A Semiclassical Approach to the Kramers--Smoluchowski Equation
نویسندگان
چکیده
منابع مشابه
Non-Abelian linear Boltzmann equation and quantum correction to Kramers and Smoluchowski equation.
A quantum linear Boltzmann equation, constructed in terms of the operator-valued dynamic structure factor of the macroscopic system the test particle is interacting with, is proposed. Due to this operator structure it is a non-Abelian linear Boltzmann equation and when expressed through the Wigner function it allows for a direct comparison with the classical one. Considering a Brownian particle...
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In certain applications one is interested in the long-time behavior of systems described by a linear partial differential equation. For example, in kinetic equations one studies the decay to equilibrium of various linear and nonlinear systems. For the Kramers–Fokker–Planck equation, which will be studied here, exponential decay was shown in Talay (1999) and an explicit rate was given in Hérau a...
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According to the Smoluchowski-Kramers approximation, the solution of the equation μq̈ t = b(q μ t ) − q̇ t + Σ(q t )Ẇt, q 0 = q, q̇ 0 = p converges to the solution of the equation q̇t = b(qt) + Σ(qt)Ẇt, q0 = q as μ → 0. We consider here a similar result for the Langevin process with elastic reflection on the boundary.
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ژورنال
عنوان ژورنال: SIAM Journal on Mathematical Analysis
سال: 2018
ISSN: 0036-1410,1095-7154
DOI: 10.1137/17m1124826