Symmetry Breaking

A pedagogical review on supersymmetry in quantum mechanis is presented which provides a comprehensive coverage of the subject. First, the key ingredients on the quantization of the systems with anticommuting variables are discussed. The supersymmetric Hamiltotian in quantum mechanics is then constructed by emphasizing the role of partner potentials and the superpotentials. We also make explicit the mathematical formulation of the Hamiltonian by considering in detail the N=1 and N=2 supersymmetric (quantum) mechanics. Supersymmetry is then discussed in the context of one-dimensional problems and the importance of the factorization method is highlighted. We treat in detail the technique of constructing a hierarchy of Hamiltonians employing the so-called ‘shape-invariance’ of potentials. To make transparent the relationship between supersymmetry and solvable potentials, we also solve several examples. We then go over to the formulation of supersymmetry in radial problems, paying a spec...

We consider the theoretical setting of a superfluid like 3He in a rotating container, which is set between the two layers of a type-II superconductor. We describe the superfluid vortices as a 2-dimensional Ising-like model on a triangular lattice in presence of local magnetic fields. The interaction term of the superfluid vortices with the Abrikosov vortices of the superconductor appears then as a symmetry breaking term in the free energy. Such a term gives a higher probability of quantum tunnelling across the potential barrier for bubbles nucleation, thus favouring quantum cavitation.

In a recent paper (S. Kumar, A. Pandey, Phys. Rev. E, 79, 2009, p. 026211) we considered Jacobi family (including Laguerre and Gaussian cases) of random matrix ensembles and reported exact solutions of crossover problems involving time-reversal symmetry breaking. In the present paper we give details of the work. We start with Dyson’s Brownian motion description of random matrix ensembles

In the Higgs mechanism, mediators of the weak force acquire masses by interacting with the Higgs condensate, leading to a vector boson mass matrix. On the other hand, a rigid body accelerated through an inviscid, incompressible and irrotational fluid feels an opposing force linearly related to its acceleration, via an added-mass tensor. We uncover a striking physical analogy between the two effects and propose a dictionary relating them. The correspondence turns the gauge Lie algebra into the space of directions in which the body can move, encodes the pattern of gauge symmetry breaking in the shape of an associated body and relates symmetries of the body to those of the scalar vacuum manifold. The new viewpoint is illustrated with numerous examples, and raises interesting questions, notably on the fluid analogues of the broken symmetry and Higgs particle, and the field-theoretic analogue of the added mass of a composite body.

We clarify several subtle points in the CPN-1 model in 2 + 1 dimensions. It is shown that as a consequence of local gauge invariance the nA particles, belonging to fundamental representation of SU(N) do not appear in the spectrum (in any number of dimensions) regardless of the nature of the interaction between them. In 2 + 1 dimensions we analyse the phase structure of the theory from the point of view of realization of the relevant symmetries: SU(N)/ZN ⊗ UΦ(1) ⊗ UE(1). The symmetries UΦ(1) and UE(1) are gauge invariant analogs of the magnetic flux and electric charge symmetries in scalar QED. The charge of UE(1) is not related to the global part of the local U(1) transformations (which counts the difference between the number of n and the number of n∗ excitations). At the phase transition point the flavour SU(N) ZN is broken down to U(N−1) while the mode of implementation of the UΦ(1) is changed from Kosterlitz-Thouless to Wigner-Weyl. We provide a gauge invariant order parameter for the flavour symmetry breaking and identify the massless “photon” with the Kosterlitz-Thouless zero mode of UΦ(1).

The fine structure of excitons is studied by magnetophotoluminescence spectroscopy of single self-assembled In(Ga)As/(Al)GaAs quantum dots. Both strength and orientation of the magnetic field are varied. In a combination with a detailed theoretical analysis, these studies allow ...

In this thesis, we are concerned with the dynamics of spiral wave solutions to Reaction-Diffsion systems of equations, and how they behave when subject to symmetry breaking perturbations. We present an asymptotic theory of the study of meandering (quasiperiodic spiral wave solutions) spiral waves which are drifting due to symmetry breaking perturbations. This theory is based on earlier theories: the 1995 Biktashev et al theory of drift of rigidly rotating spirals, and the 1996 Biktashev et al theory of meander of spirals in unperturbed systems. We combine the two theories by first rewriting the 1995 drift theory using the symmetry quotient system method of the 1996 meander theory, and then go on to extend the approach to meandering spirals by considering Floquet theory and using a singular perturbation method. We demonstrate the work of the newly developed theory on simple examples. We also develop a numerical implementation of the quotient system method, demonstrate its numerical convergence and its use in calculations which would be difficult to do by the standard methods, and also link this study to the problem of calculation of response functions of spiral waves.

This article presents an analysis of the positive disintegration as a process of symmetry breaking. Symmetry breaking plays a major role in self-organized patterns formation and correlates directly to increasing complexity and function specialization. According to Dąbrowski, a creator of the Theory of Positive Disintegration, the change from lower to higher levels of human development requires a major restructuring of an individual's psychological makeup. Each level of human development is a relatively stable and coherent configuration of emotional-cognitive patterns called developmental dynamisms. Their main function is to restructure a mental structure by breaking the symmetry of a low level and bringing differentiation and then integration to higher levels. The positive disintegration is then the process of transitions from a lower level of high symmetry and low complexity to higher levels of low symmetry and high complexity of mental structure.

We study the gravity duals of symmetry-breaking deformations of superconfor- mal field theories, AdS/CFT dual to Type IIB string theory on AdS5 ×Y where Y is a Sasaki-Einstein manifold. In these vacua both conformal invariance and baryonic symmetries are spontaneously broken. We present a detailed discussion of the supergravity moduli space, which involves flat form fields on asymptotically conical Calabi-Yau

In 'The Hitchhiker's Guide to the Galaxy', by Douglas Adams, the Answer to the Ultimate Question of Life, the Universe, and Everything is found to be 42 { but
the meaning of this is left open to interpretation. We take it to mean that there are 42
fundamental questions which must be answered on the road to full enlightenment, and we attempt a first draft (or personal selection) of these ultimate questions, on topics ranging from the cosmological constant and origin of the universe to the origin of life and consciousness.

L’auto-organisation est une notion aux multiples traditions, mobilisée entre autres par de nombreux physiciens depuis les années soixante-dix, aux frontières de la physique, de la chimie et de la biologie. Malgré des débats philosophiques nombreux, peu de travaux historiques y sont aujourd’hui consacrés, au même titre qu’à un grand nombre d’autres approches interdisciplinaires qui prennent leur essor au cours de la seconde moitié du XXe siècle. Nous étudions dans ce travail la genèse d’un concept d’auto-organisation chez le physico-chimiste belge Ilya Prigogine, prix Nobel de chimie 1977 et figure polémique chez les physiciens. Nous retraçons d’abord la préhistoire scientifique du mot, et l’arrière-plan embryologique auquel Prigogine l’emprunte, avant d’examiner le contexte de l’école de Bruxelles de thermodynamique des processus irréversibles, fondée par son maître Théophile De Donder, et la reconnaissance acquise par Prigogine dans la communauté physico-chimique des années soixante. Dans un second temps nous examinons l’élaboration de son concept d’auto-organisation de 1945 à 1975, le rôle qu’y joue l’entropie et son rapport à la biologie, à travers un projet philosophico-scientifique que l’on peut qualifer d’évolutionnisme thermodynamique. Enfin, nous nous penchons plus en détails sur l’impact qu’eut sur son travail l’article de Turing de 1952 sur le modèle de réaction-diffusion de la morphogenèse. Nous voyons comment le « concept-frontière » de structure dissipative permit à Prigogine de tisser un réseau d’analogies autour du travail de Turing et ainsi contribuer à son regain de succès dans des contextes variés.

// Self-organization is a notion with many traditions, among others mobilized by many physicists since the seventies, at the boundaries of physics, chemistry and biology. Despite the many philosophical debates, as yet few historical works are devoted to it, as well as to many others interdisciplinary approaches that are growing during the second half of the 20th century. In this work, the genesis of a concept of self-organization is studied among the Belgian chemical physicist Ilya Prigogine, Nobel Prize in Chemistry 1977 and a controversial figure among physicists. First we retrace the scientific prehistory of this word and the embryological background from which Prigogine borrows it, before examining the context of the Brussels School of thermodynamics of irreversible processes, founded by his master Théophile De Donder, and the recognition acquired by Prigogine during the sixties among the community of chemical physics. Secondly we look at the development of his concept of self-organization from 1945 to 1975, the role played by entropy and its relation to biology, through a philosophical and scientific project that can be qualified as thermodynamical evolutionism. Finally, we look in more detail the impact the Turing paper of 1952 about the reaction-diffusion model of morphogenesis had on his work. We see how the « boundary-concept » of dissipative structure allowed Prigogine to build a network of analogies about the work of Turing and to contribute to its renewed success in various contexts.

We describe flux tubes and their interactions in a low energy sigma model induced by $SU({N_f}) \rightarrow SO({N_f})$ flavor symmetry breaking in $SO(N_c)$ QCD. Unlike standard QCD, this model allows gauge confinement to manifest itself in the low energy theory, which has unscreened spinor color sources and global $Z_2$ flux tubes. We construct the flux tubes and show how they mediate the confinement of spinor sources. We further examine the flux tubes' quantum stability, spectrum and interactions. We find that flux tubes are Alice strings, despite ambiguities in defining parallel transport. Furthermore, twisted loops of flux tube support skyrmion number, just as gauged Alice strings form loops that support monopole charge. This model, while phenomenologically nonviable, thus affords a perspective on both the dynamics of confinement and on subtleties which arise for global Alice strings.

The main subject of this thesis rests on the study ---at different levels of description--- of instabilities in systems which are driven, i.e., maintained far from equilibrium by an external forcing. We focus here on two main classes, namely, driven--diffusive fluids and driven granular gases. A particular driven-diffusive lattice model, prototype for nonequilibrium phase transitions, is investigated. A well-known disadvantage

The Bose-Einstein condensation (BEC) in a binary mixture of Bose gases is studied by means of the Cornwall-Jackiw-Tomboulis (CJT) effective action approach. The equations of state (EoS) and various scenarios of phase transitions of the system are considered in detail, in particular, the numerical computations are carried out for symmetry restoration (SR), symmetry nonrestoration (SNR) and inverse symmetry breaking (ISB) for getting an insight into their physical nature. It is shown that due to the cross interaction between distinct components of mixture there occur two interesting phenomena: the high temperature BEC and the inverse BEC, which could be tested in experiments.