Derivation of the Schroedinger--Langevin equation. [Nonlinear and random potential]

Antonio Boulhosa Nassar

Antonio Boulhosa Nassar

Via quantum fluid dynamics the author presents a general method to obtain a solution of the nonlinear Schrodinger-Langevin equation with a multiterm potential for the description of interactions in non-conservative systems. The nonlinear complete set of equations forming the basis of the model are derived. The corresponding solutions are exhibited in terms of auxiliary ordinary differential equations which provide relations between the potential coefficients and other coefficients prescribing the fluid-particle behaviour.

Iwo Białynicki‐Birula

The problem of linearity of the Schroedinger equation is analyzed in the light of new experiments performed at MIT and the Laue-Langevin Institute. In these experiments slow neutrons were used to place an upper limit on the strength of the logarithmic nonlinear term in the Schroedinger equation introduced in an earlier work by Jerzy Mycielski and me.

N. G. van Kampen

Mário J. de Oliveira

Natsuki Hashitsume, Michiyo Mori, Tomoko Takahashi

A new derivation of the Langevin equation for a system in contact with a heat reservoir in equilibrium is given based on the concept of path probability inherent in the Feynman approach to quantum mechanics. The derived Langevin equation is a generalization of the Magalinski type, i.e., it is a second order differential equation and contains a shift term, a retarded damping term, a destruction term and a random force term in addition to the usual external potential force term. It is a semi-classical equation in the sense that it is a classical equation but contains a quantal response function of the Kubo formula type and the second moment of the random force is given by a quantal symmetrized correlation function. The fluctuation-dissipation theorem of the second kind is exactly valid between the response and the correlation functions.