Perturbative Analysis of Spectral Singularities and Their Optical Realizations

We develop a perturbative method of computing spectral singularities of a Schreodinger operator defined by a general complex potential that vanishes outside a closed interval. These can be realized as zero-width resonances in optical gain media and correspond to a lasing effect that occurs at the threshold gain. Their time-reversed copies yield coherent perfect absorption of light that is also known as an antilaser. We use our general results to establish the exactness of the n-th order perturbation theory for an arbitrary complex potential consisting of n delta-functions, obtain an exact expression for the transfer matrix of these potentials, and examine spectral singularities of complex barrier potentials of arbitrary shape. In the context of optical spectral singularities, these correspond to inhomogeneous gain media.Comment: 13 pages, 2 figures, one table, a reference added, typos correcte

A Comparison of the LVDP and {\Lambda}CDM Cosmological Models

We compare the cosmological kinematics obtained via our law of linearly varying deceleration parameter (LVDP) with the kinematics obtained in the {\Lambda}CDM model. We show that the LVDP model is almost indistinguishable from the {\Lambda}CDM model up to the near future of our universe as far as the current observations are concerned, though their predictions differ tremendously into the far future.Comment: 6 pages, 5 figures, 1 table, matches the version to be published in International Journal of Theoretical Physic

Exact Semiclassical Evolutions in Relativistic and Nonrelativistic Scalar Quantum Mechanics and Quantum Cosmology

The necessary and sufficient conditions for the exactness of the semiclassical approximation for the solution of the Schr\"odinger and Klein-Gordon equations are obtained. It is shown that the existence of an exact semiclassical solution of the Schr\"odinger equation determines both the semiclassical wave function and the interaction potential uniquely up to the choice of the boundary conditions. This result also holds for the Klein-Gordon equation. Its implications for the solution of the Wheeler-DeWitt equation for the FRW scalar field minisuperspace models are discussed. In particular, exact semiclassical solutions of the Wheeler-DeWitt equation for the case of massless scalar field and exponential matter potentials are constructed. The existence of exact semiclassical solutions for polynomial matter potentials of the form $\lambda\phi^{2p}$ is also analyzed. It is shown that for p=1, 2 and 3, right-going semiclassical solutions do not exist. A generalized semiclassical perturbation expansion is also developed which is quite different from the traditional $\hbar$ and $M_p^{-1}$-expansions.Comment: Few minor correction

Phase diagram of the hardcore Bose-Hubbard model on a checkerboard superlattice

We obtain the complete phase diagram of the hardcore Bose-Hubbard model in the presence of a period-two superlattice in two and three dimensions. First we acquire the phase boundaries between the superfluid phase and the `trivial' insulating phases of the model (the completely-empty and completely-filled lattices) analytically. Next, the boundary between the superfluid phase and the half-filled Mott-insulating phase is obtained numerically, using the stochastic series expansion (SSE) algorithm followed by finite-size scaling. We also compare our numerical results against the predictions of several approximation schemes, including two mean-field approaches and a fourth-order strong-coupling expansion (SCE), where we show that the latter method in particular is successful in producing an accurate picture of the phase diagram. Finally, we examine the extent to which several approximation schemes, such as the random phase approximation and the strong-coupling expansion, give an accurate description of the momentum distribution of the bosons inside the insulating phases.Comment: 11 pages, 7 figure

Pseudo-Supersymmetric Quantum Mechanics and Isospectral Pseudo-Hermi tian Hamiltonians

We examine the properties and consequences of pseudo-supersymmetry for quantum systems admitting a pseudo-Hermitian Hamiltonian. We explore the Witten index of pseudo-supersymmetry and show that every pair of diagonalizable (not necessarily Hermitian) Hamiltonians with discrete spectra and real or complex-conjugate pairs of eigenvalues are isospectral and have identical degeneracy structure except perhaps for the zero eigenvalue if and only if they are pseudo-supersymmetric partners. This implies that pseudo-supersymmetry is the basic framework for generating non-Hermitian PT-symmetric and non-PT-symmetric Hamiltonians with a real spectrum via a Darboux transformation, and shows that every diagonalizable Hamiltonian H with a discrete spectrum and real or complex-conjugate pairs of eigenvalues may be factored as H=L^# L where L is a linear operator with pseudo-adjoint L^#. In particular, this factorization applies to PT-symmetric and Hermitian Hamiltonians. The nondegenerate two-level systems provide a class of Hamiltonians that are pseudo-Hermitian. We demonstrate the implications of our general results for this class in some detail.Comment: Minor corrections, accepted for publication in Nucl. Phys.

Counterflow of spontaneous mass currents in trapped spin-orbit coupled Fermi gases

We use the Bogoliubov-de Gennes formalism and study the ground-state phases of trapped spin-orbit coupled Fermi gases in two dimensions. Our main finding is that the presence of a symmetric (Rashba type) spin-orbit coupling spontaneously induces counterflowing mass currents in the vicinity of the trap edge, i.e. $\uparrow$ and $\downarrow$ particles circulate in opposite directions with equal speed. These currents flow even in noninteracting systems, but their strength decreases toward the molecular BEC limit, which can be achieved either by increasing the spin-orbit coupling or the interaction strength. These currents are also quite robust against the effects of asymmetric spin-orbit couplings in $x$ and $y$ directions, gradually reducing to zero as the spin-orbit coupling becomes one dimensional. We compare our results with those of chiral p-wave superfluids/superconductors.Comment: 6 pages with 4 figures; to appear in PR

FASTSUBS: An Efficient and Exact Procedure for Finding the Most Likely Lexical Substitutes Based on an N-gram Language Model

Lexical substitutes have found use in areas such as paraphrasing, text simplification, machine translation, word sense disambiguation, and part of speech induction. However the computational complexity of accurately identifying the most likely substitutes for a word has made large scale experiments difficult. In this paper I introduce a new search algorithm, FASTSUBS, that is guaranteed to find the K most likely lexical substitutes for a given word in a sentence based on an n-gram language model. The computation is sub-linear in both K and the vocabulary size V. An implementation of the algorithm and a dataset with the top 100 substitutes of each token in the WSJ section of the Penn Treebank are available at http://goo.gl/jzKH0.Comment: 4 pages, 1 figure, to appear in IEEE Signal Processing Letter

Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian

We introduce the notion of pseudo-Hermiticity and show that every Hamiltonian with a real spectrum is pseudo-Hermitian. We point out that all the PT-symmetric non-Hermitian Hamiltonians studied in the literature belong to the class of pseudo-Hermitian Hamiltonians, and argue that the basic structure responsible for the particular spectral properties of these Hamiltonians is their pseudo-Hermiticity. We explore the basic properties of general pseudo-Hermitian Hamiltonians, develop pseudo-supersymmetric quantum mechanics, and study some concrete examples, namely the Hamiltonian of the two-component Wheeler-DeWitt equation for the FRW-models coupled to a real massive scalar field and a class of pseudo-Hermitian Hamiltonians with a real spectrum.Comment: Revised version, to appear in J. Math. Phy

Erratum: Pseudo-Hermiticity for a class of nondiagonalizable Hamiltonians [J. Math. Phys. 43, 6343 (2002); math-ph/0207009]

An error in the paper [J. Math. Phys. 43, 6343 (2002); math-ph/0207009] is corrected. Further explanation is given.Comment: 2 page

Denaturation of Circular DNA: Supercoil Mechanism

The denaturation transition which takes place in circular DNA is analyzed by extending the Poland-Scheraga model to include the winding degrees of freedom. We consider the case of a homopolymer whereby the winding number of the double stranded helix, released by a loop denaturation, is absorbed by \emph{supercoils}. We find that as in the case of linear DNA, the order of the transition is determined by the loop exponent $c$. However the first order transition displayed by the PS model for $c>2$ in linear DNA is replaced by a continuous transition with arbitrarily high order as $c$ approaches 2, while the second-order transition found in the linear case in the regime $1<c\le2$ disappears. In addition, our analysis reveals that melting under fixed linking number is a \emph{condensation transition}, where the condensate is a macroscopic loop which appears above the critical temperature.Comment: 9 pages, 4 figure