Supersymmetric Oscillator: Novel Symmetries

We discuss various continuous and discrete symmetries of the supersymmetric simple harmonic oscillator (SHO) in one (0 + 1)-dimension of spacetime and show their relevance in the context of mathematics of differential geometry. We show the existence of a novel set of discrete symmetries in the theory which has, hitherto, not been discussed in the literature on theoretical aspects of SHO. We also point out the physical relevance of our present investigation.Comment: REVTeX file, 5 pages, minor changes in title, text and abstract, references expanded, version to appear in EP

New SU(1, 1) Position-Dependent Effective Mass Coherent States for the Generalized Shifted Harmonic Oscillator

A new SU(1, 1) position-dependent effective mass coherent states (PDEM CS) related to the shifted harmonic oscillator (SHO) are deduced. This is accomplished by applying a similarity transformation to the generally deformed oscillator algebra (GDOA) generators for PDEM system and construct a new set of operators which close the su(1, 1) Lie algebra, being the PDEM CS of the basis for its unitary irreducible representation. The residual potential is associated to the SHO. From the Lie algebra generators, we evaluate the uncertainty relationship for a position and momentum-like operators in the PDEM CS and show that it is minimized in the sense of Barut-Girardello CS. We prove that the deduced PDEM CS preserve the same analytical form than those of Glauber states. We show that the probability density of dynamical evolution in the PDEM CS oscillates back and forth as time goes by and behaves as classical wave packet.Comment: 13 page

Vortex pinning with bounded fields for the Ginzburg-Landau equation

The coefficient, tivity is nonnega applied magnet κ = 1/ε, we sho of local minimi

Simulating quantum transport for a quasi-one-dimensional Bose gas in an optical lattice: the choice of fluctuation modes in the truncated Wigner approximation

We study the effect of quantum fluctuations on the dynamics of a quasi-one-dimensional Bose gas in an optical lattice at zero-temperature using the truncated Wigner approximation with a variety of basis sets for the initial fluctuation modes. The initial spatial distributions of the quantum fluctuations are very different when using a limited number of plane-wave (PW), simple-harmonic-oscillator (SHO) and self-consistently determined Bogoliubov (SCB) modes. The short-time transport properties of the Bose gas, characterized by the phase coherence in the PW basis are distinct from those gained using the SHO and SCB basis. The calculations using the SCB modes predict greater phase decoherence and stronger number fluctuations than the other choices. Furthermore, we observe that the use of PW modes overestimates the extent to which atoms are expelled from the core of the cloud, while the use of the other modes only breaks the cloud structure slightly which is in agreement with the experimental observations [1].Comment: 12 pages, 5 figure

Selbsthilfeorganisationen und -gruppen in der Verhaltensmedizin: Übersicht und Beschreibung

Background: Over the past years self-help organizations have become an essential part of prevention and rehabilitation in German health care. It was the aim of our enquiry to inform experts and interested persons about the most important self-help organizations (SHO) and self-help groups (SHG) of different fields in behavioral medicine. Methods: 70 SHO and SHG of different fields in behavioral medicine were selected dealing with allergy and asthma, congenital disorders, relatives of patients with psychic disorders, anxiety disorders, chronic pain disorders, eating disorders, diseases of the musculoskeletal system, diseases of the gastrointestinal tract and incontinence, skin diseases, hearing and speech disorders, life crises, disorders pertaining to the nervous system, personality disorders and psychic problems, abuse, or obsessive-compulsive disorders. The selected SHO and SHG received a structured questionnaire including questions regarding (1) address, (2) means of contact, (3) group of interest, (4) tasks and aims, (5) provision, (6) structure of organizations, and (7) comments. Results: 90% of SHO replied, 56 SHO sent back the questionnaire completely answered, 5 institutions sent material of information instead, and 30 included both questionnaire and information material. The data clearly show the extensive support SHO might offer to sufferers. Conclusions: This report provides an informative overview of SHO. It might help to support the already existing cooperation between experts and SHO in this field

Maximal Subalgebras for Modular Graded Lie Superalgebras of Odd Cartan Type

The purpose of this paper is to determine all maximal graded subalgebras of the four infinite series of finite-dimensional graded Lie superalgebras of odd Cartan type over an algebraically closed field of characteristic $p>3$. All maximal graded subalgebras consist of three types (\MyRoman{1}), (\MyRoman{2}) and (\MyRoman{3}). Maximal graded subalgebras of type (\MyRoman{3}) fall into reducible maximal graded subalgebras and irreducible maximal graded subalgebras. In this paper we classify maximal graded subalgebras of types (\MyRoman{1}), (\MyRoman{2}) and reducible maximal g raded subalgebras.The classification of irreducible maximal graded subalgebras is reduced to that of the irreducible maximal subalgebras of the classical Lie superalgebra $\mathfrak{p}(n)$.Comment: For the final version, see Transformation Groups 20(4)(2015)1075--110

Discrete adjoint approximations with shocks

This paper is concerned with the formulation and discretisation of adjoint equations when there are shocks in the underlying solution to the original nonlinear hyperbolic p.d.e. For the model problem of a scalar unsteady one-dimensional p.d.e. with a convex flux function, it is shown that the analytic formulation of the adjoint equations requires the imposition of an interior boundary condition along any shock. A 'discrete adjoint' discretisation is defined by requiring the adjoint equations to give the same value for the linearised functional as a linearisation of the original nonlinear discretisation. It is demonstrated that convergence requires increasing numerical smoothing of any shocks. Without this, any consistent discretisation of the adjoint equations without the inclusion of the shock boundary condition may yield incorrect values for the adjoint solution