Quasiclassical analysis of Bloch oscillations in non-Hermitian tight-binding lattices

Many features of Bloch oscillations in one-dimensional quantum lattices with a static force can be described by quasiclassical considerations for example by means of the acceleration theorem, at least for Hermitian systems. Here the quasiclassical approach is extended to non-Hermitian lattices, which are of increasing interest. The analysis is based on a generalised non-Hermitian phase space dynamics developed recently. Applications to a single-band tight-binding system demonstrate that many features of the quantum dynamics can be understood from this classical description qualitatively and even quantitatively. Two non-Hermitian and $PT$-symmetric examples are studied, a Hatano-Nelson lattice with real coupling constants and a system with purely imaginary couplings, both for initially localised states in space or in momentum. It is shown that the time-evolution of the norm of the wave packet and the expectation values of position and momentum can be described in a classical picture.Comment: 20 pages, 8 figures, typos corrected, slightly extended, accepted for publication in New Journal of Physics in Focus Issue on Parity-Time Symmetry in Optics and Photonic

Bose-Einstein condensates in accelerated double-periodic optical lattices: Coupling and Crossing of resonances

We study the properties of coupled linear and nonlinear resonances. The fundamental phenomena and the level crossing scenarios are introduced for a nonlinear two-level system with one decaying state, describing the dynamics of a Bose-Einstein condensate in a mean-field approximation (Gross-Pitaevskii or nonlinear Schroedinger equation). An important application of the discussed concepts is the dynamics of a condensate in tilted optical lattices. In particular the properties of resonance eigenstates in double-periodic lattices are discussed, in the linear case as well as within mean-field theory. The decay is strongly altered, if an additional period-doubled lattice is introduced. Our analytic study is supported by numerical computations of nonlinear resonance states, and future applications of our findings for experiments with ultracold atoms are discussed.Comment: 12 pages, 17 figure

Muir-Torre syndrome - Treatment with isotretinoin and interferon alpha-2a can prevent tumour development

Muir-Torre syndrome is a genodermatosis in which multiple internal malignancies are associated with cutaneous sebaceous tumours and kerato-acanthomas. A 57-year-old man presented with multiple sebaceous tumours, kerato-acanthomas, verrucous carcinoma of the nose, renal cell and transitional cell carcinomas of the left kidney, adenoma of the colon and a positive family history of colon carcinoma. He was treated with interferon (IFN-alpha Pa) s.c. 3 x 10(6) U three times a week along with 50 mg isotretinoin daily as well as topical isotretinoin gel. During a follow-up of 29 months, only 1 sebaceous skin tumour developed and was removed, whereas more than 30 such skin tumours had been surgically removed during the last 3 years. No evidence of internal tumour development or recurrence was found. The combination of IFN with retinoids seems to be of promise to prevent tumour development in Muir-Torre syndrome. Copyright (C) 2000 S. Karger AG, Basel

Mean-field dynamics of a non-Hermitian Bose-Hubbard dimer

We investigate an $N$-particle Bose-Hubbard dimer with an additional effective decay term in one of the sites. A mean-field approximation for this non-Hermitian many-particle system is derived, based on a coherent state approximation. The resulting nonlinear, non-Hermitian two-level dynamics, in particular the fixed point structures showing characteristic modifications of the self-trapping transition, are analyzed. The mean-field dynamics is found to be in reasonable agreement with the full many-particle evolution.Comment: 4 pages, 3 figures, published versio

PT-Symmetric Sinusoidal Optical Lattices at the Symmetry-Breaking Threshold

The $PT$ symmetric potential $V_0[\cos(2\pi x/a)+i\lambda\sin(2\pi x/a)]$ has a completely real spectrum for $\lambda\le 1$, and begins to develop complex eigenvalues for $\lambda>1$. At the symmetry-breaking threshold $\lambda=1$ some of the eigenvectors become degenerate, giving rise to a Jordan-block structure for each degenerate eigenvector. In general this is expected to result in a secular growth in the amplitude of the wave. However, it has been shown in a recent paper by Longhi, by numerical simulation and by the use of perturbation theory, that for a broad initial wave packet this growth is suppressed, and instead a saturation leading to a constant maximum amplitude is observed. We revisit this problem by explicitly constructing the Bloch wave-functions and the associated Jordan functions and using the method of stationary states to find the dependence on the longitudinal distance $z$ for a variety of different initial wave packets. This allows us to show in detail how the saturation of the linear growth arises from the close connection between the contributions of the Jordan functions and those of the neighbouring Bloch waves.Comment: 15 pages, 7 figures Minor corrections, additional reference

Bloch oscillations of Bose-Einstein condensates: Quantum counterpart of dynamical instability

We study the Bloch dynamics of a quasi one-dimensional Bose-Einstein condensate of cold atoms in a tilted optical lattice modeled by a Hamiltonian of Bose-Hubbard type: The corresponding mean-field system described by a discrete nonlinear Schr\"odinger equation can show a dynamical (or modulation) instability due to chaotic dynamics and equipartition over the quasimomentum modes. It is shown, that these phenomena are related to a depletion of the Floquet-Bogoliubov states and a decoherence of the condensate in the many-particle description. Three different types of dynamics are distinguished: (i) decaying oscillations in the region of dynamical instability, and (ii) persisting Bloch oscillations or (iii) periodic decay and revivals in the region of stability.Comment: 12 pages, 14 figure

Nonlinear Schr\"odinger equation for a PT symmetric delta-functions double well

The time-independent nonlinear Schr\"odinger equation is solved for two attractive delta-function shaped potential wells where an imaginary loss term is added in one well, and a gain term of the same size but with opposite sign in the other. We show that for vanishing nonlinearity the model captures all the features known from studies of PT symmetric optical wave guides, e.g., the coalescence of modes in an exceptional point at a critical value of the loss/gain parameter, and the breaking of PT symmetry beyond. With the nonlinearity present, the equation is a model for a Bose-Einstein condensate with loss and gain in a double well potential. We find that the nonlinear Hamiltonian picks as stationary eigenstates exactly such solutions which render the nonlinear Hamiltonian itself PT symmetric, but observe coalescence and bifurcation scenarios different from those known from linear PT symmetric Hamiltonians.Comment: 16 pages, 9 figures, to be published in Journal of Physics

Outdoor Recreation Participation of Pennsylvanians with Disabilities

Abstract Approximately 16% of United States residents report having some sort of physical disability that limits their recreation participation. Many of these individuals may have an abundance of free time due to unemployment, part-time work status, or retirement, and therefore recreation and leisure have the potential to provide great meaning in their lives. Qualitative and quantitative data from a State Comprehensive Outdoor Recreation Plan was used to better understand the outdoor recreation habits and perceptions of Pennsylvania residents with disabilities. Using descriptive, chi square, and ANOVA statistics, results indicate that these individuals perceive fewer benefits from outdoor activities, experience different types of constraints to participation, and have different perceptions of accessibility compared to individuals without disabilities. Results of this data analysis provide a better understanding of the perceptions that Pennsylvanians with disabilities have regarding future outdoor recreation participation, benefits of participation, and accommodations to facilitate participation

Towards a Landau-Zener formula for an interacting Bose-Einstein condensate

We consider the Landau-Zener problem for a Bose-Einstein condensate in a linearly varying two-level system, for the full many-particle system as well and in the mean-field approximation. The many-particle problem can be solved approximately within an independent crossings approximation, which yields an explicit Landau-Zener formula.Comment: RevTeX, 8 pages, 9 figure