# Investigation of the Lorentz gas in terms of periodic orbits.

@article{Cvitanovi1992InvestigationOT, title={Investigation of the Lorentz gas in terms of periodic orbits.}, author={Predrag Cvitanovi{\'c} and Pierre Gaspard and Thomas Schreiber}, journal={Chaos}, year={1992}, volume={2 1}, pages={ 85-90 } }

The diffusion constant and the Lyapunov exponent for the spatially periodic Lorentz gas are evaluated numerically in terms of periodic orbits. A symbolic description of the dynamics reduced to a fundamental domain is used to generate the shortest periodic orbits. Applied to a dilute Lorentz gas with finite horizon, the theory works well, but for the dense Lorentz gas the convergence is hampered by the strong pruning of the admissible orbits.

## 61 Citations

### Periodic orbit expansions for the Lorentz gas

- Physics, Mathematics
- 1994

We apply the periodic orbit expansion to the calculation of transport, thermodynamic, and chaotic properties of the finite-horizon triangular Lorentz gas. We show numerically that the inverse of the…

### An approximate formula for the diffusion coefficient for the periodic Lorentz gas

- Mathematics, Physics
- 2012

### A dynamical partition function for the Lorentz gas

- Physics, Mathematics
- 1995

In this paper we introduce a dynamically defined partition function for the Lorentz gas and investigate its connection with the classical ensembles and the phase-space probability measure derived…

### Lyapunov exponents and anomalous diffusion of a Lorentz gas with infinite horizon using approximate zeta functions

- Mathematics
- 1996

We compute the Lyapunov exponent, the generalized Lyapunov exponents, and the diffusion constant for a Lorentz gas on a square lattice, thus having infinite horizon. Approximate zeta functions,…

### Periodic orbit theory of strongly anomalous transport

- Physics
- 2004

We establish a deterministic technique to investigate transport moments of an arbitrary order. The theory is applied to the analysis of different kinds of intermittent one-dimensional maps and the…

### The nonequilibrium Lorentz gas.

- Physics, MathematicsChaos
- 1995

This work presents a detailed dynamical study of the transitions in the bifurcation sequence in both the elementary cell and the fundamental domain of a Lorentz gas system.

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