Spatial symmetry of head-related transfer function

Methods for analyzing the spatial symmetry of head-related transfer function (HRTF) are proposed. The influences of anatomical structures on the symmetry of HRTF are investigated using HRTFs measured on KEMAR mannequin and human subjects. Results show that for KEMAR mannequin, pinnae destroy the front-back symmetry of HRTF above 5 to 6 kHz, while for human subjects the frequency reduces to 2.5 kHz because of the locations of ears. Furthermore, at low and median frequencies, HRTF is approximately left-right symmetrical. While as frequencies increase, the asymmetry caused by the fine anatomical leftright differences appears. The starting frequency and the extent of the left-right asymmetry in HRTF depend on individuals. The analyses demonstrate the spatial symmetrical characteristics of HRTF and the frequency ranges in which the current binaural models are valid.     

Optical Möbius symmetry in metamaterials

We experimentally observed a new topological symmetry in optical composites, namely, metamaterials. While it is not found yet in nature materials, the electromagnetic M?bius symmetry discovered in metamaterials is equivalent to the structural symmetry of a M?bius strip, with the number of twists controlled by the sign change of the electromagnetic coupling between the meta-atoms. We further demonstrate that metamaterials with different coupling signs exhibit resonance frequencies that depend only on the number but not the locations of the "twists," thus confirming its topological nature. The new topological symmetry found in metamaterials may enable unique functionalities in optical materials.     

Double-heavy tetraquark states with heavy diquark-antiquark symmetry

We calculate the masses of the QQqq(Q=c,b:q=u,d,s)tetraquark states with the aid of heavy diquark-antiquark symmetry(HDAS)and the chromomagnetic interaction(CMI)model.The masses of the highestspin(J=2)tetraquarks that have only the(QQ)(3):(qq)₃.color structure are related with those of conventional hadrons using HDAS.Thereafter,the masses of their partner states are determined with the mass splittings in the CMI model.Our numerical results reveal that(i)the lightest ccnn(n=u,d)is an I(J^P)=0(1⁺)state around 3929 MeV(53 MeV above the DD^* threshold),and none of the double-charm tetraquarks are stable;(ii)the stable double-bottom tetraquarks are the lowest 0(1⁺)bbin around 10488 MeV(≈116 MeV below the BB^*threshold)and the lowest 1/2(1⁺)bbns around 10671 MeV(≈20 MeV below the BB_s^*/B_sB^*threshold);and(iii)the two lowest bcnn tetraquarks,namely the lowest 0(0⁺)around 7167 MeV and the lowest 0(1)around 7223 MeV,are in the nearthreshold states.Moreover,we discuss the constraints on the masses of double-heavy hadrons.Specifically,for the lowest nonstrange tetraquarks,we obtain T_cc<3965 MeV,T_bb<10627 MeV,and T_bc<7199 MeV.     

Newton–Hooke-type symmetry of anisotropic oscillators

Rotation-less Newton–Hooke-type symmetry, found recently in the Hill problem, and instrumental for explaining the center-of-mass decomposition, is generalized to an arbitrary anisotropic oscillator in the plane. Conversely, the latter system is shown, by the orbit method, to be the most general one with such a symmetry. Full Newton–Hooke symmetry is recovered in the isotropic case. Star escape from a galaxy is studied as an application.     

Tri-bimaximal mixing from twisted Friedberg–Lee symmetry

We investigate the Friedberg–Lee (FL) symmetry and its promotion to include the μ–τ symmetry, and call this the twisted FL symmetry. Based on the twisted FL symmetry, two possible schemes are presented toward the realistic neutrino mass spectrum and the tri-bimaximal mixing. In the first scheme, we suggest the semi-uniform translation of the FL symmetry. The second one is based on the S ₃ permutation family symmetry. The breaking terms, which are twisted FL symmetric, are introduced. Some viable models in each scheme are also presented.     

Axial crystals – macroscopic symmetry and tensor properties

ABSTRACT

Axial crystals have axial symmetry which keeps invariant straight line with a fixed point. Axial symmetry groups include 27 non-cubic crystallographic point groups and 5 limit groups describing symmetry of textures and liquid crystals. We show that, except for four cases, each axial symmetry belongs to one of five axial types: polar, chiral, pseudopolar (three basic axial types), directional (possessing none of characteristic properties of basic types) or rotational (exhibiting characteristic properties of all basic types). Each basic type can appear in two structurally different variants with the same symmetry. These variants can coexist and form a mesoscopic structure (antiparallel ferroelectric or chiral domain structure, mixture of enantiomers). We examine macroscopic properties of axial types and variants, and experimental accessivity of their characteristic features.     

Can symmetry non-restoration solve the monopole problem?

We reexamine a recently proposed non-inflationary solution to the monopole problem, based on the possibility that spontaneously broken Grand-Unified symmetries do not get restored at high temperature. We go beyond leading order by studying the self-consistent one-loop equations of the model. We find large next-to-leading corrections that reverse the lowest order results and cause symmetry restoration at high temperature.     

BRST symmetry for Regge–Teitelboim-based minisuperspace models

The Einstein–Hilbert action in the context of higher derivative theories is considered for finding their BRST symmetries. Being a constraint system, the model is transformed in the minisuperspace language with the FRLW background and the gauge symmetries are explored. Exploiting the first order formalism developed by Banerjee et al. the diffeomorphism symmetry is extracted. From the general form of the gauge transformations of the field, the analogous BRST transformations are calculated. The effective Lagrangian is constructed by considering two gauge-fixing conditions. Further, the BRST (conserved) charge is computed, which plays an important role in defining the physical states from the total Hilbert space of states. The finite field-dependent BRST formulation is also studied in this context where the Jacobian for the functional measure is illustrated specifically.     

Physical implications of Fisher-information’s scaling symmetry

We study the scaling properties of Fisher’s information measure (FIM) and show that from these one can straightforwardly deduce significant quantum-mechanical results. Specifically, we investigate the scaling properties of Fisher’s measure I and encounter that, from the concomitant operating rules, several interesting, albeit known, results can be derived. This entails that such results can be regarded as pre-configured by the conjunction of scaling and information theory. The central notion to be arrived at is that scaling entails that I must obey a certain partial differential equation (PDE). These PDE-solutions have properties that enable the application of a Legendre-transform (LT). The conjunction PDE+LT leads one to obtain several quantum results without recourse to the Schrödinger’s equation.     

Noether symmetry for Gauss–Bonnet dilatonic gravity

Noether symmetry for Gauss–Bonnet Dilatonic interaction exists for a constant dilatonic scalar potential and a linear functional dependence of the coupling parameter on the scalar field. The symmetry with the same form of the potential and coupling parameter exists all in the vacuum, radiation and matter dominated era. The late time acceleration is driven by the effective cosmological constant rather than the Gauss–Bonnet term, while the later compensates for the large value of the effective cosmological constant giving a plausible answer to the well-known coincidence problem.     

Kac-Moody symmetry of generalized non-linear Schrödinger equations

The classical non-linear Schrödinger equation associated with a symmetric Lie algebra =km is known to possess a class of conserved quantities which from a realization of the algebrak []. The construction is now extended to provide a realization of the Kac-Moody algebrak[, ^–1] (with central extension). One can then define auxiliary quantities to obtain the full algebra [, ^–1]. This leads to the formal linearization of the system.     

Magnetic charge as a “hidden” gauge symmetry

A theory containing both electric and magnetic charges is formulated using two vectors potentials,A andC . This has the aesthetic advantage of treating electric and magnetic charges both as gauge symmetries, but it has the experimental disadvantage of introducing a second massless gauge boson (the magnetic photon) which is not observed. This problem is dealt with by using the Higgs mechanism to give a mass to one of the gauge bosons while the other remains massless. This effectively hides the magnetic charge, and the symmetry associated with it, when one is at an energy scale far enough removed from the scale of the symmetry breaking.This paper is dedicated to my grandparents Herbert and Anneliese Schmidt.     

“Statistical” symmetry with applications to phase transitions

Hermann proposed that mesomorphic media should be classified by assigning certain statistical symmetry groups to each possible partially ordered array. Two translational groups introduced were called superordinate and subordinate. We find that the average density in such a partially ordered medium has the superordinate symmetry ₁, while the pair correlation function has the subordinate symmetry ₂. A complete listing is made of all compatible combinations of ₁ and ₂ in two and three dimensions. This leads to more possible symmetries than Hermann obtained, e.g., also to nonstoichiometric crystals. The order parameter space for the systems is found to be the quotient space ₁/₂. In most cases it is identical to the order parameter space of low-dimensionalXY spin systems. The Landau free energy is expanded as functional of the two-particle correlation functionK; the translation group is found to be ₁×₂. A Landau mean-field theory can then be carried out by expanding the system free energy into a series of invariants of the active irreducible representations ofK and mapping the free energy onto that for anXY planar spin system. We predict novel critical behavior for transitions between mesomorphic phases and go nogo selection rules for continuous transitions. We give the structure factors for X-ray scattering so changes in all such phase transitions are observable. The statistical symmetry groups, which describe point and translational symmetries of the mesophases, are classified. Proposals are made to include quasi-long-range or topological order in the classification scheme.This work supported in part by National Science Foundation (Division of International Programs), the PSC-BHE—Faculty Research Award CUNY and Deutsche Forschungsgemeinschaft.     

The symmetry energy γ parameter of relativistic mean-field models

The relativistic mean-field models tested in previous works against nuclear matter experimental values,critical parameters and macroscopic stellar properties are revisited and used in the evaluation of the symmetry energyγ parameter obtained in three different ways. We have checked that, independent of the choice made to calculate theγ values, a trend of linear correlation is observed between γ and the symmetry energy(S_0) and a more clear linear relationship is established between γ and the slope of the symmetry energy(L_0). These results directly contribute to the arising of other linear correlations between γ and the neutron star radii of R_(1.0) and R_(1.4), in agreement with recent findings. Finally, we have found that short-range correlations induce two specific parametrizations, namely,IU-FSU and DD-MEδ, simultaneously compatible with the neutron star mass constraint of 1.93≤M_(max)/M_☉≤2.05 and with the overlap band for the L_0 ×S_0 region, to present γ in the range of γ=0.25±0.05.     

Ultrarelativistic Bose–Einstein gas on Lorentz symmetry violation

In this paper, we study the effects of Lorentz Symmetry Breaking on the thermodynamic properties of ideal gases. Inspired by the dispersion relation coming from the Carroll–Field–Jackiw model for Electrodynamics with Lorentz and CPT violation term, we compute the thermodynamics quantities for a Boltzmann, Fermi–Dirac and Bose–Einstein distributions. Two regimes are analyzed: the large and the small Lorentz violation. In the first case, we show that the topological mass induced by the Chern–Simons term behaves as a chemical potential. For Bose–Einstein gases, a condensation in both regimes can be found.