© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Journal of Physics A Mathematical and General

New energetic and dynamic quantum effects originating from the breaking of time-reversal symmetry

Dieter Schuch

Published Sep 24, 2002• 10 citations

Abstract

The reduction of spatial symmetry can have qualitative effects for a given quantum system, such as splitting of energy levels that are degenerate in the unperturbed case. Can the breaking of temporal symmetry have a similar effect? Using a nonlinear quantum mechanical model to describe the effective interaction of simple, exactly solvable quantum systems with some dissipative environment, the time-symmetry-breaking effect of this interaction on the ground-state energy of these systems can be studied analytically. Also, in the case of dynamical properties such as tunnelling currents, the breaking of time-reversal symmetry can have quite unexpected effects. In general, a dissipative environment is assumed to inhibit the motion of a dynamical system, e.g., by reducing the frequency and amplitude of a harmonic oscillator. Our study shows, however, that under certain resonance-like conditions, the interaction with the environment can also create currents that are not present in the unperturbed system. These results follow directly from the analytical solutions of our model.

DOI: 10.1088/0305-4470/35/40/318

Related papers

Quantum transport enhancement by time-reversal symmetry breaking

Zoltán Zimborás, Mauro Faccin, Kadar, Z +3 more

Quantum mechanics still provides new unexpected effects when considering the transport of energy and information. Models of continuous time quantum walks, which implicitly use time-reversal symmetric Hamiltonians, have been intensely used to investigate the effectiveness of transport. Here we show how breaking time-reversal symmetry of the unitary dynamics in this model can enable directional control, enhancement, and suppression of quantum transport. Examples ranging from exciton transport to complex networks are presented. This opens new prospects for more efficient methods to transport energy and information.

•Jan 1, 2012•27 citations

Quantum Transport Enhancement by Time-Reversal Symmetry Breaking

Zoltán Zimborás, Mauro Faccin, Zoltán Kádár +3 more

Quantum mechanics still provides new unexpected effects when considering the transport of energy and information. Models of continuous time quantum walks, which implicitly use time-reversal symmetric Hamiltonians, have been intensely used to investigate the effectiveness of transport. Here we show how breaking time-reversal symmetry of the unitary dynamics in this model can enable directional control, enhancement, and suppression of quantum transport. Examples ranging from exciton transport to complex networks are presented. This opens new prospects for more efficient methods to transport energy and information.

arXiv:1208.4049•Scientific Reports•Aug 6, 2013•64 citations

Spontaneous Breakdown of the Time Reversal Symmetry

János Polonyi

The role of the environment initial conditions in the breaking of the time reversal symmetry of effective theories and in generating the soft irreversibility is studied by the help of Closed Time Path formalism. The initial conditions break the time reversal symmetry of the solution of the equation of motion in a trivial manner. When open systems are considered then the initial conditions of the environment must be included in the effective dynamics. This is achieved by means of a generalized ϵ-prescription where the non-uniform convergence of the limit ϵ → 0 leaves behind a spontaneous breakdown of the time reversal symmetry.

arXiv:1503.08500•Symmetry•Apr 20, 2016•8 citations

Explicit, spontaneous and dynamical breakdown of the time reversal symmetr

János Polonyi

The role of the environment initial conditions in the breaking of the time reversal symmetry of effective theories and in generating the soft irreversibility is studied by the help of Closed Time Path formalism. The initial conditions break the time reversal symmetry of the solution of the equation of motion in a trivial manner. When open systems are considered then the initial conditions of the environment must be included in the effective dynamics. This is achieved by means of a generalized $\epsilon$-prescription where the non-uniform convergence of the limit $\epsilon\to0$ leaves behind a spontaneous breakdown of the time reversal symmetry.

•Mar 29, 2015•0 citations

On the law of increasing entropy and the cause of the dynamics irreversibility of quantum systems

Gordey B. Lesovik

It has been shown that time reversal symmetry breaking in the dynamics of large systems originates from symmetry breaking in the occupation of the Hilbert space. The states ϕ, for which the entropy of the system (sub-system) increases, are automatically created in nature or can be prepared experimentally, in contrast to the respective complex-conjugate states (ϕ*), for which the entropy decreases (although formally, according to the superposition principle, they can exist). It is indicated that, in the general case, the dynamics reversal of unknown states is impossible because the complex conjugation operator is antilinear. The complexity of reversal of the known state is exponential in the typical case of a large system. The formulated statements are illustrated by simple models.

Journal of Experimental and Theoretical Physics Letters•Oct 1, 2013•4 citations

Discrete time symmetry breaking in quantum circuits: exact solutions and tunneling

Feng-Xiao Sun, Qiongyi He, Qihuang Gong +3 more

Abstract We discuss general properties of discrete time quantum symmetry breaking in degenerate parametric oscillators. Recent experiments in superconducting quantum circuit with Josephson junction nonlinearities give rise to new properties of strong parametric coupling and nonlinearities. Exact analytic solutions are obtained for the steady-state of this single-mode case of subharmonic generation. We also obtain analytic solutions for the tunneling time over which the time symmetry-breaking is lost above threshold. We find that additional anharmonic terms found in the superconducting case increase the tunneling rate, and can also lead to new regimes of tristability as well as bistability. Our analytic results are confirmed by number state calculations.

arXiv:1904.05010•New Journal of Physics•Aug 30, 2019•14 citations

The reduction of spatial symmetry can have qualitative effects for a given quantum system, such as splitting of energy levels that are degenerate in the unperturbed case. Can the breaking of temporal symmetry have a similar effect? Using a nonlinear quantum mechanical model to describe the effective interaction of simple, exactly solvable quantum systems with some dissipative environment, the time-symmetry-breaking effect of this interaction on the ground-state energy of these systems can be studied analytically. Also, in the case of dynamical properties such as tunnelling currents, the breaking of time-reversal symmetry can have quite unexpected effects. In general, a dissipative environment is assumed to inhibit the motion of a dynamical system, e.g., by reducing the frequency and amplitude of a harmonic oscillator. Our study shows, however, that under certain resonance-like conditions, the interaction with the environment can also create currents that are not present in the unperturbed system. These results follow directly from the analytical solutions of our model.

Quantum mechanics still provides new unexpected effects when considering the transport of energy and information. Models of continuous time quantum walks, which implicitly use time-reversal symmetric Hamiltonians, have been intensely used to investigate the effectiveness of transport. Here we show how breaking time-reversal symmetry of the unitary dynamics in this model can enable directional control, enhancement, and suppression of quantum transport. Examples ranging from exciton transport to complex networks are presented. This opens new prospects for more efficient methods to transport energy and information.

Quantum mechanics still provides new unexpected effects when considering the transport of energy and information. Models of continuous time quantum walks, which implicitly use time-reversal symmetric Hamiltonians, have been intensely used to investigate the effectiveness of transport. Here we show how breaking time-reversal symmetry of the unitary dynamics in this model can enable directional control, enhancement, and suppression of quantum transport. Examples ranging from exciton transport to complex networks are presented. This opens new prospects for more efficient methods to transport energy and information.

The role of the environment initial conditions in the breaking of the time reversal symmetry of effective theories and in generating the soft irreversibility is studied by the help of Closed Time Path formalism. The initial conditions break the time reversal symmetry of the solution of the equation of motion in a trivial manner. When open systems are considered then the initial conditions of the environment must be included in the effective dynamics. This is achieved by means of a generalized ϵ-prescription where the non-uniform convergence of the limit ϵ → 0 leaves behind a spontaneous breakdown of the time reversal symmetry.

The role of the environment initial conditions in the breaking of the time reversal symmetry of effective theories and in generating the soft irreversibility is studied by the help of Closed Time Path formalism. The initial conditions break the time reversal symmetry of the solution of the equation of motion in a trivial manner. When open systems are considered then the initial conditions of the environment must be included in the effective dynamics. This is achieved by means of a generalized

\epsilon

-prescription where the non-uniform convergence of the limit

\epsilon\to0

leaves behind a spontaneous breakdown of the time reversal symmetry.

It has been shown that time reversal symmetry breaking in the dynamics of large systems originates from symmetry breaking in the occupation of the Hilbert space. The states ϕ, for which the entropy of the system (sub-system) increases, are automatically created in nature or can be prepared experimentally, in contrast to the respective complex-conjugate states (ϕ*), for which the entropy decreases (although formally, according to the superposition principle, they can exist). It is indicated that, in the general case, the dynamics reversal of unknown states is impossible because the complex conjugation operator is antilinear. The complexity of reversal of the known state is exponential in the typical case of a large system. The formulated statements are illustrated by simple models.

Abstract We discuss general properties of discrete time quantum symmetry breaking in degenerate parametric oscillators. Recent experiments in superconducting quantum circuit with Josephson junction nonlinearities give rise to new properties of strong parametric coupling and nonlinearities. Exact analytic solutions are obtained for the steady-state of this single-mode case of subharmonic generation. We also obtain analytic solutions for the tunneling time over which the time symmetry-breaking is lost above threshold. We find that additional anharmonic terms found in the superconducting case increase the tunneling rate, and can also lead to new regimes of tristability as well as bistability. Our analytic results are confirmed by number state calculations.