Exact infinite-time statistics of the Loschmidt echo for a quantum quench

Abstract

The equilibration dynamics of a closed quantum system is encoded in the long-time distribution function of generic observables. In this paper we consider the Loschmidt echo generalized to finite temperature, and show that we can obtain an exact expression for its long-time distribution for a closed system described by a quantum XY chain following a sudden quench. In the thermodynamic limit the logarithm of the Loschmidt echo becomes normally distributed, whereas for small quenches in the opposite, quasi-critical regime, the distribution function acquires a universal double-peaked form indicating poor equilibration. These findings, obtained by a central limit theorem-type result, extend to completely general models in the small-quench regime.

4 pages, 2 figures

References in corpus (13)

• Thermalization and its mechanism for generic isolated quantum systems
• Ground state overlap and quantum phase transitions
• Environment-independent decoherence rate in classically chaotic systems
• Quantum critical scaling of the geometric tensors
• Absence of Thermalization in Nonintegrable Systems
• Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
• Mixed-state fidelity and quantum criticality at finite temperature
• Decoherence induced by interacting quantum spin baths
• On the Approach to Thermal Equilibrium of Macroscopic Quantum Systems
• Unitary equilibrations: probability distribution of the Loschmidt echo
• Universal equilibrium distribution after a small quantum quench
• Decoherence by engineered quantum baths
• Equivalence between XY and dimerized models

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