234 research outputs found

    Bargmann representations for deformed harmonic oscillators

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    Generalizing the case of the usual harmonic oscillator, we look for Bargmann representations corresponding to deformed harmonic oscillators. Deformed harmonic oscillator algebras are generated by four operators a,a†,Na, a^\dagger, N and the unity 1 such as [a,N]=a,[a†,N]=−a†[a,N] = a, [a^\dagger,N] = -a^\dagger, a†a=ψ(N)a^\dagger a = \psi(N) and aa†=ψ(N+1)aa^\dagger =\psi(N+1). We discuss the conditions of existence of a scalar product expressed with a true integral on the space spanned by the eigenstates of aa (or a†a^\dagger). We give various examples, in particular we consider functions ψ\psi that are linear combinations of qNq^N, q−Nq^{-N} and unity and that correspond to q-oscillators with Fock-representations or with non-Fock-representations.Comment: 23 pages, Late

    q-Supersymmetric Generalization of von Neumann's Theorem

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    Assuming that there exist operators which form an irreducible representation of the q-superoscillator algebra, it is proved that any two such representations are equivalent, related by a uniquely determined superunitary transformation. This provides with a q-supersymmetric generalization of the well-known uniqueness theorem of von Neumann for any finite number of degrees of freedom.Comment: 10 pages, Latex, HU-TFT-93-2

    Model for the on-site matrix elements of the tight-binding hamiltonian of a strained crystal: Application to silicon, germanium and their alloys

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    We discuss a model for the on-site matrix elements of the sp3d5s* tight-binding hamiltonian of a strained diamond or zinc-blende crystal or nanostructure. This model features on-site, off-diagonal couplings between the s, p and d orbitals, and is able to reproduce the effects of arbitrary strains on the band energies and effective masses in the full Brillouin zone. It introduces only a few additional parameters and is free from any ambiguities that might arise from the definition of the macroscopic strains as a function of the atomic positions. We apply this model to silicon, germanium and their alloys as an illustration. In particular, we make a detailed comparison of tight-binding and ab initio data on strained Si, Ge and SiGe.Comment: Submitted to Phys. Rev.

    Localized Endomorphisms of the Chiral Ising Model

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    Based on the treatment of the chiral Ising model by Mack and Schomerus, we present examples of localized endomorphisms ϱ1loc\varrho_1^{\rm loc} and ϱ1/2loc\varrho_{1/2}^{\rm loc}. It is shown that they lead to the same superselection sectors as the global ones in the sense that unitary equivalence π0∘ϱ1loc≅π1\pi_0\circ\varrho_1^{\rm loc}\cong\pi_1 and π0∘ϱ1/2loc≅π1/2\pi_0\circ\varrho_{1/2}^{\rm loc}\cong\pi_{1/2} holds. Araki's formalism of the selfdual CAR algebra is used for the proof. We prove local normality and extend representations and localized endomorphisms to a global algebra of observables which is generated by local von Neumann algebras on the punctured circle. In this framework, we manifestly prove fusion rules and derive statistics operators.Comment: 41 pages, latex2

    Coherent states for a quantum particle on a circle

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    The coherent states for the quantum particle on the circle are introduced. The Bargmann representation within the actual treatment provides the representation of the algebra [J^,U]=U[\hat J,U]=U, where UU is unitary, which is a direct consequence of the Heisenberg algebra [Ï•^,J^]=i[\hat \phi, \hat J]=i, but it is more adequate for the study of the circlular motion.Comment: 23 pages LaTeX, uses ioplppt.st
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