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Symmetry
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Broken Symmetry
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Broken Symmetry

A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: closed (30 April 2018) | Viewed by 14594

Special Issue Editor

Prof. Dr. Boris Malomed

E-Mail Website
Guest Editor
Department of Interdisciplinary Studies, the Iby and Aladar Fleischman Faculty of Engineering, Tel Aviv University, Ramat Aviv 69978, Israel
Interests: optical solitons and optical communications; dynamics of long josephson junctions nonlinear dynamical lattices; pattern formation in one- and two-dimensional homogeneous and inhomogeneous nonlinear dissipative media Perturbation theory and variational methods; Ginzburg-Landau equations
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Special Issue Information

Dear Colleagues,

Dynamics of collective excitations is the central topic in experimental and theoretical studies in a great variety of physical settings. Spatial symmetry of collective excitations is determined by the shape of the underlying potential, the presence of which is necessary to confine the setting to a finite size, thus making it amenable to experimental realization. In particular, a ubiquitous type of the confinement is provided by double-well potentials (DWPs), which feature symmetry between two wells separated by a barrier. A principle commonly known in quantum mechanics, which is equally valid in many other areas, such as guided light transmission in linear optical media, is that the ground state (GS) of the linear system exactly follows the symmetry of the underlying confining potential. Other representations of the same symmetry may be realized by the system's excited states. In particular, the GS wave function trapped in the one-dimensional DWP is symmetric (spatially even), while the first excited state is antisymmetric (odd). The situation is made completely different by the inclusion of self-focusing nonlinearity (in particular, it is the Kerr nonlinearity affecting the guided light propagation, and the collisional nonlinearity in trapped Bose-Einstein condensates (BECs)): if the nonlinearity strength exceeds a critical value, the former symmetric GS becomes unstable, being replaced by a couple of asymmetric GSs, which are mirror images to each other. The fact that this spontaneous-symmetry-breaking (SSB) transition creates two coexisting GSs also breaks another fundamental principle of the linear theory (quantum mechanics, in particular), viz., that the GS cannot be degenerate. The nonlinearity with the self-defocusing sign does not destabilize the symmetric GS, but breaks the antisymmetry of the first excited state. These effects are elementary examples of the huge field of the SBB phenomenology, which has been developing at an accelerating pace in the course of the last 30 years, the progress being especially spectacular in nonlinear optics and the studies of BEC. The objective of the present Special Issue is to publish a selection of original papers and reviews which adequately represent the ongoing progress in this vast research area.

Prof. Boris Malomed
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Nonlinearity
  • Self-trapping
  • Solitons
  • Ground state
  • Double-well potentials
  • Phase transitions
  • Parity
  • Josephson oscillations

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Published Papers (4 papers)

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Research

8 pages, 2172 KiB  
Article
Ultrathin Terahertz Dual-Band Perfect Metamaterial Absorber Using Asymmetric Double-Split Rings Resonator
by Taiguo Lu, Dawei Zhang, Peizhen Qiu, Jiqing Lian, Ming Jing, Binbin Yu and Jing Wen
Symmetry 2018, 10(7), 293; https://doi.org/10.3390/sym10070293 - 20 Jul 2018
Cited by 24 | Viewed by 4077
Abstract
In this article, an ultrathin terahertz dual band metamaterial absorber made up of patterned asymmetrical double-split rings and a continuous metal layer separated by a thin FR-4 layer is designed. Simulation results show that two almost identical strong absorption peaks appear in the [...] Read more.
In this article, an ultrathin terahertz dual band metamaterial absorber made up of patterned asymmetrical double-split rings and a continuous metal layer separated by a thin FR-4 layer is designed. Simulation results show that two almost identical strong absorption peaks appear in the terahertz band. When the incident electric field is perpendicular to the ring gaps located at 11 μm asymmetrically, the absorptivity of 98.6% at 4.48 THz and 98.5% at 4.76 THz can be obtained. The absorption frequency and the absorptivity of the absorber can be modulated by the asymmetric distribution of the gaps. The perfect metamaterial absorber is expected to provide important reference for the design of terahertz modulator, filters, absorbers, and polarizers. Full article
(This article belongs to the Special Issue Broken Symmetry)
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13 pages, 3458 KiB  
Article
Vortex Creation without Stirring in Coupled Ring Resonators with Gain and Loss
by Aleksandr Ramaniuk, Nguyen Viet Hung, Michael Giersig, Krzysztof Kempa, Vladimir V. Konotop and Marek Trippenbach
Symmetry 2018, 10(6), 195; https://doi.org/10.3390/sym10060195 - 1 Jun 2018
Cited by 4 | Viewed by 3258
Abstract
We present the study of the dynamics of a two-ring waveguide structure with space-dependent coupling, linear gain and nonlinear absorption; the system that can be implemented in polariton condensates, optical waveguides and nanocavities. We show that by turning on and off local coupling [...] Read more.
We present the study of the dynamics of a two-ring waveguide structure with space-dependent coupling, linear gain and nonlinear absorption; the system that can be implemented in polariton condensates, optical waveguides and nanocavities. We show that by turning on and off local coupling between rings, one can selectively generate a permanent vortex in one of the rings. We find that due to the modulation instability, it is also possible to observe several complex nonlinear phenomena, including spontaneous symmetry breaking, stable inhomogeneous states with an interesting structure of currents flowing between rings, the generation of stable symmetric and asymmetric circular flows with various vorticities, etc. The latter can be created in pairs (for relatively narrow coupling length) or as a single vortex in one of the channels, which later alternates between channels. Full article
(This article belongs to the Special Issue Broken Symmetry)
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14 pages, 1584 KiB  
Article
Symmetry Breakings in Dual-Core Systems with Double-Spot Localization of Nonlinearity
by Krzysztof B. Zegadlo, Nguyen Viet Hung, Aleksandr Ramaniuk, Marek Trippenbach and Boris A. Malomed
Symmetry 2018, 10(5), 156; https://doi.org/10.3390/sym10050156 - 13 May 2018
Viewed by 3339
Abstract
We introduce a dual-core system with double symmetry, one between the cores, and one along each core, imposed by the spatial modulation of local nonlinearity in the form of two tightly localized spots, which may be approximated by a pair of ideal delta-functions. [...] Read more.
We introduce a dual-core system with double symmetry, one between the cores, and one along each core, imposed by the spatial modulation of local nonlinearity in the form of two tightly localized spots, which may be approximated by a pair of ideal delta-functions. The analysis aims to investigate effects of spontaneous symmetry breaking in such systems. Stationary one-dimensional modes are constructed in an implicit analytical form. These solutions include symmetric ones, as well as modes with spontaneously broken inter-core and along-the-cores symmetries. Solutions featuring the simultaneous (double) breaking of both symmetries are produced too. In the model with the ideal delta-functions, all species of the asymmetric modes are found to be unstable. However, numerical consideration of a two-dimensional extension of the system, which includes symmetric cores with a nonzero transverse thickness, and the nonlinearity-localization spots of a small finite size, produces stable asymmetric modes of all the types, realizing the separate breaking of each symmetry, and states featuring simultaneous (double) breaking of both symmetries. Full article
(This article belongs to the Special Issue Broken Symmetry)
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15 pages, 277 KiB  
Article
Spontaneous Symmetry Breaking and Higgs Mode: Comparing Gross-Pitaevskii and Nonlinear Klein-Gordon Equations
by Marco Faccioli and Luca Salasnich
Symmetry 2018, 10(4), 80; https://doi.org/10.3390/sym10040080 - 23 Mar 2018
Cited by 8 | Viewed by 3178
Abstract
We discuss the mechanism of spontaneous symmetry breaking and the elementary excitations for a weakly-interacting Bose gas at a finite temperature. We consider both the non-relativistic case, described by the Gross-Pitaevskii equation, and the relativistic one, described by the cubic nonlinear Klein-Gordon equation. [...] Read more.
We discuss the mechanism of spontaneous symmetry breaking and the elementary excitations for a weakly-interacting Bose gas at a finite temperature. We consider both the non-relativistic case, described by the Gross-Pitaevskii equation, and the relativistic one, described by the cubic nonlinear Klein-Gordon equation. We analyze similarities and differences in the two equations and, in particular, in the phase and amplitude modes (i.e., Goldstone and Higgs modes) of the bosonic matter field. We show that the coupling between phase and amplitude modes gives rise to a single gapless Bogoliubov spectrum in the non-relativistic case. Instead, in the relativistic case the spectrum has two branches: one is gapless and the other is gapped. In the non-relativistic limit we find that the relativistic spectrum reduces to the Bogoliubov one. Finally, as an application of the above analysis, we consider the Bose-Hubbard model close to the superfluid-Mott quantum phase transition and we investigate the elementary excitations of its effective action, which contains both non-relativistic and relativistic terms. Full article
(This article belongs to the Special Issue Broken Symmetry)
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