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

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

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

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

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

Bulk vs. Boundary Dynamics in Anti-de Sitter Spacetime

We investigate the details of the bulk-boundary correspondence in Lorentzian signature anti-de Sitter space. Operators in the boundary theory couple to sources identified with the boundary values of non-normalizable bulk modes. Such modes do not fluctuate and provide classical backgrounds on which bulk excitations propagate. Normalizable modes in the bulk arise as a set of saddlepoints of the action for a fixed boundary condition. They fluctuate and describe the Hilbert space of physical states. We provide an explicit, complete set of both types of modes for free scalar fields in global and Poincar\'e coordinates. For \ads{3}, the normalizable and non-normalizable modes originate in the possible representations of the isometry group \SL_L\times\SL_R for a field of given mass. We discuss the group properties of mode solutions in both global and Poincar\'e coordinates and their relation to different expansions of operators on the cylinder and on the plane. Finally, we discuss the extent to which the boundary theory is a useful description of the bulk spacetime.Comment: Standard LaTeX, 28 pages, 2 postscript figures. v2: References added. Substantial revision in section 3 of treatment of global modes; non-normalizable modes have arbitrary time dependence. Revised discussion of low-mass modes and puzzle raised re: coupling of the dual boundary operators. v3: unwanted paragraph removed. v4: Sec. 5.2 correcte

Multiple PLDs Required for High Salinity and Water Deficit Tolerance in Plants

High salinity and drought have received much attention because they severely affect crop production worldwide. Analysis and comprehension of the plant's response to excessive salt and dehydration will aid in the development of stress-tolerant crop varieties. Signal transduction lies at the basis of the response to these stresses, and numerous signaling pathways have been implicated. Here, we provide further evidence for the involvement of phospholipase D (PLD) in the plant's response to high salinity and dehydration. A tomato (Lycopersicon esculentum) α-class PLD, LePLDα1, is transcriptionally up-regulated and activated in cell suspension cultures treated with salt. Gene silencing revealed that this PLD is indeed involved in the salt-induced phosphatidic acid production, but not exclusively. Genetically modified tomato plants with reduced LePLDα1 protein levels did not reveal altered salt tolerance. In Arabidopsis (Arabidopsis thaliana), both AtPLDα1 and AtPLDδ were found to be activated in response to salt stress. Moreover, pldα1 and pldδ single and double knock-out mutants exhibited enhanced sensitivity to high salinity stress in a plate assay. Furthermore, we show that both PLDs are activated upon dehydration and the knock-out mutants are hypersensitive to hyperosmotic stress, displaying strongly reduced growth