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Classical Theory of the Weak Interaction and Foundations of Nuclear Beta Decay
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
Elementary particle theory predicts the existence of such bosons, which should be massless, as a consequence of a spontaneously broken global symmetry (see Section 4.3). One very attractive global symmetry is the chiral symmetry, which is a symmetry of the Lagrange function under the particle field transformation ψ → eiγ5ψ. This symmetry would assume the masslessness of fermions, which corresponds to the concept of massless quarks. (Quark masses, e.g. in comparison with the mass of the proton are indeed relatively small.) However, since the observed hadrons are not massless the chiral symmetry must be (spontaneously) broken. As a consequence of a spontaneous symmetry breaking there should then exist a massless ‘Goldstone boson’ (Goldstone (1961)).
Magnetic dipolar modes in magnon-polariton condensates
Published in Journal of Modern Optics, 2021
As it was noted above, observation of condensed states of dipolar magnetization is hardly possible, since spin superfluidity is destroyed on the scales of magnetic dipole–dipole interactions. It means that dipole-carrying excitations in a high-quality confined ferrite-disk structure cannot be identified as the quantum states of microscopic short-range excitations stabilized by the condensate phase. Nonetheless, following the studies with ultra-cold atomic gas structures [30,31], one can assume that microwave detection of dipole–dipole condensed structures will be realizable when MDM magnons are strongly trapped by rotational superflow in a ring geometry of a quasi-2D ferrite disk. In a pattern of the rotating magnetization, the spin angular momentum is converted into the orbital angular momentum of spin-vortex state via the spin–orbit interaction. The sum of the spin or orbital angular momenta is conserved. For energetically favourable angular velocity, the vortex is formed. The magnetic-dipolar condensate is shown to exhibit a novel ground state, which has a net orbital angular momentum with broken chiral symmetry. The effect of orbitally rotating MDM magnons in a quasi-2D ferrite disk was observed both numerically and experimentally. Theoretically, this can be explained based on an analysis of boundary value problems for MS resonances. In this case, non-trivial questions arise.
Emergence of a new symmetry class for Bogoliubov–de Gennes (BdG) Hamiltonians: expanding 10-fold symmetry classes
Published in Phase Transitions, 2020
Here we study BdG Hamiltonian in spinful background. It is well known to us that the symmetry operators for TR symmetry are different for the spinless and spinful background. We also try to find there is any emergence of extra symmetry class. We consider the Hamiltonians , , and as spinful systems with symmetry operators for TR, for PH and for chiral symmetries. One may also consider the BdG Hamiltonians in the form of the spinful fermionic system as where , and t is spin-independent hopping term. Now we consider and study its symmetry properties in spinful background. We check for invariance of the model Hamiltonians under the TR, PH and chiral symmetry operations.Here we observe that the Hamiltonian satisfies the condition for both PH and chiral symmetry but not TR symmetry.This is an interesting result since this set of symmetry does not belong to any symmetry class of Table 1. The Hamiltonian has gapless state for the condition at k=0 and also for the condition at . From the energy dispersion curve (Figure 1a) we can observe that the energy spectrum is symmetric about zero. This is clearly one of the implications of PH and chiral symmetries. In Table 1, one can observe the presence of chiral symmetry only in the presence or absence of both TR and PH symmetries. There is no symmetry class with either TR or PH along with chiral symmetry. But this symmetry class has PH symmetry along with chiral symmetry.
Twist-bend nematic phase in the presence of molecular chirality
Published in Liquid Crystals, 2018
where the number of the constitutive parameters has been reduced by taking suitable units and by assuming that deformations appear only in a quadratic part of the free energy. There are 8 phenomenological parameters left, namely, and , which are the reduced temperatures associated with and fields, respectively; is the relative elastic constant; is the strength of longitudinal contribution from the steric polarization; is the strength of flexopolarization; is the strength of coupling between and fields. Taking eliminates spontaneous polar order () in the absence of . For the sake of thermodynamic stability of it is mandatory that and . The term proportional to in violates parity and hence only appears in the elastic free energies of cholesteric liquid crystals. Its presence in the expansion results from intrinsic molecular chirality (which is measured by ) and is responsible for the formation of phases with broken chiral symmetry. Furthermore, the theory given by is fundamental to our present understanding not only of the cholesteric phase but also of the Blue Phases [31,32]. We would like to mention, however, that the role of the chirality parameter is not quite clear (see discussion afterEquation (19)). Note that in and . Finally, under the assumption that is uniaxial