Time-Reversal Symmetry in Non-Hermitian Systems

For ordinary hermitian Hamiltonians, the states show the Kramers degeneracy when the system has a half-odd-integer spin and the time reversal operator obeys \Theta^2=-1, but no such a degeneracy exists when \Theta^2=+1. Here we point out that for non-hermitian systems, there exists a degeneracy similar to Kramers even when \Theta^2=+1. It is found that the new degeneracy follows from the mathematical structure of split-quaternion, instead of quaternion from which the Kramers degeneracy follows in the usual hermitian cases. Furthermore, we also show that particle/hole symmetry gives rise to a pair of states with opposite energies on the basis of the split quaternion in a class of non-hermitian Hamiltonians. As concrete examples, we examine in detail NxN Hamiltonians with N=2 and 4 which are non-hermitian generalizations of spin 1/2 Hamiltonian and quadrupole Hamiltonian of spin 3/2, respectively.Comment: 40 pages, 2 figures; typos fixed, references adde

Subwavelength fractional Talbot effect in layered heterostructures of composite metamaterials

We demonstrate that under certain conditions, fractional Talbot revivals can occur in heterostructures of composite metamaterials, such as multilayer positive and negative index media, metallodielectric stacks, and one-dimensional dielectric photonic crystals. Most importantly, without using the paraxial approximation we obtain Talbot images for the feature sizes of transverse patterns smaller than the illumination wavelength. A general expression for the Talbot distance in such structures is derived, and the conditions favorable for observing Talbot effects in layered heterostructures is discussed.Comment: To be published in Phys. Rev.

A polyphonic acoustic vortex and its complementary chords

Using an annular phased array of eight loudspeakers, we generate sound beams that simultaneously contain phase singularities at a number of different frequencies. These frequencies correspond to different musical notes and the singularities can be set to overlap along the beam axis, creating a polyphonic acoustic vortex. Perturbing the drive amplitudes of the speakers means that the singularities no longer overlap, each note being nulled at a slightly different lateral position, where the volume of the other notes is now nonzero. The remaining notes form a tri-note chord. We contrast this acoustic phenomenon to the optical case where the perturbation of a white light vortex leads to a spectral spatial distribution

Quantum hamiltonians and prime numbers

A short review of Schroedinger hamiltonians for which the spectral problem has been related in the literature to the distribution of the prime numbers is presented here. We notice a possible connection between prime numbers and centrifugal inversions in black holes and suggest that this remarkable link could be directly studied within trapped Bose-Einstein condensates. In addition, when referring to the factorizing operators of Pitkanen and Castro and collaborators, we perform a mathematical extension allowing a more standard supersymmetric approachComment: 10 pages, 2 figures, accepted as a Brief Review at MPL

Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-Liquid Property

The intrinsic anomalous Hall effect in metallic ferromagnets is shown to be controlled by Berry phases accumulated by adiabatic motion of quasiparticles on the Fermi surface, and is purely a Fermi-liquid property, not a ``bulk'' Fermi sea property like Landau diamagnetism, as has been previously supposed. Berry phases are a new topological ingredient that must be added to Landau Fermi-liquid theory in the presence of broken inversion or time-reversal symmetry.Comment: 4 pages, 0 figures; to appear in Physical Review Letters; cleaner form of main formula+note added confirming continued validity of result in interacting Fermi liquids: + improved summary paragraph stating result; final published version (minor changes

Statistical Properties of Many Particle Eigenfunctions

Wavefunction correlations and density matrices for few or many particles are derived from the properties of semiclassical energy Green functions. Universal features of fixed energy (microcanonical) random wavefunction correlation functions appear which reflect the emergence of the canonical ensemble as the number of particles approaches infinity. This arises through a little known asymptotic limit of Bessel functions. Constraints due to symmetries, boundaries, and collisions between particles can be included.Comment: 13 pages, 4 figure

Appearance of Gauge Fields and Forces beyond the adiabatic approximation

We investigate the origin of quantum geometric phases, gauge fields and forces beyond the adiabatic regime. In particular, we extend the notions of geometric magnetic and electric forces discovered in studies of the Born-Oppenheimer approximation to arbitrary quantum systems described by matrix valued quantum Hamiltonians. The results are illustrated by several physical relevant examples

The Effects of Childhood Social Support and Family Resiliency on Mental Health in Adulthood

The effect of social support on the overall health and quality of life in adulthood has been well documented particularly in chronic disease populations. Very few studies examined the relationships between childhood social support, family resiliency and mental health in adulthood in the community and among disadvantaged minority populations. We examined the role of social support and family resilience during childhood on subsequent mental health-related quality of life (HRQoL) in adulthood among racial/ethnic minorities. A needs assessment survey which was designed to explore health determinants and quality of life indicators using a community-based participatory research (CBPR) approach in a low-income community in Tampa was analyzed. Participants were predominantly low-income non-Hispanic black and Hispanic population (n=187). The outcome mental HRQoL was measured using the validated Centers for Disease Control and Prevention’s (CDC) “Healthy Days Measure” instrument. We utilized sequential multivariable logistic regression models to examine the independent effects of childhood social support and family resiliency on mental HRQoL in adulthood. Approximately 12.3% of study participants reported poor mental HRQoL (i.e. ≥14 unhealthy days due to mental health). Childhood social support and family resiliency were significant predictors of mental HRQoL in adulthood, after controlling for sociodemographic characteristics. Sleep and composite health issues in adulthood were also associated with mental HRQoL. Our analyses highlight an opportunity to promote mental health through support of interventions that improve positive family relationships and reduce the burden of chronic health issues among non-Hispanic black and Hispanic children

Decoherence-free dynamical and geometrical entangling phase gates

It is shown that entangling two-qubit phase gates for quantum computation with atoms inside a resonant optical cavity can be generated via common laser addressing, essentially, within one step. The obtained dynamical or geometrical phases are produced by an evolution that is robust against dissipation in form of spontaneous emission from the atoms and the cavity and demonstrates resilience against fluctuations of control parameters. This is achieved by using the setup introduced by Pachos and Walther [Phys. Rev. Lett. 89, 187903 (2002)] and employing entangling Raman- or STIRAP-like transitions that restrict the time evolution of the system onto stable ground states.Comment: 10 pages, 9 figures, REVTEX, Eq. (20) correcte

Strong Evidence of Normal Heat Conduction in a one-Dimensional Quantum System

We investigate how the normal energy transport is realized in one-dimensional quantum systems using a quantum spin system. The direct investigation of local energy distribution under thermal gradient is made using the quantum master equation, and the mixing properties and the convergence of the Green-Kubo formula are investigated when the number of spin increases. We find that the autocorrelation function in the Green-Kubo formula decays as $\sim t^{-1.5}$ to a finite value which vanishes rapidly with the increase of the system size. As a result, the Green-Kubo formula converges to a finite value in the thermodynamic limit. These facts strongly support the realization of Fourier heat law in a quantum system.Comment: 7 pages 6 figure