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arXiv:1502.02540

Dissipation and decoherence by ideal quantum gas

János Polonyi

Published Feb 9, 2015• 1 citation
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Abstract

The effective Lagrangian of a test particle, interacting with an ideal gas, is calculated with in the closed time path formalism in the one-loop and the leading order of the particle trajectory. The expansion in the time derivative is available for slow enough motion and it uncovers diffusive effective forces and decoherence for the coordinate and the momentum. A pure Newtonian friction force and an anisotrop coordinate decoherence are found for zero temperature ideal gas of fermions.

DOI
10.48550/arxiv.1502.02540

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The effective Lagrangian of a test particle, interacting with an ideal gas, is calculated with in the closed time path formalism in the one-loop and the leading order of the particle trajectory. The expansion in the time derivative is available for slow enough motion and it uncovers diffusive effective forces and decoherence for the coordinate and the momentum. A pure Newtonian friction force and an anisotrop coordinate decoherence are found for zero temperature ideal gas of fermions.
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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.
In this paper we study the dissipative effects and decoherence induced on a particle moving at constant speed in front of a dielectric plate in quantum vacuum, developing a closed-time-path (CTP) integral formulation in order to account for the corrections to these phenomena generated by finite temperatures. We compute the frictional force of the moving particle and find that it contains two different contributions: a pure quantum term due to quantum fluctuations (even present at vanishing temperatures) and a temperature-dependent component generated by thermal fluctuations (the bigger the contribution, the higher the temperature). We further estimate the decoherence timescale for the internal degree of freedom of the quantum particle. As expected, decoherence time is reduced by temperature; however, this feature is stronger for large velocities and for resonant situations. When the particle approaches relativistic speed, decoherence time becomes independent of temperature. The finite temperature corrections to the force or even in the decoherence timescale could be used to track traces of quantum friction through the study of the velocity dependence since the sole evidence of this dependence provides an indirect testimony of the existence of a quantum frictional force.