Microscopic expression for the heat in the adiabatic basis

Abstract

We derive a microscopic expression for the instantaneous diagonal elements of the density matrix ${\rho }_{nn}(t)$ in the adiabatic basis for an arbitrary time dependent process in a closed Hamiltonian system. If the initial density matrix is stationary (diagonal) then this expression contains only squares of absolute values of matrix elements of the evolution operator, which can be interpreted as transition probabilities. We then derive the microscopic expression for the heat defined as the energy generated due to transitions between instantaneous energy levels. If the initial density matrix is passive (diagonal with ${\rho }_{nn}(0)$ monotonically decreasing with energy) then the heat is non-negative in agreement with basic expectations of thermodynamics. Our findings also can be used for systematic expansion of various observables around the adiabatic limit.

4+, no figures. Revised version, corrected errors related to the lack of detailed balance in transition probabilities

References in corpus (6)

• Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons
• Universal adiabatic dynamics across a quantum critical point
• Supplementary Information to the paper ``Breakdown of the adiabatic limit in low dimensional gapless systems''
• Breakdown of the adiabatic limit in low dimensional gapless systems
• Minimal work principle: proof and counterexamples
• A mathematical theorem as the basis for the second law: Thomson's formulation applied to equilibrium

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