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 $AdS_{5}\times S^{5}$ 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 $(J,0,0)$ and $(J,J,J)$ 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 $\mathcal{N}=1$ Leigh-Strassler deformation of ${\cal N}=4$ 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

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