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Rayleigh approximation to ground state of the Bose and Coulomb glasses.

Ryan SD, Mityushev V, Vinokur VM, Berlyand L - Sci Rep (2015)

Bottom Line: Glasses are rigid systems in which competing interactions prevent simultaneous minimization of local energies.This leads to frustration and highly degenerate ground states the nature and properties of which are still far from being thoroughly understood.Our findings break ground for analytical studies of glassy systems, marking an important step towards understanding their properties.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA.

ABSTRACT
Glasses are rigid systems in which competing interactions prevent simultaneous minimization of local energies. This leads to frustration and highly degenerate ground states the nature and properties of which are still far from being thoroughly understood. We report an analytical approach based on the method of functional equations that allows us to construct the Rayleigh approximation to the ground state of a two-dimensional (2D) random Coulomb system with logarithmic interactions. We realize a model for 2D Coulomb glass as a cylindrical type II superconductor containing randomly located columnar defects (CD) which trap superconducting vortices induced by applied magnetic field. Our findings break ground for analytical studies of glassy systems, marking an important step towards understanding their properties.

No MeSH data available.


Related in: MedlinePlus

Superconducting cylinder with columnar defects and corresponding single-particle potential relief.(a): Sketch of a superconducting cylinder with arbitrarily distributed columnar defects. The characteristic lengths are related by the inequalities chain, . (b): Egg-crate energy potential relief for a single particle in the related two-dimensional Coulomb gas of charged particles. (c): Cross-section of the egg-crate potential relief for a charge emphasizing its random character.
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f1: Superconducting cylinder with columnar defects and corresponding single-particle potential relief.(a): Sketch of a superconducting cylinder with arbitrarily distributed columnar defects. The characteristic lengths are related by the inequalities chain, . (b): Egg-crate energy potential relief for a single particle in the related two-dimensional Coulomb gas of charged particles. (c): Cross-section of the egg-crate potential relief for a charge emphasizing its random character.

Mentions: Here we address this challenge and offer an analytical approach to construct an approximation to a ground state of the 2D random finite system in the first order with respect to disorder. We consider a two-dimensional Coulomb gas subject to quenched disorder and take advantage of the latter's equivalence to the system of 3D vortices in type II superconductors containing randomly distributed columnar defects9, see Fig. 1a. Complete identity is achieved by choosing a lateral size for the system not exceeding the London penetration depth, λ. Then vortex-vortex logarithmic interactions remain unscreened, and the vortex system becomes isomorphic to the 2D Coulomb gas of logarithmically interacting electric charges, Fig. 1b, c. Hence the equivalence of the problems of the lowest energy states of these two systems: the global minimum of the Ginzburg-Landau (GL) functional, describing the configuration of vortices corresponding to the lowest energy, defines the ground state of both.


Rayleigh approximation to ground state of the Bose and Coulomb glasses.

Ryan SD, Mityushev V, Vinokur VM, Berlyand L - Sci Rep (2015)

Superconducting cylinder with columnar defects and corresponding single-particle potential relief.(a): Sketch of a superconducting cylinder with arbitrarily distributed columnar defects. The characteristic lengths are related by the inequalities chain, . (b): Egg-crate energy potential relief for a single particle in the related two-dimensional Coulomb gas of charged particles. (c): Cross-section of the egg-crate potential relief for a charge emphasizing its random character.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4296301&req=5

f1: Superconducting cylinder with columnar defects and corresponding single-particle potential relief.(a): Sketch of a superconducting cylinder with arbitrarily distributed columnar defects. The characteristic lengths are related by the inequalities chain, . (b): Egg-crate energy potential relief for a single particle in the related two-dimensional Coulomb gas of charged particles. (c): Cross-section of the egg-crate potential relief for a charge emphasizing its random character.
Mentions: Here we address this challenge and offer an analytical approach to construct an approximation to a ground state of the 2D random finite system in the first order with respect to disorder. We consider a two-dimensional Coulomb gas subject to quenched disorder and take advantage of the latter's equivalence to the system of 3D vortices in type II superconductors containing randomly distributed columnar defects9, see Fig. 1a. Complete identity is achieved by choosing a lateral size for the system not exceeding the London penetration depth, λ. Then vortex-vortex logarithmic interactions remain unscreened, and the vortex system becomes isomorphic to the 2D Coulomb gas of logarithmically interacting electric charges, Fig. 1b, c. Hence the equivalence of the problems of the lowest energy states of these two systems: the global minimum of the Ginzburg-Landau (GL) functional, describing the configuration of vortices corresponding to the lowest energy, defines the ground state of both.

Bottom Line: Glasses are rigid systems in which competing interactions prevent simultaneous minimization of local energies.This leads to frustration and highly degenerate ground states the nature and properties of which are still far from being thoroughly understood.Our findings break ground for analytical studies of glassy systems, marking an important step towards understanding their properties.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, PA 16802, USA.

ABSTRACT
Glasses are rigid systems in which competing interactions prevent simultaneous minimization of local energies. This leads to frustration and highly degenerate ground states the nature and properties of which are still far from being thoroughly understood. We report an analytical approach based on the method of functional equations that allows us to construct the Rayleigh approximation to the ground state of a two-dimensional (2D) random Coulomb system with logarithmic interactions. We realize a model for 2D Coulomb glass as a cylindrical type II superconductor containing randomly located columnar defects (CD) which trap superconducting vortices induced by applied magnetic field. Our findings break ground for analytical studies of glassy systems, marking an important step towards understanding their properties.

No MeSH data available.


Related in: MedlinePlus