1,383 research outputs found
Chaos Thresholds in finite Fermi systems
The development of Quantum Chaos in finite interacting Fermi systems is
considered. At sufficiently high excitation energy the direct two-particle
interaction may mix into an eigen-state the exponentially large number of
simple Slater-determinant states. Nevertheless, the transition from Poisson to
Wigner-Dyson statistics of energy levels is governed by the effective high
order interaction between states very distant in the Fock space. The concrete
form of the transition depends on the way one chooses to work out the problem
of factorial divergency of the number of Feynman diagrams. In the proposed
scheme the change of statistics has a form of narrow phase transition and may
happen even below the direct interaction threshold.Comment: 9 pages, REVTEX, 2 eps figures. Enlarged versio
Comparison of perturbative expansions using different phonon bases for two-site Holstein model
The two-site single-polaron problem is studied within the perturbative
expansions using different standard phonon basis obtained through the Lang
Firsov (LF), modified LF (MLF) and modified LF transformation with squeezed
phonon states (MLFS). The role of these convergent expansions using the above
prescriptions in lowering the energy and in determining the correlation
functions are compared for different values of coupling strength. The
single-electron energy, oscillator wave functions and correlation functions are
calculated for the same system. The applicability of different phonon basis in
different regimes of the coupling strength as well as in different regimes of
hopping are also discussed.Comment: 24 pages (RevTEX), 12 postscript figures, final version accepted in
PRB(2000) Jornal Ref: Phys. Rev. B, 61, 4592-4602 (2000
Chemotactic response and adaptation dynamics in Escherichia coli
Adaptation of the chemotaxis sensory pathway of the bacterium Escherichia
coli is integral for detecting chemicals over a wide range of background
concentrations, ultimately allowing cells to swim towards sources of attractant
and away from repellents. Its biochemical mechanism based on methylation and
demethylation of chemoreceptors has long been known. Despite the importance of
adaptation for cell memory and behavior, the dynamics of adaptation are
difficult to reconcile with current models of precise adaptation. Here, we
follow time courses of signaling in response to concentration step changes of
attractant using in vivo fluorescence resonance energy transfer measurements.
Specifically, we use a condensed representation of adaptation time courses for
efficient evaluation of different adaptation models. To quantitatively explain
the data, we finally develop a dynamic model for signaling and adaptation based
on the attractant flow in the experiment, signaling by cooperative receptor
complexes, and multiple layers of feedback regulation for adaptation. We
experimentally confirm the predicted effects of changing the enzyme-expression
level and bypassing the negative feedback for demethylation. Our data analysis
suggests significant imprecision in adaptation for large additions.
Furthermore, our model predicts highly regulated, ultrafast adaptation in
response to removal of attractant, which may be useful for fast reorientation
of the cell and noise reduction in adaptation.Comment: accepted for publication in PLoS Computational Biology; manuscript
(19 pages, 5 figures) and supplementary information; added additional
clarification on alternative adaptation models in supplementary informatio
Chaotic scattering with direct processes: A generalization of Poisson's kernel for non-unitary scattering matrices
The problem of chaotic scattering in presence of direct processes or prompt
responses is mapped via a transformation to the case of scattering in absence
of such processes for non-unitary scattering matrices, \tilde S. In the absence
of prompt responses, \tilde S is uniformly distributed according to its
invariant measure in the space of \tilde S matrices with zero average, < \tilde
S > =0. In the presence of direct processes, the distribution of \tilde S is
non-uniform and it is characterized by the average (\neq 0). In
contrast to the case of unitary matrices S, where the invariant measures of S
for chaotic scattering with and without direct processes are related through
the well known Poisson kernel, here we show that for non-unitary scattering
matrices the invariant measures are related by the Poisson kernel squared. Our
results are relevant to situations where flux conservation is not satisfied.
For example, transport experiments in chaotic systems, where gains or losses
are present, like microwave chaotic cavities or graphs, and acoustic or elastic
resonators.Comment: Added two appendices and references. Corrected typo
Quantum Graphs: A simple model for Chaotic Scattering
We connect quantum graphs with infinite leads, and turn them to scattering
systems. We show that they display all the features which characterize quantum
scattering systems with an underlying classical chaotic dynamics: typical
poles, delay time and conductance distributions, Ericson fluctuations, and when
considered statistically, the ensemble of scattering matrices reproduce quite
well the predictions of appropriately defined Random Matrix ensembles. The
underlying classical dynamics can be defined, and it provides important
parameters which are needed for the quantum theory. In particular, we derive
exact expressions for the scattering matrix, and an exact trace formula for the
density of resonances, in terms of classical orbits, analogous to the
semiclassical theory of chaotic scattering. We use this in order to investigate
the origin of the connection between Random Matrix Theory and the underlying
classical chaotic dynamics. Being an exact theory, and due to its relative
simplicity, it offers new insights into this problem which is at the fore-front
of the research in chaotic scattering and related fields.Comment: 28 pages, 13 figures, submitted to J. Phys. A Special Issue -- Random
Matrix Theor
Correlation functions of scattering matrix elements in microwave cavities with strong absorption
The scattering matrix was measured for microwave cavities with two antennas.
It was analyzed in the regime of overlapping resonances. The theoretical
description in terms of a statistical scattering matrix and the rescaled
Breit-Wigner approximation has been applied to this regime. The experimental
results for the auto-correlation function show that the absorption in the
cavity walls yields an exponential decay. This behavior can only be modeled
using a large number of weakly coupled channels. In comparison to the
auto-correlation functions, the cross-correlation functions of the diagonal
S-matrix elements display a more pronounced difference between regular and
chaotic systems
A note on the universality of the Hagedorn behavior of pp-wave strings
Following on from recent studies of string theory on a one-parameter family
of integrable deformations of proposed by Lunin and
Maldacena, we carry out a systematic analysis of the high temperature
properties of type IIB strings on the associated pp-wave geometries. In
particular, through the computation of the thermal partition function and free
energy we find that not only does the theory exhibit a Hagedorn transition in
both the and class of pp-waves, but that the Hagedorn
temperature is insensitive to the deformation suggesting an interesting
universality in the high temperature behaviour of the pp-wave string theory. We
comment also on the implications of this universality on the
confinement/deconfinement transition in the dual
Leigh-Strassler deformation of Yang-Mills theory.Comment: 25 pages; fixed minor typo; added reference
Fundamental Strings in Open String Theory at the Tachyonic Vacuum
We show that the world-volume theory on a D-p-brane at the tachyonic vacuum
has solitonic string solutions whose dynamics is governed by the Nambu-Goto
action of a string moving in (25+1) dimensional space-time. This provides
strong evidence for the conjecture that at this vacuum the full (25+1)
dimensional Poincare invariance is restored. We also use this result to argue
that the open string field theory at the tachyonic vacuum must contain closed
string excitations.Comment: LaTeX file, 16 pages, references and clarification adde
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Overview of mathematical approaches used to model bacterial chemotaxis I: the single cell
Mathematical modeling of bacterial chemotaxis systems has been influential and insightful in helping to understand experimental observations. We provide here a comprehensive overview of the range of mathematical approaches used for modeling, within a single bacterium, chemotactic processes caused by changes to external gradients in its environment. Specific areas of the bacterial system which have been studied and modeled are discussed in detail, including the modeling of adaptation in response to attractant gradients, the intracellular phosphorylation cascade, membrane receptor clustering, and spatial modeling of intracellular protein signal transduction. The importance of producing robust models that address adaptation, gain, and sensitivity are also discussed. This review highlights that while mathematical modeling has aided in understanding bacterial chemotaxis on the individual cell scale and guiding experimental design, no single model succeeds in robustly describing all of the basic elements of the cell. We conclude by discussing the importance of this and the future of modeling in this area
Zero-point fluctuations in the ground state of a mesoscopic normal ring
We investigate the persistent current of a ring with an in-line quantum dot
capacitively coupled to an external circuit. Of special interest is the
magnitude of the persistent current as a function of the external impedance in
the zero temperature limit when the only fluctuations in the external circuit
are zero-point fluctuations. These are time-dependent fluctuations which
polarize the ring-dot structure and we discuss in detail the contribution of
displacement currents to the persistent current. We have earlier discussed an
exact solution for the persistent current and its fluctuations based on a Bethe
ansatz. In this work, we emphasize a physically more intuitive approach using a
Langevin description of the external circuit. This approach is limited to weak
coupling between the ring and the external circuit. We show that the zero
temperature persistent current obtained in this approach is consistent with the
persistent current calculated from a Bethe ansatz solution. In the absence of
coupling our system is a two level system consisting of the ground state and
the first excited state. In the presence of coupling we investigate the
projection of the actual state on the ground state and the first exited state
of the decoupled ring. With each of these projections we can associate a phase
diffusion time. In the zero temperature limit we find that the phase diffusion
time of the excited state projection saturates, whereas the phase diffusion
time of the ground state projection diverges.Comment: 12 pages, 5 figure
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