Work fluctuations in quantum spin chains

Abstract

We study the work fluctuations of two types of finite quantum spin chains under the application of a time-dependent magnetic field in the context of the fluctuation relation and Jarzynski equality. The two types of quantum chains correspond to the integrable Ising quantum chain and the nonintegrable XX quantum chain in a longitudinal magnetic field. For several magnetic field protocols, the quantum Crooks and Jarzynski relations are numerically tested and fulfilled. As a more interesting situation, we consider the forcing regime where a periodic magnetic field is applied. In the Ising case we give an exact solution in terms of double-confluent Heun functions. We show that the fluctuations of the work performed by the external periodic drift are maximum at a frequency proportional to the amplitude of the field. In the nonintegrable case, we show that depending on the field frequency a sharp transition is observed between a Poisson-limit work distribution at high frequencies toward a normal work distribution at low frequencies.

Entanglement in a periodic quench

“…Other experiments [12,13] have motivated studies of chains where the parameters in the Hamiltonian were assumed to vary harmonically. In this case, however, the focus was either on the energy absorption [14,15,16] or on work fluctuations [17].…”

Emergent Thermodynamics in a Quenched Quantum Many-Body System

“…Given the current experimental interest in the nonequilibrium dynamics of ultracold atomic systems and the recent developments in statistical mechanics, it is natural to study the quench dynamics of quantum many-body systems in this new thermodynamical formulation. In this work we use the transverse quantum Ising model [8] to provide an exact analysis of the Tasaki-Crooks and Jarzynski fluctuation relations in a quenched many-body system. Furthermore, we compute the irreversible entropy production and show that the emergence of thermodynamics provides an elegant interpretation of the essential physics.…”

Particle-number scaling of the quantum work statistics and Loschmidt echo in Fermi gases with time-dependent traps

“…In this section we focus on the statistics of the work done on the Fermi gas, when this is driven out of equilibrium by suddenly switching the control parameter associated with the external potential. Several issues related to the definition and computation of the work statistics in quantum systems have been already discussed in a variety of physical implementations [30,31], including spin chains [32][33][34][35][36][37][38][39][40], fermionic and bosonic systems [40][41][42][43][44].…”