arXiv subjects

G. M. Schutz

Publications and source records attributed to G. M. Schutz.

7 recordsLinked to original sources

arXiv2008

Exact solution of the Bernoulli matching model of sequence alignment

Through a series of exact mappings we reinterpret the Bernoulli model of sequence alignment in terms of the discrete-time totally asymmetric exclusion process with backward sequential update and step function initial condition. Using earlier results from the Bethe ansatz we obtain analytically the exact distribution of the length of the longest common subsequence of two sequences of finite lengths $X,Y$. Asymptotic analysis adapted from random matrix theory allows us to derive the thermodynamic limit directly from the finite-size result.

cond-mat.stat-mech↗

arXiv2004

Zero-range process with open boundaries

We calculate the exact stationary distribution of the one-dimensional zero-range process with open boundaries for arbitrary bulk and boundary hopping rates. When such a distribution exists, the steady state has no correlations between sites and is uniquely characterized by a space-dependent fugacity which is a function of the boundary rates and the hopping asymmetry. For strong boundary drive the system has no stationary distribution. In systems which on a ring geometry allow for a condensation transition, a condensate develops at one or both boundary sites. On all other sites the particle distribution approaches a product measure with the finite critical density ρ_c. In systems which do not support condensation on a ring, strong boundary drive leads to a condensate at the boundary. However, in this case the local particle density in the interior exhibits a complex algebraic growth in time. We calculate the bulk and boundary growth exponents as a function of the system parameters.

cond-mat.stat-mech↗

arXiv2004

Long-range attraction between probe particles mediated by a driven fluid

The effective interaction between two probe particles in a one-dimensional driven system is studied. The analysis is carried out using an asymmetric simple exclusion process with nearest-neighbor interactions. It is found that the driven fluid mediates an effective long-range attraction between the two probes, with a force that decays at large distances x as -b/x, where b is a function of the interaction parameters. Depending on the amplitude b the two probes may form one of three states: (a) an unbound state, where the distance grows diffusively with time; (b) a weakly bound state, in which the distance grows sub-diffusively; and (c) a strongly bound state, where the average distance stays finite in the long time limit. Similar results are found for the behavior of any finite number of probes.

cond-mat.stat-mech↗

arXiv2002

Novel phase-separation transition in one-dimensional driven models

A class of models of driven diffusive systems which is shown to exhibit phase separation in $d=1$ dimensions is introduced. Unlike all previously studied models exhibiting similar phenomena, here the phase separated state is fluctuating in the bulk of the macroscopic domains. The nature of the phase transition from the homogeneous to the phase separated state is discussed in view of a recently introduced criterion for phase separation in one-dimensional driven systems.

cond-mat.stat-mech↗

arXiv2002

Criterion for phase separation in one-dimensional driven systems

A general criterion for the existence of phase separation in driven one-dimensional systems is proposed. It is suggested that phase separation is related to the size dependence of the steady-state currents of domains in the system. A quantitative criterion for the existence of phase separation is conjectured using a correspondence made between driven diffusive models and zero-range processes. Several driven diffusive models are discussed in light of the conjecture.

cond-mat.stat-mech↗

arXiv2000

Boundary-induced phase transitions in traffic flow

Boundary-induced phase transitions are one of the surprising phenomena appearing in nonequilibrium systems. These transitions have been found in driven systems, especially the asymmetric simple exclusion process. However, so far no direct observations of this phenomenon in real systems exists. Here we present evidence for the appearance of such a nonequilibrium phase transition in traffic flow occurring on highways in the vicinity of on- and off-ramps. Measurements on a German motorway close to Cologne show a first-order nonequilibrium phase transition between a free-flow phase and a congested phase. It is induced by the interplay of density waves (caused by an on-ramp) and a shock wave moving on the motorway. The full phase diagram, including the effect of off-ramps, is explored using computer simulations and suggests means to optimize the capacity of a traffic network.

cond-mat.stat-mech↗

arXiv1997

Isotropic Transverse XY Chain with Energy- and Magnetization Currents

The ground-state correlations are investigated for an isotropic transverse XY chain which is constrained to carry either a current of magnetization J_M or a current of energy J_E. We find that the effect of nonzero J_M on the large-distance decay of correlations is twofold: i) oscillations are introduced and ii) the amplitude of the power law decay increases with increasing current. The effect of energy current is more complex. Generically, correlations in current carrying states are found to decay faster than in the J_E=0 states, contrary to expectations that correlations are increased by the presence of currents. However, increasing the current, one reaches a special line where the correlations become comparable to those of the J_E=0 states. On this line, the symmetry of the ground state is enhanced and the transverse magnetization vanishes. Further increase of the current destroys the extra symmetry but the transverse magnetization remains at the high-symmetry, zero value.

cond-mat↗