Quantum work for sudden quenches in Gaussian random Hamiltonians

Abstract

In the context of nonequilibrium quantum thermodynamics, variables like work behave stochastically. A particular definition of the work probability density function (pdf) for coherent quantum processes allows the verification of the quantum version of the celebrated fluctuation theorems, due to Jarzynski and Crooks, that apply when the system is driven away from an initial equilibrium thermal state. Such a particular pdf depends basically on the details of the initial and final Hamiltonians, on the temperature of the initial thermal state, and on how some external parameter is changed during the coherent process. Using random matrix theory we derive a simple analytic expression that describes the general behavior of the work characteristic function G(u), associated with this particular work pdf for sudden quenches, valid for all the traditional Gaussian ensembles of Hamiltonians matrices. This formula well describes the general behavior of G(u) calculated from single draws of the initial and final Hamiltonians in all ranges of temperatures.

Theory of quantum work in metallic grains

“…Along with this amazing experimental progress, exact fluctuation theorems have been derived and experimentally verified [2,[4][5][6][7][8][9][10], links between energy transfer (work), Loschmidt echo, and quantum information scrambling have been established [11][12][13][14], and the full distribution of work has been investigated in many-body systems such as Luttinger liquids [15][16][17][18][19] or systems close to quantum criticality [20,21]. So far, however, only very few studies investigate the effect of randomness [22][23][24], playing a crucial role in most nanosystems, and even these studies focus on sudden quenches and do not address quantum statistics and/or interactions.…”

Classical Theory of Quantum Work Distribution in Chaotic Fermion Systems

“…The full distribution of work has been studied extensively in many-body systems [14][15][16][17][18][19][20], and its characteristic function of this distribution has been related to the Loschmidt echo [14,21] and to quantum information scrambling [21]. However, the effect of disorder and randomness is much less studied [22][23][24] despite their relevance in mesoscopic systems.…”

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].…”