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Physical Review A

Dissipation and decoherence by a homogeneous ideal gas

János Polonyi

Published Oct 19, 2015• 9 citations
Publisher

Abstract

The effective Lagrangian of a test particle, interacting within an ideal gas, is calculated within the closed-time-path formalism in the one-loop approximation and in the leading order of the particle trajectory. The expansion in the time derivative, available for slow enough motion, uncovers diffusive forces and decoherence in the particle coordinate basis. The master equation, generated by the effective Lagrangian, is derived and its consistency is verified for a finite-temperature gas.

DOI
10.1103/physreva.92.042111

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The effective Lagrangian of a test particle, interacting within an ideal gas, is calculated within the closed-time-path formalism in the one-loop approximation and in the leading order of the particle trajectory. The expansion in the time derivative, available for slow enough motion, uncovers diffusive forces and decoherence in the particle coordinate basis. The master equation, generated by the effective Lagrangian, is derived and its consistency is verified for a finite-temperature gas.
The decoherence of a test particle interacting with an ideal gas is studied by the help of the effective Lagrangian, derived in the leading order of the perturbation expansion and in order $O({\ensuremath{\partial}}_{t}^{2})$. The stationary decoherence time is found to be comparable to or longer than the diffusion time. The decoherence time reaches its minimal value for classical, completely decohered environment, suggesting that physical decoherence is slowed down as compared with diffusion by the quantum coherence of the environment.
To study the phenomenon of decoherence the effective Lagrangian of a test particle interacting with an ideal gas is derived in the leading order of the perturbation expansion and in order $\ord{\partial^2_t}$. Two concepts of decoherence are distinguished and investigated in details: The general dynamical decoherence and the stationary decoherence, an approximation of the dynamical phenomenon corresponding to the assumption of a static test particle trajectory. Comparison of the stationary decoherence described by the present effective theory with the traditional description of decoherence based on collision theory reveals a qualitative similarity within their domain of applicability. However, the effective theory predicts comparable time scales for decoherence and dissipation in contrast to the deviation of this scales by many orders of magnitudes, estimated by referring to the collision approach. In particular the extremely fast decoherence predicted by the collisional approach can only be reproduced by the effective theory for parameter values which violate the applicability of both approaches. On the other hand, in harmonic systems, the true dynamical decoherence is indeed an extremely fast process involving a double exponential time dependence. It is argued that, in realistic systems, the dissipative effective dynamics is non-perturbative in nature and its asymptotic, relaxed state incorporates strong quantum fluctuations.
The time evolution of a Gaussian density matrix of a one dimensional particle, generated by a quadratic, O(∂t2){\cal O}(\partial_t^2)O(∂t2​) effective Lagrangian, describing a harmonic potential, a friction force and decoherence, is studied within the Closed Time Path formalism. The density matrix converges to an asymptotic form, given by a completely decohered thermal state with an O(ℏ){\cal O}(\hbar)O(ℏ) temperature in the translation invariant case. The time evolution of the state of a harmonic oscillator is followed numerically. The asymptotic density matrix, the fixed point of the master equation, is found analytically and its dependence on the oscillator frequency, the friction constant and the decoherence strength is explored.