Transport process and local thermal reservoirs.
A random walk of N particles on a lattice with M sites is studied under the constraint that each lattice site is coupled to its own mesoscopic heat bath. Such a situation can be conveniently described by using the master equation in a quantized Hamiltonian formulation where the exclusion principle is included by using Pauli operators. If all reservoirs are mutually in contact, giving rise to a temperature gradient, an evolution equation for the particle density with two different currents already results in the mean-field approximation. One is the conventional diffusive current, driven by the density gradient, whereas the other includes a coupling between the local density and the temperature gradient. Due to the competitive currents, the system exhibits a stationary solution, where the local density is determined by the local temperature field and depends on the filling factor M/N. The stability of the solution is related to the eigenvalues of a Schrödinger-like equation. In the case of a fixed temperature gradient the stationary density distribution remains stable. The approach used is totally different from and an alternative to the conventional Onsager ansatz.
Trimper
Steffen
S
Institute of Physics, Martin-Luther-University, D-06099 Halle, Germany. steffen.trimper@physik.uni-halle.de
Schulz
Michael
M