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arXiv:hep-th/9406024 · Physica A Statistical Mechanics and its Applications

Classical and quantum dissipation in non-homogeneous environments

Fabrizio Illuminati, Marco Patriarca, Pasquale Sodano

Published Nov 1, 1994• 7 citations
arXivHTMLPDF
DOI
10.1016/0378-4371(94)00171-5

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The theory of non-dissipative diffusion is constructed on an example of diffusion of a light particle in a dilute medium of heavy particles and it is shown that in low dissipative systems there are specific effects of non-dissipativity similar to quantum effects.In a non-dissipativity region mean energy of the light particle is conserved and processes are described by two non-linear diffusion equations with forward and backward time derivatives.Then these two diffusion equations are linearized and give one linear Schrödinger equation for complex amplitudes of probability.As a result, in the non-dissipative classical diffusion should be added probability amplitudes and there holds the superposition principle for these amplitudes.A mean square length of free passage and a mean square momentum define an elementary phase volume and a diffusion constant and they obey the uncertainty relations.It is shown that the formalism of quantum mechanics describes the classical non-dissipative diffusion with a homogeneous diffusion constant and that quantum mechanics is only a particular case when the elementary phase volume of free passage is universal and equal to the Planck constant.
Open quantum systems are inherently coupled to their environments, which in turn also obey quantum dynamical rules. Restricting ourselves to dissipative dynamics, here we propose a measure that quantifies how far the action of an environment on a system departs from the influence of classical noise fluctuations. It is based on the lack of commutativity between the initial reservoir state and the total system-environment Hamiltonian. Independently of the nature of the dissipative system evolution, Markovian or non-Markovian, the measure can be written in terms of the dual propagator that defines the evolution of system operators. The physical meaning and properties of the proposed definition are discussed in detail and also characterized through different paradigmatic dissipative Markovian and non-Markovian open quantum dynamics.
Abstract This study investigates the parameters affecting the entanglement time evolution of product separable (PS) and extended Werner-like (EWL) states in homogeneous, white noise, and mixed environments. In a pure homogeneous environment, both states demonstrate complete entanglement revivals, where an increase in the number of environments leads to an attenuation of concurrence. The PS state exhibits gaps and never reaches a maximum entanglement, whereas maximum purity EWL states (Bell states) maintain or periodically reach maximum entanglement. Hence, the PS and EWL states have a disjoint entanglement time evolution subspaces. Interestingly, the environment interaction and subsystem coupling interaction that influence entanglement have an inverse time relationship under a constant value of concurrence. Placing the system of interest in a white noise environment induces entanglement dissipation, with the dissipation time dependent on the width of random distribution of interaction strengths rather than the magnitude of interaction strength. In a distinct qubit environment, the entanglement time evolution of the PS state depends on the distribution of the number of environments. Moreover, combining homogeneous and white noise environments results in entanglement dynamics that exhibit characteristics of both homogeneous and white noise.