17,194 research outputs found

    Codes and Supersymmetry in One Dimension

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    Adinkras are diagrams that describe many useful supermultiplets in D=1 dimensions. We show that the topology of the Adinkra is uniquely determined by a doubly even code. Conversely, every doubly even code produces a possible topology of an Adinkra. A computation of doubly even codes results in an enumeration of these Adinkra topologies up to N=28, and for minimal supermultiplets, up to N=32.Comment: 48 pages, a new version that combines arXiv:0811.3410 and parts of arXiv:0806.0050, for submission for publicatio

    Quasi-equilibria in one-dimensional self-gravitating many body systems

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    The microscopic dynamics of one-dimensional self-gravitating many-body systems is studied. We examine two courses of the evolution which has the isothermal and stationary water-bag distribution as initial conditions. We investigate the evolution of the systems toward thermal equilibrium. It is found that when the number of degrees of freedom of the system is increased, the water-bag distribution becomes a quasi-equilibrium, and also the stochasticity of the system reduces. This results suggest that the phase space of the system is effectively not ergodic and the system with large degreees of freedom approaches to the near-integrable one.Comment: 21pages + 7 figures (available upon request), revtex, submitted to Physical Review

    Superintegrable systems with spin and second-order integrals of motion

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    We investigate a quantum nonrelativistic system describing the interaction of two particles with spin 1/2 and spin 0, respectively. We assume that the Hamiltonian is rotationally invariant and parity conserving and identify all such systems which allow additional integrals of motion that are second order matrix polynomials in the momenta. These integrals are assumed to be scalars, pseudoscalars, vectors or axial vectors. Among the superintegrable systems obtained, we mention a generalization of the Coulomb potential with scalar potential V0=αr+328r2V_0=\frac{\alpha}{r}+\frac{3\hbar^2}{8r^2} and spin orbital one V1=2r2V_1=\frac{\hbar}{2r^2}.Comment: 32 page

    Discrete Darboux transformation for discrete polynomials of hypergeometric type

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    Darboux Transformation, well known in second order differential operator theory, is applied here to the difference equation satisfied by the discrete hypergeometric polynomials(Charlier, Meixner-Krawchuk, Hahn)

    Intertwining relations of non-stationary Schr\"odinger operators

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    General first- and higher-order intertwining relations between non-stationary one-dimensional Schr\"odinger operators are introduced. For the first-order case it is shown that the intertwining relations imply some hidden symmetry which in turn results in a RR-separation of variables. The Fokker-Planck and diffusion equation are briefly considered. Second-order intertwining operators are also discussed within a general approach. However, due to its complicated structure only particular solutions are given in some detail.Comment: 18 pages, LaTeX20

    Quasi-exactly Solvable Lie Superalgebras of Differential Operators

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    In this paper, we study Lie superalgebras of 2×22\times 2 matrix-valued first-order differential operators on the complex line. We first completely classify all such superalgebras of finite dimension. Among the finite-dimensional superalgebras whose odd subspace is nontrivial, we find those admitting a finite-dimensional invariant module of smooth vector-valued functions, and classify all the resulting finite-dimensional modules. The latter Lie superalgebras and their modules are the building blocks in the construction of QES quantum mechanical models for spin 1/2 particles in one dimension.Comment: LaTeX2e using the amstex and amssymb packages, 24 page

    Quantum Pair Creation of Soliton Domain Walls

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    A large body of experimental evidence suggests that the decay of the false vacuum, accompanied by quantum pair creation of soliton domain walls, can occur in a variety of condensed matter systems. Examples include nucleation of charge soliton pairs in density waves [eg. J. H. Miller, Jr. et al., Phys. Rev. Lett. 84, 1555 (2000)] and flux soliton pairs in long Josephon junctions. Recently, Dias and Lemos [J. Math. Phys. 42, 3292 (2001)] have argued that the mass mm of the soliton should be interpreted as a line density and a surface density, respectively, for (2+1)-D and (3+1)-D systems in the expression for the pair production rate. As the transverse dimensions are increased and the total mass (energy) becomes large, thermal activation becomes suppressed, so quantum processes can dominate even at relatively high temperatures. This paper will discuss both experimental evidence and theoretical arguments for the existence of high-temperature collective quantum phenomena
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