De Physique Theorique Research Articles

Role of energy uncertainties in ergodicity breaking induced by competing interactions and disorder. A dynamical assessment through the Loschmidt echo

A local excitation in a quantum many-particle system evolves deterministically. A time-reversal procedure, involving the invertion of the signs of every energy and interaction, should produce an excitation revival: the Loschmidt echo (LE). If somewhat imperfect, only a fraction of the excitation will refocus. We use such a procedure to show how non-inverted weak disorder and interactions, when assisted by the natural reversible dynamics, fully degrade the LE. These perturbations enhance diffusion and evenly distribute the excitation throughout the system. Such a dynamical paradigm, called ergodicity, breaks down when either the disorder or the interactions are too strong. These extreme regimes give rise to the well known Anderson localization and Mott insulating phases, where quantum diffusion becomes restricted. Accordingly, regardless of the kinetic energy terms, the excitation remains mainly localized and out-of-equilibrium, and the system behaves non-ergodically. The LE constitutes a fair dynamical witness for the whole phase diagram since it evidences a surprising topography in which ergodic and non-ergodic phases interpenetrate each other. Furthermore, we provide an estimation for the critical lines separating the ergodic and non-ergodic phases around the Mott and Anderson transitions. The energy uncertainties introduced by disorder and interaction shift these thresholds towards stronger perturbations. Remarkably, the estimations of the critical lines are in good agreement with the phase diagram derived from the LE dynamics.Received: 20 Novembre 2014, Accepted: 29 June 2015; Edited by: C. A. Condat, G. J. Sibona; Reviewed by: A. De Luca, Laboratoire de Physique Theorique, ENS & Institut Philippe Meyer, Paris, France; DOI: http://dx.doi.org/10.4279/PIP.070012Cite as: P R Zangara, P R Levstein, H M Pastawski, Papers in Physics 7, 070012 (2015)This paper, by P R Zangara, P R Levstein, H M Pastawski, is licensed under the Creative Commons Attribution License 3.0.

The Physics of NeutrinosThe Physics of Neutrinos, Vernon Barger, Danny Marfatia, and Kerry Whisnant, Princeton U. Press, 2012. $99.50 (224 pp.). ISBN 978-0-691-12853-5

These lecture notes are based on a course given at Institut de Physique Theorique of CEA/Saclay in January/February 2013.

Effects of a low frequency parametric excitation

Abstract The effects of a slowly varying parametric excitation on a shallow arch model are investigated. The delay bifurcation and the sequence of visited equilibria are analyzed. The method of Melnikov and a method proposed by Berglund [Adiabatic dynamical systems and hysteresis, Ph.D. thesis, Institut de Physique Theorique EPRFL, Lausanne, Switzerland, 1998] are used to determine chaotic regions.

On the non-thermal high energy radiation of galaxy clusters

Institute de Physique Theorique, Universite de Lausanne, BSP 1015 Lausanne, SwitzerlandReceived / AcceptedAbstract. The origin of the nonthermal EUV and hard X-ray emission “excess” reported from some galaxyclusters has been intensively debated over last several years. The most favored models which refer this excessto relativistic electrons upscattering the 2.7 K CMBR generally requires very low magnetic field, significantlybelow the estimates derived from the Faraday Rotation Measurements, unless one invokes rather nonstandardassumptions concerning the energy and pitch angle distributions of nonthermal electrons. In this paper we suggesta new model assuming that the “nonthermal” excess is due to synchrotron radiation of ultrarelativistic (multi-TeV) electrons of “photonic” origin. These electrons are continuously introduced throughout the entire intraclustermedium by very high energy (hypothetical) γ-rays through interactions with the diffuse extragalactic radiationfields. We present numerical calculations for the Coma cluster, and briefly discuss implications of the model forother galaxy clusters both in the X- and γ-ray energy domains.Key words. X-rays: galaxies: clusters – Galaxies: clusters: individual: Coma – Gamma rays: theory

Recent Advances in the Theory of Quantum Integrable Systems

The theory of integrable systems is grounded in the very beginning of theoretical physics: Kepler's system is an integrable system. This field of dynamical systems, where one looks for exact solutions of the equations of motion, has attracted most of the great figures in mathematical physics: Euler, Lagrange, Jacobi, etc. Liouville was the first to formulate the precise mathematical conditions ensuring solvability `by quadrature' of the dynamical equations, and his theorem still lies at the heart of the recent developments. The modern era started about thirty years ago with the systematic formulation of soliton solutions to nonlinear wave equations. Since then, impressive developments arose both for the classical and the quantum theory. Subtle mathematical techniques were devised for the resolution of these theories, relying on algebra (group theory), analysis and algebraic geometry (Riemann theory of surfaces). We therefore clearly see that the theory of integrable systems lies ab initio at a crossing of physics and mathematics, and that the developments of these last thirty years have strengthened this dual character, which makes it into an archetypal domain of mathematical physics. As regards the classical theory, beyond the direct connections to the various domains of classical soliton physics (hydrodynamics, condensed matter physics, laser optics, particle physics, plasma, biology or information coding), one has witnessed in these recent years more unexpected (and for some of them not yet well understood) connections to a priori farther fields of theoretical physics: string theory (through matrix models), topological field theories (two dimensional Yang--Mills, three dimensional Chern--Simons--Witten), or supersymmetric field theories (for instance the correspondence discovered by Seiberg and Witten between classical integrable models and quantum potentials). Quantum integrable theories provide examples of exactly (non perturbatively) solvable physical models. They thus allow one to obtain descriptions of non trivial phenomena such as second order phase transition in condensed systems (spin lattices) and exact solution of relativistic quantum field theories (Sine--Gordon...). On the other hand, they supply an excellent example of fruitful interface between physics and mathematics: the theory of quantum groups (and the germane theory of special functions) is a perfect illustration of this role and perspectives of such new developments appear very promising. The purpose of the first RAQIS meeting was to bring together researchers from the various fields of mathematics and physics connected to the theory of quantum integrable systems. This conference was held in the framework of the European TMR network EUCLID `Integrable models and applications: from strings to condensed matter', contract number HPRN-CT-2002-00325. The RAQIS03 meeting took place at the Laboratoire d'Annecy-le-vieux de Physique Theorique (LAPTH, France) from 25 March to 28 March, 2003. The organising committee consisted of Daniel Arnaudon, Jean Avan, Luc Frappat, Eric Ragoucy and Paul Sorba. Financial support was provided by Universite de Savoie and CNRS-DRI (Centre National de la Recherche Scientifique, Direction des Relations Internationales). In particular various scientific contacts with several Japanese participants were initiated thanks to the CNRS PICS contract number 911. This special issue of Journal of Physics A: Mathematical and General is dedicated to the subject of the RAQIS03 meeting in Annecy-le-vieux. Most of the contributors to this issue took part in the meeting, but this volume does not aim to be a proceedings in the usual sense of the word: contributions do not necessarily coincide with the reports presented at the meeting, nor are the contributors restricted exclusively to those people that were present. The intention of the special issue is to benefit from the occasion offered by the RAQIS03 meeting to highlight the important new areas in quantum integrability, by collecting together in one single volume a selection of articles reflecting the scope of the meeting. All contributions to this special issue are original research papers, but by collecting together we feel that we offer a better context for the work and an insight into the new directions where this research is leading. specialists and also to newcomers in this domain. Finally, we would like to warmly thank all the participants and speakers as well as all the authors and contributors to this issue.

Sharp Rigid to Floppy Phase Transition Induced by Dangling Ends in a Network Glass

Laboratoire de Physique Theorique des Liquides, Universite Pierre et Marie Curie, Boite 121, 4 Place Jussieu,75252 Paris, Cedex 05, France(Received 29 March 2001; published 16 October 2001)The count of Lagrangian bonding constraints in ternary Ge S I glasses isestablished from the molecular structure using Raman scattering and Þrst-principles cluster calculations.The results show that decreases to 3 as y increases close to , where a sharply deÞnedglobal minimum in the nonreversing heat sow, near , is observed in scanning calorimetry.Here we have a rigidity transition induced by I dangling ends, with its sharpness resulting from theabsence of self-organization in the random network.

Nearest-neighbor functions in a one-dimensional generalized ballistic deposition model

P. Viot, P. R. Van Tassel, and J. Talbot Laboratoire de Physique Theorique des Liquides, Universite Pierre et Marie Curie, 4, place Jussieu 75252 Paris Cedex 05, France Department of Chemical Engineering and Materials Science, Wayne State University, 5050 Anthony Wayne Drive, Detroit, Michigan 48202 Department of Chemistry and Biochemistry, Duquesne University, Pittsburgh, Pennsylvania 15282 ~Received 7 November 1996; revised manuscript received 16 June 1997!

Perturbations of geodesic flows on surfaces of constant negative curvature and their mixing properties: 486 (M1,T2) P. Collet, Laboratoire de Physique Theorique, Ecole Polytechnique, 91128 Palaiseau, FRANCE, and IMA; H. Epstein, IHES, 91440, Bures S/Yvette, FRANCE; G. Gallavotti, Istituto Matematico, Universita di Roma, ITALY.

Perturbations of geodesic flows on surfaces of constant negative curvature and their mixing properties: 486 (M1,T2) P. Collet, Laboratoire de Physique Theorique, Ecole Polytechnique, 91128 Palaiseau, FRANCE, and IMA; H. Epstein, IHES, 91440, Bures S/Yvette, FRANCE; G. Gallavotti, Istituto Matematico, Universita di Roma, ITALY.

Nuclear Vibrations and Effective Interactions

We derive separable interactions which are equivalent to the zero-range Skyrme forces in the random phase approximation. The isoscalar and the isovector tl-pole-tl-pole forces proposed by Bohr and Mottelson are obtained as a special case of the separable interactions. Spin- and isospin-dependent separable forces are also discussed. 3 ) reproduces very well static properties of the nuclear ground states in the broad region of the mass table. The same interaction has been shown by many authors 4)~6) to explain very well the gross structure of the dynamic properties of nuclei like giant multipole resonances. It is well known that the separable Q-Q force developed by Bohr and Mottelson et al.7),8) has played an important role in comprehensive description of nuclear low-lying collective excitations. The introduction of the separable force makes it possible to perform the calculations of many-body correlation problems in a simple and intuitive manner and to analyze experimental data systematically throughout the periodic table. Moreover, Bohr and Mottelson et a1. 7 ),9) have extended their idea of the separable-force to the study of giant multipole resonances by using the sum-rules and the self-consistent condition between the vibrating potential and density. Their model has been Quite successful in the calculation of the excitation energies of the isoscalar and isovector giant resonances and, also, in the estimate of the core polarization effects. Up till now, some authors10),11J discussed the connection between the separable A-pole-A-pole interaction and the more sophisticated interaction, that is, the Skyrme force related with the isoscalar and the isovector giant resonances. 'l Present address: Division de Physique Theorique, Intitut de Physique Nucleaire, 91406 Orsay-Cedex, France.

Kinematical singularities, crossing matrix and kinematical constraints for two-body helicity amplitudes: G. Cohen-Tannoudji, A. Morel, and H. Navelet. Service de Physique Theorique, Centre d'Etudes Nucleaires de Saclay, Gif-sur-Yvette, France

Kinematical singularities, crossing matrix and kinematical constraints for two-body helicity amplitudes: G. Cohen-Tannoudji, A. Morel, and H. Navelet. Service de Physique Theorique, Centre d'Etudes Nucleaires de Saclay, Gif-sur-Yvette, France

One-particle densities, thermal propagation, and second sound in dielectric crystals: C. P. Enz. Institut de Physique Theorique, Université de Génève, Switzerland

One-particle densities, thermal propagation, and second sound in dielectric crystals: C. P. Enz. Institut de Physique Theorique, Université de Génève, Switzerland

Structure of the perturbation expansion for the bose liquid at zero temperature: J. Gavoret, Laboratoire de Physique Theorique et Hautes Energies, Orsay, France, and P. Nozieres, Laboratoire de Physique de l'Ecole Normale Supereure, Paris, France

Structure of the perturbation expansion for the bose liquid at zero temperature: J. Gavoret, Laboratoire de Physique Theorique et Hautes Energies, Orsay, France, and P. Nozieres, Laboratoire de Physique de l'Ecole Normale Supereure, Paris, France