We present a solution for the stationary state of an asymmetric exclusion model with sequential update and open boundary conditions. We solve the model exactly for random hopping in both directions by applying a matrix-product formalism which was recently used to solve the model with sublattice-parallel update (Hinrichsen H 1995 Weizmann Inst. Preprint cond-mat/9512172). It is shown that the matrix-algebra describing the sequential update and sublattice-parallel update are identical and can be mapped onto the random sequential case treated by Derrida et al (Derrida B, Evans M R, Hakim V and Pasquier V 1993 J. Phys. A: Math. Gen. 26 1493).We present a solution for the stationary state of an asymmetric exclusion model with sequential update and open boundary conditions. We solve the model exactly for random hopping in both directions by applying a matrix-product formalism which was recently used to solve the model with sublattice-parallel update (Hinrichsen H 1995 Weizmann Inst. Preprint cond-mat/9512172). It is shown that the matrix-algebra describing the sequential update and sublattice-parallel update are identical and can be mapped onto the random sequential case treated by Derrida et al (Derrida B, Evans M R, Hakim V and Pasquier V 1993 J. Phys. A: Math. Gen. 26 1493).

arXiv:cond-mat/9603172Journal of Physics A Mathematical and GeneralJun 21, 199660 citations

Ground-state properties of one-dimensional anyon gases

Yajiang Hao, Yunbo Zhang, Shu Chen

We investigate the ground state of the one-dimensional interacting anyonic system based on the exact Bethe ansatz solution for arbitrary coupling constant $(0\ensuremath{\leqslant}c\ensuremath{\leqslant}\ensuremath{\infty})$ and statistics parameter $(0\ensuremath{\leqslant}\ensuremath{\kappa}\ensuremath{\leqslant}\ensuremath{\pi})$. It is shown that the density of state in quasimomentum $k$ space and the ground-state energy are determined by the renormalized coupling constant ${c}^{\ensuremath{'}}$. The effect induced by the statistics parameter $\ensuremath{\kappa}$ exhibits in the momentum distribution in two aspects: Besides the effect of renormalized coupling, the anyonic statistics results in the nonsymmetric momentum distribution when the statistics parameter $\ensuremath{\kappa}$ deviates from 0 (Bose statistics) and $\ensuremath{\pi}$ (Fermi statistics) for any coupling constant $c$ . The momentum distribution evolves from a Bose distribution to a Fermi one as $\ensuremath{\kappa}$ varies from 0 to $\ensuremath{\pi}$. The asymmetric momentum distribution comes from the contribution of the imaginary part of the nondiagonal element of reduced density matrix, which is an odd function of $\ensuremath{\kappa}$. The peak at positive momentum will shift to negative momentum if $\ensuremath{\kappa}$ is negative.We investigate the ground state of the one-dimensional interacting anyonic system based on the exact Bethe ansatz solution for arbitrary coupling constant $(0\ensuremath{\leqslant}c\ensuremath{\leqslant}\ensuremath{\infty})$ and statistics parameter $(0\ensuremath{\leqslant}\ensuremath{\kappa}\ensuremath{\leqslant}\ensuremath{\pi})$. It is shown that the density of state in quasimomentum $k$ space and the ground-state energy are determined by the renormalized coupling constant ${c}^{\ensuremath{'}}$. The effect induced by the statistics parameter $\ensuremath{\kappa}$ exhibits in the momentum distribution in two aspects: Besides the effect of renormalized coupling, the anyonic statistics results in the nonsymmetric momentum distribution when the statistics parameter $\ensuremath{\kappa}$ deviates from 0 (Bose statistics) and $\ensuremath{\pi}$ (Fermi statistics) for any coupling constant $c$. The momentum distribution evolves from a Bose distribution to a Fermi one as $\ensuremath{\kappa}$ varies from 0 to $\ensuremath{\pi}$. The asymmetric momentum distribution comes from the contribution of the imaginary part of the nondiagonal element of reduced density matrix, which is an odd function of $\ensuremath{\kappa}$. The peak at positive momentum will shift to negative momentum if $\ensuremath{\kappa}$ is negative.

arXiv:0805.1988Physical Review AAug 26, 200862 citations

On the relation between coherence and monochromaticity

Jan Peřina

Physics LettersJan 1, 19654 citations

Exact solution of the asymmetric exclusion model with particles of arbitrary size

Francisco Castilho Alcaraz, R. Z. Bariev

A generalization of the simple exclusion asymmetric model is introduced. In this model an arbitrary mixture of molecules with distinct sizes s=0,1,2, ..., in units of lattice space, diffuses asymmetrically on the lattice. A related surface growth model is also presented. Variations of the distribution of the molecules sizes may change the excluded volume almost continuously. We solve the model exactly through the Bethe ansatz and the dynamical critical exponent z is calculated from the finite-size corrections of the mass gap of the related quantum chain. Our results show that for an arbitrary distribution of molecules, the dynamical critical behavior is on the Kardar-Parizi-Zhang universality.A generalization of the simple exclusion asymmetric model is introduced. In this model an arbitrary mixture of molecules with distinct sizes s=0,1,2, ..., in units of lattice space, diffuses asymmetrically on the lattice. A related surface growth model is also presented. Variations of the distribution of the molecules sizes may change the excluded volume almost continuously. We solve the model exactly through the Bethe ansatz and the dynamical critical exponent z is calculated from the finite-size corrections of the mass gap of the related quantum chain. Our results show that for an arbitrary distribution of molecules, the dynamical critical behavior is on the Kardar-Parizi-Zhang universality.

arXiv:cond-mat/9904130Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsJul 1, 199953 citations

k

space and the ground-state energy are determined by the renormalized coupling constant ${c}^{\ensuremath{'}}$. The effect induced by the statistics parameter $\ensuremath{\kappa}$ exhibits in the momentum distribution in two aspects: Besides the effect of renormalized coupling, the anyonic statistics results in the nonsymmetric momentum distribution when the statistics parameter $\ensuremath{\kappa}$ deviates from 0 (Bose statistics) and $\ensuremath{\pi}$ (Fermi statistics) for any coupling constant

c

. The momentum distribution evolves from a Bose distribution to a Fermi one as $\ensuremath{\kappa}$ varies from 0 to $\ensuremath{\pi}$. The asymmetric momentum distribution comes from the contribution of the imaginary part of the nondiagonal element of reduced density matrix, which is an odd function of $\ensuremath{\kappa}$. The peak at positive momentum will shift to negative momentum if $\ensuremath{\kappa}$ is negative.