Dynamical correlations of conserved quantities in the one-dimensional equal mass hard particle gas

Aritra Kundu; Abhishek Dhar; Sanjib Sabhapandit

doi:10.1088/1742-5468/ab5d0c

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arXiv · 1909.01698

Dynamical correlations of conserved quantities in the one-dimensional equal mass hard particle gas

Aritra Kundu·Abhishek Dhar·Sanjib Sabhapandit

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Abstract

We study a gas of point particles with hard-core repulsion in one dimension where the particles move freely in-between elastic collisions. We prepare the system with a uniform density on the infinite line. The velocities $\{v_i; i \in \mathbb{Z} \}$ of the particles are chosen independently from a thermal distribution. Using a mapping to the non-interacting gas, we analytically compute the equilibrium spatio-temporal correlations $\langle v_i^m(t) v_j^n(0)\rangle$ for arbitrary integers $m,n$. The analytical results are verified with microscopic simulations of the Hamiltonian dynamics. The correlation functions have ballistic scaling, as expected in an integrable model.

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Aritra Kundu, Abhishek Dhar, Sanjib Sabhapandit. 2019-09-04. Dynamical correlations of conserved quantities in the one-dimensional equal mass hard particle gas. https://doi.org/10.1088/1742-5468%2Fab5d0c

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