Inevitable Power-law Behavior of Isolated Many-Body Quantum Systems and How It Anticipates Thermalization

Abstract

Despite being ubiquitous, out-of-equilibrium quantum systems are much less understood than systems at equilibrium. Progress in the field has benefited from a symbiotic relationship between theoretical studies and new experiments on coherent dynamics. The present work strengthens this connection by providing a general picture of the relaxation process of isolated lattice many-body quantum systems that are routinely studied in experiments with cold atoms, ions traps, and nuclear magnetic resonance. We show numerically and analytically that the long-time decay of the probability for finding the system in its initial state necessarily shows a power-law behavior $\propto t^{-\gamma }$. This happens independently of the details of the system, such as integrability, level repulsion, and the presence or absence of disorder. Information about the spectrum, the structure of the initial state, and the number of particles that interact simultaneously is contained in the value of $\gamma$. From it, we can anticipate whether the initial state will or will not thermalize.

5 pages, 3 figures

References in corpus (13)

• Anderson Transitions
• The large deviation approach to statistical mechanics
• Time-resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices
• Dynamics of Loschmidt echoes and fidelity decay
• Breakdown of thermalization in finite one-dimensional systems
• Quantum Chaos and Thermalization in Isolated Systems of Interacting Particles
• Loschmidt Echo
• Simulations of Information Transport in Spin Chains
• Fundamental Asymmetry in Quenches Between Integrable and Nonintegrable Systems
• Initial state dependence of the quench dynamics in integrable quantum systems. II. Thermal states
• Nonexponential fidelity decay in isolated interacting quantum systems
• Return probability and scaling exponents in the critical random matrix ensemble
• General relaxation time of the fidelity for isolated quantum thermodynamic systems

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