276 research outputs found
Formation of antiwaves in gap-junction-coupled chains of neurons
Using network models consisting of gap junction coupled Wang-Buszaki neurons,
we demonstrate that it is possible to obtain not only synchronous activity
between neurons but also a variety of constant phase shifts between 0 and \pi.
We call these phase shifts intermediate stable phaselocked states. These phase
shifts can produce a large variety of wave-like activity patterns in
one-dimensional chains and two-dimensional arrays of neurons, which can be
studied by reducing the system of equations to a phase model. The 2\pi periodic
coupling functions of these models are characterized by prominent higher order
terms in their Fourier expansion, which can be varied by changing model
parameters. We study how the relative contribution of the odd and even terms
affect what solutions are possible, the basin of attraction of those solutions
and their stability. These models may be applicable to the spinal central
pattern generators of the dogfish and also to the developing neocortex of the
neonatal rat
The scaling behaviour of screened polyelectrolytes
We present a field-theoretic renormalization group (RG) analysis of a single
flexible, screened polyelectrolyte chain (a Debye-H\"uckel chain) in a polar
solvent. We point out that the Debye-H\"uckel chain may be mapped onto a local
field theory which has the same fixed point as a generalised Potts
model. Systematic analysis of the field theory shows that the system is one
with two interplaying length-scales requiring the calculation of scaling
functions as well as exponents to fully describe its physical behaviour. To
illustrate this, we solve the RG equation and explicitly calculate the
exponents and the mean end-to-end length of the chain.Comment: 6 pages, 1 figure; changed title and slight modification to tex
A Perturbative/Variational Approach to Quantum Lattice Hamiltonians
We propose a method to construct the ground state of local
lattice hamiltonians with the generic form , where
is a coupling constant and is a hamiltonian with a non degenerate ground
state . The method is based on the choice of an exponential ansatz
, which is a sort of generalized
lattice version of a Jastrow wave function. We combine perturbative and
variational techniques to get succesive approximations of the operator
. Perturbation theory is used to set up a variational method which
in turn produces non perturbative results. The computation with this kind of
ansatzs leads to associate to the original quantum mechanical problem a
statistical mechanical system defined in the same spatial dimension. In some
cases these statistical mechanical systems turn out to be integrable, which
allow us to obtain exact upper bounds to the energy. The general ideas of our
method are illustrated in the example of the Ising model in a transverse field.Comment: 27 pages, three .ps figures appended, DFTUZ 94-2
Entanglement Mean Field Theory and the Curie-Weiss Law
The mean field theory, in its different hues, form one of the most useful
tools for calculating the single-body physical properties of a many-body
system. It provides important information, like critical exponents, of the
systems that do not yield to an exact analytical treatment. Here we propose an
entanglement mean field theory (EMFT) to obtain the behavior of the two-body
physical properties of such systems. We apply this theory to predict the phases
in paradigmatic strongly correlated systems, viz. the transverse anisotropic
XY, the transverse XX, and the Heisenberg models. We find the critical
exponents of different physical quantities in the EMFT limit, and in the case
of the Heisenberg model, we obtain the Curie-Weiss law for correlations. While
the exemplary models have all been chosen to be quantum ones, classical
many-body models also render themselves to such a treatment, at the level of
correlations.Comment: 5 pages, 4 figure
Finite Temperature and Dynamical Properties of the Random Transverse-Field Ising Spin Chain
We study numerically the paramagnetic phase of the spin-1/2 random
transverse-field Ising chain, using a mapping to non-interacting fermions. We
extend our earlier work, Phys. Rev. 53, 8486 (1996), to finite temperatures and
to dynamical properties. Our results are consistent with the idea that there
are ``Griffiths-McCoy'' singularities in the paramagnetic phase described by a
continuously varying exponent , where measures the
deviation from criticality. There are some discrepancies between the values of
obtained from different quantities, but this may be due to
corrections to scaling. The average on-site time dependent correlation function
decays with a power law in the paramagnetic phase, namely
, where is imaginary time. However, the typical
value decays with a stretched exponential behavior, ,
where may be related to . We also obtain results for the full
probability distribution of time dependent correlation functions at different
points in the paramagnetic phase.Comment: 10 pages, 14 postscript files included. The discussion of the typical
time dependent correlation function has been greatly expanded. Other papers
of APY are available on-line at http://schubert.ucsc.edu/pete
Coupling between feedback loops in autoregulatory networks affects bistability range, open-loop gain and switching times
Biochemical regulatory networks governing diverse cellular processes such as stress-response,
differentiation and cell cycle often contain coupled feedback loops. We aim at understanding
how features of feedback architecture, such as the number of loops, the sign of the loops and
the type of their coupling, affect network dynamical performance. Specifically, we investigate
how bistability range, maximum open-loop gain and switching times of a network with
transcriptional positive feedback are affected by additive or multiplicative coupling with
another positive- or negative-feedback loop. We show that a network's bistability range is
positively correlated with its maximum open-loop gain and that both quantities depend on the
sign of the feedback loops and the type of feedback coupling. Moreover, we find that the
addition of positive feedback could decrease the bistability range if we control the basal level
in the signal-response curves of the two systems. Furthermore, the addition of negative
feedback has the capacity to increase the bistability range if its dissociation constant is much
lower than that of the positive feedback. We also find that the addition of a positive feedback to
a bistable network increases the robustness of its bistability range, whereas the addition of a
negative feedback decreases it. Finally, we show that the switching time for a transition from a
high to a low steady state increases with the effective fold change in gene regulation. In
summary, we show that the effect of coupled feedback loops on the bistability range and
switching times depends on the underlying mechanistic details
Aperiodic Ising model on the Bethe lattice: Exact results
We consider the Ising model on the Bethe lattice with aperiodic modulation of
the couplings, which has been studied numerically in Phys. Rev. E 77, 041113
(2008). Here we present a relevance-irrelevance criterion and solve the
critical behavior exactly for marginal aperiodic sequences. We present
analytical formulae for the continuously varying critical exponents and discuss
a relationship with the (surface) critical behavior of the aperiodic quantum
Ising chain.Comment: 7 pages, 3 figures, minor correction
Crossover between aperiodic and homogeneous semi-infinite critical behaviors in multilayered two-dimensional Ising models
We investigate the surface critical behavior of two-dimensional multilayered
aperiodic Ising models in the extreme anisotropic limit. The system under
consideration is obtained by piling up two types of layers with respectively
and spin rows coupled via nearest neighbor interactions and
, where the succession of layers follows an aperiodic sequence. Far
away from the critical regime, the correlation length is smaller
than the first layer width and the system exhibits the usual behavior of an
ordinary surface transition. In the other limit, in the neighborhood of the
critical point, diverges and the fluctuations are sensitive to the
non-periodic structure of the system so that the critical behavior is governed
by a new fixed point. We determine the critical exponent associated to the
surface magnetization at the aperiodic critical point and show that the
expected crossover between the two regimes is well described by a scaling
function. From numerical calculations, the parallel correlation length
is then found to behave with an anisotropy exponent which
depends on the aperiodic modulation and the layer widths.Comment: LaTeX file, 9 pages, 8 eps figures, to appear in Phys. Rev.
Griffiths-McCoy singularities in the transverse field Ising model on the randomly diluted square lattice
The site-diluted transverse field Ising model in two dimensions is studied
with Quantum-Monte-Carlo simulations. Its phase diagram is determined in the
transverse field (Gamma) and temperature (T) plane for various (fixed)
concentrations (p). The nature of the quantum Griffiths phase at zero
temperature is investigated by calculating the distribution of the local
zero-frequency susceptibility. It is pointed out that the nature of the
Griffiths phase is different for small and large Gamma.Comment: 21 LaTeX (JPSJ macros included), 12 eps-figures include
Thermodynamics of histories for the one-dimensional contact process
The dynamical activity K(t) of a stochastic process is the number of times it
changes configuration up to time t. It was recently argued that (spin) glasses
are at a first order dynamical transition where histories of low and high
activity coexist. We study this transition in the one-dimensional contact
process by weighting its histories by exp(sK(t)). We determine the phase
diagram and the critical exponents of this model using a recently developed
approach to the thermodynamics of histories that is based on the density matrix
renormalisation group. We find that for every value of the infection rate,
there is a phase transition at a critical value of s. Near the absorbing state
phase transition of the contact process, the generating function of the
activity shows a scaling behavior similar to that of the free energy in an
equilibrium system near criticality.Comment: 16 pages, 7 figure
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