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  • Articles  (67,058)
  • 2000-2004  (67,058)
  • Mathematics  (65,229)
  • Philosophy  (2,050)
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  • 1
    Electronic Resource
    Electronic Resource
    Bound states in straight quantum waveguides with combined boundary conditions (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 3892-3915 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We investigate the discrete spectrum of the Hamiltonian describing a quantum particle living in the two-dimensional straight strip. We impose the combined Dirichlet and Neumann boundary conditions on different parts of the boundary. Several statements on the existence or the absence of the discrete spectrum are compared for two models with combined boundary conditions. Examples of eigenfunctions and eigenvalues are computed numerically. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1491597
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  • 2
    Electronic Resource
    Electronic Resource
    Symmetry breaking regime in the nonlinear Hartree equation (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 3879-3891 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The present article is concerned with minimizers of the attractive Hartree energy functional Hg[ψ¯,ψ]=〈fraction SHAPE="CASE"〉12||∇ψ||22+(ψ,vψ)2+g(ψ,V * |ψ|2ψ)2 on Rd, d≥2, for a general class of external potentials v and two-body interactions V of positive type, with g〈0. We prove spontaneous symmetry breaking in the large coupling limit. A numerical investigation visualizes this regime in the example of an external double well potential. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1488673
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  • 3
    Electronic Resource
    Electronic Resource
    The Dirac operator in a fermion bag background in 1+1 dimensions and generalized supersymmetric quantum mechanics (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 3927-3936 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We show that the spectral theory of the Dirac operator D=i∂(Slashthrough accent mark)−σ(x)−iπ(x)γ5, in a static background (σ(x),π(x)) in 1+1 space–time dimensions, is underlined by a certain novel generalization of supersymmetric quantum mechanics, and we explore some of its mathematical and physical consequences. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1485114
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  • 4
    Electronic Resource
    Electronic Resource
    Bogoliubov transformations and exact isolated solutions for simple nonadiabatic Hamiltonians (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 3916-3926 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We present a new method for finding isolated exact solutions of a class of nonadiabatic Hamiltonians of relevance to quantum optics and allied areas. Central to our approach is the use of Bogoliubov transformations of the bosonic fields in the models. We demonstrate the simplicity and efficiency of this method by applying it to the Rabi Hamiltonian. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1490406
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  • 5
    Electronic Resource
    Electronic Resource
    Energy levels and wave functions of vector bosons in a homogeneous magnetic field (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 3952-3962 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We aimed to obtain the energy levels of massive spin-1 particles moving in a constant magnetic field. The method used here is completely algebraic. In the process to obtain the energy levels the wave function is expressed in terms of Laguerre polynomials. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1489502
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  • 6
    Electronic Resource
    Electronic Resource
    Pseudo-Hermiticity versus PT-symmetry III: Equivalence of pseudo-Hermiticity and the presence of antilinear symmetries (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 3944-3951 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We show that a diagonalizable (non-Hermitian) Hamiltonian H is pseudo-Hermitian if and only if it has an antilinear symmetry, i.e., a symmetry generated by an invertible antilinear operator. This implies that the eigenvalues of H are real or come in complex conjugate pairs if and only if H possesses such a symmetry. In particular, the reality of the spectrum of H implies the presence of an antilinear symmetry. We further show that the spectrum of H is real if and only if there is a positive-definite inner-product on the Hilbert space with respect to which H is Hermitian or alternatively there is a pseudo-canonical transformation of the Hilbert space that maps H into a Hermitian operator. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1489072
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  • 7
    Electronic Resource
    Electronic Resource
    Stabilization of impurity states in crossed magnetic and electric fields (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 3937-3943 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the renormalizability of the zero-range interaction in the two-dimensional space is always followed by the existence of a bound state, which is not true for odd-dimensional spaces. A renormalization procedure is defined and the exact retarded Green's function for electrons moving in two dimensions and interacting with both crossed magnetic and electric fields and an attractive zero-range interaction is constructed. Imaginary parts of poles of this Green's function determine lifetimes of quasibound (resonance) states. It is shown that for some particular parameters the stabilization against decay occurs even for strong electric fields. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1491596
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  • 8
    Electronic Resource
    Electronic Resource
    The propagator of the radial Dirac equation (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 3963-3983 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The propagator for the radial Dirac equation is explicitly constructed. It turns out to be a distribution of order zero, but it is shown that there exists no path-space measure associated with this equation. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1486263
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  • 9
    Electronic Resource
    Electronic Resource
    Applications of Nambu mechanics to systems of hydrodynamical type (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 4035-4040 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We show that the reduced Dubrovin–Novikov hydrodynamic type models are integrable Nambu mechanical systems admitting Lax triples. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1481955
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  • 10
    Electronic Resource
    Electronic Resource
    On the problem of algebraic completeness for the invariants of the Riemann tensor. III. (2002)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 43 (2002), S. 4020-4034 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We study the set CZ of invariants [Zakhary and Carminati, J. Math. Phys. 42, 1474 (2001)] for the class of space–times whose Ricci tensors possess a null eigenvector. We show that all cases are maximally backsolvable, in terms of sets of invariants from CZ, but that some cases are not completely backsolvable and these all possess an alignment between an eigenvector of the Ricci tensor with a repeated principal null vector of the Weyl tensor. We provide algebraically complete sets for each canonically different space–time and hence conclude with these results and those of a previous article [Carminati, Zakhary, and McLenaghan, J. Math. Phys. 43, 492 (2002)] that the CZ set is determining or maximal. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1478803
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