Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

General validity of reciprocity in quantum mechanics

Huai-Yi Xie, P. T. Leung, Din Ping Tsai

Published Dec 15, 2008• 9 citations
Publisher

Abstract

The concept of reciprocity symmetry for matter-wave propagation is established for nonrelativistic quantum mechanics with previous results in the literature extended to include nonlocal interactions. Examples are given for cases with both local and nonlocal potentials, where we show in particular that reciprocity can be violated for the motion of a charged particle in an external electromagnetic field. In addition, this symmetry is applied to interpret a recent analysis [Phys. Rev. A 64, 042716 (2001)] on the symmetry of transmission through one-dimensional complex potentials, with the emphasis that the validity of reciprocity can go beyond that of time-reversal symmetry, such as in the presence of absorption in which the latter symmetry breaks down.

DOI
10.1103/physreva.78.064101

Related papers

Gauge invariance and reciprocity in quantum mechanics

P. T. Leung, K. Young

Reciprocity in wave propagation usually refers to the symmetry of the Green's function under the interchange of the source and the observer coordinates, but this condition is not gauge invariant in quantum mechanics, a problem that is particularly significant in the presence of a vector potential. Several possible alternative criteria are given and analyzed with reference to different examples with nonzero magnetic fields and/or vector potentials, including the case of a multiply connected spatial domain. It is shown that the appropriate reciprocity criterion allows for specific phase factors separable into functions of the source and observer coordinates and that this condition is robust with respect to the addition of any scalar potential. In the Aharonov-Bohm effect, reciprocity beyond monoenergetic experiments holds only because of subsidiary conditions satisfied in actual experiments: the test charge is in units of $e$ and the flux is produced by a condensate of particles with charge $2e$.

Physical Review A•Mar 8, 2010•10 citations

Constraints on the reciprocal propagation of a quantum particle through a one-dimensional localized complex potential

Ethan Knox, P. T. Leung

In the propagation of an electron through a one-dimensional asymmetric complex potential, it is known that while the conventional Green function reciprocity symmetry will ensure transmission to be symmetric between a “left-incident” and a “right-incident” beam, no such symmetry exists for the case of reflection. Here we derive generalized reciprocity relations for both the amplitude and phase of the reflected waves as constraints on the left- and right-incident beams, in complete analogy to what was established in optics. We further provide illustrations of these relations via direct analytical calculations in the case of a real potential, and via numerical studies in the case of a complex potential.

Canadian Journal of Physics•Jan 22, 2013•0 citations

Remarks Concerning Reciprocity in Quantum Mechanics

D. E. Bilhorn, Leslie L. Foldy, Roy M. Thaler +2 more

A new derivation of the reciprocity theorem is given. The general invariance property of the Hamiltonian which leads to symmetry of the Green's function for a quantum mechanical system is exhibited. It is found that reciprocity does not necessarily imply Hermiticity of the Hamiltonian, so that the ``complex optical model potential,'' for example, satisfies the reciprocity relations. The concept of reciprocity is then generalized to include a somewhat wider class of symmetry properties. Some properties of antiunitary transformations are discussed.

Journal of Mathematical Physics•Apr 1, 1964•32 citations

Dynamics of matter wave packets in the presence of time-dependent absorption

Maximilien Barbier

Atom-laser interaction is at the heart of the vibrant field of quantum optics. The dynamical properties of a moving atom submitted to a laser radiation are strongly \ninfluenced by the position- and time-dependence of the latter. The full physical state of the atom must include information about the centre-of-mass motion and the internal structure of the atom. It is challenging to obtain a complete description of the full state of the atom. However, there exists an alternative approach to the dynamics of an atom in the presence of a laser, which is based on the concept of matter-wave absorption. \n \nIn this thesis, we theoretically study the nonrelativistic one-dimensional motion of an electrically neutral quantum particle in the presence of a thin time-dependent absorber, representing the laser radiation. Our aim is to better understand the precise connection between time-dependent matter-wave absorption and the interaction between an atom and a localised time-dependent laser. \n \nOur analysis is based on two different approaches to the problem. The first one describes the moving atom by a two-level system, and represents the laser radiation \nby an off-diagonal δ-potential. The second model treats the atom as a structureless particle, and describes the laser by a time-dependent absorbing barrier. While the \nformer model can be derived from first principles, the treatment of the absorbing barrier in the latter model lacks a rigorous quantum mechanical justification. The \nmain outcome of our work is to provide a solid physical ground for the absorber model, by explicitly connecting it to the δ-potential model. We have thus extended \nthe range of theoretical tools useful for investigating the effects of time-dependent laser radiation on quantum matter.

•Feb 1, 2017•1 citation

Dynamics of local symmetry correlators for interacting many-particle systems

P. Schmelcher, S. Krönke, F. K. Diakonos

Recently [P. A. Kalozoumis et al. Phys. Rev. Lett. 113, 050403 (2014)] the concept of local symmetries in one-dimensional stationary wave propagation has been shown to lead to a class of invariant two-point currents that allow to generalize the parity and Bloch theorem. In the present work, we establish the theoretical framework of local symmetries for higher-dimensional interacting many-body systems. Based on the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, we derive the equations of motion of local symmetry correlators which are off-diagonal elements of the reduced one-body density matrix at symmetry related positions. The natural orbital representation yields equations of motion for the convex sum of the local symmetry correlators of the natural orbitals as well as for the local symmetry correlators of the individual orbitals themselves. An alternative integral representation with a unique interpretation is provided. We discuss special cases, such as the bosonic and fermionic mean field theory, and show in particular that the invariance of two-point currents is recovered in the case of the non-interacting one-dimensional stationary wave propagation. Finally we derive the equations of motion for anomalous local symmetry correlators which indicate the breaking of a global into a local symmetry in the stationary non-interacting case.

arXiv:1604.07951•The Journal of Chemical Physics•Jan 28, 2017•8 citations

Retarded Electromagnetic Interaction and Symmetry Violation of Time Reversal in High Order Stimulated Radiation and Absorption Processes of Lights as well as Nonlinear Optics - Influence on Fundamental Theory of Laser and Non-Equilibrium Statistical Physi

Mei Xiaochun

Electromagnetic Radiation 20time reversal, for the motion equations of quantum mechanics and the Hamiltonian of electromagnetic interaction are unchanged under time reversal.However, most processes related to laser and nonlinear optics are actually high nonequilibrium ones.As we known that time reversal symmetry will generally be violated in non-equilibrium processes.It is proved in this paper that after the retarded effect of radiation fields is taken into account, the time reversal symmetry will be violated in light's high order stimulated radiation and absorption processes with ml lm BB , although the Hamiltonian of electromagnetic interaction is still unchanged under time reversal.The transition probability of third order process is calculated and the revised formula of nonlinear optics polarizability is deduced in this paper.Many phenomena of time reversal symmetry violation in non-linear optics just as sum frequency, double frequency, different frequencies, double stable states, self-focusing and self-defocusing, echo phenomena, as well as optical self-transparence and self absorptions and so on are analyzed.The reason to cause symmetry violation is that some filial or partial transition processes of bounding state atoms are forbidden or can't be achieved due to the law of energy conservation.These restrictions can cause the symmetry violation of time reversal of other partial transition processes which can be actualized really.These realizable filial or partial processes which violate time reversal symmetry generally are just the practically observed physical processes.The symmetry violation is also relative to the initial state's asymmetries of bounding atoms before and after time reversal.For the electromagnetic interaction between non-bounding atoms and radiation fields, there is no this kind of symmetry violation of time reversal.For example, in the experiments of particle physics in accelerators, we can not observe the symmetry violation of time reversal.At last, the influences of symmetry violation of time reversal on the foundation theory of laser and non-equilibrium statistical physics are discussed.The phenomena of producing laser without the reversion of particle population and transition without radiation can be well explained.The result indicates that the irreversibility of evolution processes of macrosystems originates from the irreversibility of micro-processes.The irreversibility paradox can be eliminated thoroughly.By introducing retarded electromagnetic interaction, the forces between classical changed particles are not conservative ones.Based on them, we can establish the revised Liouville equation which is irreversible under time reversal.In this way, we can lay a really rational dynamic foundation for classical non-equilibrium statistical mechanics. The transition probability of the first order processFor simplification, we consider an atom with an electron in its external layer.Electron's mass is  , charge is q .When there is no external interaction, the Hamiltonian and the wave function of electron are individually  2 2 0 ˆ2 HU r m     1 0 n Et n en      (1) www.intechopen.comRetarded Electromagnetic Interaction and Symmetry Violation of Time Reversal in High Order Stimulated Radiation and Absorption Processes of Lights as Well as Nonlinear Optics ... 21 After external electromagnetic field is introduced, the interaction Hamiltonian is 2 2 2 ˆˆ ˆ2 qq HA pA q c c How to reference In order to correctly reference this scholarly work, feel free to copy and paste the following: Mei Xiaochun (2012).Retarded Electromagnetic Interaction and Symmetry Violation of Time Reversal in High Order Stimulated Radiation and Absorption Processes of Lights as well as Nonlinear Optics -Influence on Fundamental Theory of Laser and Non-Equilibrium Statistical Physi, Electromagnetic Radiation, Prof. S. O.

InTech eBooks•Jun 5, 2012•0 citations
The concept of reciprocity symmetry for matter-wave propagation is established for nonrelativistic quantum mechanics with previous results in the literature extended to include nonlocal interactions. Examples are given for cases with both local and nonlocal potentials, where we show in particular that reciprocity can be violated for the motion of a charged particle in an external electromagnetic field. In addition, this symmetry is applied to interpret a recent analysis [Phys. Rev. A 64, 042716 (2001)] on the symmetry of transmission through one-dimensional complex potentials, with the emphasis that the validity of reciprocity can go beyond that of time-reversal symmetry, such as in the presence of absorption in which the latter symmetry breaks down.
Reciprocity in wave propagation usually refers to the symmetry of the Green's function under the interchange of the source and the observer coordinates, but this condition is not gauge invariant in quantum mechanics, a problem that is particularly significant in the presence of a vector potential. Several possible alternative criteria are given and analyzed with reference to different examples with nonzero magnetic fields and/or vector potentials, including the case of a multiply connected spatial domain. It is shown that the appropriate reciprocity criterion allows for specific phase factors separable into functions of the source and observer coordinates and that this condition is robust with respect to the addition of any scalar potential. In the Aharonov-Bohm effect, reciprocity beyond monoenergetic experiments holds only because of subsidiary conditions satisfied in actual experiments: the test charge is in units of eee and the flux is produced by a condensate of particles with charge 2e2e2e.
In the propagation of an electron through a one-dimensional asymmetric complex potential, it is known that while the conventional Green function reciprocity symmetry will ensure transmission to be symmetric between a “left-incident” and a “right-incident” beam, no such symmetry exists for the case of reflection. Here we derive generalized reciprocity relations for both the amplitude and phase of the reflected waves as constraints on the left- and right-incident beams, in complete analogy to what was established in optics. We further provide illustrations of these relations via direct analytical calculations in the case of a real potential, and via numerical studies in the case of a complex potential.
A new derivation of the reciprocity theorem is given. The general invariance property of the Hamiltonian which leads to symmetry of the Green's function for a quantum mechanical system is exhibited. It is found that reciprocity does not necessarily imply Hermiticity of the Hamiltonian, so that the ``complex optical model potential,'' for example, satisfies the reciprocity relations. The concept of reciprocity is then generalized to include a somewhat wider class of symmetry properties. Some properties of antiunitary transformations are discussed.
Atom-laser interaction is at the heart of the vibrant field of quantum optics. The dynamical properties of a moving atom submitted to a laser radiation are strongly \ninfluenced by the position- and time-dependence of the latter. The full physical state of the atom must include information about the centre-of-mass motion and the internal structure of the atom. It is challenging to obtain a complete description of the full state of the atom. However, there exists an alternative approach to the dynamics of an atom in the presence of a laser, which is based on the concept of matter-wave absorption. \n \nIn this thesis, we theoretically study the nonrelativistic one-dimensional motion of an electrically neutral quantum particle in the presence of a thin time-dependent absorber, representing the laser radiation. Our aim is to better understand the precise connection between time-dependent matter-wave absorption and the interaction between an atom and a localised time-dependent laser. \n \nOur analysis is based on two different approaches to the problem. The first one describes the moving atom by a two-level system, and represents the laser radiation \nby an off-diagonal δ-potential. The second model treats the atom as a structureless particle, and describes the laser by a time-dependent absorbing barrier. While the \nformer model can be derived from first principles, the treatment of the absorbing barrier in the latter model lacks a rigorous quantum mechanical justification. The \nmain outcome of our work is to provide a solid physical ground for the absorber model, by explicitly connecting it to the δ-potential model. We have thus extended \nthe range of theoretical tools useful for investigating the effects of time-dependent laser radiation on quantum matter.
Recently [P. A. Kalozoumis et al. Phys. Rev. Lett. 113, 050403 (2014)] the concept of local symmetries in one-dimensional stationary wave propagation has been shown to lead to a class of invariant two-point currents that allow to generalize the parity and Bloch theorem. In the present work, we establish the theoretical framework of local symmetries for higher-dimensional interacting many-body systems. Based on the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, we derive the equations of motion of local symmetry correlators which are off-diagonal elements of the reduced one-body density matrix at symmetry related positions. The natural orbital representation yields equations of motion for the convex sum of the local symmetry correlators of the natural orbitals as well as for the local symmetry correlators of the individual orbitals themselves. An alternative integral representation with a unique interpretation is provided. We discuss special cases, such as the bosonic and fermionic mean field theory, and show in particular that the invariance of two-point currents is recovered in the case of the non-interacting one-dimensional stationary wave propagation. Finally we derive the equations of motion for anomalous local symmetry correlators which indicate the breaking of a global into a local symmetry in the stationary non-interacting case.
Electromagnetic Radiation 20time reversal, for the motion equations of quantum mechanics and the Hamiltonian of electromagnetic interaction are unchanged under time reversal.However, most processes related to laser and nonlinear optics are actually high nonequilibrium ones.As we known that time reversal symmetry will generally be violated in non-equilibrium processes.It is proved in this paper that after the retarded effect of radiation fields is taken into account, the time reversal symmetry will be violated in light's high order stimulated radiation and absorption processes with ml lm BB , although the Hamiltonian of electromagnetic interaction is still unchanged under time reversal.The transition probability of third order process is calculated and the revised formula of nonlinear optics polarizability is deduced in this paper.Many phenomena of time reversal symmetry violation in non-linear optics just as sum frequency, double frequency, different frequencies, double stable states, self-focusing and self-defocusing, echo phenomena, as well as optical self-transparence and self absorptions and so on are analyzed.The reason to cause symmetry violation is that some filial or partial transition processes of bounding state atoms are forbidden or can't be achieved due to the law of energy conservation.These restrictions can cause the symmetry violation of time reversal of other partial transition processes which can be actualized really.These realizable filial or partial processes which violate time reversal symmetry generally are just the practically observed physical processes.The symmetry violation is also relative to the initial state's asymmetries of bounding atoms before and after time reversal.For the electromagnetic interaction between non-bounding atoms and radiation fields, there is no this kind of symmetry violation of time reversal.For example, in the experiments of particle physics in accelerators, we can not observe the symmetry violation of time reversal.At last, the influences of symmetry violation of time reversal on the foundation theory of laser and non-equilibrium statistical physics are discussed.The phenomena of producing laser without the reversion of particle population and transition without radiation can be well explained.The result indicates that the irreversibility of evolution processes of macrosystems originates from the irreversibility of micro-processes.The irreversibility paradox can be eliminated thoroughly.By introducing retarded electromagnetic interaction, the forces between classical changed particles are not conservative ones.Based on them, we can establish the revised Liouville equation which is irreversible under time reversal.In this way, we can lay a really rational dynamic foundation for classical non-equilibrium statistical mechanics. The transition probability of the first order processFor simplification, we consider an atom with an electron in its external layer.Electron's mass is  , charge is q .When there is no external interaction, the Hamiltonian and the wave function of electron are individually  2 2 0 ˆ2 HU r m     1 0 n Et n en      (1) www.intechopen.comRetarded Electromagnetic Interaction and Symmetry Violation of Time Reversal in High Order Stimulated Radiation and Absorption Processes of Lights as Well as Nonlinear Optics ... 21 After external electromagnetic field is introduced, the interaction Hamiltonian is 2 2 2 ˆˆ ˆ2 qq HA pA q c c How to reference In order to correctly reference this scholarly work, feel free to copy and paste the following: Mei Xiaochun (2012).Retarded Electromagnetic Interaction and Symmetry Violation of Time Reversal in High Order Stimulated Radiation and Absorption Processes of Lights as well as Nonlinear Optics -Influence on Fundamental Theory of Laser and Non-Equilibrium Statistical Physi, Electromagnetic Radiation, Prof. S. O.