Dynamics of a two-level system coupled to Ohmic bath: a perturbation approach

H. Zheng

doi:10.1140/epjb/e2004-00152-7

EPJ

Dynamics of a two-level system coupled to Ohmic bath: a perturbation approach

H. Zheng^a

Department of Physics, Shanghai Jiao Tong University, Shanghai 200030, P.R. China

Corresponding authors: ^a This email address is being protected from spambots. You need JavaScript enabled to view it. This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 24 April 2003
Revised: 14 October 2003
Published online: 8 June 2004

Abstract

The quantum dynamics, both non-equilibrium and equilibrium, of the dissipative two-level system is studied by means of the perturbation approach based on a unitary transformation. It works well for the whole parameter range $Mathematical equation: $0<\alpha<1$$ and $Mathematical equation: $0<\Delta<\omega_c$$ and our main results are: the coherence-incoherence transition is at $Mathematical equation: $\alpha_c={1\over 2}[1+\Delta_r/\omega_c]$$ ; for $Mathematical equation: $\alpha<\alpha_c$$ the non-equilibrium correlation $Mathematical equation: $P(t)=\cos(\omega_0 t)\exp(-\gamma t)$$ ; the susceptibility $Mathematical equation: $\chi^{\prime\prime}(\omega)/\omega$$ is of a double peak structure for $Mathematical equation: $\alpha<\alpha_c$$ and the Shiba's relation is exactly satisfied; at the transition point $Mathematical equation: $\alpha=\alpha_c$$ the equilibrium correlation $Mathematical equation: $C(t)\approx -1/\gamma^2_c t^2$$ in the long time limit.

PACS: 72.20.Dp – General theory, scattering mechanisms / 05.30.-d – Quantum statistical mechanics

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EPJ

Dynamics of a two-level system coupled to Ohmic bath: a perturbation approach

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