Work statistics for sudden quenches in interacting quantum many-body systems

Abstract

Work in isolated systems, defined by the two projective energy measurement scheme, is a random variable whose the distribution function obeys the celebrated fluctuation theorems of Crooks and Jarzynski. In this study, we provide a simple way to calculate the work distribution associated to sudden quench processes in a given class of quantum many-body systems. Due to the large Hilbert space dimension of these systems, we show that there is an energy coarse-grained description of the exact work distribution that can be constructed from two elements: the level density of the initial Hamiltonian, and the strength function, which provides information about the influence of the perturbation over the eigenvectors in the quench process. We also show how random Hamiltonian models can be helpful to find the energy coarse-grained work probability distribution and apply this approach to different spin-1/2 chain models. Our finding provides an accurate description of the work distribution of such systems in the cases of intermediate and high temperatures in both chaotic and integrable regimes.arXiv:1907.06285v1 [quant-ph]

Work-distribution quantumness and irreversibility when crossing a quantum phase transition in finite time

“…Quantum phase transitions (QPTs) are an exquisitely quantum phenomenon, so there is interest in studying their signatures on quantum thermodynamic quantities and their distributions (fluctuations) [14,16,18,[21][22][23][24][25][26][27][28]. In addition, many-body interactions, which are ubiquitous and notoriously difficult to treat, assume an even more complex role in out-of-equilibrium quantum systems [29,30] where, e.g., they may affect the way the system reaches or settles into different phases. Relevant questions are as follows: what is the role of many-body interactions for quantum particles driven out of equilibrium, and how do they affect quantum thermodynamical quantities?…”

Tensor-Network Approach to Work Statistics for 1D Quantum Lattice Systems

“…Over the last decades, extensive efforts were devoted to prove and experimentally test the Jarzynski equality or closely related Crooks fluctuation theorem in various systems [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. However, what's more informative is the detailed probability distribution of work under an arbitrary protocol (instead of a sudden quench) [27,28]. Since it encodes essential information about not only the equilibrium properties, but also the nonequilibrium driving processes [29][30][31][32][33][34][35][36][37].…”

Quantum fluctuation theorem for initial near-equilibrium system

“…Transverse Ising model.-Recently, to study the dynamics of quantum many-body systems in this nonequilibrium thermodynamical formulation has aroused widespread interest. There has been quite a remarkable amount of activity uncovering the features of work statistics in a range of physical models including spin chains [40][41][42][43][44][45], Fermionic systems [46][47][48][49], Bosonic systems and Luttinger liquids [50][51][52][53] and periodically driven quantum systems [54][55][56][57]. Work statistics have also proved to be useful in the analysis of dynamical quantum criticality [58][59][60][61][62] and more recently to shed light on the phenomenon of information scrambling [63][64][65][66][67].…”