2014
DOI: 10.1007/s10955-013-0908-4
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Energy Diffusion in Harmonic System with Conservative Noise

Abstract: Abstract. A linear Boltzmann equation is interpreted as the forward equation for the probability density of a Markov process (is the two-dimensional torus. Here (K(t), i(t)) is an autonomous reversible jump process, with waiting times between two jumps with finite expectation value but infinite variance.

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Cited by 11 publications
(26 citation statements)
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“…This condition can be shown to be satisfied by W (x) in (13). We also note that (63) can be written as…”
Section: Luttinger Model With An External Field: Proof Of Theorem 21mentioning
confidence: 85%
See 2 more Smart Citations
“…This condition can be shown to be satisfied by W (x) in (13). We also note that (63) can be written as…”
Section: Luttinger Model With An External Field: Proof Of Theorem 21mentioning
confidence: 85%
“…To anticipate the properties of a final steady state in this set-up we consider first a system of length L > 0 in contact with infinite reservoirs at its left and right boundaries with different fixed chemical potentials or temperatures (µ L , T L ) and (µ R , T R ), respectively. The coupling between system and reservoirs is done stochastically for classical systems [10][11][12][13][14][15], and for quantum systems one uses Lindblad-type operators [7][8][9]16]. Such a system will in general approach a steady state for fixed L. We can then define the electrical conductivity σ as the ratio of the steady particle current I to the average gradient (µ L − µ R ) L:…”
Section: Introductionmentioning
confidence: 99%
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“…By general probabilistic arguments, one expects that this distribution satisfies a partial differential equation as in (10) [27], which our results confirm. Previous works deriving diffusion from static impurities in microscopic models using precise mathematical arguments include [33][34][35] for classical systems and [36] for a noninteracting quantum system. As far as we know, there are no such previous rigorous results for interacting quantum systems.…”
mentioning
confidence: 99%
“…In reality the bodies are in contact with the exterior that can be thought as a thermal reservoir at some given temperature. This is, of course, an extremely important 6 Note that here we abuse notation and use P 0 , E 0 to designate, respectively, the measure and expectation in path space determined by the initial measure (that we also called P 0 , hence the abuse). Of course, in the deterministic case all is determined by the initial condition, but in the random case the measure in path space describes also the randomness of the dynamics.…”
Section: The Models: Microscopic Dynamicsmentioning
confidence: 99%