Generalized Bethe ansatz solution of a one-dimensional asymmetric exclusion process on a ring with blockage

Journal Article · Sat May 01 00:00:00 EDT 1993 · Journal of Statistical Physics; (United States)

DOI:https://doi.org/10.1007/BF01058433· OSTI ID:6327482

Schuetz, G ^[1]

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1. Weizmann Institute, Rehovot (Israel)

A model is presented for a one-dimensional anisotropic exclusion process describing particles moving deterministically on a ring of length L with a single defect, across which they move with probability O[le]p[le]1. This model is equivalent to a two-dimensional, six-vertex model in an extreme anisotropic limit with a defect line interpolating between open and periodic boundary conditions. The model os solved with a Bethe ansatz generalized to this kind of boundary condition. The authors discuss in detail the steady state and derive exact expressions for the current j, the density profile n(x), and the two-point density correlation function. In the thermodynamic limit L[r arrow][infinity] the phase diagram shows three phases, a low-density phase, a coexistence phase, and a high-density phase related to the low-density phase by a particle-hole symmetry. In the low-density phase the density profile decays exponentially with the distance from the boundary to its bulk value on a length scale [xi]. On the phase transition line [xi] diverges and the current j approaches its critical value j[sub c] = p as a power law, J[sub c]-j [proportional to] [xi][sup [minus]1/2]. In the coexistence phase the width [Delta] of the interface between the high-density region and the low-density region is proportional to L[sup 1/2] if the density [rho][ne]1/2 and [Delta] = 0 relation function turns out to be of a scaling form with a space-dependent amplitude n(x[sub 1], x[sub 2]) = A(x[sub 2])r[sup x]e[sup [minus]r/[xi]] with r = x[sub 2]-x[sub 1] and a critical exponent [kappa]=0. 15 refs., 5 figs.

• OSTI ID: 6327482
• Journal Information: Journal of Statistical Physics; (United States), Journal Name: Journal of Statistical Physics; (United States) Vol. 71:3-4; ISSN JSTPBS; ISSN 0022-4715
• Country of Publication: United States
• Language: English

Related Subjects

661300 -- Other Aspects of Physical Science-- (1992-)
662100* -- General Theory of Particles & Fields-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOUNDARY CONDITIONS
CORRELATION FUNCTIONS
DENSITY
DIAGRAMS
FUNCTIONS
MANY-BODY PROBLEM
MECHANICS
ONE-DIMENSIONAL CALCULATIONS
PARTICLE KINEMATICS
PHASE DIAGRAMS
PHASE TRANSFORMATIONS
PHYSICAL PROPERTIES
PROBABILITY
STATISTICAL MECHANICS
SYMMETRY