1,436 research outputs found
Lieb-Thirring inequalities for geometrically induced bound states
We prove new inequalities of the Lieb-Thirring type on the eigenvalues of
Schr\"odinger operators in wave guides with local perturbations. The estimates
are optimal in the weak-coupling case. To illustrate their applications, we
consider, in particular, a straight strip and a straight circular tube with
either mixed boundary conditions or boundary deformations.Comment: LaTeX2e, 14 page
Magnetic transport in a straight parabolic channel
We study a charged two-dimensional particle confined to a straight
parabolic-potential channel and exposed to a homogeneous magnetic field under
influence of a potential perturbation . If is bounded and periodic along
the channel, a perturbative argument yields the absolute continuity of the
bottom of the spectrum. We show it can have any finite number of open gaps
provided the confining potential is sufficiently strong. However, if
depends on the periodic variable only, we prove by Thomas argument that the
whole spectrum is absolutely continuous, irrespectively of the size of the
perturbation. On the other hand, if is small and satisfies a weak
localization condition in the the longitudinal direction, we prove by Mourre
method that a part of the absolutely continuous spectrum persists
Initial state maximizing the nonexponentially decaying survival probability for unstable multilevel systems
The long-time behavior of the survival probability for unstable multilevel
systems that follows the power-decay law is studied based on the N-level
Friedrichs model, and is shown to depend on the initial population in unstable
states. A special initial state maximizing the asymptote of the survival
probability at long times is found and examined by considering the spontaneous
emission process for the hydrogen atom interacting with the electromagnetic
field.Comment: 5 pages, 1 table. Accepted for publication in Phys. Rev.
Time-Energy coherent states and adiabatic scattering
Coherent states in the time-energy plane provide a natural basis to study
adiabatic scattering. We relate the (diagonal) matrix elements of the
scattering matrix in this basis with the frozen on-shell scattering data. We
describe an exactly solvable model, and show that the error in the frozen data
cannot be estimated by the Wigner time delay alone. We introduce the notion of
energy shift, a conjugate of Wigner time delay, and show that for incoming
state the energy shift determines the outgoing state.Comment: 11 pages, 1 figur
Atomically dispersed Pt-N-4 sites as efficient and selective electrocatalysts for the chlorine evolution reaction
Chlorine evolution reaction (CER) is a critical anode reaction in chlor-alkali electrolysis. Although precious metal-based mixed metal oxides (MMOs) have been widely used as CER catalysts, they suffer from the concomitant generation of oxygen during the CER. Herein, we demonstrate that atomically dispersed Pt-N-4 sites doped on a carbon nanotube (Pt-1/CNT) can catalyse the CER with excellent activity and selectivity. The Pt-1/CNT catalyst shows superior CER activity to a Pt nanoparticle-based catalyst and a commercial Ru/Ir-based MMO catalyst. Notably, Pt-1/CNT exhibits near 100% CER selectivity even in acidic media, with low Cl- concentrations (0.1M), as well as in neutral media, whereas the MMO catalyst shows substantially lower CER selectivity. In situ electrochemical X-ray absorption spectroscopy reveals the direct adsorption of Cl- on Pt-N-4 sites during the CER. Density functional theory calculations suggest the PtN4C12 site as the most plausible active site structure for the CER
Generalized local interactions in 1D: solutions of quantum many-body systems describing distinguishable particles
As is well-known, there exists a four parameter family of local interactions
in 1D. We interpret these parameters as coupling constants of delta-type
interactions which include different kinds of momentum dependent terms, and we
determine all cases leading to many-body systems of distinguishable particles
which are exactly solvable by the coordinate Bethe Ansatz. We find two such
families of systems, one with two independent coupling constants deforming the
well-known delta interaction model to non-identical particles, and the other
with a particular one-parameter combination of the delta- and (so-called)
delta-prime interaction. We also find that the model of non-identical particles
gives rise to a somewhat unusual solution of the Yang-Baxter relations. For the
other model we write down explicit formulas for all eigenfunctions.Comment: 23 pages v2: references adde
Exterior-Interior Duality for Discrete Graphs
The Exterior-Interior duality expresses a deep connection between the Laplace
spectrum in bounded and connected domains in , and the scattering
matrices in the exterior of the domains. Here, this link is extended to the
study of the spectrum of the discrete Laplacian on finite graphs. For this
purpose, two methods are devised for associating scattering matrices to the
graphs. The Exterior -Interior duality is derived for both methods.Comment: 15 pages 1 figur
Transport and dynamics on open quantum graphs
We study the classical limit of quantum mechanics on graphs by introducing a
Wigner function for graphs. The classical dynamics is compared to the quantum
dynamics obtained from the propagator. In particular we consider extended open
graphs whose classical dynamics generate a diffusion process. The transport
properties of the classical system are revealed in the scattering resonances
and in the time evolution of the quantum system.Comment: 42 pages, 13 figures, submitted to PR
Spectral and localization properties of the Dirichlet wave guide with two concentric Neumann discs
Bound states of the Hamiltonian describing a quantum particle living on three
dimensional straight strip of width are investigated. We impose the Neumann
boundary condition on the two concentric windows of the radii and
located on the opposite walls and the Dirichlet boundary condition on the
remaining part of the boundary of the strip. We prove that such a system
exhibits discrete eigenvalues below the essential spectrum for any .
When and tend to the infinity, the asymptotic of the eigenvalue is
derived. A comparative analysis with the one-window case reveals that due to
the additional possibility of the regulating energy spectrum the anticrossing
structure builds up as a function of the inner radius with its sharpness
increasing for the larger outer radius. Mathematical and physical
interpretation of the obtained results is presented; namely, it is derived that
the anticrossings are accompanied by the drastic changes of the wave function
localization. Parallels are drawn to the other structures exhibiting similar
phenomena; in particular, it is proved that, contrary to the two-dimensional
geometry, at the critical Neumann radii true bound states exist.Comment: 25 pages, 7 figure
Duality and Anholonomy in Quantum Mechanics of 1D Contact Interactions
We study systems with parity invariant contact interactions in one dimension.
The model analyzed is the simplest nontrivial one --- a quantum wire with a
point defect --- and yet is shown to exhibit exotic phenomena, such as strong
vs weak coupling duality and spiral anholonomy in the spectral flow. The
structure underlying these phenomena is SU(2), which arises as accidental
symmetry for a particular class of interactions.Comment: 4 pages ReVTeX with 4 epsf figures. KEK preprint 2000-3. Correction
in Eq.(14
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