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The Weak Interaction in the Framework of Grand Unification Theories
Published in K Grotz, H V Klapdor, S S Wilson, The Weak Interaction in Nuclear, Particle and Astrophysics, 2020
K Grotz, H V Klapdor, S S Wilson
Normally, spontaneous symmetry breaking is considered at this point. Above a certain, very high energy density, this symmetry breaking is suspended, and the symmetry, which we shall call the GUT symmetry is again established. According to the cosmological standard model, this was the case in the first 10−35 seconds after the birth of the universe (see Chapter 9). Above the critical energy density at which the symmetry breaking occurs, we actually expect one uniform interaction mediated by n massless gauge bosons. The difference between the strong, the weak and the electromagnetic interactions should vanish at such high energies. At lower energies, below the symmetry breaking, the n massless gauge bosons are transformed into the already familiar W bosons, Z bosons, photons and gluons. In addition, further, as yet unknown, gauge bosons are to be expected.
Rotational Motion
Published in P. F. Bortignon, A. Bracco, R. A. Broglia, Giant Resonances, 2019
P. F. Bortignon, A. Bracco, R. A. Broglia
It is well established that closed shell nuclei are spherical in their ground state. Adding nucleons polarizes the closed shells and eventually the polarization effects may become so large that the mean field becomes deformed. In other words, the mean field solution of the nuclear many-body system displaying the lowest energies may not be spherically symmetric. As a rule, these solutions display quadrupole deformation. This is the phenomenon of spontaneous symmetry breaking of rotational invariance that makes it possible to specify an orientation of the system in ordinary space. Restoration of symmetry arises from the rotation of the system as a whole, as evidenced by the presence of rotational bands. In fact, rotations represent the collective mode associated with such a spontaneous symmetry breaking phenomenon.
Dynamical Systems in Space
Published in LM Pismen, Working with Dynamical Systems, 2020
Passing to two-variable RDS, we first encounter the phenomenon of spontaneous symmetry breaking. We concentrate on a simple model system with widely separated time and length scales, which is capable to generate a variety of stationary and propagating structures. While still restricting to 1D, we will be also capable to analyze their instabilities.
Observation of string defects in liquid crystal
Published in Liquid Crystals, 2021
Kirandeep Kaur Matharu, Samriti Khosla, Sapna Sethi, Nitin Sood
Phase transitions associated with change of symmetry are described through Spontaneous symmetry breaking [14]. In this case the higher symmetry phase (less ordered) is associated with a unique true vacuum whereas in the ordered phase, the vacuum has degenerated structure and the system can choose any one of the degenerate vacua randomly after the phase transition. Consequently, a set of minimum energy configurations forms which represent vacuum manifold (M). For topological excitations manifold defines the order parameter [11]. The topology of ‘M’ represents the kind of defect to be formed while approaching the more ordered state [6,7]. These defects are represented by different homotopy groups ᴨn(M). The homotopy groups characterise mapping from the n-sphere Sn enclosing the topological excitation in real space into the vacuum manifold M [11]. In general, πn (Mo) gives the number of topologically distinct noncontractible n-spheres and π1(Mo) gives the number of topologically distinct noncontractible loops. Strings occur in theories with nontrivial π1(Mo) [2,6,7].
Symmetry and asymmetry induced dynamics in a memristive twin-T circuit
Published in International Journal of Electronics, 2022
Léandre Kamdjeu Kengne, Justin Roger Mboupda Pone, Hilaire Bertrand Fotsin
First of all, a clear distinction should be made between explicit and spontaneous symmetry breaking. Explicit symmetry breaking arises when the law governing its behaviour is changed and is no longer invariant; and spontaneous symmetry breaking occurs when the underlying laws are invariant under the symmetry but the particular realisation of the observed system is not. This latter case corresponds, for example, of solutions that appear in pairs of asymmetric attractors in various symmetric models (Kingni et al., 2019; Leutcho et al., 2018; Njitacke & Kengne, 2018; Pone et al., 2019; Tabekoueng Njitacke et al.).
Ferroelectric liquid crystal nanocomposites: recent development and future perspective
Published in Liquid Crystals Reviews, 2018
Satya Prakash Yadav, Kanchan Yadav, Jayeeta Lahiri, Avanish Singh Parmar
The most basic characteristics of LCs, at least from a macroscopic point of view, are the presence of long-range orientational order while the positional order is limited or absent altogether. Often these correlations are described in terms of order parameters (OPs). The transition from one phase to another is a symmetry breaking event. The extent to which the orientational and positional correlations among molecules in the less symmetric (more ordered) phase differ from that in the more symmetric (less ordered) phase is expressed in terms of order parameters [19,32,33].