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Volumn 80, Issue 5, 2009, Pages

Diffusion of finite-sized hard-core interacting particles in a one-dimensional box: Tagged particle dynamics

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC LIMITS; ASYMPTOTIC TECHNIQUE; BETHE ANSATZ; COLLISION TIME; CONDITIONAL PROBABILITY DENSITY; DIFFUSION CONSTANT; FINITE LENGTH; FINITE-SIZED SYSTEMS; GAUSSIANS; HYPERGEOMETRIC FUNCTIONS; INFINITE SYSTEM; INITIAL POSITION; INTERACTING PARTICLES; JACOBI POLYNOMIALS; LARGE N; MEAN-SQUARE DISPLACEMENT; NON EQUILIBRIUM; ONE-DIMENSIONAL SYSTEMS; PARTICLE CONCENTRATIONS; REFLECTING BOUNDARY; TAGGED PARTICLE; TIME REGIME;

EID: 70449687989     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.80.051103     Document Type: Article
Times cited : (71)

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    • The Bethe ansatz solution for particles jumping on a infinite lattice was given in. Our solution for the infinite system, Eqs. d12 d13 d14 and φ (kj, xj,0) = e-i kj xj,0, can be obtained from the solution in by the replacements ∫0 2π d kj /2π → - d kj /2π and by expanding the energy E (k1,..., kN) and the scattering coefficients Sij in a power series in momenta to lowest order.
    • The Bethe ansatz solution for particles jumping on a infinite lattice was given in. Our solution for the infinite system, Eqs. d12 d13 d14 and φ (kj, xj,0) = e-i kj xj,0, can be obtained from the solution in by the replacements ∫0 2π d kj /2π → - d kj /2π and by expanding the energy E (k1,..., kN) and the scattering coefficients Sij in a power series in momenta to lowest order.
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    • Alternatively, one may be interested in the tPDF for a fixed initial particle distribution x 0: ρ T (xT, t x 0) = R d x1′ d xN′ δ (xT - xT′) P (x ′, t x0). For the case where all particles start at the same position a straightforward integration yields, using Eq., a result for ρ T (xT, t x 0) which in the limit → is identical to that obtained in, as it should.
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