A generalized fluctuation-dissipation theorem for the one-dimensional diffusion process

Abstract The process of diffusion-limited cell dehydration is modeled for a planar system by writing the one-dimensional diffusion-equation for a cell with moving, semipermeable boundaries. For the simplifying case of isothermal dehydration with constant diffusivity, an approximate analytical solution is obtained by linearizing the governing partial differential equations. The general problem must be solved numerically. The Forward Time Center Space (FTCS) and Crank-Nicholson differencing schemes are implemented, and evaluated by comparison with the analytical solution. Putative stability criteria for the two algorithms are proposed based on numerical experiments, and the Crank-Nicholson method is shown to be accurate for a mesh with as few as six nodes.

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Probing non-thermal density fluctuations in the one-dimensional Bose gas

SciPost Physics ◽

10.21468/scipostphys.3.3.023 ◽

2017 ◽

Vol 3 (3) ◽

Cited By ~ 12

Author(s):

Jacopo De Nardis ◽

Milosz Panfil ◽

Andrea Gambassi ◽

Leticia Cugliandolo ◽

Robert Konik ◽

...

Keyword(s):

Spatial Dimension ◽

Bose Gas ◽

Density Fluctuations ◽

Dynamical Structure ◽

Many Body ◽

Initial State ◽

One Dimensional ◽

Fluctuation Dissipation ◽

Quantum Integrable Models ◽

The One

Quantum integrable models display a rich variety of non-thermal excited states with unusual properties. The most common way to probe them is by performing a quantum quench, i.e., by letting a many-body initial state unitarily evolve with an integrable Hamiltonian. At late times these systems are locally described by a generalized Gibbs ensemble with as many effective temperatures as their local conserved quantities. The experimental measurement of this macroscopic number of temperatures remains elusive. Here we show that they can be obtained for the Bose gas in one spatial dimension by probing the dynamical structure factor of the system after the quench and by employing a generalized fluctuation-dissipation theorem that we provide. Our procedure allows us to completely reconstruct the stationary state of a quantum integrable system from state-of-the-art experimental observations.

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Limit theorem for one-dimensional diffusion process in brownian environment

Lecture Notes in Mathematics - Stochastic Analysis ◽

10.1007/bfb0077874 ◽

1988 ◽

pp. 156-172 ◽

Cited By ~ 2

Author(s):

Hiroshi Tanaka

Keyword(s):

Limit Theorem ◽

Diffusion Process ◽

One Dimensional ◽

Dimensional Diffusion

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Numerical Solution of the Differential Diffusion Equation for a Steel Carburizing Process

Solid State Phenomena ◽

10.4028/www.scientific.net/ssp.284.1230 ◽

2018 ◽

Vol 284 ◽

pp. 1230-1234

Author(s):

Mikhail V. Maisuradze ◽

Alexandra A. Kuklina

Keyword(s):

Diffusion Equation ◽

Numerical Solution ◽

Differential Diffusion ◽

One Dimensional ◽

The Third ◽

Dimensional Diffusion ◽

Simplified Algorithm ◽

The One ◽

Carburizing Process ◽

Precise Assessment

The simplified algorithm of the numerical solution of the differential diffusion equation is presented. The solution is based on the one-dimensional diffusion model with the third kind boundary conditions and the finite difference method. The proposed approach allows for the quick and precise assessment of the carburizing process parameters – temperature and time.

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