Bargmann-Michel-Telegdi equation and one-particle relativistic approach

A reexamination of the semiclassical approach of the relativistic electron indicates a possible variation of its helicity for electric and magnetic static fields applied along its global motion due to zitterbewegung effects, proportional to the anomalous part of the magnetic moment.Comment: 10 pages, LATEX2E, uses amsb

Quantum Chaotic Dynamics and Random Polynomials

We investigate the distribution of roots of polynomials of high degree with random coefficients which, among others, appear naturally in the context of "quantum chaotic dynamics". It is shown that under quite general conditions their roots tend to concentrate near the unit circle in the complex plane. In order to further increase this tendency, we study in detail the particular case of self-inversive random polynomials and show that for them a finite portion of all roots lies exactly on the unit circle. Correlation functions of these roots are also computed analytically, and compared to the correlations of eigenvalues of random matrices. The problem of ergodicity of chaotic wave-functions is also considered. For that purpose we introduce a family of random polynomials whose roots spread uniformly over phase space. While these results are consistent with random matrix theory predictions, they provide a new and different insight into the problem of quantum ergodicity. Special attention is devoted all over the paper to the role of symmetries in the distribution of roots of random polynomials.Comment: 33 pages, Latex, 6 Figures not included (a copy of them can be requested at [email protected]); to appear in Journal of Statistical Physic

Group Theory Approach to Band Structure: Scarf and Lame Hamiltonians

The group theoretical treatment of bound and scattering state problems is extended to include band structure. We show that one can realize Hamiltonians with periodic potentials as dynamical symmetries, where representation theory provides analytic solutions, or which can be treated with more general spectrum generating algebraic methods. We find dynamical symmetries for which we derive the transfer matrices and dispersion relations. Both compact and non-compact groups are found to play a role.Comment: 4 pages + 2 figs. Revtex/epsf. To appear: Phys Rev Lett, v.83 199

Hit-and-run transcriptional control by bZIP1 mediates rapid nutrient signaling in Arabidopsis

The dynamic nature of gene regulatory networks allows cells to rapidly respond to environmental change. However, the underlying temporal connections are missed, even in kinetic studies, as transcription factor (TF) binding within at least one time point is required to identify primary targets. The TF-regulated but unbound genes are dismissed as secondary targets. Instead, we report that these genes comprise transient TF-target interactions most relevant to rapid signal transduction. We temporally perturbed a master TF (Basic Leucine Zipper 1, bZIP1) and the nitrogen (N) signal it transduces and integrated TF regulation and binding data from the same cell samples. Our enabling approach could identify primary TF targets based solely on gene regulation, in the absence of TF binding. We uncovered three classes of primary TF targets: (i) poised (TF-bound but not TF-regulated), (ii) stable (TF-bound and TF-regulated), and (iii) transient (TF-regulated but not TF-bound), the largest class. Unexpectedly, the transient bZIP1 targets are uniquely relevant to rapid N signaling in planta, enriched in dynamic N-responsive genes, and regulated by TF and N signal interactions. These transient targets include early N responders nitrate transporter 2.1 and NIN-like protein 3, bound by bZIP1 at 1-5 min, but not at later time points following TF perturbation. Moreover, promoters of these transient targets are uniquely enriched with cis-regulatory motifs coinherited with bZIP1 binding sites, suggesting a recruitment role for bZIP1. This transient mode of TF action supports a classic, but forgotten, "hit-and-run" transcription model, which enables a "catalyst TF" to activate a large set of targets within minutes of signal perturbation

Projective Fourier Duality and Weyl Quantization

The Weyl-Wigner correspondence prescription, which makes large use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for noncommutative Fourier analysis allowing for that property. It is shown how the standard Kac structure has to be extended in order to accommodate the physical requirements. An Abelian and a symmetric projective Kac algebras are shown to provide, in close parallel to the standard case, a new dual framework and a well-defined notion of projective Fourier duality for the group of translations on the plane. The Weyl formula arises naturally as an irreducible component of the duality mapping between these projective algebras.Comment: LaTeX 2.09 with NFSS or AMSLaTeX 1.1. 102Kb, 44 pages, no figures. requires subeqnarray.sty, amssymb.sty, amsfonts.sty. Final version with text improvements and crucial typos correction

Group Approach to the Quantization of the P\"oschl-Teller dynamics

The quantum dynamics of a particle in the Modified P\"oschl-Teller potential is derived from the group $SL(2,R)$ by applying a Group Approach to Quantization (GAQ). The explicit form of the Hamiltonian as well as the ladder operators is found in the enveloping algebra of this basic symmetry group. The present algorithm provides a physical realization of the non-unitary, finite-dimensional, irreducible representations of the $SL(2,R)$ group. The non-unitarity manifests itself in that only half of the states are normalizable, in contrast with the representations of SU(2) where all the states are physical.Comment: 17 pages, LaTe

Radiation reaction for multipole moments

We propose a Poincare-invariant description for the effective dynamics of systems of charged particles by means of intrinsic multipole moments. To achieve this goal we study the effective dynamics of such systems within two frameworks -- the particle itself and hydrodynamical one. We give a relativistic-invariant definition for the intrinsic multipole moments both pointlike and extended relativistic objects. Within the hydrodynamical framework we suggest a covariant action functional for a perfect fluid with pressure. In the case of a relativistic charged dust we prove the equivalence of the particle approach to the hydrodynamical one to the problem of radiation reaction for multipoles. As the particular example of a general procedure we obtain the effective model for a neutral system of charged particles with dipole moment.Comment: 12 pages, 1 figure, RevTeX 4; references updated, minor textual correction

Vacuum Fluctuations, Geometric Modular Action and Relativistic Quantum Information Theory

A summary of some lines of ideas leading to model-independent frameworks of relativistic quantum field theory is given. It is followed by a discussion of the Reeh-Schlieder theorem and geometric modular action of Tomita-Takesaki modular objects associated with the quantum field vacuum state and certain algebras of observables. The distillability concept, which is significant in specifying useful entanglement in quantum information theory, is discussed within the setting of general relativistic quantum field theory.Comment: 26 pages. Contribution for the Proceedings of a Conference on Special Relativity held at Potsdam, 200

Analytic representations based on SU(1,1) coherent states and their applications

We consider two analytic representations of the SU(1,1) Lie group: the representation in the unit disk based on the SU(1,1) Perelomov coherent states and the Barut-Girardello representation based on the eigenstates of the SU(1,1) lowering generator. We show that these representations are related through a Laplace transform. A ``weak'' resolution of the identity in terms of the Perelomov SU(1,1) coherent states is presented which is valid even when the Bargmann index $k$ is smaller than one half. Various applications of these results in the context of the two-photon realization of SU(1,1) in quantum optics are also discussed.Comment: LaTeX, 15 pages, no figures, to appear in J. Phys. A. More information on http://www.technion.ac.il/~brif/science.htm

Gain control network conditions in early sensory coding

Gain control is essential for the proper function of any sensory system. However, the precise mechanisms for achieving effective gain control in the brain are unknown. Based on our understanding of the existence and strength of connections in the insect olfactory system, we analyze the conditions that lead to controlled gain in a randomly connected network of excitatory and inhibitory neurons. We consider two scenarios for the variation of input into the system. In the first case, the intensity of the sensory input controls the input currents to a fixed proportion of neurons of the excitatory and inhibitory populations. In the second case, increasing intensity of the sensory stimulus will both, recruit an increasing number of neurons that receive input and change the input current that they receive. Using a mean field approximation for the network activity we derive relationships between the parameters of the network that ensure that the overall level of activity of the excitatory population remains unchanged for increasing intensity of the external stimulation. We find that, first, the main parameters that regulate network gain are the probabilities of connections from the inhibitory population to the excitatory population and of the connections within the inhibitory population. Second, we show that strict gain control is not achievable in a random network in the second case, when the input recruits an increasing number of neurons. Finally, we confirm that the gain control conditions derived from the mean field approximation are valid in simulations of firing rate models and Hodgkin-Huxley conductance based models