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Transport process and local thermal reservoirs
Steffen Trimper1, Michael Schulz
1Institute of Physics, Martin-Luther-University, D-06099 Halle, Germany. steffen.trimper@physik.uni-halle.de
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 13, 2007
Summary
This study explores particle density on a lattice with heat baths, revealing a new current driven by temperature gradients. The system achieves a stable density distribution influenced by temperature and particle filling factor.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Quantum Mechanics
Background:
- Investigates N-particle random walks on M-site lattices with mesoscopic heat baths.
- Utilizes a quantized Hamiltonian formulation of the master equation, incorporating the exclusion principle via Pauli operators.
Purpose of the Study:
- To analyze particle density evolution and stationary states in a lattice system with coupled heat baths and temperature gradients.
- To explore the emergence of novel transport phenomena beyond conventional diffusion.
Main Methods:
- Employs a master equation in a quantized Hamiltonian formulation.
- Applies mean-field approximation to derive evolution equations for particle density.
- Analyzes the stability of stationary solutions using a Schrödinger-like equation.
Main Results:
- Derives an evolution equation for particle density featuring two distinct currents: a diffusive current and a temperature-gradient-driven current.
- Identifies a stationary solution where local density depends on the local temperature field and the filling factor (M/N).
- Demonstrates the stability of the stationary density distribution under a fixed temperature gradient.
Conclusions:
- The proposed model offers a novel, alternative approach to the conventional Onsager ansatz for studying transport phenomena.
- The interplay between density and temperature gradients leads to complex, yet stable, stationary states in mesoscopic systems.
- This work provides insights into non-equilibrium statistical mechanics and the behavior of driven systems.
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