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Open Quantum Systems Decoherence
Ranked diffusion, delta Bose gas and Burgers equation
arXiv
Authors: Pierre Le Doussal
Year
2021
Paper ID
62195
Status
Preprint
Abstract Read
~2 min
Abstract Words
116
Citations
N/A
Abstract
We study the diffusion of N particles in one dimension interacting via a drift proportional to their rank. In the attractive case (self-gravitating gas) a mapping to the Lieb Liniger quantum model allows to obtain stationary time correlations, return probabilities and the decay rate to the stationary state. The rank field obeys a Burgers equation, which we analyze. It allows to obtain the stationary density at large N in an external potential V(x) (in the repulsive case). In the attractive case the decay rate to the steady state is found to depend on the initial condition if its spatial decay is slow enough. Coulomb gas methods allow to study the final equilibrium at large N.
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- This paper contributes to the Open Quantum Systems & Decoherence research area in the Quantum Articles archive.
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- We study the diffusion of N particles in one dimension interacting via a drift proportional to their rank.
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