1,348 research outputs found
A Hardy inequality in twisted waveguides
We show that twisting of an infinite straight three-dimensional tube with
non-circular cross-section gives rise to a Hardy-type inequality for the
associated Dirichlet Laplacian. As an application we prove certain stability of
the spectrum of the Dirichlet Laplacian in locally and mildly bent tubes.
Namely, it is known that any local bending, no matter how small, generates
eigenvalues below the essential spectrum of the Laplacian in the tubes with
arbitrary cross-sections rotated along a reference curve in an appropriate way.
In the present paper we show that for any other rotation some critical strength
of the bending is needed in order to induce a non-empty discrete spectrum.Comment: LaTeX, 20 page
Spectrum of the Schr\"odinger operator in a perturbed periodically twisted tube
We study Dirichlet Laplacian in a screw-shaped region, i.e. a straight
twisted tube of a non-circular cross section. It is shown that a local
perturbation which consists of "slowing down" the twisting in the mean gives
rise to a non-empty discrete spectrum.Comment: LaTeX2e, 10 page
Neutrino scattering off pair-breaking and collective excitations in superfluid neutron matter and in color-flavor locked quark matter
We calculate the correlation functions needed to describe the linear response
of superfluid matter, and go on to calculate the differential cross section for
neutral-current neutrino scattering in superfluid neutron matter and in
color-flavor locked quark matter (CFL). We report the first calculation of
scattering rates that includes neutrino interactions with both pair-breaking
excitations and low-lying collective excitations (Goldstone modes). Our results
apply both above and below the critical temperature, allowing use in
simulations of neutrino transport in supernovae and neutron stars.Comment: 22 pages, 9 figure
Neutrino Masses and the Gluino Axion Model
We extend the recently proposed gluino axion model to include neutrino
masses. We discuss how the canonical seesaw model and the Higgs triplet model
may be realized in this framework. In the former case, the heavy singlet
neutrinos are contained in superfields which do not have any vacuum expectation
value, whereas the gluino axion is contained in one which does. We also
construct a specific renormalizable model which realizes the mass scale
relationship , where is the axion decay constant
and is a large effective mass parameter.Comment: 8 pages, no figur
Coupling curvature to a uniform magnetic field; an analytic and numerical study
The Schrodinger equation for an electron near an azimuthally symmetric curved
surface in the presence of an arbitrary uniform magnetic field
is developed. A thin layer quantization procedure is implemented to
bring the electron onto , leading to the well known geometric potential
and a second potential that couples , the component of
normal to to mean surface curvature, as well as a term
dependent on the normal derivative of
evaluated on . Numerical results in the form of ground state
energies as a function of the applied field in several orientations are
presented for a toroidal model.Comment: 12 pages, 3 figure
Effects of bariatric surgery and dietary interventions for obesity on brain neurotransmitter systems and metabolism: A systematic review of positron emission tomography (PET) and single‐photon emission computed tomography (SPECT) studies
Spatial search by quantum walk
Grover's quantum search algorithm provides a way to speed up combinatorial
search, but is not directly applicable to searching a physical database.
Nevertheless, Aaronson and Ambainis showed that a database of N items laid out
in d spatial dimensions can be searched in time of order sqrt(N) for d>2, and
in time of order sqrt(N) poly(log N) for d=2. We consider an alternative search
algorithm based on a continuous time quantum walk on a graph. The case of the
complete graph gives the continuous time search algorithm of Farhi and Gutmann,
and other previously known results can be used to show that sqrt(N) speedup can
also be achieved on the hypercube. We show that full sqrt(N) speedup can be
achieved on a d-dimensional periodic lattice for d>4. In d=4, the quantum walk
search algorithm takes time of order sqrt(N) poly(log N), and in d<4, the
algorithm does not provide substantial speedup.Comment: v2: 12 pages, 4 figures; published version, with improved arguments
for the cases where the algorithm fail
Once again on electromagnetic properties of a domain wall interacting with charged fermions
The response to a magnetic flux is considered of the vacuum state of charged
Dirac fermions interacting with a domain wall made of a neutral spinless field
in (3+1) dimensions with the fermion mass having a phase variation across the
wall. It is pointed out that due to simple C parity arguments the spontaneous
magnetization for this system is necessarily zero, thus invalidating some
claims to the contrary in the literature. The cancellation of the spontaneous
magnetization is explicitly demonstrated in a particular class of models. The
same calculation produces a general formula for the electric charge density
induced by the magnetic flux -- an effect previously discussed in the
literature for axionic domain walls. The distribution of the induced charge is
calculated in specific models.Comment: 15 page
Quantization of Field Theories Generalizing Gravity-Yang-Mills Systems on the Cylinder
Pure gravity and gauge theories in two dimensions are shown to be special
cases of a much more general class of field theories each of which is
characterized by a Poisson structure on a finite dimensional target space. A
general scheme for the quantization of these theories is formulated. Explicit
examples are studied in some detail. In particular gravity and gauge theories
with equivalent actions are compared. Big gauge transformations as well as the
condition of metric nondegeneracy in gravity turn out to cause significant
differences in the structure of the corresponding reduced phase spaces and the
quantum spectra of Dirac observables. For gravity coupled to SU(2) Yang
Mills the question of quantum dynamics (`problem of time') is addressed. [This
article is a contribution to the proceedings (to appear in LNP) of the 3rd
Baltic RIM Student Seminar (1993). Importance is attached to concrete examples.
A more abstract presentation of the ideas underlying this article (including
new developments) is found in hep-th/9405110.]Comment: 26, pages, TUW-94-
Curvature induced toroidal bound states
Curvature induced bound state (E < 0) eigenvalues and eigenfunctions for a
particle constrained to move on the surface of a torus are calculated. A limit
on the number of bound states a torus with minor radius a and major radius R
can support is obtained. A condition for mapping constrained particle wave
functions on the torus into free particle wave functions is established.Comment: 6 pages, no figures, Late
- …