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  • 1
    Electronic Resource
    Electronic Resource
    Extended Hilbert space approach to few-body problems (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1681-1690 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A general formulation of the quantum scattering theory for a system of few particles, which have an internal structure, is given. Due to freezing out the internal degrees of freedom in the external channels, a certain class of energy-dependent potentials is generated. By means of potential theory, a modified Faddeev equation is derived both in external and internal channels. The Fredholmity of these equations is proven and this is what provides a sound basis for solving the addressed scattering problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528715
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  • 2
    Electronic Resource
    Electronic Resource
    An extensions theory setting for scattering by breathing bag (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 199-201 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A model of the scattering of a structureless pointlike particle on a spherical bag with an internal structure, imitating "quark'' degrees of freedom, is considered. It is assumed that the bag is a dynamical object and its radius plays the role of additional dynamical variable. The energy of the collision is distributed among the quark excitations and the vibration degrees of freedom of the bag surface. In the frame of the theory of extensions the Hamiltonian of the coupled bag-quark system interacting with the pointlike particle is constructed. The formal multichannel S matrix of the problem is obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528860
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  • 3
    Electronic Resource
    Electronic Resource
    Two-body scattering on a graph and application to simple nanoelectronic devices (1995)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 2813-2825 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The two-body system on a graph with one junction is considered. The effective three-body scattering problem turns out to be exactly solvable for pointwise interactions. Additional degrees of freedom corresponding to a dynamics of some structure (e.g., an atomic cluster) located in the junction (point of common contact) of three thin electrodes are considered. These degrees of freedom bring effective energy-dependent interaction into the effective Schrödinger equation in the scattering channel. The wave function of the system is constructed in the explicit form using the extension theory methods. The obtained results are applied to the qualitative description of a simple three-electrode nanoelectronic device. The perturbation theory approach based on the analysis of the Liouville equation is suggested for calculation of the conductivity for such a device in terms of the obtained wave function. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531068
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  • 4
    Electronic Resource
    Electronic Resource
    Estimations for negative spectral bands of three-dimensional periodical Schrödinger operator (1993)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 34 (1993), S. 936-942 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The asymptotic estimations, as period tends to infinity, for negative spectral bands of three-dimensional periodical Schrödinger operator who's potential was generated by shifting along the cubic lattice of a negative function with compact support are described herein. The problem is of primary importance for solid state physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530202
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  • 5
    Electronic Resource
    Electronic Resource
    Electron transport in quasi-one-dimensional random structure (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 2916-2922 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A model of the Markovian chain of N atoms is constructed with the help of extension theory. Behavior of averaged wave functions of random Dirac operator is studied for finite and large N with respect to parameters of the model and Markovian process. Study of a random Dirac operator is connected with the study of nonrandom double-dimensional non-self-adjoint Dirac operator. Dynamics of bands of effective periodic operator with respect to the Markovian parameter is presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.529560
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  • 6
    Electronic Resource
    Electronic Resource
    Spectral properties of a charged particle in antidot array: A limiting case of quantum billiard (1996)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 37 (1996), S. 5171-5194 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A model of the periodic array of quantum antidots in the presence of a uniform magnetic field is suggested. The model can be conceived as a periodic lattice of resonators (curvilinear triangles) connected through "infinitely small'' openings at the vertices of the triangles. The model Hamiltonian is obtained by means of operator extension theory in indefinite metric spaces. In the case of rational magnetic flux through an elementary cell of the lattice, the dispersion equation is found in an explicit form with the help of harmonic analysis on the magnetic translation group. It is proved, at least in the case of integer flux, that the spectrum of the model Hamiltonian consists of three parts: (1) Landau levels (they correspond to the classical orbits lying between antidots); (2) extended states that correspond to the classical propagation trajectories; and (3) bound states satisfying the dispersion equation; they correspond to the classical chaotic orbits rotating around single antidots. Among other things, methods of finding the Green's function for some planar domains with curvilinear boundaries are derived. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.531679
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  • 7
    Electronic Resource
    Electronic Resource
    7.4. Spectral decompositions and the carleson condition (1984)
    Springer
    Journal of mathematical sciences 26 (1984), S. 2152-2153 
    Details
    ISSN: 1573-8795
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01221513
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  • 8
    Electronic Resource
    Electronic Resource
    Spectral analysis of unitary perturbations of contractions (1985)
    Springer
    Journal of mathematical sciences 28 (1985), S. 768-776 
    Details
    ISSN: 1573-8795
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract By the methods of the theory of extensions, for a unitary operator U with a simple spectrum one constructs all possible contractions Tv, differing from U by a one-dimensional one, and with the aid of the unitary dilation Ũ of the contraction T one carries out a comparative spectral analysis of the operators U and T. Writing the contraction T in the spectral representation of the operator U, we construct a model of a contraction which turns out to be useful in the investigation of the process of the “disconnection of a communication channel” of a conservative system with an exterior universe. The technique described in the paper is useful for the construction of explicitly solved problems of resonance scattering and in the investigation of the serial structure of resonators.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02112342
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  • 9
    Electronic Resource
    Electronic Resource
    Nonphysical sheet for the Friedrichs model (1995)
    Springer
    Journal of mathematical sciences 77 (1995), S. 3232-3235 
    Details
    ISSN: 1573-8795
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A method of deducing an expansion theorem in resonance states for the two-dimensional Friedrichs model $$A = \tfrac{1}{{2i}}(U_\varphi - U_\varphi ^ + )$$ is suggested. The construction is based on detailed Lax-Phillips analogs of the corresponding unitary Friedrichs model $$U_\varphi = z(1 + \tfrac{{2i\alpha }}{{1 - i\alpha }}P_\varphi )$$ , perturbed by the projector Pϕ, generated by an element ϕ possessing special analytic properties. Bibliography: 11 titles.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02364716
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  • 10
    Electronic Resource
    Electronic Resource
    Embedding theorems for weighted classes of harmonic and analytic functions (1974)
    Springer
    Journal of mathematical sciences 2 (1974), S. 135-142 
    Details
    ISSN: 1573-8795
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01099672
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