624 research outputs found
Four-Parameter Point-Interaction in 1-D Quantum Systems
We construct a four-parameter point-interaction for a non-relativistic
particle moving on a line as the limit of a short range interaction with range
tending toward zero. For particular choices of the parameters, we can obtain a
delta-interaction or the so-called delta'-interaction. The Hamiltonian
corresponding to the four-parameter point-interaction is shown to correspond to
the four-parameter self-adjoint Hamiltonian of the free particle moving on the
line with the origin excluded.Comment: 6 pages, Plain Tex file. BU-HEP-92-
Perturbation Theory for Singular Potentials in Quantum Mechanics
We study perturbation theory in certain quantum mechanics problems in which
the perturbing potential diverges at some points, even though the energy
eigenvalues are smooth functions of the coefficient of the potential. We
discuss some of the unusual techniques which are required to obtain
perturbative expansions of the energies in such cases. These include a
point-splitting prescription for expansions around the Dirichlet (fermionic)
limit of the -function potential, and performing a similarity
transformation to a non-Hermitian potential in the Calogero-Sutherland model.
As an application of the first technique, we study the ground state of the
-function Bose gas near the fermionic limit.Comment: LaTeX, 19 pages, no figure
Novel A-B type oscillations in a 2-D electron gas in inhomogenous magnetic fields
We present results from a quantum and semiclassical theoretical study of the
and resistivities of a high mobility 2-D electron gas
in the presence of a dilute random distribution of tubes with magnetic flux
and radius , for arbitrary values of and . We
report on novel Aharonov-Bohm type oscillations in and ,
related to degenerate quantum flux tube resonances, that satisfy the selection
rule , with an integer. We discuss possible
experimental conditions where these oscillations may be observed.Comment: 11 pages REVTE
Spectral properties on a circle with a singularity
We investigate the spectral and symmetry properties of a quantum particle
moving on a circle with a pointlike singularity (or point interaction). We find
that, within the U(2) family of the quantum mechanically allowed distinct
singularities, a U(1) equivalence (of duality-type) exists, and accordingly the
space of distinct spectra is U(1) x [SU(2)/U(1)], topologically a filled torus.
We explore the relationship of special subfamilies of the U(2) family to
corresponding symmetries, and identify the singularities that admit an N = 2
supersymmetry. Subfamilies that are distinguished in the spectral properties or
the WKB exactness are also pointed out. The spectral and symmetry properties
are also studied in the context of the circle with two singularities, which
provides a useful scheme to discuss the symmetry properties on a general basis.Comment: TeX, 26 pages. v2: one reference added and two update
Particle Production near an AdS Crunch
We numerically study the dual field theory evolution of five-dimensional
asymptotically anti-de Sitter solutions of supergravity that develop
cosmological singularities. The dual theory is an unstable deformation of the N
= 4 gauge theory on R S3, and the big crunch singularity in the bulk
occurs when a boundary scalar field runs to infinity. Consistent quantum
evolution requires one imposes boundary conditions at infinity. Modeling these
by a steep regularization of the scalar potential, we find that when an
initially nearly homogeneous wavepacket rolls down the potential, most of the
potential energy of the initial configuration is converted into gradient energy
during the first oscillation of the field. This indicates there is no
transition from a big crunch to a big bang in the bulk for dual boundary
conditions of this kind.Comment: 20 pages, 6 figure
The regulated four parameter one dimensional point interaction
The general four parameter point interaction in one dimensional quantum
mechanics is regulated. It allows the exact solution, but not the perturbative
one. We conjecture that this is due to the interaction not being asymptotically
free. We then propose a different breakup of unperturbed theory and
interaction, which now is asymptotically free but leads to the same physics.
The corresponding regulated potential can be solved both exactly and
perturbatively, in agreement with the conjecture.Comment: 17 pages, no figures, Tex fil
Comparing Formulations of Generalized Quantum Mechanics for Reparametrization-Invariant Systems
A class of decoherence schemes is described for implementing the principles
of generalized quantum theory in reparametrization-invariant `hyperbolic'
models such as minisuperspace quantum cosmology. The connection with
sum-over-histories constructions is exhibited and the physical equivalence or
inequivalence of different such schemes is analyzed. The discussion focuses on
comparing constructions based on the Klein-Gordon product with those based on
the induced (a.k.a. Rieffel, Refined Algebraic, Group Averaging, or Spectral
Analysis) inner product. It is shown that the Klein-Gordon and induced products
can be simply related for the models of interest. This fact is then used to
establish isomorphisms between certain decoherence schemes based on these
products.Comment: 21 pages ReVTe
Equivalence of Local and Separable Realizations of the Discontinuity-Inducing Contact Interaction and Its Perturbative Renormalizability
We prove that the separable and local approximations of the
discontinuity-inducing zero-range interaction in one-dimensional quantum
mechanics are equivalent. We further show that the interaction allows the
perturbative treatment through the coupling renormalization.
Keywords: one-dimensional system, generalized contact interaction,
renormalization, perturbative expansion. PACS Nos: 3.65.-w, 11.10.Gh, 31.15.MdComment: ReVTeX 7pgs, doubl column, no figure, See also the website
http://www.mech.kochi-tech.ac.jp/cheon
Green functions for generalized point interactions in 1D: A scattering approach
Recently, general point interactions in one dimension has been used to model
a large number of different phenomena in quantum mechanics. Such potentials,
however, requires some sort of regularization to lead to meaningful results.
The usual ways to do so rely on technicalities which may hide important
physical aspects of the problem. In this work we present a new method to
calculate the exact Green functions for general point interactions in 1D. Our
approach differs from previous ones because it is based only on physical
quantities, namely, the scattering coefficients, and , to construct .
Renormalization or particular mathematical prescriptions are not invoked. The
simple formulation of the method makes it easy to extend to more general
contexts, such as for lattices of general point interactions; on a line; on
a half-line; under periodic boundary conditions; and confined in a box.Comment: Revtex, 9 pages, 3 EPS figures. To be published in PR
Holographic renormalization as a canonical transformation
The gauge/string dualities have drawn attention to a class of variational
problems on a boundary at infinity, which are not well defined unless a certain
boundary term is added to the classical action. In the context of supergravity
in asymptotically AdS spaces these problems are systematically addressed by the
method of holographic renormalization. We argue that this class of a priori ill
defined variational problems extends far beyond the realm of holographic
dualities. As we show, exactly the same issues arise in gravity in non
asymptotically AdS spaces, in point particles with certain unbounded from below
potentials, and even fundamental strings in flat or AdS backgrounds. We show
that the variational problem in all such cases can be made well defined by the
following procedure, which is intrinsic to the system in question and does not
rely on the existence of a holographically dual theory: (i) The first step is
the construction of the space of the most general asymptotic solutions of the
classical equations of motion that inherits a well defined symplectic form from
that on phase space. The requirement of a well defined symplectic form is
essential and often leads to a necessary repackaging of the degrees of freedom.
(ii) Once the space of asymptotic solutions has been constructed in terms of
the correct degrees of freedom, then there exists a boundary term that is
obtained as a certain solution of the Hamilton-Jacobi equation which
simultaneously makes the variational problem well defined and preserves the
symplectic form. This procedure is identical to holographic renormalization in
the case of asymptotically AdS gravity, but it is applicable to any Hamiltonian
system.Comment: 37 pages; v2 minor corrections in section 2, 2 references and a
footnote on Palatini gravity added. Version to appear in JHE
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