A Diffusion Equation for Quantum Adiabatic Systems

Sudhir R. Jain

Published Jan 1, 1998• 4 citations

Abstract

For ergodic adiabatic quantum systems, we study the evolution of energy distribution as the system evolves in time. Starting from the von Neumann equation for the density operator, we obtain the quantum analogue of the Smoluchowski equation on coarse-graining over the energy spectrum. This result brings out the precise notion of quantum diffusion. 1 There are many physical situations where a separation of time scales occurs, the adiabatic approximation to an evolution is one of the expressions of such a separation [1]. Classically, an important problem in this context is to describe the evolution in phase space of an ensemble of systems under an ergodic adiabatic Hamiltonian [2]. An ergodic adiabatic Hamiltonian can be defined as one which describes ergodic (usually specialized to chaotic) dynamics under a slowly time-dependent Hamiltonian. In this paper, we study the quantal version of this treatment and obtain results which, in an

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