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Driven inelastic Maxwell gas in one dimension.

V V Prasad1, Sanjib Sabhapandit2, Abhishek Dhar3

  • 1The Institute of Mathematical Sciences, Taramani, Chennai - 600113, India.

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|March 17, 2017
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Summary
This summary is machine-generated.

This study investigates a one-dimensional lattice model of a driven inelastic Maxwell gas. Researchers found that spatial correlations decay exponentially, and spatiotemporal correlations show unique time-dependent behavior in specific regions.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Non-equilibrium Systems

Background:

  • Investigates a lattice version of the driven inelastic Maxwell gas in one dimension.
  • Focuses on systems with periodic boundary conditions and nearest-neighbor interactions.
  • Examines the role of external driving in sustaining a steady state.

Purpose of the Study:

  • To derive and analyze the behavior of variance and two-point correlation functions.
  • To determine steady-state properties and spatial correlation functions.
  • To characterize the spatiotemporal correlation function C(x,t).

Main Methods:

  • Developed a set of closed coupled equations for variance and two-point correlation evolution.
  • Calculated steady-state values for variance and spatial correlation functions.
  • Analyzed the exact form of the spatiotemporal correlation function C(x,t).

Main Results:

  • The spatial correlation function decays exponentially with distance, with an exact determination of the correlation length for large systems.
  • The spatiotemporal correlation C(x,t) exhibits a time-dependent form in an interior region (-x* < x < x*) and a time-independent form in the exterior region (|x| > x*).
  • Second-order discontinuities in C(x,t) occur at transition points x=±x*, which propagate outwards at a constant speed.

Conclusions:

  • The study provides an exact analytical solution for the driven inelastic Maxwell gas model on a lattice.
  • The findings reveal distinct spatial and temporal correlation behaviors, including propagating discontinuities.
  • This work contributes to the understanding of non-equilibrium statistical mechanics in low-dimensional systems.