Density Profiles in Open Superdiffusive Systems

Abstract

We numerically solve a discretized model of Levy random walks on a finite one-dimensional domain in the presence of sources and with a reflection coefficient $r$. At the domain boundaries, the steady-state density profile is non-analytic. The meniscus exponent $\mu$, introduced to characterize this singular behavior, uniquely identifies the whole profile. Numerical data suggest that $\mu =\alpha /2+r(\alpha /2-1)$, where $\alpha$ is the Levy exponent of the step-length distribution. As an application, we show that this model reproduces the temperature profiles obtained for a chain of oscillators displaying anomalous heat conduction. Remarkably, the case of free-boundary conditions in the chain correspond to a Levy walk with negative reflection coefficient.

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• Derivation of fluctuating hydrodynamics and crossover from diffusive to anomalous transport in a hard-particle gas
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• Crossover between different universality classes: Scaling for thermal transport in one dimension
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• Anomalous transmission and drifts in one-dimensional Levy structures
• Kinetic and hydrodynamic regimes in multi-particle-collision dynamics of a one-dimensional fluid with thermal walls
• Solitons as candidates for energy carriers in Fermi-Pasta-Ulam lattices
• Anomalous heat equation in a system connected to thermal reservoirs
• Heat conduction in a three-dimensional momentum-conserving fluid
• Hydrodynamics and transport in the long-range-interacting ${\phi }^4$ chain
• Nonequilibrium phenomena in nonlinear lattices: from slow relaxation to anomalous transport
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• L{é}vy walks on finite intervals: A step beyond asymptotics
• Thermalization of isolated harmonic networks under conservative noise
• Energy current cumulants in one-dimensional systems in equilibrium
• Classical and quantum harmonic mean-field models coupled intensively and extensively with external baths
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