Nonequilibrium solutions of the Boltzmann equation under the action of an external force.

@article{GuryOdelin2014NonequilibriumSO,
  title={Nonequilibrium solutions of the Boltzmann equation under the action of an external force.},
  author={D. Gu{\'e}ry-Odelin and Juan Gonzalo Muga and M. J. Ruiz-Montero and Emmanuel Trizac},
  journal={Physical review letters},
  year={2014},
  volume={112 18},
  pages={
          180602
        }
}
We construct a novel class of exact solutions to the Boltzmann equation, in both its classical and quantum formulation, for arbitrary collision laws. When the system is subjected to a specific external forcing, the precise form of which is worked out, nonequilibrium dampingless solutions are admissible. They do not contradict the H theorem, but are constructed from its requirements. Interestingly, these solutions hold for time-dependent confinement. We exploit them, in a reverse-engineering… 

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References

SHOWING 1-10 OF 18 REFERENCES

The Boltzmann equation and its applications

I. Basic Principles of The Kinetic Theory of Gases.- 1. Introduction.- 2. Probability.- 3. Phase space and Liouville's theorem.- 4. Hard spheres and rigid walls. Mean free path.- 5. Scattering of a

Molecular Gas Dynamics and the Direct Simulation of Gas Flows

The direct simulation Monte Carlo (or DSMC) method has, in recent years, become widely used in engineering and scientific studies of gas flows that involve low densities or very small physical

Hydrodynamic Limits of the Boltzmann Equation

The Boltzmann equation and its formal hydrodynamic limits.- Mathematical tools for the derivation of hydrodynamic limits.- The incompressible Navier-Stokes limit.- The incompressible Euler limit.-

An Introduction to the Boltzmann Equation and Transport Processes in Gases

Basic Principles of the Kinetic Theory.- The Boltzmann Equation.- The Chapman-Enskog Method.- Moment Methods.- Polyatomic Gases.- Dense Gases.- Granular Gases.- Mixtures of Monatomic Gases.-

Lectures on Gas Theory

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