Abstract
We generalize Anderson's orthogonality determinant formula to describe the statistics of work performed on generic disordered, non-interacting fermionic nanograins during quantum quenches. The energy absorbed increases linearly with time, while its variance exhibits a superdiffusive behavior due to Pauli's exclusion principle. The probability of adiabatic evolution decays as a stretched exponential. In slowly driven systems, work statistics exhibits universal features, and can be understood in terms of fermion diffusion in energy space, generated by Landau-Zener transitions. This diffusion is very well captured by a Markovian symmetrical exclusion process, with the diffusion constant identified as the energy absorption rate. The energy absorption rate shows an anomalous frequency dependence at small energies, reflecting the symmetry class of the underlying Hamiltonian. Our predictions can be experimentally verified by calorimetric measurements performed on nanoscale circuits.
Highlights
Heat, and work are fundamental concepts in thermodynamics and statistical physics, it is far from trivial to extend their concepts to generic nonequilibrium quantum systems [1,2], where energy becomes a fluctuating statistical quantity even in pure quantum states, and energy transfer can only be understood in terms of a precise measurement protocol
We have derived and used a determinant formula to compute the distribution of work, Pt (W ), in the course of a quantum quench in generic, disordered, fermionic nanosystems, and have shown that it displays a large degree of universality, especially in the slow quench limit
Our results demonstrate that quantum work statistics in these systems is, after all, to a large extent classical
Summary
Heat, and work are fundamental concepts in thermodynamics and statistical physics, it is far from trivial to extend their concepts to generic nonequilibrium quantum systems [1,2], where energy becomes a fluctuating statistical quantity even in pure quantum states, and energy transfer can only be understood in terms of a precise measurement protocol. We study the properties and universal aspects of quantum work produced in the course of time-dependent quantum quenches in generic, noninteracting, but disordered fermionic many-body nanosystems These systems provide an ideal platform to study quantum thermodynamics and the interplay of quantum time evolution, disorder, and quantum statistics. We assume that the system is in its M-particle ground state at time t = 0, and work is performed by changing external gate voltages or by applying time-dependent magnetic fields [27] (see Fig. 1) We describe this situation by performing a quench (ramp) at a constant pace, v ≡ Tr(dt H2) 1/2, related to the frequency ω of external parameters, and investigate the distribution of the internal energy injected, Pt (W ) ≡ δ[W − (H (t ) − EGS(t ))] RM,.
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