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تسجيل مستخدم جديدEquilibration of a one-dimensional Wigner crystal
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Equilibration of a one-dimensional system of interacting electrons requires processes that change the numbers of left- and right-moving particles. At low temperatures such processes are strongly suppressed, resulting in slow relaxation towards equilibrium. We study this phenomenon in the case of spinless electrons with strong long-range repulsion, when the electrons form a one-dimensional Wigner crystal. We find the relaxation rate by accounting for the Umklapp scattering of phonons in the crystal. For the integrable model of particles with inverse-square repulsion, the relaxation rate vanishes.
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We consider a system of one-dimensional spinless particles interacting via long-range repulsion. In the limit of strong interactions the system is a Wigner crystal, with excitations analogous to phonons in solids. In a harmonic crystal the phonons do
not interact, and the system never reaches thermal equilibrium. We account for the anharmonism of the Wigner crystal and find the rate at which it approaches equilibrium. The full equilibration of the system requires umklapp scattering of phonons, resulting in exponential suppression of the equilibration rate at low temperatures.
In one-dimensional quantum systems with strong long-range repulsion particles arrange in a quasi-periodic chain, the Wigner crystal. We demonstrate that besides the familiar phonons, such one-dimensional Wigner crystal supports an additional mode of
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A system of confined charged electrons interacting via the long-range Coulomb force can form a Wigner crystal due to their mutual repulsion. This happens when the potential energy of the system dominates over its kinetic energy, i.e., at low temperat
ures for a classical system and at low densities for a quantum one. At $T=0$, the system is governed by quantum mechanics, and hence, the spatial density peaks associated with crystalline charge localization are sharpened for a lower average density. Conversely, in the classical limit of high temperatures, the crystalline spatial density peaks are suppressed (recovered) at a lower (higher) average density. In this paper, we study those two limits separately using an exact diagonalization of small one-dimensional (1D) systems containing few ($<10$) electrons and propose an approximate method to connect them into a unified effective phase diagram for Wigner few-electron crystallization. The result is a qualitative quantum-classical crossover phase diagram of an effective 1D Wigner crystal. We show that the spatial density peaks associated with the quasi-crystallization should be experimentally observable in a few-electron 1D system. We find that the effective crystalline structure slowly disappears with both the crossover average density and crossover temperature for crystallization decreasing with increasing particle number, consistent with the absence of any true long-range 1D order. In fact, one peculiar aspect of the effective finite-size nature of 1D Wigner crystallization we find is that even a short-range interaction would lead to a finite-size 1D crystal, except that the crystalline order vanishes much faster with increasing system size in the short-range interacting system compared with the long-range interacting one.
The spatial Fourier spectrum of the electron density distribution in a finite 1D system and the distribution function of electrons over single-particle states are studied in detail to show that there are two universal features in their behavior, whic
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