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Response of a quantum system to a time-dependent external field anddynamical symmetry of the system

Wang, SJTypel, SWeiguny, AWiese

Published Jan 1, 1998• 0 citations
OpenAlex

Abstract

The response of a quantum system to a time-dependent periodic external The response of a quantum system to a time-dependent periodic external

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The response of a quantum system to a time-dependent periodic external field is investigated in connection with the dynamical symmetry breaking and level dynamics of the adiabatic states of the system. The main results are as follows. (A) When the periodic external field preserves the dynamical symmetry of the system, its response is like that of elastic matter. (B) When the periodic external field breaks the dynamical symmetry, several cases may occur: (a) in the adiabatic limit, the system still responds elastically; (b) if the initial state is an eigenstate of the evolution operator U ( T ) for one period T of the external field, the system evolves in time cyclically and responds quasi-elastically; (c) if the initial state is not an eigenstate of the evolution operator U ( T ), the system evolves in time non-cyclically and responds non-elastically. The detailed non-elastic behaviour depends on the statistical nature of the adiabatic eigenstates of the system. If the adiabatic spectrum is chaotic, the non-elastic response is expected to be strongly dissipative. The avoided level crossings of the adiabatic eigenstates play a crucial role in both producing chaoticity of the adiabatic levels and causing dissipation of the non-elastic response. The non-elastic role played by the adiabatic progressive phase is also addressed. Computer experiments are performed for the su(2) dynamical model to illustrate the above general results.

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A Solvable Model for Discrete Time Crystal Enforced by Nonsymmorphic Dynamical Symmetry

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Discrete time crystal is a class of nonequilibrium quantum systems exhibiting subharmonic responses to external periodic driving. Here we propose a class of discrete time crystals enforced by nonsymmorphic dynamical symmetry. We start with a system with nonsymmorphic dynamical symmetry, in which the instantaneous eigenstates become Möbius twisted, hence doubling the period of the instantaneous state. The exact solution of the time-dependent Schrödinger equation shows that the system spontaneously exhibits a period extension without undergoing quantum superposition states for a series of specifc evolution frequencies or in the limit of long evolution period. Moreover, in such case the system gains a π Berry phase after two periods' evolution. Finally, we show that the subharmonic response is stable even when many-body interactions are introduced, indicating a DTC phase in the thermodynamic limit.

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In this paper, the single-spin transition dynamics is used to investigate the kinetic Gaussian model in a periodic external field. We first derive the fundamental dynamic equations, and then treat an isotropic d-dimensional hypercubic lattice Gaussian spin system with Fourier's transformation method. We obtain exactly the local magnetization and the equal-time pair-correlation function. The critical characteristics of the dynamical relaxation tau(q), the complex susceptibility chi(omega,q), and the dynamical response are discussed. The results show that the time evolution of the dynamical quantities and the dynamical responses of the system strongly depend on the frequency and the wave vector of the external field.

arXiv:cond-mat/0207007•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jan 1, 2000•11 citations
The response of a quantum system to a time-dependent periodic external field is investigated in connection with the dynamical symmetry breaking and level dynamics of the adiabatic states of the system. The main results are as follows. (A) When the periodic external field preserves the dynamical symmetry of the system, its response is like that of elastic matter. (B) When the periodic external field breaks the dynamical symmetry, several cases may occur: (a) in the adiabatic limit, the system still responds elastically; (b) if the initial state is an eigenstate of the evolution operator U ( T ) for one period T of the external field, the system evolves in time cyclically and responds quasi-elastically; (c) if the initial state is not an eigenstate of the evolution operator U ( T ), the system evolves in time non-cyclically and responds non-elastically. The detailed non-elastic behaviour depends on the statistical nature of the adiabatic eigenstates of the system. If the adiabatic spectrum is chaotic, the non-elastic response is expected to be strongly dissipative. The avoided level crossings of the adiabatic eigenstates play a crucial role in both producing chaoticity of the adiabatic levels and causing dissipation of the non-elastic response. The non-elastic role played by the adiabatic progressive phase is also addressed. Computer experiments are performed for the su(2) dynamical model to illustrate the above general results.
Discrete time crystal is a class of nonequilibrium quantum systems exhibiting subharmonic responses to external periodic driving. Here we propose a class of discrete time crystals enforced by nonsymmorphic dynamical symmetry. We start with a system with nonsymmorphic dynamical symmetry, in which the instantaneous eigenstates become Möbius twisted, hence doubling the period of the instantaneous state. The exact solution of the time-dependent Schrödinger equation shows that the system spontaneously exhibits a period extension without undergoing quantum superposition states for a series of specifc evolution frequencies or in the limit of long evolution period. Moreover, in such case the system gains a π Berry phase after two periods' evolution. Finally, we show that the subharmonic response is stable even when many-body interactions are introduced, indicating a DTC phase in the thermodynamic limit.
In this paper, the single-spin transition dynamics is used to investigate the kinetic Gaussian model in a periodic external field. We first derive the fundamental dynamic equations, and then treat an isotropic d-dimensional hypercubic lattice Gaussian spin system with Fourier's transformation method. We obtain exactly the local magnetization and the equal-time pair-correlation function. The critical characteristics of the dynamical relaxation tau(q), the complex susceptibility chi(omega,q), and the dynamical response are discussed. The results show that the time evolution of the dynamical quantities and the dynamical responses of the system strongly depend on the frequency and the wave vector of the external field.