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Physica A Statistical Mechanics and its Applications

Equilibrium reduced-density operator for nanoscopic systems

Zbigniew Jacyna‐Onyszkiewicz

Published Mar 1, 2002• 7 citations
Publisher
DOI
10.1016/s0378-4371(01)00555-6

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A new type of projection operator is used to derive homogeneous equations of motion for the reduced density operator of a system coupled to a bath. Crucial simplifications of these equations are obtained without assuming that the projection operator and the zeroth-order Hamiltonian commute. No factorization assumption for the initial density matrix is made. The applicability of the general formalism, which is valid also for nonergodic initial conditions, to physically relevant situations is investigated. It turns out to be particularly useful for the treatment of a system initially submitted to some constraints but otherwise in equilibrium. The relaxation towards the unconstrained equilibrium of a two-level system in contact with an Ohmic bath is treated as an example. The reduced equilibrium density operator of this system is obtained analytically for the case of extremely low temperatures. The result shows and it is then proved rigorously that the zero-temperature reduced density operator does not describe a pure state in general, except in the zero-coupling limit.