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Journal of Modern Physics

Schrodinger-Langevin Equation and Ion Transport atNano Scale

Samyadeb Bhattacharya, Suman Dutta, Sisir Roy

Published Jan 1, 2011• 2 citations
Publisher

Abstract

Schrodinger-Langevin equation has been constructed for the ion-transport for K-ion channel. The stability of the solutions of this equation has been discussed under various physical situations. This will shed new light on the ion transport at nano-scale as well as the possibility of ion trapping and quantum information processing.
DOI
10.4236/jmp.2011.24032

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The Brownian motion of a particle coupled to a heat bath can be derived from an exactly solvable many-body system. This motion is governed by the Langevin equation in Newtonian mechanics, and by an operator equation formally identical to the Langevin equation when the system composed of the particle plus the heat bath is quantized. To get this formal similarity between the classical and the quantal equations of motion of the particle, the classical dissipative system is formulated in terms of a modified Hamilton–Jacobi equation and is then quantized using the Schrödinger method. The result is identical with the Schrödinger–Langevin equation that has been obtained by quantizing the entire system and then isolating the motion of the particle. The non-linear wave equation describing the motion of a particle subject to conservative and time-dependent forces as well as frictional forces has been applied to the problems of motion of a wave-packet, and of the scattering and trapping of heavy-ions.
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