Dynamical Critical Exponent for Two-Species Totally Asymmetric Diffusion on a Ring

被引：6

作者：

Wehefritz-Kaufmann, Birgit ^{[1
]}

机构：

[1] Purdue Univ, Dept Math & Phys, W Lafayette, IN 47906 USA

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2010年 / 6卷

基金：

美国国家科学基金会;

关键词：

asymmetric diffusion; nested U(q)(SU(3)) Bethe ansatz; dynamical critical exponent; SIMPLE EXCLUSION PROCESS; SPONTANEOUS SYMMETRY-BREAKING; CURRENT FLUCTUATIONS; STATIONARY MEASURE; QUANTUM CHAINS; STEADY-STATE; MODEL; SYSTEM; SHOCKS; REPRESENTATION;

D O I：

10.3842/SIGMA.2010.039

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present a study of the two species totally asymmetric diffusion model using the Bethe ansatz. The Hamiltonian has U(q)(SU(3)) symmetry. We derive the nested Bethe ansatz equations and obtain the dynamical critical exponent from the finite-size scaling properties of the eigenvalue with the smallest real part. The dynamical critical exponent is 3/2 which is the exponent corresponding to KPZ growth in the single species asymmetric diffusion model.

引用

页数：15

共 46 条

[11] Exact connections between current fluctuations and the second class particle in a class of deposition models [J].

Balazs, Marton ;

Seppaelaeinen, Timo .

JOURNAL OF STATISTICAL PHYSICS, 2007, 127 (02) :431-455

[12] Random Walk of Second Class Particles in Product Shock Measures [J].

Balazs, Marton ;

Farkas, Gyoergy ;

Kovacs, Peter ;

Rakos, Attila .

JOURNAL OF STATISTICAL PHYSICS, 2010, 139 (02) :252-279

[13]

Bulirsch R., 1964, Numer. Math, V6, P413, DOI [10.1007/BF01386092, DOI 10.1007/BF01386092]

[14] Algebraic Bethe ansatz for the two species ASEP with different hopping rates [J].

Cantini, Luigi .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2008, 41 (09)

[15] Statistical physics of vehicular traffic and some related systems [J].

Chowdhury, D ;

Santen, L ;

Schadschneider, A .

PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 2000, 329 (4-6) :199-329

[16]

Christe P., 1993, LECT NOTES PHYS, V16

[17] REACTION-DIFFUSION PROCESSES DESCRIBED BY 3-STATE QUANTUM CHAINS AND INTEGRABILITY [J].

DAHMEN, SR .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1995, 28 (04) :905-922

[18] Exact spectral gaps of the asymmetric exclusion process with open boundaries [J].

de Gier, Jan ;

Essler, Fabian H. L. .

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT, 2006,

[19] Slowest relaxation mode of the partially asymmetric exclusion process with open boundaries [J].

de Gier, Jan ;

Essler, Fabian H. L. .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2008, 41 (48)

[20] Shock profiles for the asymmetric simple exclusion process in one dimension [J].

Derrida, B ;

Lebowitz, JL ;

Speer, ER .

JOURNAL OF STATISTICAL PHYSICS, 1997, 89 (1-2) :135-167

← 1 2 3 4 5 →