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Europhysics Letters (EPL)

Zero-Width Slit Model and Resonances in Mesoscopic Systems

I. Yu. Popov, S. L. Popova

Published Nov 10, 1993• 40 citations
Publisher

Abstract

The resonance effects in a quantum waveguide connected with a resonator is studied in the framework of the zero-width slits model based on the operator extensions theory approach.
DOI
10.1209/0295-5075/24/5/009

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Order,Disorder and Chaos in Quantum Systems: Proceedings of a conference held at Dubna, USSR on October 17–21 1989

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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.- Green's 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.

•Jul 2, 1990•1 citation
We investigate the quantum signatures of classical nonlinear resonances by making the analytic connection between the quantum wave functions and the classical periodic orbits for the uncoupled systems. It is found that the highly efficient extension of the localized coherent states within the classical caustics is an intriguing phenomenon in mesoscopic systems with nonlinear resonances. With the theoretical analysis, we experimentally demonstrate that the laser resonator with an intracavity saturable absorber can be employed to visualize the wave patterns analogous to the quantum wave functions associated with Fermi resonance.
The coupling of a quantum mechanical system to open decay channels has been theoretically studied in numerous works, mainly in the context of nuclear physics but also in atomic, molecular, and mesoscopic physics. Theory predicts that with increasing coupling strength to the channels the resonance widths of all states should first increase but finally decrease again for most of the states. In this Letter, the first direct experimental verification of this effect, known as resonance trapping, is presented. In the experiment a microwave Sinai cavity with an attached waveguide with variable slit width was used.
We develop and analyze a theoretical model which yields the shifts and widths of Feshbach resonances in an atomic waveguide. It is based on a multichannel approach for confinement-induced resonances (CIRs) and atomic transitions in the waveguides in the multimode regime. In this scheme we replace the single-channel scalar interatomic interaction by the four-channel tensorial potential modeling resonances of broad, narrow, and overlapping character according to the two-channel parametrization of Lange et al. [Phys. Rev. A 79, 013622 (2009)]. As an input the experimentally known parameters of Feshbach resonances in the absence of the waveguide are used. We calculate the shifts and widths of sss-, ddd-, and ggg-wave magnetic Feshbach resonances of Cs atoms emerging in harmonic waveguides as CIRs and resonant enhancement of the transmission at zeros of the free space scattering length. We have found the linear dependence of the width of the resonance on the longitudinal atomic momentum and quadratic dependence on the waveguide width. Our model opens possibilities for quantitative studies of the scattering processes in ultracold atomic gases in waveguides beyond the framework of sss-wave resonant scattering.
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.- Green's 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.