Spectral singularities in PT-symmetric periodic finite-gap systems

The origin of spectral singularities in finite-gap singly periodic PT-symmetric quantum systems is investigated. We show that they emerge from a limit of band-edge states in a doubly periodic finite gap system when the imaginary period tends to infinity. In this limit, the energy gaps are contracted and disappear, every pair of band states of the same periodicity at the edges of a gap coalesces and transforms into a singlet state in the continuum. As a result, these spectral singularities turn out to be analogous to those in the non-periodic systems, where they appear as zero-width resonances. Under the change of topology from a non-compact into a compact one, spectral singularities in the class of periodic systems we study are transformed into exceptional points. The specific degeneration related to the presence of finite number of spectral singularities and exceptional points is shown to be coherently reflected by a hidden, bosonized nonlinear supersymmetry.Comment: 16 pages, 3 figures; a difference between spectral singularities and exceptional points specified, the version to appear in PR

Twist Deformations of the Supersymmetric Quantum Mechanics

The N-extended Supersymmetric Quantum Mechanics is deformed via an abelian twist which preserves the super-Hopf algebra structure of its Universal Enveloping Superalgebra. Two constructions are possible. For even N one can identify the 1D N-extended superalgebra with the fermionic Heisenberg algebra. Alternatively, supersymmetry generators can be realized as operators belonging to the Universal Enveloping Superalgebra of one bosonic and several fermionic oscillators. The deformed system is described in terms of twisted operators satisfying twist-deformed (anti)commutators. The main differences between an abelian twist defined in terms of fermionic operators and an abelian twist defined in terms of bosonic operators are discussed.Comment: 18 pages; two references adde

No Ending Point in The Bragg-to-Vortex Glass Phase Transition Line at Low Temperatures

We have measured the magnetic hysteresis loops and the magnetic relaxation for $Bi_2Sr_2CaCu_2O_{8+\delta}$ (Bi-2212) single crystals which exhibit the second magnetization peak effect. Although no second peak effect is observed below 20 K in the measurement with fast field sweeping rate, it is found that the second peak effect will appear again after long time relaxation or in a measurement with very slow field sweeping rate at 16 K. It is anticipated that the peak effect will appear at very low temperatures (approaching zero K) when the relaxation time is long enough. We attribute this phenomenon to the profile of the interior magnetic field and conclude that the phase transition line of Bragg glass to vortex glass has no ending point at low temperatures.Comment: 4 pages, 5 figure

Nonlinear Supersymmetry as a Hidden Symmetry

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Aspects of Higher Order Gravity and Holography

Some thermodynamical properties of Lovelock gravity are discussed in several space-time dimensions, the holographic principle being one of the ingredients of the discussion. As it turns out, the area law and the brickwall method, though correct for the Einstein-Hilbert theory, may fail to work in general.Comment: 15 page