scholarly journals Extended Divisibility Relations for Constraint Polynomials of the Asymmetric Quantum Rabi Model

2020 ◽  
pp. 149-168
Author(s):  
Cid Reyes-Bustos
Keyword(s):  
Symmetry Breaking ◽  
Quantum Optics ◽  
Bargmann Space ◽  
Asymmetric Quantum ◽  
Rabi Model ◽  
Symmetry Breaking Term ◽  
Divisibility Properties ◽  
Breaking Term ◽  
Insight Into

Abstract The quantum Rabi model (QRM) is widely regarded as one of the fundamental models of quantum optics. One of its generalizations is the asymmetric quantum Rabi model (AQRM), obtained by introducing a symmetry-breaking term depending on a parameter $$\varepsilon \in \mathbb {R}$$ to the Hamiltonian of the QRM. The AQRM was shown to possess degeneracies in the spectrum for values $$\epsilon \in 1/2\mathbb {Z}$$ via the study of the divisibility of the so-called constraint polynomials. In this article, we aim to provide further insight into the structure of Juddian solutions of the AQRM by extending the divisibility properties and the relations between the constraint polynomials with the solution of the AQRM in the Bargmann space. In particular we discuss a conjecture proposed by Masato Wakayama.

scholarly journals Novel thick brane solutions with U(1) symmetry breaking

2021 ◽  
Vol 81 (3) ◽  
Author(s):  
Marzieh Peyravi ◽  
Nematollah Riazi ◽  
Francisco S. N. Lobo
Keyword(s):  
Symmetry Breaking ◽  
Scalar Fields ◽  
Einstein Tensor ◽  
Vacuum Structure ◽  
Different Types ◽  
Dimensional Gravity ◽  
Breaking Parameter ◽  
Symmetry Breaking Term ◽  
The Stability ◽  
Breaking Term

AbstractIn this work, using two scalar fields ($$\phi $$ ϕ , $$\psi $$ ψ ) coupled to 4 + 1 dimensional gravity, we construct novel topological brane solutions through an explicit U(1) symmetry breaking term. The potential of this model is constructed so that two distinct degenerate vacua in the $$\phi $$ ϕ field exist, in analogy to the $$\phi ^{4}$$ ϕ 4 potential. Therefore, brane solutions appear due to the vacuum structure of the $$\phi $$ ϕ field. However, the topology and vacuum structure in the $$\psi $$ ψ direction depends on the symmetry breaking parameter $$\beta ^{2}$$ β 2 , which leads to different types of branes. As a result, one can interpret the present model as a combination of a $$\phi ^{4}$$ ϕ 4 brane with an auxiliary field, which leads to deviations from the $$\phi ^{4}$$ ϕ 4 system with the brane achieving a richer internal structure. Furthermore, we analyse in detail the behaviour of the superpotentials, the warp factors, the Ricci and Kretschmann scalars and the Einstein tensor components. In addition to this, we explore the stability of the brane in terms of the free parameters of the model. The analysis presented here complements previous work and is sufficiently novel to be interesting.

scholarly journals Inverse mass hierarchy of light scalar mesons driven by anomaly-induced flavor breaking

2020 ◽  
Vol 2020 (5) ◽  
Author(s):  
Yoshiki Kuroda ◽  
Masayasu Harada ◽  
Shinya Matsuzaki ◽  
Daisuke Jido
Keyword(s):  
Symmetry Breaking ◽  
Chiral Symmetry ◽  
Scalar Meson ◽  
Chiral Symmetry Breaking ◽  
Linear Sigma Model ◽  
Mass Hierarchy ◽  
Scalar Mesons ◽  
Light Scalar ◽  
Symmetry Breaking Term ◽  
Breaking Term

Abstract We propose a novel mechanism to reproduce the observed mass hierarchy for scalar mesons lighter than 1 GeV (called the inverse hierarchy), regarding them as mesons made of a quark and an anti-quark ($q\bar{q}$ mesons). The source is provided by the SU(3) flavor-symmetry breaking induced by the U(1) axial anomaly. In particular, the anomaly term including the explicit chiral symmetry breaking plays a significant role in the light scalar meson spectrum. To be concrete, we construct a linear sigma model for scalar mesons of $q\bar{q}$ type together with their pseudoscalar chiral partners, including an anomaly-induced explicit chiral symmetry-breaking term. We find that, due to the proposed mechanism, the inverse hierarchy, i.e., $m\left[ a_0 (980) \right] \simeq m\left[ f_0 (980) \right] > m \left[ K_0^\ast (700) \right] > m \left[ f_0(500) \right]$, is indeed realized. Consequently, the quark content of $f_0 (500)$ is dominated by the isoscalar $\bar uu+ \bar dd$ component, and $f_0 (980)$ by the strange quark bilinear one, $s\bar{s}$.

PATTERN FORMATION AND DYNAMICS IN AN ANNULAR CO2 LASER

2001 ◽  
Vol 11 (11) ◽  
pp. 2759-2770
Author(s):  
M. L. RAMÓN ◽  
S. BOCCALETTI ◽  
R. MEUCCI ◽  
E. ALLARIA
Keyword(s):  
Pattern Formation ◽  
Symmetry Breaking ◽  
Co2 Laser ◽  
Temporal Evolution ◽  
Spatial Structures ◽  
Bloch Equations ◽  
Model Based ◽  
Symmetry Breaking Term ◽  
Breaking Term ◽  
Maxwell Bloch Equations

The formation and competition of patterns in an annular CO 2 laser has been experimentally and numerically analyzed. The temporal evolution of the different spatial structures increases its richness and complexity during the coexistence of different patterns. A model based on the Maxwell–Bloch equations, including a symmetry breaking term, provides a numerical interpretation of the main experimental features.

scholarly journals Corrections to Wigner–Eckart Relations by Spontaneous Symmetry Breaking

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1120
Author(s):  
Carlo Heissenberg ◽  
Franco Strocchi
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Irreducible Representations ◽  
Matrix Elements ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Goldstone Bosons ◽  
The Matrix ◽  
Symmetry Breaking Term ◽  
Breaking Term

The matrix elements of operators transforming as irreducible representations of an unbroken symmetry group G are governed by the well-known Wigner–Eckart relations. In the case of infinite-dimensional systems, with G spontaneously broken, we prove that the corrections to such relations are provided by symmetry breaking Ward identities, and simply reduce to a tadpole term involving Goldstone bosons. The analysis extends to the case in which an explicit symmetry breaking term is present in the Hamiltonian, with the tadpole term now involving pseudo Goldstone bosons. An explicit example is discussed, illustrating the two cases.

scholarly journals Dark matter from a complex scalar singlet: the role of dark CP and other discrete symmetries

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Leonardo Coito ◽  
Carlos Faubel ◽  
Juan Herrero-García ◽  
Arcadi Santamaria
Keyword(s):  
Dark Matter ◽  
Symmetry Breaking ◽  
Parameter Space ◽  
Dark Matter Candidate ◽  
Theory Approach ◽  
Complex Scalar ◽  
Symmetry Breaking Term ◽  
Pseudo Scalar ◽  
Breaking Term ◽  
Scalar Singlet

Abstract We study the case of a pseudo-scalar dark matter candidate which emerges from a complex scalar singlet, charged under a global U(1) symmetry, which is broken both explicitly and spontaneously. The pseudo-scalar is naturally stabilized by the presence of a remnant discrete symmetry: dark CP. We study and compare the phenomenology of several simplified models with only one explicit symmetry breaking term. We find that several regions of the parameter space are able to reproduce the observed dark matter abundance while respecting direct detection and invisible Higgs decay limits: in the resonances of the two scalars, featuring the known as forbidden or secluded dark matter, and through non-resonant Higgs-mediated annihilations. In some cases, combining different measurements would allow one to distinguish the breaking pattern of the symmetry. Moreover, this setup admits a light DM candidate at the sub-GeV scale. We also discuss the situation where more than one symmetry breaking term is present. In that case, the dark CP symmetry may be spontaneously broken, thus spoiling the stability of the dark matter candidate. Requiring that this does not happen imposes a constraint on the allowed parameter space. Finally, we consider an effective field theory approach valid in the pseudo-Nambu-Goldstone boson limit and when the U(1) breaking scale is much larger than the electroweak scale.

scholarly journals DARK ENERGY IN AN AXION MODEL WITH EXPLICIT Z(N) SYMMETRY BREAKING

2005 ◽  
Vol 20 (23) ◽  
pp. 1763-1766 ◽  
Author(s):  
PANKAJ JAIN
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Symmetry Breaking ◽  
Cold Dark Matter ◽  
Symmetry Breaking Term ◽  
The Universe ◽  
Breaking Term

We point out that a well-known axion model with an explicit Z(N) symmetry breaking term predicts both dark energy and cold dark matter. We estimate the parameters of this model which fit the observed densities of the dark components of the universe. We find that the parameters do not conflict with any observations.

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