Statistics of the Work in Quantum Quenches, Universality and the Critical Casimir Effect

Abstract

We consider the dynamics of an isolated quantum many-body system after a sudden change of one control parameter, focusing on the statistics of the work done. We establish a connection between the generating function of the distribution of the work and the partition function of a classical system in a film geometry. Using this connection, we first show that the scaling of the fidelity susceptibilities close to a quantum phase transition can be understood in terms of the critical behavior of the excess entropy and specific heat in the classical model. Remarkably, we show that the statistics of the work close to the threshold and to criticality is connected to the so-called critical Casimir free energy which is responsible for the interaction between the boundaries of the classical system. On the basis of this relation, we highlight the emerging universal features of the statistics of the work. Our findings are exemplified for a global quench of the transverse Ising chain at zero temperature.

arXiv comment4.5 pages

Cited by in corpus (9)

• Quantum Quench in the Transverse Field Ising chain I: Time evolution of order parameter correlators
• Dynamical Quantum Phase Transitions in Spin Chains with Long-Range Interactions: Merging different concepts of non-equilibrium criticality
• The quantum Ising chain for beginners
• Quench echo and work statistics in integrable quantum field theories
• Nonequilibrium quench dynamics in quantum quasicrystals
• Equilibration times in clean and noisy systems
• Formation probabilities in quantum critical chains and Casimir effect
• Finite size corrections to scaling of the formation probabilities and the Casimir effect in the conformal field theories
• Evolution of the magnetization after a local quench in the critical transverse-field Ising chain