Identical Particles and Quantum Symmetries

We propose a solution to the problem of compatibility of Bose-Fermi statistics with symmetry transformations implemented by compact quantum groups of Drinfel'd type. We use unitary transformations to conjugate multi-particle symmetry postulates, so as to obtain a twisted realization of the symmetric groups S_n.Comment: latex, 30 pages; final version (Nucl. Phys. B, in print

PT-symmetry and its spontaneous breakdown explained by anti-linearity

The impact of an anti-unitary symmetry on the spectrum of non-Hermitian operators is studied. Wigner's normal form of an anti-unitary operator accounts for the spectral properties of non-Hermitian, PE-symmetric Harniltonians. The occurrence of either single real or complex conjugate pairs of eigenvalues follows from this theory. The corresponding energy eigenstates span either one- or two-dimensional irreducible representations of the symmetry PE. In this framework, the concept of a spontaneously broken PE-symmetry is not needed

Oriented Associativity Equations and Symmetry Consistent Conjugate Curvilinear Coordinate Nets

This paper is devoted to description of the relationship among oriented associativity equations, symmetry consistent conjugate curvilinear coordinate nets, and the widest associated class of semi- Hamiltonian hydrodynamic-type systems.Comment: 19 page

Carbon K-shell Photo Ionization of CO: Molecular frame angular Distributions of normal and conjugate shakeup Satellites

We have measured the molecular frame angular distributions of photoelectrons emitted from the Carbon K shell of fixed-in-space CO molecules for the case of simultaneous excitation of the remaining molecular ion. Normal and conjugate shake up states are observed. Photo electrons belonging to normal \Sigma -satellite lines show an angular distribution resembling that observed for the main photoline at the same electron energy. Surprisingly a similar shape is found for conjugate shake up states with \Pi -symmetry. In our data we identify shake rather than electron scattering (PEVE) as the mechanism producing the conjugate lines. The angular distributions clearly show the presence of a \Sigma -shape resonance for all of the satellite lines.Comment: 8 pages, 2 figure

Conjugate coupling induced symmetry breaking and quenched oscillations

Spontaneous symmetry breaking (SSB) is essential and plays a vital role many natural phenomena, including the formation of Turing pattern in organisms and complex patterns in brain dynamics. In this work, we investigate whether a set of coupled Stuart-Landau oscillators can exhibit spontaneous symmetry breaking when the oscillators are interacting through dissimilar variables or conjugate coupling. We find the emergence of SSB state with coexisting distinct dynamical states in the parametric space and show how the system transits from symmetry breaking state to out-of-phase synchronized (OPS) state while admitting multistabilities among the dynamical states. Further, we also investigate the effect of feedback factor on SSB as well as oscillation quenching states and we point out that the decreasing feedback factor completely suppresses SSB and oscillation death states. Interestingly, we also find the feedback factor completely diminishes only symmetry breaking oscillation and oscillation death (OD) states but it does not affect the nontrivial amplitude death (NAD) state. Finally, we have deduced the analytical stability conditions for in-phase and out-of-phase oscillations, as well as amplitude and oscillation death states.Comment: Accepted for publication in Europhysics Letter