350397, and the DARPA Quiness Program through US Army Research Office award W31P4Q-12-1-0019.
Propensity, Probability, and Quantum Theory
NASA Astrophysics Data System (ADS)
Ballentine, Leslie E.
2016-08-01
Quantum mechanics and probability theory share one peculiarity. Both have well established mathematical formalisms, yet both are subject to controversy about the meaning and interpretation of their basic concepts. Since probability plays a fundamental role in QM, the conceptual problems of one theory can affect the other. We first classify the interpretations of probability into three major classes: (a) inferential probability, (b) ensemble probability, and (c) propensity. Class (a) is the basis of inductive logic; (b) deals with the frequencies of events in repeatable experiments; (c) describes a form of causality that is weaker than determinism. An important, but neglected, paper by P. Humphreys demonstrated that propensity must differ mathematically, as well as conceptually, from probability, but he did not develop a theory of propensity. Such a theory is developed in this paper. Propensity theory shares many, but not all, of the axioms of probability theory. As a consequence, propensity supports the Law of Large Numbers from probability theory, but does not support Bayes theorem. Although there are particular problems within QM to which any of the classes of probability may be applied, it is argued that the intrinsic quantum probabilities (calculated from a state vector or density matrix) are most naturally interpreted as quantum propensities. This does not alter the familiar statistical interpretation of QM. But the interpretation of quantum states as representing knowledge is untenable. Examples show that a density matrix fails to represent knowledge.
Light-scattering theory of diffraction.
Guo, Wei
2010-03-01
Since diffraction is a scattering process in principle, light propagation through one aperture in a screen is discussed in the light-scattering theory. Through specific calculation, the expression of the electric field observed at an observation point is obtained and is used not only to explain why Kirchhoff's diffraction theory is a good approximation when the screen is both opaque and sufficiently thin but also to demonstrate that the mathematical and physical problems faced by Kirchhoff's theory are avoided in the light-scattering theory. PMID:20208939
Construction of relativistic quantum theory: a progress report
Noyes, H.P.
1986-06-01
We construct the particulate states of quantum physics using a recursive computer program that incorporates non-determinism by means of locally arbitrary choices. Quantum numbers and coupling constants arise from the construction via the unique 4-level combinatorial hierarchy. The construction defines indivisible quantum events with the requisite supraluminal correlations, yet does not allow supraluminal communication. Measurement criteria incorporate c, h-bar and m/sub p/ or (not ''and'') G, connected to laboratory events via finite particle number scattering theory and the counter paradigm. The resulting theory is discrete throughout, contains no infinities, and, as far as we have developed it, is in agreement with quantum mechanical and cosmological fact.
Quantum and semiclassical theories of chemical reaction rates
Miller, W.H. |
1995-09-01
A rigorous quantum mechanical theory (and a semiclassical approximation thereto) is described for calculating chemical reaction rates ``directly``, i.e., without having to solve the complete state-to-state reactive scattering problem. The approach has many vestiges of transition state theory, for which it may be thought of as the rigorous generalization.
Unstable states in quantum theory
NASA Astrophysics Data System (ADS)
Kuksa, V. I.
2014-05-01
Various approaches to the problem of describing unstable particles are reviewed. Fundamental problems that arise in quantum field description of these particles and the ways of their solution are considered. Among them, there is an approach related to the notion of the smeared (continuous) mass, which originates from the finite lifetime of unstable particles. The quantum field model of unstable particles with smeared mass, which is built upon two basic axiomatic elements, is considered in detail. The basic processes with unstable particles (decay and scattering) are considered within the framework of the model and the formalism for describing physical characteristics of those processes is developed. The model is successfully applied to describing the processes of pair and triple boson production at the linear collider, top quark pair production, and certain hadronic decays. Based on this model, the factorization method is developed, which allows a description of complicated and multistep scattering and decay processes with unstable particles to be considerably simplified.
Scattering theory with path integrals
Rosenfelder, R.
2014-03-15
Starting from well-known expressions for the T-matrix and its derivative in standard nonrelativistic potential scattering, I rederive recent path-integral formulations due to Efimov and Barbashov et al. Some new relations follow immediately.
NASA Astrophysics Data System (ADS)
Modesto, Leonardo; Piva, Marco; Rachwał, Lesław
2016-07-01
We explicitly compute the one-loop exact beta function for a nonlocal extension of the standard gauge theory, in particular, Yang-Mills and QED. The theory, made of a weakly nonlocal kinetic term and a local potential of the gauge field, is unitary (ghost-free) and perturbatively super-renormalizable. Moreover, in the action we can always choose the potential (consisting of one "killer operator") to make zero the beta function of the running gauge coupling constant. The outcome is a UV finite theory for any gauge interaction. Our calculations are done in D =4 , but the results can be generalized to even or odd spacetime dimensions. We compute the contribution to the beta function from two different killer operators by using two independent techniques, namely, the Feynman diagrams and the Barvinsky-Vilkovisky traces. By making the theories finite, we are able to solve also the Landau pole problems, in particular, in QED. Without any potential, the beta function of the one-loop super-renormalizable theory shows a universal Landau pole in the running coupling constant in the ultraviolet regime (UV), regardless of the specific higher-derivative structure. However, the dressed propagator shows neither the Landau pole in the UV nor the singularities in the infrared regime (IR).
Generalized Quantum Theory and Mathematical Foundations of Quantum Field Theory
NASA Astrophysics Data System (ADS)
Maroun, Michael Anthony
This dissertation is divided into two main topics. The first is the generalization of quantum dynamics when the Schrodinger partial differential equation is not defined even in the weak mathematical sense because the potential function itself is a distribution in the spatial variable, the same variable that is used to define the kinetic energy operator, i.e. the Laplace operator. The procedure is an extension and broadening of the distributional calculus and offers spectral results as an alternative to the only other two known methods to date, namely a) the functional calculi; and b) non-standard analysis. Furthermore, the generalizations of quantum dynamics presented within give a resolution to the time asymmetry paradox created by multi-particle quantum mechanics due to the time evolution still being unitary. A consequence is the randomization of phases needed for the fundamental justification Pauli master equation. The second topic is foundations of the quantum theory of fields. The title is phrased as ``foundations'' to emphasize that there is no claim of uniqueness but rather a proposal is put forth, which is markedly different than that of constructive or axiomatic field theory. In particular, the space of fields is defined as a space of generalized functions with involutive symmetry maps (the CPT invariance) that affect the topology of the field space. The space of quantum fields is then endowed the Frechet property and interactions change the topology in such a way as to cause some field spaces to be incompatible with others. This is seen in the consequences of the Haag theorem. Various examples and discussions are given that elucidate a new view of the quantum theory of fields and its (lack of) mathematical structure.
Revisiting Bohr's semiclassical quantum theory.
Ben-Amotz, Dor
2006-10-12
Bohr's atomic theory is widely viewed as remarkable, both for its accuracy in predicting the observed optical transitions of one-electron atoms and for its failure to fully correspond with current electronic structure theory. What is not generally appreciated is that Bohr's original semiclassical conception differed significantly from the Bohr-Sommerfeld theory and offers an alternative semiclassical approximation scheme with remarkable attributes. More specifically, Bohr's original method did not impose action quantization constraints but rather obtained these as predictions by simply matching photon and classical orbital frequencies. In other words, the hydrogen atom was treated entirely classically and orbital quantized emerged directly from the Planck-Einstein photon quantization condition, E = h nu. Here, we revisit this early history of quantum theory and demonstrate the application of Bohr's original strategy to the three quintessential quantum systems: an electron in a box, an electron in a ring, and a dipolar harmonic oscillator. The usual energy-level spectra, and optical selection rules, emerge by solving an algebraic (quadratic) equation, rather than a Bohr-Sommerfeld integral (or Schroedinger) equation. However, the new predictions include a frozen (zero-kinetic-energy) state which in some (but not all) cases lies below the usual zero-point energy. In addition to raising provocative questions concerning the origin of quantum-chemical phenomena, the results may prove to be of pedagogical value in introducing students to quantum mechanics. PMID:17020371
Benchmark calculations of thermal reaction rates. I - Quantal scattering theory
NASA Technical Reports Server (NTRS)
Chatfield, David C.; Truhlar, Donald G.; Schwenke, David W.
1991-01-01
The thermal rate coefficient for the prototype reaction H + H2 yields H2 + H with zero total angular momentum is calculated by summing, averaging, and numerically integrating state-to-state reaction probabilities calculated by time-independent quantum-mechanical scattering theory. The results are very carefully converged with respect to all numerical parameters in order to provide high-precision benchmark results for confirming the accuracy of new methods and testing their efficiency.
Topics in electromagnetic, acoustic, and potential scattering theory
NASA Astrophysics Data System (ADS)
Nuntaplook, Umaporn
With recent renewed interest in the classical topics of both acoustic and electromagnetic aspects for nano-technology, transformation optics, fiber optics, metamaterials with negative refractive indices, cloaking and invisibility, the topic of time-independent scattering theory in quantum mechanics is becoming a useful field to re-examine in the above contexts. One of the key areas of electromagnetic theory scattering of plane electromagnetic waves --- is based on the properties of the refractive indices in the various media. It transpires that the refractive index of a medium and the potential in quantum scattering theory are intimately related. In many cases, understanding such scattering in radially symmetric media is sufficient to gain insight into scattering in more complex media. Meeting the challenge of variable refractive indices and possibly complicated boundary conditions therefore requires accurate and efficient numerical methods, and where possible, analytic solutions to the radial equations from the governing scalar and vector wave equations (in acoustics and electromagnetic theory, respectively). Until relatively recently, researchers assumed a constant refractive index throughout the medium of interest. However, the most interesting and increasingly useful cases are those with non-constant refractive index profiles. In the majority of this dissertation the focus is on media with piecewise constant refractive indices in radially symmetric media. The method discussed is based on the solution of Maxwell's equations for scattering of plane electromagnetic waves from a dielectric (or "transparent") sphere in terms of the related Helmholtz equation. The main body of the dissertation (Chapters 2 and 3) is concerned with scattering from (i) a uniform spherical inhomogeneity embedded in an external medium with different properties, and (ii) a piecewise-uniform central inhomogeneity in the external medium. The latter results contain a natural generalization of
Massive supersymmetric quantum gauge theory
NASA Astrophysics Data System (ADS)
Grigore, D. R.; Gut, M.; Scharf, G.
2005-08-01
We continue the study of the supersymmetric vector multiplet in a purely quantum framework. We obtain some new results which make the connection with the standard literature. First we construct the one-particle physical Hilbert space taking into account the (quantum) gauge structure of the model. Then we impose the condition of positivity for the scalar product only on the physical Hilbert space. Finally we obtain a full supersymmetric coupling which is gauge invariant in the supersymmetric sense in the first order of perturbation theory. By integrating out the Grassmann variables we get an interacting Lagrangian for a massive Yang-Mills theory related to ordinary gauge theory; however the number of ghost fields is doubled so we do not obtain the same ghost couplings as in the standard model Lagrangian.
Theory of waves incoherently scattered
NASA Technical Reports Server (NTRS)
Bauer, P.
1974-01-01
Electromagnetic waves impinging upon a plasma at frequencies larger than the plasma frequency, suffer weak scattering. The scattering arises from the existence of electron density fluctuations. The received signal corresponds to a particular spatial Fourier component of the fluctuations, the wave vector of which is a function of the wavelength of the radiowave. Wavelengths short with respect to the Debye length of the medium relate to fluctuations due to non-interacting Maxwellian electrons, while larger wavelengths relate to fluctuations due to collective Coulomb interactions. In the latter case, the scattered signal exhibits a spectral distribution which is characteristic of the main properties of the electron and ion gases and, therefore, provides a powerful diagnosis of the state of the ionosphere.
Theory of Light Scattering in Axion Electrodynamics
NASA Astrophysics Data System (ADS)
Ochiai, Tetsuyuki
2012-09-01
Taking account of the axion term in the Maxwell Lagrangian, we present a rigorous theory of light scattering in piecewise-constant axion fields. In particular, we focus on axionic substances with confined and/or curved geometries, and the scattering matrices of an axionic slab, cylinder, and sphere are derived analytically. The axion term generates a surface current with off-diagonal optical conductivity, giving rise to a new type of photospin--orbit interaction. As a result, various novel light-scattering phenomena can take place. We demonstrate enhanced Faraday rotation, parity-violating light scattering, and strong perturbation of dipole radiation.
Siegert pseudostate formulation of scattering theory: General three-dimensional case
NASA Astrophysics Data System (ADS)
Krainov, Lev O.; Batishchev, Pavel A.; Tolstikhin, Oleg I.
2016-04-01
This paper generalizes the Siegert pseudostate (SPS) formulation of scattering theory to arbitrary finite-range potentials without any symmetry in the three-dimensional (3D) case. The orthogonality and completeness properties of 3D SPSs are established. The SPS expansions for scattering states, outgoing-wave Green's function, scattering matrix, and scattering amplitude, that is, all major objects of scattering theory, are derived. The theory is illustrated by calculations for several model potentials. The results enable one to apply 3D SPSs as a purely discrete basis capable of representing both discrete and continuous spectra in solving various stationary and time-dependent quantum-mechanical problems.
Haag's theorem in noncommutative quantum field theory
Antipin, K. V.; Mnatsakanova, M. N.; Vernov, Yu. S.
2013-08-15
Haag's theorem was extended to the general case of noncommutative quantum field theory when time does not commute with spatial variables. It was proven that if S matrix is equal to unity in one of two theories related by unitary transformation, then the corresponding one in the other theory is equal to unity as well. In fact, this result is valid in any SO(1, 1)-invariant quantum field theory, an important example of which is noncommutative quantum field theory.
NASA Astrophysics Data System (ADS)
Huang, Yi-Ping; Hermele, Michael
Some pyrochlore oxides realize novel dipolar-octupolar (DO) doublets on the sites of the pyrochlore lattice of corner-sharing tetrahedra. With magnetic field along the (111) direction, such systems can approximately be described as decoupled layers of a S =1/2 XYZ model on Kagome planes, with perpendicular magnetic field. A recent quantum Monte Carlo study found a zero temperature disordered phase in this model, dubbed quantum kagome ice, and proposed that it is a type of Z2 quantum spin liquid (J. Carrasquilla, Z. Hao and R. G. Melko, Nat. Comm., 6, 7421). We will describe an effective theory for this putative Z2 spin liquid, and present results on its symmetry fractionalization and resulting properties that may be tested in future numerical simulations. the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award # DE-SC0014415.
NASA Astrophysics Data System (ADS)
Roiban, Radu; Spradlin, Marcus; Volovich, Anastasia
2011-11-01
This issue aims to serve as an introduction to our current understanding of the structure of scattering amplitudes in gauge theory, an area which has seen particularly rapid advances in recent years following decades of steady progress. The articles contained herein provide a snapshot of the latest developments which we hope will serve as a valuable resource for graduate students and other scientists wishing to learn about the current state of the field, even if our continually evolving understanding of the subject might soon render this compilation incomplete. Why the fascination with scattering amplitudes, which have attracted the imagination and dedicated effort of so many physicists? Part of it stems from the belief, supported now by numerous examples, that unexpected simplifications of otherwise apparently complicated calculations do not happen by accident. Instead they provide a strong motivation to seek out an underlying explanation. The insight thereby gained can subsequently be used to make the next class of seemingly impossible calculations not only possible, but in some cases even trivial. This two-pronged strategy of exploring and exploiting the structure of gauge theory amplitudes appeals to a wide audience from formal theorists interested in mathematical structure for the sake of its own beauty to more phenomenologically-minded physicists eager to speed up the next generation of analysis software. Understandably it is the maximally supersymmetric 𝒩 = 4 Yang-Mills theory (SYM) which has the simplest structure and has correspondingly received the most attention. Rarely in theoretical physics are we fortunate enough to encounter a toy model which is simple enough to be solved completely yet rich enough to possess interesting non-trivial structure while simultaneously, and most importantly, being applicable (even if only as a good approximation) to a wide range of 'real' systems. The canonical example in quantum mechanics is of course the harmonic
Inconstancy-theory/quantum-gravity
NASA Astrophysics Data System (ADS)
Murtaza, Faheem
1999-05-01
Inconstancy-theory is the union of "relativity" and "quantum" theories which rests upon the answers of the simple questions. 1) That if only the simple motion of a particle can not be observed without the "reference-frame" then how the whole universe can be expected to be observable without any "reference-frame". 2) Does not the inter-influence (Unity) of space-time-mass suggest that these are generated by common source and might not there be some invisible "flow" (dynamical-equilibrium) that is the cause of space-time-mass,as time itself is a flow. "Inconstancy" proposes, interalia, the principle that "relativity (generalised) is the universal law of nature in each and every respect". For that "inconstancy" admits only the light, being absolute, a real reference-frame and medium(mirror) for the display of relative "space-time-mass". Light as reference-frame in "Inconstancy" unifies "relativity" and "quantum" theories and establishes the inter-connection between "quantum-gravity" and strong-nuclear interactions, which offers the velocity of light in terms of physical and spatial-temporal components. "Inconstancy" introduces another "constant" operative in "quantum-gravity" and unveils the "graviton" location for its novel range as previously "relativity" escaped detection for v<<
Quantum Simulation of Quantum Field Theories in Trapped Ions
Casanova, J.; Lamata, L.; Egusquiza, I. L.; Gerritsma, R.; Roos, C. F.; Garcia-Ripoll, J. J.; Solano, E.
2011-12-23
We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.
Effective equilibrium theory of nonequilibrium quantum transport
NASA Astrophysics Data System (ADS)
Dutt, Prasenjit; Koch, Jens; Han, Jong; Le Hur, Karyn
2011-12-01
The theoretical description of strongly correlated quantum systems out of equilibrium presents several challenges and a number of open questions persist. Here, we focus on nonlinear electronic transport through an interacting quantum dot maintained at finite bias using a concept introduced by Hershfield [S. Hershfield, Phys. Rev. Lett. 70 2134 (1993)] whereby one can express such nonequilibrium quantum impurity models in terms of the system's Lippmann-Schwinger operators. These scattering operators allow one to reformulate the nonequilibrium problem as an effective equilibrium problem associated with a modified Hamiltonian. In this paper, we provide a pedagogical analysis of the core concepts of the effective equilibrium theory. First, we demonstrate the equivalence between observables computed using the Schwinger-Keldysh framework and the effective equilibrium approach, and relate Green's functions in the two theoretical frameworks. Second, we expound some applications of this method in the context of interacting quantum impurity models. We introduce a novel framework to treat effects of interactions perturbatively while capturing the entire dependence on the bias voltage. For the sake of concreteness, we employ the Anderson model as a prototype for this scheme. Working at the particle-hole symmetric point, we investigate the fate of the Abrikosov-Suhl resonance as a function of bias voltage and magnetic field.
Quantum theory of bilayer quantum Hall smectics
NASA Astrophysics Data System (ADS)
Papa, Emiliano; Schliemann, John; MacDonald, A. H.; Fisher, Matthew P.
2003-03-01
Mean-field theory predicts that bilayer quantum Hall systems at odd integer total filling factors can have stripe ground states, in which the top Landau level is occupied alternately by electrons in one of the two layers. We report on an analysis of the properties of these states based on a coupled-Luttinger-liquid description that is able to account for quantum fluctuations of charge-density and position along each stripe edge. The soft modes associated with the broken symmetries of the stripe state lead to an unusual coupled-Luttinger-liquid system with strongly enhanced low-temperature heat capacity and strongly suppressed low-energy tunneling density of states. We assess the importance of the intralayer and interlayer backscattering terms in the microscopic Hamiltonian, which are absent in the Luttinger liquid description, by employing a perturbative renormalization group approach which rescales time and length along but not transverse to the stripes. With interlayer backscattering interactions present the Luttinger-liquid states are unstable either to an incompressible striped state that has spontaneous interlayer phase coherence and a sizable charge gap even at relatively large layer separations, or to Wigner crystal states. Our quantitative estimates of the gaps produced by backscattering interactions are summarized in Fig. 11 by a schematic phase diagram intended to represent predicted experimental findings in very high mobility bilayer systems at dilution refrigerator temperatures as a function of layer separation and bilayer density balance. We predict that the bilayer will form incompressible isotropic interlayer phase-coherent states for small layer separations, say d⩽1.5l. At larger interlayer spacings, however, the bilayer will tend to form one of several different anisotropic states depending on the layer charge balance, which we parametrize by the fractional filling factor ν contributed by one of the two layers. For large charge imbalances (
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
Minimal unitary (covariant) scattering theory
Lindesay, J.V.; Markevich, A.
1983-06-01
In the minimal three particle equations developed by Lindesay the two body input amplitude was an on shell relativistic generalization of the non-relativistic scattering model characterized by a single mass parameter ..mu.. which in the two body (m + m) system looks like an s-channel bound state (..mu.. < 2m) or virtual state (..mu.. > 2m). Using this driving term in covariant Faddeev equations generates a rich covariant and unitary three particle dynamics. However, the simplest way of writing the relativisitic generalization of the Faddeev equations can take the on shell Mandelstam parameter s = 4(q/sup 2/ + m/sup 2/), in terms of which the two particle input is expressed, to negative values in the range of integration required by the dynamics. This problem was met in the original treatment by multiplying the two particle input amplitude by THETA(s). This paper provides what we hope to be a more direct way of meeting the problem.
Noyes, H.P.
1990-01-29
We construct discrete space-time coordinates separated by the Lorentz-invariant intervals h/mc in space and h/mc{sup 2} in time using discrimination (XOR) between pairs of independently generated bit-strings; we prove that if this space is homogeneous and isotropic, it can have only 1, 2 or 3 spacial dimensions once we have related time to a global ordering operator. On this space we construct exact combinatorial expressions for free particle wave functions taking proper account of the interference between indistinguishable alternative paths created by the construction. Because the end-points of the paths are fixed, they specify completed processes; our wave functions are born collapsed''. A convenient way to represent this model is in terms of complex amplitudes whose squares give the probability for a particular set of observable processes to be completed. For distances much greater than h/mc and times much greater than h/mc{sup 2} our wave functions can be approximated by solutions of the free particle Dirac and Klein-Gordon equations. Using a eight-counter paradigm we relate this construction to scattering experiments involving four distinguishable particles, and indicate how this can be used to calculate electromagnetic and weak scattering processes. We derive a non-perturbative formula relating relativistic bound and resonant state energies to mass ratios and coupling constants, equivalent to our earlier derivation of the Bohr relativistic formula for hydrogen. Using the Fermi-Yang model of the pion as a relativistic bound state containing a nucleon-antinucleon pair, we find that (G{sub {pi}N}{sup 2}){sup 2} = (2m{sub N}/m{sub {pi}}){sup 2} {minus} 1. 21 refs., 1 fig.
Gravity and Quantum Theory Unified
NASA Astrophysics Data System (ADS)
Warren, Gary
Historic arguments against Aether theories disappear if the Aether is a 4D compressible hyperfluid in which each particle is our observation of a hypervortex, formed in and comprised of hyperfluid. Such Aether resolves ``spooky action at a distance'' which allows unification of gravity and quantum theory. Light is transverse waves in free space (away from hypervortices) in the hyperfluid. Their detailed behavior is why we observe a curved 3D Lorentz universe - a slice through the 4D hyperverse. Meanwhile, detailed hypervortex behavior, including faster-than-light longitudinal waves in and along hypervortices, explain quantum phenomena. A particular Lagrangian for such a hyperfluid regenerates Maxwell's equations, plus an equation for gravity, and an equation for electric charge. Couplings among these equations generate a discrete spectrum of hypervortex solutions that we observe as a spectrum of particles. Gravity results from gradients in the fluid density near vortices. Observed clock rates depend on fluid density, and vortex motion thus intertwining gravity, clock rates and quantum phenomena. Implied experiments will be discussed.
Quantum Information Theory for Quantum Communication
NASA Astrophysics Data System (ADS)
Koashi, Masato
This chapter gives a concise description of the fundamental concepts of quantum information and quantum communication, which is pertinent to the discussions in the subsequent chapters. Beginning with the basic set of rules that dictate quantum mechanics, the chapter explains the most general ways to describe quantum states, measurements, and state transformations. Convenient mathematical tools are also presented to provide an intuitive picture of a qubit, which is the simplest unit of quantum information. The chapter then elaborates on the distinction between quantum communication and classical communication, with emphasis on the role of quantum entanglement as a communication resource. Quantum teleportation and dense coding are then explained in the context of optimal resource conversions among quantum channels, classical channels, and entanglement.
Collective field theory for quantum Hall states
NASA Astrophysics Data System (ADS)
Laskin, M.; Can, T.; Wiegmann, P.
2015-12-01
We develop a collective field theory for fractional quantum Hall (FQH) states. We show that in the leading approximation for a large number of particles, the properties of Laughlin states are captured by a Gaussian free field theory with a background charge. Gradient corrections to the Gaussian field theory arise from the covariant ultraviolet regularization of the theory, which produces the gravitational anomaly. These corrections are described by a theory closely related to the Liouville theory of quantum gravity. The field theory simplifies the computation of correlation functions in FQH states and makes manifest the effect of quantum anomalies.
Magnetization dissipation in ferromagnets from scattering theory
NASA Astrophysics Data System (ADS)
Brataas, Arne; Tserkovnyak, Yaroslav; Bauer, Gerrit E. W.
2011-08-01
The magnetization dynamics of ferromagnets is often formulated in terms of the Landau-Lifshitz-Gilbert (LLG) equation. The reactive part of this equation describes the response of the magnetization in terms of effective fields, whereas the dissipative part is parametrized by the Gilbert damping tensor. We formulate a scattering theory for the magnetization dynamics and map this description on the linearized LLG equation by attaching electric contacts to the ferromagnet. The reactive part can then be expressed in terms of the static scattering matrix. The dissipative contribution to the low-frequency magnetization dynamics can be described as an adiabatic energy pumping process to the electronic subsystem by the time-dependent magnetization. The Gilbert damping tensor depends on the time derivative of the scattering matrix as a function of the magnetization direction. By the fluctuation-dissipation theorem, the fluctuations of the effective fields can also be formulated in terms of the quasistatic scattering matrix. The theory is formulated for general magnetization textures and worked out for monodomain precessions and domain-wall motions. We prove that the Gilbert damping from scattering theory is identical to the result obtained by the Kubo formalism.
Effective string theory and QCD scattering amplitudes
Makeenko, Yuri
2011-01-15
QCD string is formed at distances larger than the confinement scale and can be described by the Polchinski-Strominger effective string theory with a nonpolynomial action, which has nevertheless a well-defined semiclassical expansion around a long-string ground state. We utilize modern ideas about the Wilson-loop/scattering-amplitude duality to calculate scattering amplitudes and show that the expansion parameter in the effective string theory is small in the Regge kinematical regime. For the amplitudes we obtain the Regge behavior with a linear trajectory of the intercept (d-2)/24 in d dimensions, which is computed semiclassically as a momentum-space Luescher term, and discuss an application to meson scattering amplitudes in QCD.
Quantum field perturbation theory revisited
NASA Astrophysics Data System (ADS)
Matone, Marco
2016-03-01
Schwinger's formalism in quantum field theory can be easily implemented in the case of scalar theories in D dimension with exponential interactions, such as μDexp (α ϕ ). In particular, we use the relation exp (α δ/δ J (x ) )exp (-Z0[J ])=exp (-Z0[J +αx]) with J the external source, and αx(y )=α δ (y -x ). Such a shift is strictly related to the normal ordering of exp (α ϕ ) and to a scaling relation which follows by renormalizing μ . Next, we derive a new formulation of perturbation theory for the potentials V (ϕ )=λ/n ! :ϕn: , using the generating functional associated to :exp (α ϕ ):. The Δ (0 )-terms related to the normal ordering are absorbed at once. The functional derivatives with respect to J to compute the generating functional are replaced by ordinary derivatives with respect to auxiliary parameters. We focus on scalar theories, but the method is general and similar investigations extend to other theories.
Scattering theory for Floquet-Bloch states
NASA Astrophysics Data System (ADS)
Bilitewski, Thomas; Cooper, Nigel R.
2015-03-01
Motivated by recent experimental implementations of artificial gauge fields for gases of cold atoms, we study the scattering properties of particles that are subjected to time-periodic Hamiltonians. Making use of Floquet theory, we focus on translationally invariant situations in which the single-particle dynamics can be described in terms of spatially extended Floquet-Bloch waves. We develop a general formalism for the scattering of these Floquet-Bloch waves. An important role is played by the conservation of Floquet quasienergy, which is defined only up to the addition of integer multiples of ℏ ω for a Hamiltonian with period T =2 π /ω . We discuss the consequences of this for the interpretation of "elastic" and "inelastic" scattering in cases of physical interest. We illustrate our general results with applications to the scattering of a single particle in a Floquet-Bloch state from a static potential and the scattering of two bosonic particles in Floquet-Bloch states through their interparticle interaction. We analyze examples of these scattering processes that are closely related to the schemes used to generate artificial gauge fields in cold-atom experiments, through optical dressing of internal states, or through time-periodic modulations of tight-binding lattices. We show that the effects of scattering cannot, in general, be understood by an effective time-independent Hamiltonian, even in the limit ω →∞ of rapid modulation. We discuss the relative sizes of the elastic scattering (required to stabilize many-body phases) and of the inelastic scattering (leading to deleterious heating effects). In particular, we describe how inelastic processes that can cause significant heating in the current experimental setup can be switched off by additional confinement of transverse motion.
Quantum theory of Manakov solitons
Rand, Darren; Prucnal, Paul R.; Steiglitz, Ken
2005-05-15
A fully quantum mechanical model of two-component Manakov solitons is developed in both the Heisenberg and Schroedinger representations, followed by an analytical, linearized quantum theory of Manakov solitons in the Heisenberg picture. This theory is used to analyze the vacuum-induced fluctuations of Manakov soliton propagation and collision. The vacuum fluctuations induce phase diffusion and dispersion in Manakov soliton propagation. Calculations of the position, polarization angle, and polarization state fluctuations show an increase in collision-induced noise with a decrease in the relative velocity between the two solitons, as expected because of an increase in the interaction length. Fluctuations in both the polarization angle and state are shown to be independent of propagation distance, opening up possibilities for communications, switching, and logic, exploiting these properties of Manakov solitons. Calculations of the phase noise reveal, surprisingly, that the collision-induced fluctuations can be reduced slightly below the level of fluctuations in the absence of collision, due to cross-correlation effects between the collision-induced phase and amplitude fluctuations of the soliton. The squeezing effect of Manakov solitons is also studied and proven, unexpectedly, to have the same theoretical optimum as scalar solitons.
Surface-integral formulation of scattering theory
Kadyrov, A.S. Bray, I.; Mukhamedzhanov, A.M.; Stelbovics, A.T.
2009-07-15
We formulate scattering theory in the framework of a surface-integral approach utilizing analytically known asymptotic forms of the two-body and three-body scattering wavefunctions. This formulation is valid for both short-range and long-range Coulombic interactions. New general definitions for the potential scattering amplitude are presented. For the Coulombic potentials, the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure. New post and prior forms for the Coulomb three-body breakup amplitude are derived. This resolves the problem of the inability of the conventional scattering theory to define the post form of the breakup amplitude for charged particles. The new definitions can be written as surface-integrals convenient for practical calculations. The surface-integral representations are extended to amplitudes of direct and rearrangement scattering processes taking place in an arbitrary three-body system. General definitions for the wave operators are given that unify the currently used channel-dependent definitions.
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.
Theory of Multiple Coulomb Scattering from Extended Nuclei
DOE R&D Accomplishments Database
Cooper, L. N.; Rainwater, J.
1954-08-01
Two independent methods are described for calculating the multiple scattering distribution for projected angle scattering resulting when very high energy charged particles traverse a thick scatterer. The results are compared with the theories of Moliere and Olbert.
Space--Time from Topos Quantum Theory
NASA Astrophysics Data System (ADS)
Flori, Cecilia
One of the main challenges in theoretical physics in the past 50 years has been to define a theory of quantum gravity, i.e. a theory which consistently combines general relativity and quantum theory in order to define a theory of space-time itself seen as a fluctuating field. As such, a definition of space-time is of paramount importance, but it is precisely the attainment of such a definition which is one of the main stumbling blocks in quantum gravity. One of the striking features of quantum gravity is that although both general relativity and quantum theory treat space-time as a four-dimensional (4D) manifold equipped with a metric, quantum gravity would suggest that, at the microscopic scale, space-time is somewhat discrete. Therefore the continuum structure of space-time suggested by the two main ingredients of quantum gravity seems to be thrown into discussion by quantum gravity itself. This seems quite an odd predicament, but it might suggest that perhaps a different mathematical structure other than a smooth manifold should model space-time. These considerations seem to shed doubts on the use of the continuum in general in a possible theory of quantum gravity. An alternative would be to develop a mathematical formalism for quantum gravity in which no fundamental role is played by the continuum and where a new concept of space-time, not modeled on a differentiable manifold, will emerge. This is precisely one of the aims of the topos theory approach to quantum theory and quantum gravity put forward by Isham, Butterfield, and Doering and subsequently developed by other authors. The aim of this article is to precisely elucidate how such an approach gives rise to a new definition of space-time which might be more appropriate for quantum gravity.
Uncertainty relation revisited from quantum estimation theory
Watanabe, Yu; Sagawa, Takahiro; Ueda, Masahito
2011-10-15
We use quantum estimation theory to formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two noncommuting observables satisfy Heisenberg-type uncertainty relation, find the achievable bound, and propose a strategy to achieve it.
VLF scattering from Red Sprites-Theory
NASA Astrophysics Data System (ADS)
Rodger, C. J.; Wait, J. R.; Dowden, R. L.
1998-05-01
A relatively simple model of Red Sprites as a set of conducting columns reproduces the radio physics properties of VLF sprites. The columnar structure of optical sprites is represented by thin vertical conducting columns (or `Spritelets') in free space, with dimensions taken from optical observations. The scattered field from a set of coupled Spritelets has a complex amplitude pattern which normally includes some deep minima reproducing the `perturbation shadows' seen in some experimental events. It is not uncommon for the back scattered amplitudes to be similar to those for forward scatter in the theoretical model, as in experimental reports. As some sprite events appear to have closely spaced Spritelets, the results presented here indicate that there will be a high degree of electrical shielding. This is an application of the theory presented by[Rodger et al. (1997a)].
Multiscale quantum simulation of quantum field theory using wavelets
NASA Astrophysics Data System (ADS)
Brennen, Gavin K.; Rohde, Peter; Sanders, Barry C.; Singh, Sukhwinder
2015-09-01
A successful approach to understand field theories is to resolve the physics into different length or energy scales using the renormalization group framework. We propose a quantum simulation of quantum field theory which encodes field degrees of freedom in a wavelet basis—a multiscale description of the theory. Since wavelet families can be constructed to have compact support at all resolutions, this encoding allows for quantum simulations to create particle excitations which are local at some chosen scale and provides a natural way to associate observables in the theory to finite-resolution detectors.
Whiteheadian process and quantum theory
Stapp, H.
1998-08-01
There are deep similarities between Whitehead's idea of the process by which nature unfolds and the ideas of quantum theory. Whitehead says that the world is made of ''actual occasions'', each of which arises from potentialities created by prior actual occasions. These actual occasions are happenings modeled on experiential events, each of which comes into being and then perishes, only to be replaced by a successor. It is these experience-like happenings that are the basic realities of nature, according to Whitehead, not the persisting physical particles that Newtonian physics took be the basic entities. Similarly, Heisenberg says that what is really happening in a quantum process is the emergence of an actual from potentialities created by prior actualities. In the orthodox Copenhagen interpretation of quantum theory the actual things to which the theory refer are increments in ''our knowledge''. These increments are experiential events. The particles of classical physics lose their fundamental status: they dissolve into diffuse clouds of possibilities. At each stage of the unfolding of nature the complete cloud of possibilities acts like the potentiality for the occurrence of a next increment in knowledge, whose occurrence can radically change the cloud of possibilities/potentialities for the still-later increments in knowledge. The fundamental difference between these ideas about nature and the classical ideas that reigned from the time of Newton until this century concerns the status of the experiential aspects of nature. These are things such as thoughts, ideas, feelings, and sensations. They are distinguished from the physical aspects of nature, which are described in terms of quantities explicitly located in tiny regions of space and time. According to the ideas of classical physics the physical world is made up exclusively of things of this latter type, and the unfolding of the physical world is determined by causal connections involving only these things
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 Theory of Laser Amplifiers.
NASA Astrophysics Data System (ADS)
Mander, Gillian Linda
Available from UMI in association with The British Library. Requires signed TDF. We calculate the input-output characteristics of a below threshold laser amplifier. Expressions are derived for the output second- and fourth-order spectral and temporal correlation functions in terms of the corresponding input quantities, and for the photocount first and second factorial moments for both homodyne and direct detection. The general results are applied to several cases of practical interest, including specific non-classical input states. We show that a maximum of twofold amplification is permitted if squeezing in the input is to survive at the output. Similarly, for preservation of photon antibunching in amplification we show that only very small gains are allowed. The model treated here provides a detailed example of the amplifier noise limitations imposed by quantum mechanics. In particular, we show that minimum noise occurs in a cavity that is asymmetric with respect to the mirror reflectivities. The latter part of this work treats the above threshold laser amplifier. The laser output is back-scattered from a moving target to provide a weak Doppler-shifted signal which re-enters the laser cavity and is amplified. We show that the three-level atomic lasing medium is equivalent to a two-level medium pumped by an inverted bath. We use the methods of quantum statistical analysis to obtain time -evolution equations for the c-number amplitudes of the laser and signal fields. We show that the results may be applied to the below threshold regime for appropriate values of the pump parameter. By considering the amplitude differential gain we show explicitly that the behaviour of the laser around threshold is characteristic of a second -order phase transition. We calculate the output intensity gain appropriate to a heterodyne detection process, and find good agreement between the predicted gain profiles and measured data for both carbon dioxide and argon-ion lasers.
Nuclear Quantum Gravitation - The Correct Theory
NASA Astrophysics Data System (ADS)
Kotas, Ronald
2016-03-01
Nuclear Quantum Gravitation provides a clear, definitive Scientific explanation of Gravity and Gravitation. It is harmonious with Newtonian and Quantum Mechanics, and with distinct Scientific Logic. Nuclear Quantum Gravitation has 10 certain, Scientific proofs and 21 more good indications. With this theory the Physical Forces are obviously Unified. See: OBSCURANTISM ON EINSTEIN GRAVITATION? http://www.santilli- Foundation.org/inconsistencies-gravitation.php and Einstein's Theory of Relativity versus Classical Mechanics http://www.newtonphysics.on.ca/einstein/
Multiloop calculations in perturbative quantum field theory
NASA Astrophysics Data System (ADS)
Blokland, Ian Richard
This thesis deals with high-precision calculations in perturbative quantum field theory. In conjunction with detailed experimental measurements, perturbative quantum field theory provides the quantitative framework with which much of modern particle physics is understood. The results of three new theoretical calculations are presented. The first is a definitive resolution of a recent controversy involving the interaction of a muon with a magnetic field. Specifically, the light-by-light scattering contribution to the anomalous magnetic moment of the muon is shown to be of positive sign, thereby decreasing the discrepancy between theory and experiment. Despite this adjustment to the theoretical prediction, the remaining discrepancy might be a subtle signature of new kinds of particles. The second calculation involves the energy levels of a bound state formed from two charged particles of arbitrary masses. By employing recently developed mass expansion techniques, new classes of solutions are obtained for problems in a field of particle physics with a very rich history. The third calculation provides an improved prediction for the decay of a top quark. In order to obtain this result, a large class of multiloop integrals has been solved for the first time. Top quark decay is just one member of a family of interesting physical processes to which these new results apply. Since specialized calculational techniques are essential ingredients in all three calculations, they are motivated and explained carefully in this thesis. These techniques, once automated with symbolic computational software, have recently opened avenues of solution to a wide variety of important problems in particle physics.
Free Quantum Field Theory from Quantum Cellular Automata
NASA Astrophysics Data System (ADS)
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo; Tosini, Alessandro
2015-10-01
After leading to a new axiomatic derivation of quantum theory (see D'Ariano et al. in Found Phys, 2015), the new informational paradigm is entering the domain of quantum field theory, suggesting a quantum automata framework that can be regarded as an extension of quantum field theory to including an hypothetical Planck scale, and with the usual quantum field theory recovered in the relativistic limit of small wave-vectors. Being derived from simple principles (linearity, unitarity, locality, homogeneity, isotropy, and minimality of dimension), the automata theory is quantum ab-initio, and does not assume Lorentz covariance and mechanical notions. Being discrete it can describe localized states and measurements (unmanageable by quantum field theory), solving all the issues plaguing field theory originated from the continuum. These features make the theory an ideal framework for quantum gravity, with relativistic covariance and space-time emergent solely from the interactions, and not assumed a priori. The paper presents a synthetic derivation of the automata theory, showing how the principles lead to a description in terms of a quantum automaton over a Cayley graph of a group. Restricting to Abelian groups we show how the automata recover the Weyl, Dirac and Maxwell dynamics in the relativistic limit. We conclude with some new routes about the more general scenario of non-Abelian Cayley graphs. The phenomenology arising from the automata theory in the ultra-relativistic domain and the analysis of corresponding distorted Lorentz covariance is reviewed in Bisio et al. (Found Phys 2015, in this same issue).
Generalized Rayleigh scattering. I. Basic theory.
NASA Astrophysics Data System (ADS)
Ivanov, V. V.
1995-11-01
The classsical problem of multiple molecular (in particular, Rayleigh) scattering in plane-parallel atmospheres is considered from a somewhat broader viewpoint than usual. The general approach and ideology are borrowed from non-LTE line formation theory. The main emphasis is on the depth dependence of the corresponding source matrix rather than on the emergent radiation. We study the azimuth-averaged radiation field of polarized radiation in a semi-infinite atmosphere with embedded primary sources. The corresponding 2x2 phase matrix of molecular scattering is P=(1-W) P_I_+W P_R_, where P_I_ and P_R_ are the phase matrices of the scalar isotropic scattering and of the Rayleigh scattering, respectively, and W is the depolarization parameter. Contrary to the usual assumption that W{in}[0,1], we assume W{in} [0,{infinity}) and call this generalized Rayleigh scattering (GRS). Using the factorization of P which is intimately related to its diadic expansion, we reduce the problem to an integral equation for the source matrix S(τ) with a matrix displacement kernel. In operator form this equation is S={LAMBDA}S+S^*^, where {LAMBDA} is the matrix {LAMBDA}-operator and S^*^ is the primary source term. This leads to a new concept, the matrix albedo of single scattering λ =diag(λ_I_,λ_Q_), where λ_I_ is the usual (scalar) single scattering albedo and λ_Q_=0.7Wλ_I_. Its use enables one to formulate matrix equivalents of many of the results of the scalar theory in exactly the same form as in the scalar case. Of crucial importance is the matrix equivalent of the sqrt(ɛ) law of the scalar theory. Another useful new concept is the λ-plane, i.e., the plane with the axes (λ_I_,λ_Q_). Systematic use of the matrix sqrt(ɛ) law and of the λ-plane proved to be a useful instrument in classifying various limiting and particular cases of GRS and in discussing numerical data on the matrix source functions (to be given in Paper II of the series).
Reconstruction and Reinvention in Quantum Theory
NASA Astrophysics Data System (ADS)
Dickson, Michael
2015-10-01
I consider the fact that there are a number of interesting ways to `reconstruct' quantum theory, and suggest that, very broadly speaking, a form of `instrumentalism' makes good sense of the situation. This view runs against some common wisdom, which dismisses instrumentalism as `cheap'. In contrast, I consider how an instrumentalist might think about the reconstruction theorems, and, having made a distinction between `reconstructing' quantum theory and `reinventing' quantum theory, I suggest that there is an adequate (not `cheap') instrumentalist approach to the theory (and to these theorems) that invokes both.
Quantum Probability Theory and the Foundations of Quantum Mechanics
NASA Astrophysics Data System (ADS)
Fröhlich, Jürg; Schubnel, Baptiste
By and large, people are better at coining expressions than at filling them with interesting, concrete contents. Thus, it may not be very surprising that there are many professional probabilists who may have heard the expression but do not appear to be aware of the need to develop "quantum probability theory" into a thriving, rich, useful field featured at meetings and conferences on probability theory. Although our aim, in this essay, is not to contribute new results on quantum probability theory, we hope to be able to let the reader feel the enormous potential and richness of this field. What we intend to do, in the following, is to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras).
Theory of scattering by complex potentials
Thylwe, K.; Froeman, N.
1983-10-15
The scattering problem for a non-relativistic spinless particle under the influence of a complex effective potential, which is spherically symmetric and tends to zero faster than 1/r at infinity, is considered. Certain general relations, which illuminate the influence of the imaginary part of the potential on the scattering process, are derived with the use of the expression for the probability current density. The rigorous phase-integral method developed by N. Froeman and P. O. Froeman is used for obtaining an exact, general formula for the scattering matrix, or equivalently, for the phase shift. The formula is expressed in terms of phase-integral approximations of an arbitrary order and certain quantities defined by convergent series. Estimating the latter quantities and omitting small corrections, an approximate formula is derived for the phase shift, valid for the case that only one complex turning point contributes essentially to the phase shift. Criteria for classifying a scattering problem as such a one-turning-point problem are given. The treatment is made general enough to also cover situations of interest in Regge-pole or complex angular momentum theory.
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.
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 general theory of quantum relativity
NASA Astrophysics Data System (ADS)
Minic, Djordje; Tze, Chia-Hsiung
2004-02-01
The geometric form of standard quantum mechanics is compatible with the two postulates: (1) the laws of physics are invariant under the choice of experimental setup and (2) every quantum observation or event is intrinsically statistical. These postulates remain compatible within a background independent extension of quantum theory with a local intrinsic time implying the relativity of the concept of a quantum event. In this extension the space of quantum events becomes dynamical and only individual quantum events make sense observationally. At the core of such a general theory of quantum relativity is the three-way interplay between the symplectic form, the dynamical metric and non-integrable almost complex structure of the space of quantum events. Such a formulation provides a missing conceptual ingredient in the search for a background independent quantum theory of gravity and matter. The crucial new technical element in our scheme derives from a set of recent mathematical results on certain infinite-dimensional almost Kahler manifolds which replace the complex projective spaces of standard quantum mechanics.
Asymptotic theory of quantum statistical inference
NASA Astrophysics Data System (ADS)
Hayashi, Masahito
Part I: Hypothesis Testing: Introduction to Part I -- Strong Converse and Stein's lemma in quantum hypothesis testing/Tomohiro Ogawa and Hiroshi Nagaoka -- The proper formula for relative entropy and its asymptotics in quantum probability/Fumio Hiai and Dénes Petz -- Strong Converse theorems in Quantum Information Theory/Hiroshi Nagaoka -- Asymptotics of quantum relative entropy from a representation theoretical viewpoint/Masahito Hayashi -- Quantum birthday problems: geometrical aspects of Quantum Random Coding/Akio Fujiwara -- Part II: Quantum Cramèr-Rao Bound in Mixed States Model: Introduction to Part II -- A new approach to Cramèr-Rao Bounds for quantum state estimation/Hiroshi Nagaoka -- On Fisher information of Quantum Statistical Models/Hiroshi Nagaoka -- On the parameter estimation problem for Quantum Statistical Models/Hiroshi Nagaoka -- A generalization of the simultaneous diagonalization of Hermitian matrices and its relation to Quantum Estimation Theory/Hiroshi Nagaoka -- A linear programming approach to Attainable Cramèr-Rao Type Bounds/Masahito Hayashi -- Statistical model with measurement degree of freedom and quantum physics/Masahito Hayashi and Keiji Matsumoto -- Asymptotic Quantum Theory for the Thermal States Family/Masahito Hayashi -- State estimation for large ensembles/Richard D. Gill and Serge Massar -- Part III: Quantum Cramèr-Rao Bound in Pure States Model: Introduction to Part III-- Quantum Fisher Metric and estimation for Pure State Models/Akio Fujiwara and Hiroshi Nagaoka -- Geometry of Quantum Estimation Theory/Akio Fujiwara -- An estimation theoretical characterization of coherent states/Akio Fujiwara and Hiroshi Nagaoka -- A geometrical approach to Quantum Estimation Theory/Keiji Matsumoto -- Part IV: Group symmetric approach to Pure States Model: Introduction to Part IV -- Optimal extraction of information from finite quantum ensembles/Serge Massar and Sandu Popescu -- Asymptotic Estimation Theory for a Finite-Dimensional Pure
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
Teaching Quantum Theory in the Introductory Course.
ERIC Educational Resources Information Center
Hobson, Art
1996-01-01
Describes an approach to teaching quantum theory without math with emphasis on some innovative approaches and topics such as nonlocality and Bell's theorem. Written in the form of suggestions to prospective instructors. (JRH)
Effective theories for dark matter nucleon scattering
NASA Astrophysics Data System (ADS)
Hisano, Junji; Nagai, Ryo; Nagata, Natsumi
2015-05-01
We reformulate the calculation of the dark matter-nucleon scattering cross sections based on the method of effective field theories. We assume that the scatterings are induced by the exchange of colored mediators, and construct the effective theories by integrating out the colored particles. All of the leading order matching conditions as well as the renormalization group equations are presented. We consider a Majorana fermion, and real scalar and vector bosons for the dark matter and show the results for each case. The treatment for the twist-2 operators is discussed in detail, and it is shown that the scale of evaluating their nucleon matrix elements does not have to be the hadronic scale. The effects of the QCD corrections are evaluated on the assumption that the masses of the colored mediators are much heavier than the electroweak scale. Our formulation is systematic and model-independent, and thus suitable to be implemented in numerical packages, such as micrOMEGAs and DarkSUSY.
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.
Quantum theory - essential from cosmos to consciousness
NASA Astrophysics Data System (ADS)
Görnitz, T.
2010-06-01
Quantum theory is the most successful physical theory. About one third of the gross national product in the developed countries results from its applications. But very often quantum theory is still declared as "crazy" or "not understandable". However, quantum theory has a clear mathematical structure that expresses well-known experiences from every day life: A whole is often more than the sum of its parts, and not only the facts also the possibilities can act. If such structures become important then the consequences differ from the models of classical physics which rests on the fundamental differences between matter and motion, material and force, localization and extension, fullness and emptiness. From quantum theory one can learn that all these differences are useful in many cases but are not fundamental. There are equivalences between them, and these can be extended even to the equivalence between matter, energy and abstract quantum information. It is cosmological funded and is denominated as "Protyposis" to avoid the connotation of information and meaning. Protyposis enables a fundamentally new understanding of matter which can be seen as "formed", "condensed" or "designed" abstract quantum information. One result of the Protyposis is a derivation of Einstein's equations from the abstract quantum information. Another consequence is the ontological reality of the mind and its connection to a brain which can be explained without any dualistic model.
Geometric continuum regularization of quantum field theory
Halpern, M.B. . Dept. of Physics)
1989-11-08
An overview of the continuum regularization program is given. The program is traced from its roots in stochastic quantization, with emphasis on the examples of regularized gauge theory, the regularized general nonlinear sigma model and regularized quantum gravity. In its coordinate-invariant form, the regularization is seen as entirely geometric: only the supermetric on field deformations is regularized, and the prescription provides universal nonperturbative invariant continuum regularization across all quantum field theory. 54 refs.
A supersymmetric extension of quantum gauge theory
NASA Astrophysics Data System (ADS)
Grigore, D. R.; Scharf, G.
2003-01-01
We consider a supersymmetric extension of quantum gauge theory based on a vector multiplet containing supersymmetric partners of spin 3/2 for the vector fields. The constructions of the model follows closely the usual construction of gauge models in the Epstein-Glaser framework for perturbative field theory. Accordingly, all the arguments are completely of quantum nature without reference to a classical supersymmetric theory. As an application we consider the supersymmetric electroweak theory. The resulting self-couplings of the gauge bosons agree with the standard model up to a divergence.
The Nature of Quantum Truth: Logic, Set Theory, & Mathematics in the Context of Quantum Theory
NASA Astrophysics Data System (ADS)
Frey, Kimberly
The purpose of this dissertation is to construct a radically new type of mathematics whose underlying logic differs from the ordinary classical logic used in standard mathematics, and which we feel may be more natural for applications in quantum mechanics. Specifically, we begin by constructing a first order quantum logic, the development of which closely parallels that of ordinary (classical) first order logic --- the essential differences are in the nature of the logical axioms, which, in our construction, are motivated by quantum theory. After showing that the axiomatic first order logic we develop is sound and complete (with respect to a particular class of models), this logic is then used as a foundation on which to build (axiomatic) mathematical systems --- and we refer to the resulting new mathematics as "quantum mathematics." As noted above, the hope is that this form of mathematics is more natural than classical mathematics for the description of quantum systems, and will enable us to address some foundational aspects of quantum theory which are still troublesome --- e.g. the measurement problem --- as well as possibly even inform our thinking about quantum gravity. After constructing the underlying logic, we investigate properties of several mathematical systems --- e.g. axiom systems for abstract algebras, group theory, linear algebra, etc. --- in the presence of this quantum logic. In the process, we demonstrate that the resulting quantum mathematical systems have some strange, but very interesting features, which indicates a richness in the structure of mathematics that is classically inaccessible. Moreover, some of these features do indeed suggest possible applications to foundational questions in quantum theory. We continue our investigation of quantum mathematics by constructing an axiomatic quantum set theory, which we show satisfies certain desirable criteria. Ultimately, we hope that such a set theory will lead to a foundation for quantum
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.
The decoupling approach to quantum information theory
NASA Astrophysics Data System (ADS)
Dupuis, Frédéric
2010-04-01
Quantum information theory studies the fundamental limits that physical laws impose on information processing tasks such as data compression and data transmission on noisy channels. This thesis presents general techniques that allow one to solve many fundamental problems of quantum information theory in a unified framework. The central theorem of this thesis proves the existence of a protocol that transmits quantum data that is partially known to the receiver through a single use of an arbitrary noisy quantum channel. In addition to the intrinsic interest of this problem, this theorem has as immediate corollaries several central theorems of quantum information theory. The following chapters use this theorem to prove the existence of new protocols for two other types of quantum channels, namely quantum broadcast channels and quantum channels with side information at the transmitter. These protocols also involve sending quantum information partially known by the receiver with a single use of the channel, and have as corollaries entanglement-assisted and unassisted asymptotic coding theorems. The entanglement-assisted asymptotic versions can, in both cases, be considered as quantum versions of the best coding theorems known for the classical versions of these problems. The last chapter deals with a purely quantum phenomenon called locking. We demonstrate that it is possible to encode a classical message into a quantum state such that, by removing a subsystem of logarithmic size with respect to its total size, no measurement can have significant correlations with the message. The message is therefore "locked" by a logarithmic-size key. This thesis presents the first locking protocol for which the success criterion is that the trace distance between the joint distribution of the message and the measurement result and the product of their marginals be sufficiently small.
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.
Generalizing Prototype Theory: A Formal Quantum Framework.
Aerts, Diederik; Broekaert, Jan; Gabora, Liane; Sozzo, Sandro
2016-01-01
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper. PMID:27065436
The facets of relativistic quantum field theory
NASA Astrophysics Data System (ADS)
Dosch, H. G.; Müller, V. F.
2010-04-01
Relativistic quantum field theory is generally recognized to form the adequate theoretical frame for subatomic physics, with the Standard Model of Particle Physics as a major achievement. We point out that quantum field theory in its present form is not a monolithic theory, but rather consists of distinct facets, which aim at a common ideal goal. We give a short overview of the strengths and limitations of these facets. We emphasize the theory-dependent relation between the quantum fields, and the basic objects in the empirical domain, the particles. Given the marked conceptual differences between the facets, we argue to view these, and therefore also the Standard Model, as symbolic constructions. We finally note that this view of physical theories originated in the 19th century and is related to the emergence of the classical field as an autonomous concept.
The facets of relativistic quantum field theory
NASA Astrophysics Data System (ADS)
Dosch, H. G.; Müller, V. F.
2011-04-01
Relativistic quantum field theory is generally recognized to form the adequate theoretical frame for subatomic physics, with the Standard Model of Particle Physics as a major achievement. We point out that quantum field theory in its present form is not a monolithic theory, but rather consists of distinct facets, which aim at a common ideal goal. We give a short overview of the strengths and limitations of these facets. We emphasize the theory-dependent relation between the quantum fields, and the basic objects in the empirical domain, the particles. Given the marked conceptual differences between the facets, we argue to view these, and therefore also the Standard Model, as symbolic constructions. We finally note that this view of physical theories originated in the 19th century and is related to the emergence of the classical field as an autonomous concept.
Generalizing Prototype Theory: A Formal Quantum Framework
Aerts, Diederik; Broekaert, Jan; Gabora, Liane; Sozzo, Sandro
2016-01-01
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has instead been successful in capturing these phenomena such as graded membership, situational meaning, composition of categories, and also more complex decision making situations, which cannot be modeled in traditional probabilistic approaches. We show how a formal quantum approach to concepts and their combinations can provide a powerful extension of prototype theory. We explain how prototypes can interfere in conceptual combinations as a consequence of their contextual interactions, and provide an illustration of this using an intuitive wave-like diagram. This quantum-conceptual approach gives new life to original prototype theory, without however making it a privileged concept theory, as we explain at the end of our paper. PMID:27065436
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.
Toward a physical theory of quantum cognition.
Takahashi, Taiki
2014-01-01
Recently, mathematical models based on quantum formalism have been developed in cognitive science. The target articles in this special issue of Topics in Cognitive Science clearly illustrate how quantum theoretical formalism can account for various aspects of human judgment and decision making in a quantitatively and mathematically rigorous manner. In this commentary, we show how future studies in quantum cognition and decision making should be developed to establish theoretical foundations based on physical theory, by introducing Taketani's three-stage theory of the development of science. Also, implications for neuroeconomics (another rapidly evolving approach to human judgment and decision making) are discussed. PMID:24482329
Categorical aspects of reconstructing quantum theory
NASA Astrophysics Data System (ADS)
Lal, Raymond; Coecke, Bob
2012-02-01
We present steps towards a new understanding of reconstructions of quantum theory. Chiribella, D'Ariano, and Perinotti (CDP) have recently produced a fascinating reconstruction of the formalism of quantum theory, which brings to light its operational origins. We use parts of the formalism of categorical quantum mechanics to expose the underlying mathematical structures of information flow in the CDP reconstruction. Our results include an elegant relation between teleportation and local tomography, and an equivalence betweeen a purely category-theoretic description of the purification of a mixed state, and the purification axiom of CDP.
Tests of alternative quantum theories with neutrons
Sponar, S.; Durstberger-Rennhofer, K.; Badurek, G.; Hasegawa, Y.; Klepp, J.; Schmitzer, C.; Bartosik, H.
2014-12-04
According to Bell’s theorem, every theory based on local realism is at variance with certain predictions of quantum mechanics. A theory that maintains realism but abandons reliance on locality, which has been proposed by Leggett, is incompatible with experimentally observable quantum correlations. In our experiment correlation measurements of spin-energy entangled single-neutrons violate a Leggett-type inequality by more than 7.6 standard deviations. The experimental data falsify the contextual realistic model and are fully in favor of quantum mechanics.
α∗-cohomology, and classification of translation-invariant non-commutative quantum field theories
NASA Astrophysics Data System (ADS)
Varshovi, Amir Abbass
2014-09-01
Translation-invariant ⋆ products are studied in the setting of α∗-cohomology. It is explicitly shown that all quantum behaviors including Green's functions and the scattering matrix of translation-invariant non-commutative quantum field theories are thoroughly characterized by α∗-cohomology classes of the star products.
Inelastic neutron scattering studies of novel quantum magnets
NASA Astrophysics Data System (ADS)
Plumb, Kemp W.
excitations. Dynamic spin correlations in BiCu 2PO6 are the quantum analog of the incommensurate spiral order that appears in classical frustrated magnets and the dispersion minimum occurs at an incommensurate wavevector with a gap of Delta1 = 1.67(2) meV. Neutron scattering measurements in applied magnetic field show that the triplon degeneracy in zero field is completely broken by anisotropic magnetic interactions and each branch was observed to exhibit an anomalous Zeeman behavior. The lowest energy excitation spectrum and anomalous Zeeman splitting is captured by a bond-operator theory, incorporating very significant anisotropic magnetic exchange interactions. At high energies, we have also observed a continuum of two-triplon scattering and a unique two-triplon bound state excitation. Anharmonic terms in the magnetic Hamiltonian of BiCu2PO6 result in a spectacular spontaneous decay of the triplon quasiparticles.
Quantum Theory of Atomic and Molecular Structures and Interactions
NASA Astrophysics Data System (ADS)
Makrides, Constantinos
This dissertation consists of topics in two related areas of research that together provide quantum mechanical descriptions of atomic and molecular interactions and reactions. The first is the ab initio electronic structure calculation that provides the atomic and molecular interaction potential, including the long-range potential. The second is the quantum theory of interactions that uses such potentials to understand scattering, long-range molecules, and reactions. In ab initio electronic structure calculations, we present results of dynamic polarizabilities for a variety of atoms and molecules, and the long-range dispersion coefficients for a number of atom-atom and atom-molecule cases. We also present results of a potential energy surface for the triatomic lithium-ytterbium-lithium system, aimed at understanding the related chemical reactions. In the quantum theory of interactions, we present a multichannel quantum-defect theory (MQDT) for atomic interactions in a magnetic field. This subject, which is complex especially for atoms with hyperfine structure, is essential for the understanding and the realization of control and tuning of atomic interactions by a magnetic field: a key feature that has popularized cold atom physics in its investigations of few-body and many-body quantum systems. Through the example of LiK, we show how MQDT provides a systematic and an efficient understanding of atomic interaction in a magnetic field, especially magnetic Feshbach resonances in nonzero partial waves.
Relativistic Quantum Mechanics and Field Theory
NASA Astrophysics Data System (ADS)
Gross, Franz
1999-04-01
An accessible, comprehensive reference to modern quantum mechanics and field theory. In surveying available books on advanced quantum mechanics and field theory, Franz Gross determined that while established books were outdated, newer titles tended to focus on recent developments and disregard the basics. Relativistic Quantum Mechanics and Field Theory fills this striking gap in the field. With a strong emphasis on applications to practical problems as well as calculations, Dr. Gross provides complete, up-to-date coverage of both elementary and advanced topics essential for a well-rounded understanding of the field. Developing the material at a level accessible even to newcomers to quantum mechanics, the book begins with topics that every physicist should know-quantization of the electromagnetic field, relativistic one body wave equations, and the theoretical explanation of atomic decay. Subsequent chapters prepare readers for advanced work, covering such major topics as gauge theories, path integral techniques, spontaneous symmetry breaking, and an introduction to QCD, chiral symmetry, and the Standard Model. A special chapter is devoted to relativistic bound state wave equations-an important topic that is often overlooked in other books. Clear and concise throughout, Relativistic Quantum Mechanics and Field Theory boasts examples from atomic and nuclear physics as well as particle physics, and includes appendices with background material. It is an essential reference for anyone working in quantum mechanics today.
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.
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.
Quantum theory of laser-stimulated desorption
NASA Technical Reports Server (NTRS)
Slutsky, M. S.; George, T. F.
1978-01-01
A quantum theory of laser-stimulated desorption (LSDE) is presented and critically analyzed. It is shown how LSDE depends on laser-pulse characteristics and surface-lattice dynamics. Predictions of the theory for a Debye model of the lattice dynamics are compared to recent experimental results.
Dual field theories of quantum computation
NASA Astrophysics Data System (ADS)
Vanchurin, Vitaly
2016-06-01
Given two quantum states of N q-bits we are interested to find the shortest quantum circuit consisting of only one- and two- q-bit gates that would transfer one state into another. We call it the quantum maze problem for the reasons described in the paper. We argue that in a large N limit the quantum maze problem is equivalent to the problem of finding a semiclassical trajectory of some lattice field theory (the dual theory) on an N +1 dimensional space-time with geometrically flat, but topologically compact spatial slices. The spatial fundamental domain is an N dimensional hyper-rhombohedron, and the temporal direction describes transitions from an arbitrary initial state to an arbitrary target state and so the initial and final dual field theory conditions are described by these two quantum computational states. We first consider a complex Klein-Gordon field theory and argue that it can only be used to study the shortest quantum circuits which do not involve generators composed of tensor products of multiple Pauli Z matrices. Since such situation is not generic we call it the Z-problem. On the dual field theory side the Z-problem corresponds to massless excitations of the phase (Goldstone modes) that we attempt to fix using Higgs mechanism. The simplest dual theory which does not suffer from the massless excitation (or from the Z-problem) is the Abelian-Higgs model which we argue can be used for finding the shortest quantum circuits. Since every trajectory of the field theory is mapped directly to a quantum circuit, the shortest quantum circuits are identified with semiclassical trajectories. We also discuss the complexity of an actual algorithm that uses a dual theory prospective for solving the quantum maze problem and compare it with a geometric approach. We argue that it might be possible to solve the problem in sub-exponential time in 2 N , but for that we must consider the Klein-Gordon theory on curved spatial geometry and/or more complicated (than N -torus
Zhang, Yu Chen, GuanHua; Yam, ChiYung
2015-04-28
A time-dependent inelastic electron transport theory for strong electron-phonon interaction is established via the equations of motion method combined with the small polaron transformation. In this work, the dissipation via electron-phonon coupling is taken into account in the strong coupling regime, which validates the small polaron transformation. The corresponding equations of motion are developed, which are used to study the quantum interference effect and phonon-induced decoherence dynamics in molecular junctions. Numerical studies show clearly quantum interference effect of the transport electrons through two quasi-degenerate states with different couplings to the leads. We also found that the quantum interference can be suppressed by the electron-phonon interaction where the phase coherence is destroyed by phonon scattering. This indicates the importance of electron-phonon interaction in systems with prominent quantum interference effect.
Theory of Nematic Fractional Quantum Hall States
NASA Astrophysics Data System (ADS)
You, Yizhi; Cho, Gil Young; Fradkin, Eduardo
2014-10-01
We derive an effective field theory for the isotropic-nematic quantum phase transition of fractional quantum Hall states. We demonstrate that for a system with an isotropic background the low-energy effective theory of the nematic order parameter has z =2 dynamical scaling exponent, due to a Berry phase term of the order parameter, which is related to the nondissipative Hall viscosity. Employing the composite fermion theory with a quadrupolar interaction between electrons, we show that a sufficiently attractive quadrupolar interaction triggers a phase transition from the isotropic fractional quantum Hall fluid into a nematic fractional quantum Hall phase. By investigating the spectrum of collective excitations, we demonstrate that the mass gap of the Girvin-MacDonald-Platzman mode collapses at the isotropic-nematic quantum phase transition. On the other hand, Laughlin quasiparticles and the Kohn collective mode remain gapped at this quantum phase transition, and Kohn's theorem is satisfied. The leading couplings between the nematic order parameter and the gauge fields include a term of the same form as the Wen-Zee term. A disclination of the nematic order parameter carries an unquantized electric charge. We also discuss the relation between nematic degrees of freedom and the geometrical response of the fractional quantum Hall fluid.
Path integral formulation of scattering theory with application to scattering by black holes
Zhang, T.R.
1985-01-01
The computational power of Feynman path integrals was exploited. Path-integration formalism for the quantum mechanics scattering and classical wave scattering was generalized. Firstly, the standard WKB approximation was generalized to the cases where the critical points of the action functional are degenerate. Three typical semiclassical scattering features served as examples for a classification of degenerate critical points: conservation laws, rainbows, glories. Secondly, the method developed for non-relativistic quantum mechanics scattering was used in the case of classical wave scattering. Scattering by Schwarzschild black holes was chosen as an example, and WKB cross sections for scalar, vector, and tensor fields were worked out. Finally, 2s-th Bessel function behavior of WKB cross section for helicity-s polarized glory scattering in curved space time was proved.
Basing quantum theory on information processing
NASA Astrophysics Data System (ADS)
Barnum, Howard
2008-03-01
I consider information-based derivations of the quantum formalism, in a framework encompassing quantum and classical theory and a broad spectrum of theories serving as foils to them. The most ambitious hope for such a derivation is a role analogous to Einstein's development of the dynamics and kinetics of macroscopic bodies, and later of their gravitational interactions, on the basis of simple principles with clear operational meanings and experimental consequences. Short of this, it could still provide a principled understanding of the features of quantum mechanics that account for its greater-than-classical information-processing power, helping guide the search for new quantum algorithms and protocols. I summarize the convex operational framework for theories, and discuss information-processing in theories therein. Results include the fact that information that can be obtained without disturbance is inherently classical, generalized no-cloning and no-broadcasting theorems, exponentially secure bit commitment in all non-classical theories without entanglement, properties of theories that allow teleportation, and properties of theories that allow ``remote steering'' of ensembles using entanglement. Joint work with collaborators including Jonathan Barrett, Matthew Leifer, Alexander Wilce, Oscar Dahlsten, and Ben Toner.
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.
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.
Knot theory and quantum gravity
Rovelli, C.; Smolin, L.
1988-09-05
A new represenatation for quantum general relativity is described, which is defined in terms of functionals of sets of loops in three-space. In this representation exact solutions of the quantum constraints may be obtained. This result is related to the simplification of the constraints in Ashtekar's new formalism. We give in closed form the general solution of the diffeomorphisms constraint and a large class of solutions of the full set of constraints. These are classified by the knot and link classes of the spatial three-manifold.
Quantum processes: A Whiteheadian interpretation of quantum field theory
NASA Astrophysics Data System (ADS)
Bain, Jonathan
Quantum processes: A Whiteheadian interpretation of quantum field theory is an ambitious and thought-provoking exercise in physics and metaphysics, combining an erudite study of the very complex metaphysics of A.N. Whitehead with a well-informed discussion of contemporary issues in the philosophy of algebraic quantum field theory. Hättich's overall goal is to construct an interpretation of quantum field theory. He does this by translating key concepts in Whitehead's metaphysics into the language of algebraic quantum field theory. In brief, this Hättich-Whitehead (H-W, hereafter) interpretation takes "actual occasions" as the fundamental ontological entities of quantum field theory. An actual occasion is the result of two types of processes: a "transition process" in which a set of initial possibly-possessed properties for the occasion (in the form of "eternal objects") is localized to a space-time region; and a "concrescence process" in which a subset of these initial possibly-possessed properties is selected and actualized to produce the occasion. Essential to these processes is the "underlying activity", which conditions the way in which properties are initially selected and subsequently actualized. In short, under the H-W interpretation of quantum field theory, an initial set of possibly-possessed eternal objects is represented by a Boolean sublattice of the lattice of projection operators determined by a von Neumann algebra R (O) associated with a region O of Minkowski space-time, and the underlying activity is represented by a state on R (O) obtained by conditionalizing off of the vacuum state. The details associated with the H-W interpretation involve imposing constraints on these representations motivated by principles found in Whitehead's metaphysics. These details are spelled out in the three sections of the book. The first section is a summary and critique of Whitehead's metaphysics, the second section introduces the formalism of algebraic quantum field
Creativity and the Quantum Theory.
ERIC Educational Resources Information Center
Goswami, Amit
1988-01-01
The idea that creative acts are quantum jumps in the brain's mechanism is explored. Descriptions of the creative process that support the central role of sudden and discontinuous leaps of thought are cited from various philosophers and scientists. Distinctions between the functions of the brain and of computers are drawn. (VW)
Quantum Computing and Number Theory
NASA Astrophysics Data System (ADS)
Sasaki, Yoshitaka
2013-09-01
The prime factorization can be efficiently solved on a quantum computer. This result was given by Shor in 1994. In the first half of this article, a review of Shor's algorithm with mathematical setups is given. In the second half of this article, the prime number theorem which is an essential tool to understand the distribution of prime numbers is given.
Reasonable fermionic quantum information theories require relativity
NASA Astrophysics Data System (ADS)
Friis, Nicolai
2016-03-01
We show that any quantum information theory based on anticommuting operators must be supplemented by a superselection rule deeply rooted in relativity to establish a reasonable notion of entanglement. While quantum information may be encoded in the fermionic Fock space, the unrestricted theory has a peculiar feature: the marginals of bipartite pure states need not have identical entropies, which leads to an ambiguous definition of entanglement. We solve this problem, by proving that it is removed by relativity, i.e., by the parity superselection rule that arises from Lorentz invariance via the spin-statistics connection. Our results hence unveil a fundamental conceptual inseparability of quantum information and the causal structure of relativistic field theory.
Spacetime states and covariant quantum theory
NASA Astrophysics Data System (ADS)
Reisenberger, Michael; Rovelli, Carlo
2002-06-01
In its usual presentation, classical mechanics appears to give time a very special role. But it is well known that mechanics can be formulated so as to treat the time variable on the same footing as the other variables in the extended configuration space. Such covariant formulations are natural for relativistic gravitational systems, where general covariance conflicts with the notion of a preferred physical-time variable. The standard presentation of quantum mechanics, in turn, again gives time a very special role, raising well known difficulties for quantum gravity. Is there a covariant form of (canonical) quantum mechanics? We observe that the preferred role of time in quantum theory is the consequence of an idealization: that measurements are instantaneous. Canonical quantum theory can be given a covariant form by dropping this idealization. States prepared by noninstantaneous measurements are described by ``spacetime smeared states.'' The theory can be formulated in terms of these states, without making any reference to a special time variable. The quantum dynamics is expressed in terms of the propagator, an object covariantly defined on the extended configuration space.
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.
Backlund Transformation in Quantum Field Theory
NASA Astrophysics Data System (ADS)
Burt, Philip
1996-11-01
Solutions of nonlinear field equations with polynomial nonlin earities are well known(P.B.Burt,Quantum Mechanics and Nonlinear Waves,Harwood Academic,Chur,1981).These solutions have been used to describe spin zero systems with self interactions. General- izations to systmes of fermions and bosons with various inter- actions lend themselves to description of quantum field theories with proper normalization. No ultraviolet divergences occur in such theories. The solutions themselves represent weak Backlund transformation of the nonlinear field equations and the related Klein Gordonequation(C.Rogers and W.F.Ames,Nonlinear Boundary Value Problems in Science and Engineering, Academic Press,New York,1989).
Quantum mechanics of 4-derivative theories
NASA Astrophysics Data System (ADS)
Salvio, Alberto; Strumia, Alessandro
2016-04-01
A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantization. We find that a 4-derivative degree of freedom involves a canonical coordinate with unusual time-inversion parity, and that a correspondingly unusual representation must be employed for the relative quantum operator. The resulting theory has positive energy eigenvalues, normalizable wavefunctions, unitary evolution in a negative-norm configuration space. We present a formalism for quantum mechanics with a generic norm.
Quantum Walks: Theory, Application, and Implementation
NASA Astrophysics Data System (ADS)
Schmitz, Albert Thomas
The quantum walk is a method for conceptualizing and designing quantum computing algorithms and it comes in two forms: the continuous-time and discrete-time quantum walk. The thesis is organized into three parts, each of which looks to develop the concept and uses of the quantum walk. The first part is the theory of the quantum walk. This includes definitions and considerations for the various incarnations of the discrete-time quantum walk and a discussion on the general method for connecting the continuous-time and discrete-time versions. As a result, it is shown that most versions of the discrete-time quantum walk can be put into a general form and this can be used to simulate any continuous-time quantum walk. The second part uses these results for a hypothetical application. The application presented is a search algorithm that appears to scale in the time for completion independent of the size of the search space. This behavior is then elaborated upon and shown to have general qualitative agreement with simulations to within the approximations that are made. The third part introduces a method of implementation. Given a universal quantum computer, the method is discussed and shown to simulate an arbitrary discrete-time quantum walk. Some of the benefits of this method are that half the unitary evolution can be achieved without the use of any gates and there may be some possibility for error detection. The three parts combined suggest a possible experiment, given a quantum computing scheme of sufficient robustness.
Continuous wavelet transform in quantum field theory
NASA Astrophysics Data System (ADS)
Altaisky, M. V.; Kaputkina, N. E.
2013-07-01
We describe the application of the continuous wavelet transform to calculation of the Green functions in quantum field theory: scalar ϕ4 theory, quantum electrodynamics, and quantum chromodynamics. The method of continuous wavelet transform in quantum field theory, presented by Altaisky [Phys. Rev. D 81, 125003 (2010)] for the scalar ϕ4 theory, consists in substitution of the local fields ϕ(x) by those dependent on both the position x and the resolution a. The substitution of the action S[ϕ(x)] by the action S[ϕa(x)] makes the local theory into a nonlocal one and implies the causality conditions related to the scale a, the region causality [J. D. Christensen and L. Crane, J. Math. Phys. (N.Y.) 46, 122502 (2005)]. These conditions make the Green functions G(x1,a1,…,xn,an)=⟨ϕa1(x1)…ϕan(xn)⟩ finite for any given set of regions by means of an effective cutoff scale A=min(a1,…,an).
Next-to-simplest quantum field theories
NASA Astrophysics Data System (ADS)
Lal, Shailesh; Raju, Suvrat
2010-05-01
We describe new on-shell recursion relations for tree amplitudes in N=1 and N=2 gauge theories and use these to show that the structure of the one-loop S-matrix in pure (i.e. without any matter) N=1 and N=2 gauge theories resembles that of pure Yang-Mills theory. We proceed to study gluon scattering in gauge theories coupled to matter in arbitrary representations. The contribution of matter to individual bubble and triangle coefficients can depend on the fourth- and sixth-order indices of the matter representation, respectively. So, the condition that one-loop amplitudes be free of bubbles and triangles can be written as a set of linear Diophantine equations involving these higher-order indices. These equations simplify for supersymmetric theories. We present new examples of supersymmetric theories that have only boxes (and no triangles or bubbles at one-loop) and nonsupersymmetric theories that are free of bubbles. These theories see simplifications in their S-matrices that cannot be deduced just from naive power-counting. In particular, our results indicate that one-loop scattering amplitudes in the N=2, SU(N) theory with a symmetric tensor hypermultiplet and an antisymmetric tensor hypermultiplet are simple like those in the N=4 theory.
Next-to-simplest quantum field theories
Lal, Shailesh; Raju, Suvrat
2010-05-15
We describe new on-shell recursion relations for tree amplitudes in N=1 and N=2 gauge theories and use these to show that the structure of the one-loop S-matrix in pure (i.e. without any matter) N=1 and N=2 gauge theories resembles that of pure Yang-Mills theory. We proceed to study gluon scattering in gauge theories coupled to matter in arbitrary representations. The contribution of matter to individual bubble and triangle coefficients can depend on the fourth- and sixth-order indices of the matter representation, respectively. So, the condition that one-loop amplitudes be free of bubbles and triangles can be written as a set of linear Diophantine equations involving these higher-order indices. These equations simplify for supersymmetric theories. We present new examples of supersymmetric theories that have only boxes (and no triangles or bubbles at one-loop) and nonsupersymmetric theories that are free of bubbles. These theories see simplifications in their S-matrices that cannot be deduced just from naive power-counting. In particular, our results indicate that one-loop scattering amplitudes in the N=2, SU(N) theory with a symmetric tensor hypermultiplet and an antisymmetric tensor hypermultiplet are simple like those in the N=4 theory.
Construction of Quantum Field Theories with Factorizing S-Matrices
NASA Astrophysics Data System (ADS)
Lechner, Gandalf
2008-02-01
A new approach to the construction of interacting quantum field theories on two-dimensional Minkowski space is discussed. In this program, models are obtained from a prescribed factorizing S-matrix in two steps. At first, quantum fields which are localized in infinitely extended, wedge-shaped regions of Minkowski space are constructed explicitly. In the second step, local observables are analyzed with operator-algebraic techniques, in particular by using the modular nuclearity condition of Buchholz, d’Antoni and Longo. Besides a model-independent result regarding the Reeh Schlieder property of the vacuum in this framework, an infinite class of quantum field theoretic models with non-trivial interaction is constructed. This construction completes a program initiated by Schroer in a large family of theories, a particular example being the Sinh-Gordon model. The crucial problem of establishing the existence of local observables in these models is solved by verifying the modular nuclearity condition, which here amounts to a condition on analytic properties of form factors of observables localized in wedge regions. It is shown that the constructed models solve the inverse scattering problem for the considered class of S-matrices. Moreover, a proof of asymptotic completeness is obtained by explicitly computing total sets of scattering states. The structure of these collision states is found to be in agreement with the heuristic formulae underlying the Zamolodchikov-Faddeev algebra.
Multigluon scattering in open superstring theory
Stieberger, Stephan; Taylor, Tomasz R.
2006-12-15
We discuss the amplitudes describing N-gluon scattering in type I superstring theory, on a disk world sheet. After reviewing the general structure of amplitudes and the complications created by the presence of a large number of vertices at the boundary, we focus on the most promising case of maximally helicity violating (MHV) configurations because in this case, the zero Regge slope limit ({alpha}{sup '}{yields}0) is particularly simple. We obtain the full-fledged MHV disk amplitudes for N=4, 5, and N=6 gluons, expressed in terms of one, two and six functions of kinematic invariants, respectively. These functions represent certain boundary integrals--generalized Euler integrals--which for N{>=}6 correspond to multiple hypergeometric series (generalized Kampe de Feriet functions). Their {alpha}{sup '} expansions lead to Euler-Zagier sums. For arbitrary N, we show that the leading string corrections to the Yang-Mills amplitude, of order O({alpha}{sup '2}), originate from the well-known {alpha}{sup '2} TrF{sup 4} effective interactions of four gauge field strength tensors. By using iteration based on the soft gluon limit, we derive a simple formula valid to that order for arbitrary N. We argue that such a procedure can be extended to all orders in {alpha}{sup '}. If nature gracefully picked a sufficiently low string mass scale, our results would be important for studying string effects in multijet production at the Large Hadron Collider (LHC)
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.
The amplitude of quantum field theory
Medvedev, B.V. ); Pavlov, V.P.; Polivanov, M.K. ); Sukhanov, A.D. )
1989-05-01
General properties of the transition amplitude in axiomatic quantum field theory are discussed. Bogolyubov's axiomatic method is chosen as the variant of the theory. The axioms of this method are analyzed. In particular, the significance of the off-shell extension and of the various forms of the causality condition are examined. A complete proof is given of the existence of a single analytic function whose boundary values are the amplitudes of all channels of a process with given particle number.
Quantum theory of dynamic nuclear polarization in quantum dots
NASA Astrophysics Data System (ADS)
Economou, Sophia; Barnes, Edwin
2013-03-01
Nuclear spins play a major role in the dynamics of spin qubits in III-V semiconductor quantum dots. Although the hyperfine interaction between nuclear and electron (or hole) spins is typically viewed as the leading source of decoherence in these qubits, understanding how to experimentally control the nuclear spin polarization can not only ameliorate this problem, but in fact turn the nuclear spins into a valuable resource for quantum computing. Beyond extending decoherence times, control of this polarization can enable universal quantum computation as shown in singlet-triplet qubits and, in addition, offers the possibility of repurposing the nuclear spins into a robust quantum memory. In, we took a first step toward taking advantage of this resource by developing a general, fully quantum theory of non-unitary electron-nuclear spin dynamics with a periodic train of delta-function pulses as the external control driving the electron spin. Here, we extend this approach to other types of controls and further expand on the predictions and physical insights that emerge from the theory.
Quantum stability of chameleon field theories.
Upadhye, Amol; Hu, Wayne; Khoury, Justin
2012-07-27
Chameleon scalar fields are dark-energy candidates which suppress fifth forces in high density regions of the Universe by becoming massive. We consider chameleon models as effective field theories and estimate quantum corrections to their potentials. Requiring that quantum corrections be small, so as to allow reliable predictions of fifth forces, leads to an upper bound m<0.0073(ρ/10 g cm(-3))(1/3) eV for gravitational-strength coupling whereas fifth force experiments place a lower bound of m>0.0042 eV. An improvement of less than a factor of two in the range of fifth force experiments could test all classical chameleon field theories whose quantum corrections are well controlled and couple to matter with nearly gravitational strength regardless of the specific form of the chameleon potential. PMID:23006073
Universality of computation in real quantum theory
NASA Astrophysics Data System (ADS)
Belenchia, A.; D'Ariano, G. M.; Perinotti, P.
2013-10-01
Recently de la Torre et al. (Phys. Rev. Lett., 109 (2012) 090403) reconstructed Quantum Theory from its local structure on the basis of local discriminability and the existence of a one-parameter group of bipartite transformations containing an entangling gate. This result relies on universality of any entangling gate for quantum computation. Here we prove universality of C-NOT with local gates for Real Quantum Theory (RQT), showing that the universality requirement would not be sufficient for the result, whereas local discriminability and the local qubit structure play a crucial role. For reversible computation, generally an extra rebit is needed for RQT. As a by-product we also provide a short proof of universality of C-NOT for CQT.
Quantum Cylindrical Waves and Parametrized Field Theory
NASA Astrophysics Data System (ADS)
Varadarajan, Madhavan
In this article, we review some illustrative results in the study of two related toy models for quantum gravity, namely cylindrical waves (which are cylindrically symmetric gravitational fields)and parametrized field theory (which is just free scalar field theory on a flat space-time in generally covariant disguise). In the former, we focus on the phenomenon of unexpected large quantum gravity effects in regions of weak classical gravitational fields and on an analysis of causality in a quantum geometry. In the latter, we focus on Dirac quantization, argue that this is related to the unitary implementability of free scalar field evolution along curved foliations of the flat space-time and review the relevant results for unitary implementability.
PT-Symmetric Quantum Field Theory
NASA Astrophysics Data System (ADS)
Bender, Carl M.
2011-09-01
In 1998 it was discovered that the requirement that a Hamiltonian be Dirac Hermitian (H = H†) can be weakened and generalized to the requirement that a Hamiltonian be PT symmetric ([H,PT] = 0); that is, invariant under combined space reflection and time reversal. Weakening the constraint of Hermiticity allows one to consider new kinds of physically acceptable Hamiltonians and, in effect, it amounts to extending quantum mechanics from the real (Hermitian) domain into the complex domain. Much work has been done on the analysis of various PT-symmetric quantum-mechanical models. However, only very little analysis has been done on PT-symmetric quantum-field-theoretic models. Here, we describe some of what has been done in the context of PT-symmetric quantum field theory and describe some possible fundamental applications.
Neutron Interference Experiments and Quantum Measurement Theory
NASA Astrophysics Data System (ADS)
Namiko, M.; Otake, Y.; Soshi, H.
1987-03-01
Physical and epistemological implications of recent experiments on the neutron interference are discussed from the viewpoint of the Machida-Namiki theory of measurement in quantum mechanics, without resort to discussion on the number-phase uncertainty relation. The same idea is also applied to the neutrino oscillation problem.
Global effects in quaternionic quantum field theory
NASA Astrophysics Data System (ADS)
Brumby, S. P.; Joshi, G. C.
1996-12-01
We present some striking global consequences of a model quaternionic quantum field theory which is locally complex. We show how making the quaternionic structure a dynamical quantity naturally leads to the prediction of cosmic strings and nonbaryonic hot dark matter candidates.
Operational quantum theory without predefined time
NASA Astrophysics Data System (ADS)
Oreshkov, Ognyan; Cerf, Nicolas J.
2016-07-01
The standard formulation of quantum theory assumes a predefined notion of time. This is a major obstacle in the search for a quantum theory of gravity, where the causal structure of space-time is expected to be dynamical and fundamentally probabilistic in character. Here, we propose a generalized formulation of quantum theory without predefined time or causal structure, building upon a recently introduced operationally time-symmetric approach to quantum theory. The key idea is a novel isomorphism between transformations and states which depends on the symmetry transformation of time reversal. This allows us to express the time-symmetric formulation in a time-neutral form with a clear physical interpretation, and ultimately drop the assumption of time. In the resultant generalized formulation, operations are associated with regions that can be connected in networks with no directionality assumed for the connections, generalizing the standard circuit framework and the process matrix framework for operations without global causal order. The possible events in a given region are described by positive semidefinite operators on a Hilbert space at the boundary, while the connections between regions are described by entangled states that encode a nontrivial symmetry and could be tested in principle. We discuss how the causal structure of space-time could be understood as emergent from properties of the operators on the boundaries of compact space-time regions. The framework is compatible with indefinite causal order, timelike loops, and other acausal structures.
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
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.
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.
Theory of ghost scattering with incoherent light sources
NASA Astrophysics Data System (ADS)
Cheng, Jing
2016-04-01
Inspired by the idea of ghost imaging, we propose a ghost scattering scheme to study light scattering with incoherent light sources through the nonlocal correlation measurement of the differential scattering cross-section fluctuations in two different optical paths. We present a rigorous formal theory to describe the ghost scattering process. Also we have derived a simple and closed-form ghost scattering formula within the first-order Born approximation which is particularly suited for weak scatterers. We find that the scattering information of a test scatterer can be obtained by using only a single-pixel detector in the corresponding optical path through the nonlocal correlation measurement with the help of another reference path.
Solvay 1927: Quantum Theory at the Crossroads
NASA Astrophysics Data System (ADS)
Valentini, Antony
2011-04-01
We reconsider the crucial 1927 Solvay conference in the context of current research in the foundations of quantum theory. Contrary to folklore, the interpretation question was not settled at this conference and no consensus was reached; instead, a range of sharply conflicting views were presented and extensively discussed. Today, there is no longer an established or dominant interpretation of quantum theory, so it is important to re-evaluate the historical sources and keep the interpretation debate open. The proceedings of the conference contain much unexpected material, and are remarkable for their clear identification of key issues that remain controversial to this day. After providing a general overview, we focus on the extensive discussions of de Broglie's pilot-wave theory, which de Broglie presented for a many-body system, including the much misunderstood critique by Pauli.
Quantum to classical transition in quantum field theory
NASA Astrophysics Data System (ADS)
Lombardo, Fernando C.
1998-12-01
We study the quatum to classical transition process in the context of quantum field theory. Extending the influence functional formalism of Feynman and Vernon, we study the decoherence process for self-interacting quantum fields in flat space. We also use this formalism for arbitrary geometries to analyze the quantum to classical transition in quantum gravity. After summarizing the main results known for the quantum Brownian motion, we consider a self-interacting field theory in Minkowski spacetime. We compute a coarse grained effective action by integrating out the field modes with wavelength shorter than a critical value. From this effective action we obtain the evolution equation for the reduced density matrix (master equation). We compute the diffusion coefficients for this equation and analyze the decoherence induced on the long-wavelength modes. We generalize the results to the case of a conformally coupled scalar field in de Sitter spacetime. We show that the decoherence is effective as long as the critical wavelength is taken to be not shorter than the Hubble radius. On the other hand, we study the classical limit for scalar-tensorial models in two dimensions. We consider different couplings between the dilaton and the scalar field. We discuss the Hawking radiation process and, from an exact evaluation of the influence functional, we study the conditions by which decoherence ensures the validity of the semiclassical approximation in cosmological metrics. Finally we consider four dimensional models with massive scalar fields, arbitrary coupled to the geometry. We compute the Einstein-Langevin equations in order to study the effect of the fluctuations induced by the quantum fields on the classical geometry.
Quantum cellular automaton theory of light
NASA Astrophysics Data System (ADS)
Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo
2016-05-01
We present a quantum theory of light based on the recent derivation of Weyl and Dirac quantum fields from general principles ruling the interactions of a countable set of abstract quantum systems, without using space-time and mechanics (D'Ariano and Perinotti, 2014). In a Planckian interpretation of the discreteness, the usual quantum field theory corresponds to the so-called relativistic regime of small wave-vectors. Within the present framework the photon is a composite particle made of an entangled pair of free Weyl Fermions, and the usual Bosonic statistics is recovered in the low photon density limit, whereas the Maxwell equations describe the relativistic regime. We derive the main phenomenological features of the theory in the ultra-relativistic regime, consisting in a dispersive propagation in vacuum, and in the occurrence of a small longitudinal polarization, along with a saturation effect originated by the Fermionic nature of the photon. We then discuss whether all these effects can be experimentally tested, and observe that only the dispersive effects are accessible to the current technology via observations of gamma-ray bursts.
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.
Imperfect Cloning Operations in Algebraic Quantum Theory
NASA Astrophysics Data System (ADS)
Kitajima, Yuichiro
2015-01-01
No-cloning theorem says that there is no unitary operation that makes perfect clones of non-orthogonal quantum states. The objective of the present paper is to examine whether an imperfect cloning operation exists or not in a C*-algebraic framework. We define a universal -imperfect cloning operation which tolerates a finite loss of fidelity in the cloned state, and show that an individual system's algebra of observables is abelian if and only if there is a universal -imperfect cloning operation in the case where the loss of fidelity is less than . Therefore in this case no universal -imperfect cloning operation is possible in algebraic quantum theory.
Theory of quantum error-correcting codes
Knill, E.; Laflamme, R.
1997-02-01
Quantum error correction will be necessary for preserving coherent states against noise and other unwanted interactions in quantum computation and communication. We develop a general theory of quantum error correction based on encoding states into larger Hilbert spaces subject to known interactions. We obtain necessary and sufficient conditions for the perfect recovery of an encoded state after its degradation by an interaction. The conditions depend only on the behavior of the logical states. We use them to give a recovery-operator-independent definition of error-correcting codes. We relate this definition to four others: the existence of a left inverse of the interaction, an explicit representation of the error syndrome using tensor products, perfect recovery of the completely entangled state, and an information theoretic identity. Two notions of fidelity and error for imperfect recovery are introduced, one for pure and the other for entangled states. The latter is more appropriate when using codes in a quantum memory or in applications of quantum teleportation to communication. We show that the error for entangled states is bounded linearly by the error for pure states. A formal definition of independent interactions for qubits is given. This leads to lower bounds on the number of qubits required to correct e errors and a formal proof that the classical bounds on the probability of error of e-error-correcting codes applies to e-error-correcting quantum codes, provided that the interaction is dominated by an identity component. {copyright} {ital 1997} {ital The American Physical Society}
On the similarity of theories of anelastic and scattering attenuation
Wennerberg, L.; Frankel, A.
1989-01-01
We point out basic parallels between theories of anelastic and scattering attenuation. We consider approximations to scattering effects presented by O'Doherty and Anstey (1971), Sato (1982), and Wu (1982). We use the linear theory of anelasticity. We note that the frequency dependence of Q can be related to a distribution of scales of physical properties of the medium. The frequency dependence of anelastic Q is related to the distribution of relaxation times in exactly the same manner as the frequency dependence of scattering Q is related to the distribution of scatterer sizes. Thus, the well-known difficulty of separating scattering from intrinsic attenuation is seen from this point of view as a consequence of the fact that certain observables can be interpreted by identical equations resulting from either of two credible physical theories describing fundamentally different processes. -from Authors
Theory for magnetic excitations in quantum spin ice
NASA Astrophysics Data System (ADS)
Onoda, Shigeki; Datta, Trinanjan
Magnetic excitations in magnetic rare-earth pyrochlore oxides called quantum spin ice (QSI) systems such as Yb2Ti2O7, Pr2Zr2O7, and Tb2Ti2O7 have attracted great interest for possible observations of the quantum dynamics of spin ice monopoles and emergent photon excitations. However, their spectral properties remain open especially for cases relevant to experimental systems. Here, we develop a theoretical framework that incorporates gauge fluctuations into a modified gauge mean-field approach, so that it reproduces key features of recent quantum Monte-Carlo results on the double broad specific heat in the simplest QSI model and can describe a continuous growth of a coherence in gauge-field correlations on cooling down to Coulomb-phase ground states. Using this new approach, we provide a theory for magnetic neutron-scattering spectra. It is found that spin-flip exchange interactions produce dispersive QSI monopole excitations which create a particle-hole continuum neutron-scattering spectrum. Gauge fluctuations give multi-particle contributions to the spectrum, which will be possibly detected in Higgs phases.
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.
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.
Electromagnetic scattering by magnetic spheres: Theory and algorithms
NASA Astrophysics Data System (ADS)
Milham, Merill E.
1994-10-01
The theory for the scattering of magnetic spheres is developed by means of scaling functions. This theory leads in a natural way to the development of scattering algorithms which use exponential scaling to overcome computational overflow problems. The design and testing of the algorithm is described. Fortran codes which implement the algorithmic design are presented and examples of code use are given. Listings of the code are included.
Quantum Theories of Self-Localization
NASA Astrophysics Data System (ADS)
Bernstein, Lisa Joan
In the classical dynamics of coupled oscillator systems, nonlinearity leads to the existence of stable solutions in which energy remains localized for all time. Here the quantum-mechanical counterpart of classical self-localization is investigated in the context of two model systems. For these quantum models, the terms corresponding to classical nonlinearities modify a subset of the stationary quantum states to be particularly suited to the creation of nonstationary wavepackets that localize energy for long times. The first model considered here is the Quantized Discrete Self-Trapping model (QDST), a system of anharmonic oscillators with linear dispersive coupling used to model local modes of vibration in polyatomic molecules. A simple formula is derived for a particular symmetry class of QDST systems which gives an analytic connection between quantum self-localization and classical local modes. This formula is also shown to be useful in the interpretation of the vibrational spectra of some molecules. The second model studied is the Frohlich/Einstein Dimer (FED), a two-site system of anharmonically coupled oscillators based on the Frohlich Hamiltonian and motivated by the theory of Davydov solitons in biological protein. The Born-Oppenheimer perturbation method is used to obtain approximate stationary state wavefunctions with error estimates for the FED at the first excited level. A second approach is used to reduce the first excited level FED eigenvalue problem to a system of ordinary differential equations. A simple theory of low-energy self-localization in the FED is discussed. The quantum theories of self-localization in the intrinsic QDST model and the extrinsic FED model are compared.
From Entropic Dynamics to Quantum Theory
Caticha, Ariel
2009-12-08
Non-relativistic quantum theory is derived from information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles so that the configuration space is a statistical manifold. The dynamics then follows from a principle of inference, the method of Maximum Entropy. The concept of time is introduced as a convenient way to keep track of change. The resulting theory resembles both Nelson's stochastic mechanics and general relativity. The statistical manifold is a dynamical entity: its geometry determines the evolution of the probability distribution which, in its turn, reacts back and determines the evolution of the geometry. There is a new quantum version of the equivalence principle: 'osmotic' mass equals inertial mass. Mass and the phase of the wave function are explained as features of purely statistical origin.
A quantum photonic dissipative transport theory
NASA Astrophysics Data System (ADS)
Lei, Chan U.; Zhang, Wei-Min
2012-05-01
In this paper, a quantum transport theory for describing photonic dissipative transport dynamics in nanophotonics is developed. The nanophotonic devices concerned in this paper consist of on-chip all-optical integrated circuits incorporating photonic bandgap waveguides and driven resonators embedded in nanostructured photonic crystals. The photonic transport through waveguides is entirely determined from the exact master equation of the driven resonators, which is obtained by explicitly eliminating all the degrees of freedom of the waveguides (treated as reservoirs). Back-reactions from the reservoirs are fully taken into account. The relation between the driven photonic dynamics and photocurrents is obtained explicitly. The non-Markovian memory structure and quantum decoherence dynamics in photonic transport can then be fully addressed. As an illustration, the theory is utilized to study the transport dynamics of a photonic transistor consisting of a nanocavity coupled to two waveguides in photonic crystals. The controllability of photonic transport through the external driven field is demonstrated.
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.
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.
Theory of helimagnons in itinerant quantum systems
NASA Astrophysics Data System (ADS)
Belitz, D.; Kirkpatrick, T. R.; Rosch, A.
2006-02-01
The nature and effects of the Goldstone mode in the ordered phase of helical or chiral itinerant magnets such as MnSi are investigated theoretically. It is shown that the Goldstone mode, or helimagnon, is a propagating mode with a highly anisotropic dispersion relation, in analogy to the Goldstone mode in chiral liquid crystals. Starting from a microscopic theory, a comprehensive effective theory is developed that allows for an explicit description of the helically ordered phase, including the helimagnons, for both classical and quantum helimagnets. The directly observable dynamical spin susceptibility, which reflects the properties of the helimagnon, is calculated.
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.
Aspects of quantum gravity theory and phenomenology
NASA Astrophysics Data System (ADS)
Zampeli, Adamantia
Quantum gravity deals with the formulation of a physical theory consistent with both quantum and gravitational principles. The formulation is based on two main methods of quantisation, the canonical and the covariant one. In the first part of the thesis, the main problems of each method of quantisation are stated. In particular, the problem of time is analysed in the canonical quantisation framework and the conformal sickness problem of the Euclidean quantum gravity is studied with covariant methods. Quantum gravity phenomenology is studied through two models. The first one is a cosmological model obtained by reduced phase space quantisation. Implications for the early era of the universe as well as how phantom fields might arise are studied. The second one deals with the calculation of the response function of a detector in the presence of Dirac fields in a 2+1 dimensional spacetime. The spectrum detected is expected to invoke the apparent inversion of statistics of a quantum field. This calculation might have potential indications for the actual detection of thermal radiation in a graphene sheet.
Theory of Thomson scattering in inhomogeneous media
NASA Astrophysics Data System (ADS)
Kozlowski, P. M.; Crowley, B. J. B.; Gericke, D. O.; Regan, S. P.; Gregori, G.
2016-04-01
Thomson scattering of laser light is one of the most fundamental diagnostics of plasma density, temperature and magnetic fields. It relies on the assumption that the properties in the probed volume are homogeneous and constant during the probing time. On the other hand, laboratory plasmas are seldom uniform and homogeneous on the temporal and spatial dimensions over which data is collected. This is particularly true for laser-produced high-energy-density matter, which often exhibits steep gradients in temperature, density and pressure, on a scale determined by the laser focus. Here, we discuss the modification of the cross section for Thomson scattering in fully-ionized media exhibiting steep spatial inhomogeneities and/or fast temporal fluctuations. We show that the predicted Thomson scattering spectra are greatly altered compared to the uniform case, and may lead to violations of detailed balance. Therefore, careful interpretation of the spectra is necessary for spatially or temporally inhomogeneous systems.
Theory of Thomson scattering in inhomogeneous media.
Kozlowski, P M; Crowley, B J B; Gericke, D O; Regan, S P; Gregori, G
2016-01-01
Thomson scattering of laser light is one of the most fundamental diagnostics of plasma density, temperature and magnetic fields. It relies on the assumption that the properties in the probed volume are homogeneous and constant during the probing time. On the other hand, laboratory plasmas are seldom uniform and homogeneous on the temporal and spatial dimensions over which data is collected. This is particularly true for laser-produced high-energy-density matter, which often exhibits steep gradients in temperature, density and pressure, on a scale determined by the laser focus. Here, we discuss the modification of the cross section for Thomson scattering in fully-ionized media exhibiting steep spatial inhomogeneities and/or fast temporal fluctuations. We show that the predicted Thomson scattering spectra are greatly altered compared to the uniform case, and may lead to violations of detailed balance. Therefore, careful interpretation of the spectra is necessary for spatially or temporally inhomogeneous systems. PMID:27068215
Multiple Scattering Theory for Inelastic Processes
NASA Astrophysics Data System (ADS)
Braun, V. M.; Shabelski, Yu. M.
The review is devoted to the description of inelastic interactions of composite systems in the framework of the multiple scattering approach. Quasielastic scattering and multiple hadron production processes are considered for hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions at high energies. We show that important information on inelastic processes follows on very general grounds from the classification of various intermediate states in the elastic amplitude, as similarly AGK cutting rules arise for reggeon diagrams. Attention is mainly given to the appropriate technique, which is illustrated with several examples of increasing complexity. The general formalism for the inelastic screening corrections is presented and its particular applications to various reactions. The review does not aim at the systematic study of numerous versions of the multiple scattering calculus confronting each other and to the extensive experimental data. Instead, we concentrate on a few simple examples to make clear the underlying physics and to work out the needed machinery employed in practical calculations.
Theory of Thomson scattering in inhomogeneous media
Kozlowski, P. M.; Crowley, B. J. B.; Gericke, D. O.; Regan, S. P.; Gregori, G.
2016-01-01
Thomson scattering of laser light is one of the most fundamental diagnostics of plasma density, temperature and magnetic fields. It relies on the assumption that the properties in the probed volume are homogeneous and constant during the probing time. On the other hand, laboratory plasmas are seldom uniform and homogeneous on the temporal and spatial dimensions over which data is collected. This is particularly true for laser-produced high-energy-density matter, which often exhibits steep gradients in temperature, density and pressure, on a scale determined by the laser focus. Here, we discuss the modification of the cross section for Thomson scattering in fully-ionized media exhibiting steep spatial inhomogeneities and/or fast temporal fluctuations. We show that the predicted Thomson scattering spectra are greatly altered compared to the uniform case, and may lead to violations of detailed balance. Therefore, careful interpretation of the spectra is necessary for spatially or temporally inhomogeneous systems. PMID:27068215
No extension of quantum theory can have improved predictive power.
Colbeck, Roger; Renner, Renato
2011-01-01
According to quantum theory, measurements generate random outcomes, in stark contrast with classical mechanics. This raises the question of whether there could exist an extension of the theory that removes this indeterminism, as suspected by Einstein, Podolsky and Rosen. Although this has been shown to be impossible, existing results do not imply that the current theory is maximally informative. Here we ask the more general question of whether any improved predictions can be achieved by any extension of quantum theory. Under the assumption that measurements can be chosen freely, we answer this question in the negative: no extension of quantum theory can give more information about the outcomes of future measurements than quantum theory itself. Our result has significance for the foundations of quantum mechanics, as well as applications to tasks that exploit the inherent randomness in quantum theory, such as quantum cryptography. PMID:21811240
Scattering theory with localized non-Hermiticities
Znojil, Miloslav
2008-07-15
In the context of the recent interest in solvable models of scattering mediated by non-Hermitian Hamiltonians (cf. H. F. Jones, Phys. Rev. D 76, 125003 (2007)) we show that the well-known variability of the ad hoc choice of the metric {theta} which defines the physical Hilbert space of states can help us to clarify several apparent paradoxes. We argue that with a suitable {theta}, a fully plausible physical picture of the scattering can be recovered. Quantitatively, our new recipe is illustrated on an exactly solvable toy model.
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)
Nonequilibrium GREEN’S Functions for High-Field Quantum Transport Theory
NASA Astrophysics Data System (ADS)
Bertoncini, Rita
A formulation of the Kadanoff-Baym-Keldysh theory of nonequilibrium quantum statistical mechanics is developed in order to describe nonperturbatively the effects of the electric field on electron-phonon scattering in nondegenerate semiconductors. We derive an analytic, gauge-invariant model for the spectral density of energy states that accounts for both intracollisional field effect and collisional broadening simultaneously. A kinetic equation for the quantum distribution function is derived and solved numerically. The nonlinear drift velocity versus applied field characteristics is also evaluated numerically. Many features of our nonlinear theory bear formal resemblance to linear-response theory.
String theory, quantum phase transitions, and the emergent Fermi liquid.
Cubrović, Mihailo; Zaanen, Jan; Schalm, Koenraad
2009-07-24
A central problem in quantum condensed matter physics is the critical theory governing the zero-temperature quantum phase transition between strongly renormalized Fermi liquids as found in heavy fermion intermetallics and possibly in high-critical temperature superconductors. We found that the mathematics of string theory is capable of describing such fermionic quantum critical states. Using the anti-de Sitter/conformal field theory correspondence to relate fermionic quantum critical fields to a gravitational problem, we computed the spectral functions of fermions in the field theory. By increasing the fermion density away from the relativistic quantum critical point, a state emerges with all the features of the Fermi liquid. PMID:19556462
Weak Quantum Theory: Formal Framework and Selected Applications
Atmanspacher, Harald; Filk, Thomas; Roemer, Hartmann
2006-01-04
Two key concepts of quantum theory, complementarity and entanglement, are considered with respect to their significance in and beyond physics. An axiomatically formalized, weak version of quantum theory, more general than the ordinary quantum theory of physical systems, is described. Its mathematical structure generalizes the algebraic approach to ordinary quantum theory. The crucial formal feature leading to complementarity and entanglement is the non-commutativity of observables.The ordinary Hilbert space quantum mechanics can be recovered by stepwise adding the necessary features. This provides a hierarchy of formal frameworks of decreasing generality and increasing specificity. Two concrete applications, more specific than weak quantum theory and more general than ordinary quantum theory, are discussed: (i) complementarity and entanglement in classical dynamical systems, and (ii) complementarity and entanglement in the bistable perception of ambiguous stimuli.
Scatter Theories and Their Application to Lunar Radar Return
NASA Technical Reports Server (NTRS)
Hayre, H. S.
1961-01-01
The research work being done under this NASA grant is divided into the following three categories: (1) An estimate of the radar return for the NASA Aerobee rocket shot at White Sands Missile Range. (WSMR) (2) Development of new scatter theories, modification and correlation of existing scatter theories, and application of the theories to moon-echo data for estimation of the surface features of the moon. (3) Acoustic modeling of the lunar surface and correlation of the theoretical with both full scale and acoustical experimental results.
Multiple-scattering theory for electromagnetic waves
Wang, X. ); Zhang, X. ); Yu, Q.; Harmon, B.N. )
1993-02-15
In this paper, a multiple-scattering formalism for electromagnetic waves is presented. Its application to the three-dimensional periodic dielectric structures is given in a form similar to the usual Korringa-Kohn-Rostoker form of scalar waves. Using this approach, the band-structure results of touching spheres of diamond structure in a dielectric medium with dielectric constant 12.96 are calculated. The application to disordered systems under the coherent-potential approximation is discussed.
Relational quadrilateralland II: The Quantum Theory
NASA Astrophysics Data System (ADS)
Anderson, Edward; Kneller, Sophie
2014-04-01
We provide the quantum treatment of the relational quadrilateral. The underlying reduced configuration spaces are ℂℙ2 and the cone over this. We consider exact free and isotropic HO potential cases and perturbations about these. Moreover, our purely relational kinematical quantization is distinct from the usual one for ℂℙ2, which turns out to carry absolutist connotations instead. Thus, this paper is the first to note absolute-versus-relational motion distinctions at the kinematical rather than dynamical level. It is also an example of value to the discussion of kinematical quantization along the lines of Isham, 1984. The relational quadrilateral is the simplest RPM whose mathematics is not standard in atomic physics (the triangle and four particles on a line are both based on 𝕊2 and ℝ3 mathematics). It is far more typical of the general quantum relational N-a-gon than the previously studied case of the relational triangle. We consider useful integrals as regards perturbation theory and the peaking interpretation of quantum cosmology. We subsequently consider problem of time (PoT) applications of this: quantum Kuchař beables, the Machian version of the semiclassical approach and the timeless naïve Schrödinger interpretation. These go toward extending the combined Machian semiclassical-Histories-Timeless Approach of [Int. J. Mod. Phys. D23 (2014) 1450014] to the case of the quadrilateral, which will be treated in subsequent papers.
Twistor Diagrams and Quantum Field Theory.
NASA Astrophysics Data System (ADS)
O'Donald, Lewis
Available from UMI in association with The British Library. Requires signed TDF. This thesis uses twistor diagram theory, as developed by Penrose (1975) and Hodges (1990c), to try to approach some of the difficulties inherent in the standard quantum field theoretic description of particle interactions. The resolution of these issues is the eventual goal of the twistor diagram program. First twistor diagram theory is introduced from a physical view-point, with the aim of studying larger diagrams than have been typically explored. Methods are evolved to tackle the double box and triple box diagrams. These lead to three methods of constructing an amplitude for the double box, and two ways for the triple box. Next this theory is applied to translate the channels of a Yukawa Feynman diagram, which has more than four external states, into various twistor diagrams. This provides a test of the skeleton hypothesis (of Hodges, 1990c) in these cases, and also shows that conformal breaking must enter into twistor diagrams before the translation of loop level Feynman diagrams. The issue of divergent Feynman diagrams is then considered. By using a twistor equivalent of the sum-over -states idea of quantum field theory, twistor translations of loop diagrams are conjectured. The various massless propagator corrections and vacuum diagrams calculated give results consistent with Feynman theory. Two diagrams are also found that give agreement with the finite parts of the Feynman "fish" diagrams of phi^4 -theory. However it is found that a more rigorous translation for the time-like fish requires new boundaries to be added to the twistor sum-over-states. The twistor diagram obtained is found to give the finite part of the relevant Feynman diagram.
Scattering Theory of Kondo Mirages and Observation of Single Kondo Atom Phase Shift*
NASA Astrophysics Data System (ADS)
Fiete, Gregory A.; Hersch, Jesse S.; Heller, Eric J.; Manoharan, H. C.; Lutz, C. P.; Eigler, D. M.
2001-03-01
We explain the origin of the Kondo mirage seen in recent quantum corral Scanning Tunneling Microscope (STM) experiments with a scattering theory of electrons on the surfaces of metals. Our theory combined with experimental data provides the first direct observation of a single Kondo atom phase shift. The Kondo mirage observed at the empty focus of an elliptical quantum corral is shown to arise from multiple electron bounces off the corral wall adatoms in a manner analagous to the formation of a real image in optics. We demonstrate our theory with direct quantitive comparision to experimental data. *This research was supported by the National Science Foundation under Grant No. CHE9610501 and by ITAMP.
Multichannel quantum defect theory for polar molecules
NASA Astrophysics Data System (ADS)
Elfimov, Sergei V.; Dorofeev, Dmitrii L.; Zon, Boris A.
2014-02-01
Our work is devoted to developing a general approach for nonpenetrating Rydberg states of polar molecules. We propose a method to estimate the accuracy of calculation of their wave functions and quantum defects. Basing on this method we estimate the accuracy of Born-Oppenheimer (BO) and inverse Born-Oppenheimer (IBO) approximations for these states. This estimation enables us to determine the space and energy regions where BO and IBO approximations are valid. It depends on the interplay between l coupling (due to dipole potential of the core) and l uncoupling (due to rotation the core). Next we consider the intermediate region where both BO and IBO are not valid. For this intermediate region we propose a modification of Fano's multichannel quantum defect theory to match BO and IBO wave functions and show that it gives more reliable results. They are demonstrated on the example of SO molecule.
Environmental management: principles from quantum theory.
Valadez, A M; Sportsman, S
1999-01-01
Management of the environment is a critical role component for any health care provider. Turmoil, multiple relationships, and new ways of "doing business" characterize today's health care system, and traditional management techniques, based on Newtonian physics may no longer be effective. Principles helpful for managing the current health care environment may be found in quantum theory. These include (1) the world is unpredictable; (2) the intent of the observer influences how the world is seen; and (3) interrelationships are what count, not the things themselves. These principles are derived from the work of Wheatley, who applied the quantum theoretical framework to leadership. Strategies for gaining competence in managing the new environment are explored. Such strategies include shared governance, the process of delegation, and coordination of services. These strategies may be helpful to colleagues in education as well as in practice. PMID:10450646
Reassessment of the theory of stimulated Raman scattering
NASA Technical Reports Server (NTRS)
Fralick, G. C.; Deck, R. T.
1985-01-01
A modification of the standard theory of stimulated Raman scattering (SRS) first proposed by Sparks (1974, 1975) is analyzed and shown to incorporate a possibly important physical effect; however, its original formulation is incorrect. The analysis is based on an exact numerical integration of the coupled equations of the modified theory, the results of which are compared with both the conventional theory of SRS and with one set of experimental data. A reformulation of the modified theory is suggested that leads to a gain which is in somewhat better agreement with the data than is the conventional theory.
NASA Astrophysics Data System (ADS)
Schempp, Walter J.
2013-09-01
Based on projective geometry, a quantum holographic approach to the orbiton / spinon dynamics of quantum blackholography and clinical magnetic resonance tomography is mathematically described. Crucial applications of the conformal steady-state free-precession modality and automorphic scattering theory are the evidence for a supermassive central black hole in the Milky Way galaxy and the modalities of clinical cardiovascular magnetic resonance tomography and diffusion weighted magnetic resonance tomography of non-invasive radiological diagnostics.
A Theory of Radar Scattering by the Moon
NASA Technical Reports Server (NTRS)
Senior, T. B. A.; Siegel, K. M.
1959-01-01
A theory is described in which the moon is regarded as a "quasi-smooth" scatterer at radar frequencies. A scattered pulse is then composed of a number of individual returns each of which is provided by a single scattering area. In this manner it is possible to account for all the major features of the pulse, and the evidence in favor of the theory is presented. From a study of the measured power received at different frequencies, it is shown that the scattering area nearest to the earth is the source of a specular return, and it is then possible to obtain information about the material of which the area is composed. The electromagnetic constants are derived and their significance discussed.
Maxwell-Garnett effective medium theory: Quantum nonlocal effects
Moradi, Afshin
2015-04-15
We develop the Maxwell-Garnett theory for the effective medium approximation of composite materials with metallic nanoparticles by taking into account the quantum spatial dispersion effects in dielectric response of nanoparticles. We derive a quantum nonlocal generalization of the standard Maxwell-Garnett formula, by means the linearized quantum hydrodynamic theory in conjunction with the Poisson equation as well as the appropriate additional quantum boundary conditions.
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.
Scattering theory approach to electrodynamic Casimir forces
Rahi, Sahand Jamal; Kardar, Mehran; Emig, Thorsten; Graham, Noah; Jaffe, Robert L.
2009-10-15
We give a comprehensive presentation of methods for calculating the Casimir force to arbitrary accuracy, for any number of objects, arbitrary shapes, susceptibility functions, and separations. The technique is applicable to objects immersed in media other than vacuum, nonzero temperatures, and spatial arrangements in which one object is enclosed in another. Our method combines each object's classical electromagnetic scattering amplitude with universal translation matrices, which convert between the bases used to calculate scattering for each object, but are otherwise independent of the details of the individual objects. The method is illustrated by rederiving the Lifshitz formula for infinite half-spaces, by demonstrating the Casimir-Polder to van der Waals crossover, and by computing the Casimir interaction energy of two infinite, parallel, perfect metal cylinders either inside or outside one another. Furthermore, it is used to obtain new results, namely, the Casimir energies of a sphere or a cylinder opposite a plate, all with finite permittivity and permeability, to leading order at large separation.
Elements of QED-NRQED effective field theory: NLO scattering at leading power
NASA Astrophysics Data System (ADS)
Dye, Steven P.; Gonderinger, Matthew; Paz, Gil
2016-07-01
The proton radius puzzle, i.e. the large discrepancy in the extraction of the proton charge radius between regular and muonic hydrogen, challenges our understanding of the structure of the proton. It can also be an indication of a new force that couples to muons, but not to electrons. An effective field theory analysis using nonrelativistic quantum electrodynamics (NRQED) indicates that the muonic hydrogen result can be interpreted as a large, compared to some model estimates, muon-proton spin-independent contact interaction. The muonic hydrogen result can be tested by a muon-proton scattering experiment, MUSE, that is planned at the Paul Scherrer Institute in Switzerland. The typical momenta of the muons in this experiment are of the order of the muon mass. In this energy regime the muons are relativistic but the protons are still nonrelativistic. The interaction between the muons and protons can be described by a hybrid QED-NRQED effective field theory. We present some elements of this effective field theory. In particular we consider O (Z α ) scattering up to power m2/M2 , where m (M ) is the muon (proton) mass and Z =1 for a proton, and O (Z2α2) scattering at leading power. We show how the former reproduces Rosenbluth scattering up to power m2/M2 and the latter the relativistic scattering off a static potential. Proton structure corrections at O (Z2α2) will be considered in a subsequent paper.
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).
Quantum defect theory for the van der Waals plus dipole-dipole interaction
NASA Astrophysics Data System (ADS)
Wang, Gao-Ren; Xie, Ting; Huang, Yin; Zhang, Wei; Cong, Shu-Lin
2012-12-01
We investigate the scattering dynamics governed by the long-range van der Waals plus dipole-dipole interaction potential, -C6/R6-C3/R3, which describes the long-range interaction between two polar molecules in an electric field. In the spirit of quantum defect theory, a set of parameters which are nearly constants in the threshold regime is defined to characterize the scattering process. Using appropriate boundary conditions for the scattering wave functions and relevant parameters, we explore the quantum reflection by and quantum tunneling through the long-range potential. As a sample application, the reactive collision rates of 40K87Rb + 40K87Rb are calculated.
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.
New optimal polynomial theory for NN-scattering
Rijken, T A; Signell, P
1980-01-01
A new optimal polynomial theory for nucleon-nucleon scattering is presented. For the first time in nucleon-nucleon scattering, the derivative amplitudes originally introduced by Fubini, Furlan, and Rosetti are applied. Based on the properties of these amplitudes we introduce K-matrix functions which have suitable analyticity properties as functions of cos theta, where theta is the center of mass scattering angle. The K-matrix functions enable introduction of a new set of functions for which the optimal mapping techniques of Cutkosky, Deo and Ciulli can be applied. Results are shown for proton-proton phase shift analyses at 210 and 330 MeV.
Quantum theory of multimode polariton condensation
NASA Astrophysics Data System (ADS)
Racine, David; Eastham, P. R.
2014-08-01
We develop a theory for the dynamics of the density matrix describing a multimode polariton condensate. In such a condensate several single-particle orbitals become highly occupied, due to stimulated scattering from reservoirs of high-energy excitons. A generic few-parameter model for the system leads to a Lindblad equation which includes saturable pumping, decay, and condensate interactions. We show how this theory can be used to obtain the population distributions, and the time-dependent first- and second-order coherence functions, in such a multimode condensate. As a specific application, we consider a polaritonic Josephson junction, formed from a double-well potential. We obtain the population distributions, emission line shapes, and widths (first-order coherence functions), and predict the dephasing time of the Josephson oscillations.
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