4,558 research outputs found
Gravitational quantum states of neutrons in a rough waveguide
A theory of gravitational quantum states of ultracold neutrons in waveguides
with absorbing/scattering walls is presented. The theory covers recent
experiments in which the ultracold neutrons were beamed between a mirror and a
rough scatterer/absorber. The analysis is based on a recently developed theory
of quantum transport along random rough walls which is modified in order to
include leaky (absorbing) interfaces and, more importantly, the low-amplitude
high-aperture roughness. The calculations are focused on a regime when the
direct transitions into the continuous spectrum above the absorption threshold
dominate the depletion of neutrons from the gravitational states and are more
efficient than the processes involving the intermediate states. The theoretical
results for the neutron count are sensitive to the correlation radius (lateral
size) of surface inhomogeneities and to the ratio of the particle energy to the
absorption threshold in a weak roughness limit. The main impediment for
observation of the higher gravitational states is the "overhang" of the
particle wave functions which can be overcome only by use scatterers with
strong roughness. In general, the strong roughness with high amplitude is
preferable if one wants just to detect the individual gravitational states,
while the strong roughness experiments with small amplitude and high aperture
are preferable for the quantitative analysis of the data. We also discuss the
ways to further improve the accuracy of calculations and to optimize the
experimental regime.Comment: 48 pages, 14 figure
The Elliptic curves in gauge theory, string theory, and cohomology
Elliptic curves play a natural and important role in elliptic cohomology. In
earlier work with I. Kriz, thes elliptic curves were interpreted physically in
two ways: as corresponding to the intersection of M2 and M5 in the context of
(the reduction of M-theory to) type IIA and as the elliptic fiber leading to
F-theory for type IIB. In this paper we elaborate on the physical setting for
various generalized cohomology theories, including elliptic cohomology, and we
note that the above two seemingly unrelated descriptions can be unified using
Sen's picture of the orientifold limit of F-theory compactification on K3,
which unifies the Seiberg-Witten curve with the F-theory curve, and through
which we naturally explain the constancy of the modulus that emerges from
elliptic cohomology. This also clarifies the orbifolding performed in the
previous work and justifies the appearance of the w_4 condition in the elliptic
refinement of the mod 2 part of the partition function. We comment on the
cohomology theory needed for the case when the modular parameter varies in the
base of the elliptic fibration.Comment: 23 pages, typos corrected, minor clarification
Holomorphic Supercurves and Supersymmetric Sigma Models
We introduce a natural generalisation of holomorphic curves to morphisms of
supermanifolds, referred to as holomorphic supercurves. More precisely,
supercurves are morphisms from a Riemann surface, endowed with the structure of
a supermanifold which is induced by a holomorphic line bundle, to an ordinary
almost complex manifold. They are called holomorphic if a generalised
Cauchy-Riemann condition is satisfied. We show, by means of an action identity,
that holomorphic supercurves are special extrema of a supersymmetric action
functional.Comment: 30 page
Duality symmetry and the form fields of M-theory
In previous work we derived the topological terms in the M-theory action in
terms of certain characters that we defined. In this paper, we propose the
extention of these characters to include the dual fields. The unified treatment
of the M-theory four-form field strength and its dual leads to several
observations. In particular we elaborate on the possibility of a twisted
cohomology theory with a twist given by degrees greater than three.Comment: 12 pages, modified material on the differentia
Drinfeld-Manin Instanton and Its Noncommutative Generalization
The Drinfeld-Manin construction of U(N) instanton is reformulated in the ADHM
formulism, which gives explicit general solutions of the ADHM constraints for
U(N) (N>=2k-1) k-instantons. For the N<2k-1 case, implicit results are given
systematically as further constraints, which can be used to the collective
coordinate integral. We find that this formulism can be easily generalized to
the noncommutative case, where the explicit solutions are as well obtained.Comment: 17 pages, LaTeX, references added, mailing address added,
clarifications adde
The curvature of semidirect product groups associated with two-component Hunter-Saxton systems
In this paper, we study two-component versions of the periodic Hunter-Saxton
equation and its -variant. Considering both equations as a geodesic flow
on the semidirect product of the circle diffeomorphism group \Diff(\S) with a
space of scalar functions on we show that both equations are locally
well-posed. The main result of the paper is that the sectional curvature
associated with the 2HS is constant and positive and that 2HS allows for a
large subspace of positive sectional curvature. The issues of this paper are
related to some of the results for 2CH and 2DP presented in [J. Escher, M.
Kohlmann, and J. Lenells, J. Geom. Phys. 61 (2011), 436-452].Comment: 19 page
A note on multi-dimensional Camassa-Holm type systems on the torus
We present a -component nonlinear evolutionary PDE which includes the
-dimensional versions of the Camassa-Holm and the Hunter-Saxton systems as
well as their partially averaged variations. Our goal is to apply Arnold's
[V.I. Arnold, Sur la g\'eom\'etrie diff\'erentielle des groupes de Lie de
dimension infinie et ses applications \`a l'hydrodynamique des fluides
parfaits. Ann. Inst. Fourier (Grenoble) 16 (1966) 319-361], [D.G. Ebin and J.E.
Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid.
Ann. of Math. 92(2) (1970) 102-163] geometric formalism to this general
equation in order to obtain results on well-posedness, conservation laws or
stability of its solutions. Following the line of arguments of the paper [M.
Kohlmann, The two-dimensional periodic -equation on the diffeomorphism group
of the torus. J. Phys. A.: Math. Theor. 44 (2011) 465205 (17 pp.)] we present
geometric aspects of a two-dimensional periodic --equation on the
diffeomorphism group of the torus in this context.Comment: 14 page
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