Approach to Equilibrium in Nano-scale Systems at Finite Temperature

Jin, F.; Yuan, S.; Katsnelson, M.I.; De Raedt, H.; Miyashita, S.; Michielsen, K.

doi:10.1143/JPSJ.79.124005

Journal Article

Approach to Equilibrium in Nano-scale Systems at Finite Temperature

Jin, F. ; De Raedt, H. ; Yuan, S. ; Katsnelson, M. I. ; Miyashita, S. ; Michielsen, K.FZJ*

2010
The Physical Society of Japan Tokyo

Journal of the Physical Society of Japan 79, 124005 (2010) [10.1143/JPSJ.79.124005]

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Please use a persistent id in citations: http://hdl.handle.net/2128/22900 doi:10.1143/JPSJ.79.124005

Abstract: We study the time evolution of the reduced density matrix of a system of spin-1/2 particles interacting with an environment of spin-1/2 particles. The initial state of the composite system is taken to be a product state of a pure state of the system and a pure state of the environment. The latter pure state is prepared such that it represents the environment at a given finite temperature in the canonical ensemble. The state of the composite system evolves according to the time-dependent Schrodinger equation, the interaction creating entanglement between the system and the environment. It is shown that independent of the strength of the interaction and the initial temperature of the environment, all the eigenvalues of the reduced density matrix converge to their stationary values, implying that also the entropy of the system relaxes to a stationary value. We demonstrate that the difference between the canonical density matrix and the reduced density matrix in the stationary state increases as the initial temperature of the environment decreases. As our numerical simulations are necessarily restricted to a modest number of spin-1/2 particles (<36), but do not rely on time-averaging of observables nor on the assumption that the coupling between system and environment is weak, they suggest that the stationary state of the system directly follows from the time evolution of a pure state of the composite system, even if the size of the latter cannot be regarded as being close to the thermodynamic limit.

Keyword(s): J ; quantum statistical mechanics (auto) ; canonical ensemble (auto) ; time-dependent Schrodinger equation (auto) ; thermalization (auto) ; decoherence (auto)

Classification:

Physics, Multidisciplinary

Note: This work is partially supported by NCF, the Netherlands, by a Grant-in-Aid for Scientific Research on Priority Areas, and the Next Generation Super Computer Project, Nano-science Program from the Ministry of Education, Culture, Sports, Science and Technology, Japan. Part of the calculations were performed on the JUGENE supercomputer at JSC.

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