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Energy Current Cumulants in One-Dimensional Systems in Equilibrium
Abhishek Dhar1, Keiji Saito2, Anjan Roy3
1International Centre for Theoretical Sciences, TIFR, Shivakote Village, Hesaraghatta Hobli, Bengaluru 560089, India.
Physical Review Letters
|June 16, 2018
Summary
Anomalous transport in 1D systems shows two universality classes. Heat current fluctuations in these systems exhibit distinct system-size dependencies, explained by Lévy walker models and fluctuating hydrodynamics.
Area of Science:
- Condensed Matter Physics
- Statistical Mechanics
- Nonlinear Dynamics
Background:
- Fluctuating hydrodynamics theory predicts two universality classes for anomalous transport in 1D systems.
- These classes are distinguished by the scaling behavior of conserved quantities and sound modes.
- Heat transport in these systems is expected to follow Lévy statistics.
Purpose of the Study:
- To investigate heat current fluctuations in two specific 1D systems representing the predicted universality classes.
- To compare the system-size dependence of heat current cumulants in these distinct systems.
- To explain observed numerical results using theoretical models.
Main Methods:
- Numerical simulations of a hard particle gas (Hamiltonian dynamics) and a harmonic chain (stochastic dynamics).
- Analysis of system-size dependence of heat current cumulants.
- Development and application of a phenomenological Lévy walker model.
- Microscopic derivation of the cumulant-generating function for the harmonic chain.
Main Results:
- Numerical simulations revealed distinct system-size dependencies of heat current cumulants for the two systems.
- A phenomenological Lévy walker model successfully explained these observed dependencies.
- Microscopic theory for the harmonic chain corroborated the system-size dependence derived from the phenomenological model.
Conclusions:
- The study confirms the existence of different universality classes for anomalous transport in 1D systems.
- Fluctuating hydrodynamics and Lévy statistics provide a consistent framework for understanding heat current fluctuations.
- The findings highlight the importance of system-size effects in characterizing transport properties.
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