844 research outputs found
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 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
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