Spectrum of a duality-twisted Ising quantum chain

The Ising quantum chain with a peculiar twisted boundary condition is considered. This boundary condition, first introduced in the framework of the spin-1/2 XXZ Heisenberg quantum chain, is related to the duality transformation, which becomes a symmetry of the model at the critical point. Thus, at the critical point, the Ising quantum chain with the duality-twisted boundary is translationally invariant, similar as in the case of the usual periodic or antiperiodic boundary conditions. The complete energy spectrum of the Ising quantum chain is calculated analytically for finite systems, and the conformal properties of the scaling limit are investigated. This provides an explicit example of a conformal twisted boundary condition and a corresponding generalised twisted partition function.Comment: LaTeX, 7 pages, using IOP style

Dynamics of an exclusion process with creation and annihilation

We examine the dynamical properties of an exclusion process with creation and annihilation of particles in the framework of a phenomenological domain-wall theory, by scaling arguments and by numerical simulation. We find that the length- and time scale are finite in the maximum current phase for finite creation- and annihilation rates as opposed to the algebraically decaying correlations of the totally asymmetric simple exclusion process (TASEP). Critical exponents of the transition to the TASEP are determined. The case where bulk creation- and annihilation rates vanish faster than the inverse of the system size N is also analyzed. We point out that shock localization is possible even for rates proportional to 1/N^a, 1<a<2.Comment: 16 pages, 8 figures, typos corrected, references added, section 4 revise

Spectral diffusion and 14N quadrupole splittings in absorption detected magnetic resonance hole burning spectra of photosynthetic reaction centers

Zero field absorption detected magnetic resonance hole burning measurements were performed on photosynthetic reaction centers of the bacteria Rhodobacter sphaeroides R26 and Rhodopseudomonas viridis. Extrapolation to zero microwave power yielded pseudohomogeneous linewidths of 2.0 MHz for Rhodopseudomonas viridis, 1.0 and 0.9 MHz for the protonated forms of Rhodobacter sphaeroides R26 with and without monomer bacteriochlorophyll exchanged, and 0.25 MHz as an upper limit for fully deuterated reaction centers of Rhodobacter sphaeroides R26. The measured linewidths were interpreted as being due to unresolved hyperfine interaction between the nuclear spins and the triplet electron spin, the line shape being determined by spectral diffusion among the nuclei. The difference in linewidths between Rhodobacter sphaeroides R26 and Rhodopseudomonas viridis is then explained by triplet delocalization on the special pair in the former, and localization on one dimer half on the latter. In the fully deuterated sample, four quadrupole satellites were observed in the hole spectra arising from the eight 14N nitrogens in the special pair. The quadrupole parameters seem to be very similar for all nitrogens and were determined to =1.25±0.1 MHz and =0.9±0.1 MHz. The Journal of Chemical Physics is copyrighted by The American Institute of Physics

Phase transitions and correlations in the bosonic pair contact process with diffusion: Exact results

The variance of the local density of the pair contact process with diffusion (PCPD) is investigated in a bosonic description. At the critical point of the absorbing phase transition (where the average particle number remains constant) it is shown that for lattice dimension d>2 the variance exhibits a phase transition: For high enough diffusion constants, it asymptotically approaches a finite value, while for low diffusion constants the variance diverges exponentially in time. This behavior appears also in the density correlation function, implying that the correlation time is negative. Yet one has dynamical scaling with a dynamical exponent calculated to be z=2.Comment: 20 pages, 5 figure

Discrete stochastic models for traffic flow

We investigate a probabilistic cellular automaton model which has been introduced recently. This model describes single-lane traffic flow on a ring and generalizes the asymmetric exclusion process models. We study the equilibrium properties and calculate the so-called fundamental diagrams (flow vs.\ density) for parallel dynamics. This is done numerically by computer simulations of the model and by means of an improved mean-field approximation which takes into account short-range correlations. For cars with maximum velocity 1 the simplest non-trivial approximation gives the exact result. For higher velocities the analytical results, obtained by iterated application of the approximation scheme, are in excellent agreement with the numerical simulations.Comment: Revtex, 30 pages, full postscript version (including figures) available by anonymous ftp from "fileserv1.mi.uni-koeln.de" in the directory "pub/incoming/" paper accepted for publication in Phys.Rev.

The asymmetric simple exclusion process: an integrable model for non-equilibrium statistical mechanics

The asymmetric simple exclusion process (ASEP) plays the role of a paradigm in non-equilibrium statistical mechanics. We review exact results for the ASEP obtained by Bethe ansatz and put emphasis on the algebraic properties of this model. The Bethe equations for the eigenvalues of the Markov matrix of the ASEP are derived from the algebraic Bethe ansatz. Using these equations we explain how to calculate the spectral gap of the model and how global spectral properties such as the existence of multiplets can be predicted. An extension of the Bethe ansatz leads to an analytic expression for the large deviation function of the current in the ASEP that satisfies the Gallavotti-Cohen relation. Finally, we describe some variants of the ASEP that are also solvable by Bethe ansatz. Keywords: ASEP, integrable models, Bethe ansatz, large deviations.Comment: 24 pages, 5 figures, published in the "special issue on recent advances in low-dimensional quantum field theories", P. Dorey, G. Dunne and J. Feinberg editor

Hidden symmetries in the asymmetric exclusion process

We present a spectral study of the evolution matrix of the totally asymmetric exclusion process on a ring at half filling. The natural symmetries (translation, charge conjugation combined with reflection) predict only two fold degeneracies. However, we have found that degeneracies of higher order also exist and, as the system size increases, higher and higher orders appear. These degeneracies become generic in the limit of very large systems. This behaviour can be explained by the Bethe Ansatz and suggests the presence of hidden symmetries in the model. Keywords: ASEP, Markov matrix, symmetries, spectral degeneracies, Bethe Ansatz.Comment: 16 page

The stochastic pump current and the non-adiabatic geometrical phase

We calculate a pump current in a classical two-state stochastic chemical kinetics by means of the non-adiabatic geometrical phase interpretation. The two-state system is attached to two particle reservoirs, and under a periodic perturbation of the kinetic rates, it gives rise to a pump current between the two-state system and the absorbing states. In order to calculate the pump current, the Floquet theory for the non-adiabatic geometrical phase is extended from a Hermitian case to a non-Hermitian case. The dependence of the pump current on the frequency of the perturbative kinetic rates is explicitly derived, and a stochastic resonance-like behavior is obtained.Comment: 11 page

Minimal Unitary Models and The Closed SU(2)-q Invariant Spin Chain

We consider the Hamiltonian of the closed $SU(2)_{q}$ invariant chain. We project a particular class of statistical models belonging to the unitary minimal series. A particular model corresponds to a particular value of the coupling constant. The operator content is derived. This class of models has charge-dependent boundary conditions. In simple cases (Ising, 3-state Potts) corresponding Hamiltonians are constructed. These are non-local as the original spin chain.Comment: 19 pages, latex, no figure