Title | Order,Disorder and Chaos in Quantum Systems [electronic resource] : Proceedings of a conference held at Dubna, USSR on October 17-21 1989 / edited by Pavel Exner, Hagen Neidhardt |
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Imprint | Basel : Birkhรคuser Basel, 1990 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-7306-2 |
Descript | XIV, 360 p. online resource |
1. Schroedinger operators : spectra, scattering and semiclassical behaviour -- Negative discrete spectrum of the Schroedinger operator with large coupling constant : qualitative discussion -- Discrete spectrum in the gaps of the continuous one in the large-coupling-constant limit -- On the asymptotics of discrete spectrum for the Schroedinger operator in electric and homogeneous magnetic fields -- Asymptotics of the discrete spectrum of Hamiltonians of quantum systems with a homogeneous magnetic field -- Asymptotics of eigenvalues for many-particle Hamiltonians at symmetry subspaces -- Spectral asymptotics with highly accurate remainder estimates -- Bound states and resonances in quantum wires -- Spectral properties of the operators H? = ??XX + p(x)? + v(?x), p is periodic -- Discrete spectrum for a periodic Schroedinger operator perturbed by a decreasing potential -- On a complete description of the principal discrete series of spectral invariants of the Hill operator -- WKB-approximations from the perturbation theory viewpoint -- Moving potentials and the completeness of wave operators. Part II : Propagating observables on scattering states -- Representation of the three-body S-matrix in terms of effective amplitudes -- A three-body one-dimensional system with increasing interaction : wave function asymptotics -- Surprises of quantum tunneling (something about the velocity of sub-barrier motion) -- 2. Point and contact interactions, self-adjoint extensions -- Lifshitz tails and non-Lifshitz tails for one-dimensional random point interactions -- Point interactions with an internal structure as limits of nonlocal point interactions -- Greenโs function for the Aharonov-Bohm effect with a non-Abelian gauge group -- A model of zero-width slits and the real diffraction problem -- Construction of an inelastic scatterer in nanoelectronics by the extension-theory methods -- On boundary theory for Schroedinger operators and stochastic processes -- Dirac Hamiltonian with Coulomb potential and contact intraction on a sphere -- Self-adjoint extensions of Schroedinger operators with singular potentials -- Currents and the extension theory -- 3. Quantum chaos -- Chaotic quantum billiards -- Relevance of the localization to quasienergy statistics in quantum chaotic systems -- Singular continuous quasi-energy spectrum in the kicked rotator with separable perturbation : onset of quantum chaos ? -- Relation between correlation functions and spectrum statistics in the region of quantum chaos -- 4. Other topics -- Localization effects in non-homogeneous dielectrics -- A self-adjoint dilation of the linear Boltzmann operator -- Kato problem for functional-differential equations and difference Schroedinger operators -- An existence theorem for some nonlinear nonlocal Schroedinger operators and the solitonlike dynamics for the corresponding dynamical systems -- The Sturm-Liouville problem with a potential linear in spectral parameter -- Stochastic model of tree growth -- Critical phenomenon in the stationary model of random growth -- On a quantum-classical connection, hidden symmetries and a model of Josephson junction -- Open multiquantum systems. Method of a generating functional -- Generalized functions and their applications -- List of unpublished contributions -- List of participants