5,108 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
Stress versus temperature dependent activation energies in creep
The activation energy for creep at low stresses and elevated temperatures is lattice diffusion, where the rate controlling mechanism for deformation is dislocation climb. At higher stresses and intermediate temperatures, the rate controlling mechanism changes from that of dislocation climb to one of obstacle-controlled dislocation glide. Along with this change, there occurs a change in the activation energy. It is shown that a temperature-dependent Gibbs free energy does a good job of correlating steady-state creep data, while a stress-dependent Gibbs free energy does a less desirable job of correlating the same data. Applications are made to copper and a LiF-22 mol. percent CaF2 hypereutectic salt
Special complex manifolds
We introduce the notion of a special complex manifold: a complex manifold
(M,J) with a flat torsionfree connection \nabla such that (\nabla J) is
symmetric. A special symplectic manifold is then defined as a special complex
manifold together with a \nabla-parallel symplectic form \omega . This
generalises Freed's definition of (affine) special K\"ahler manifolds. We also
define projective versions of all these geometries. Our main result is an
extrinsic realisation of all simply connected (affine or projective) special
complex, symplectic and K\"ahler manifolds. We prove that the above three types
of special geometry are completely solvable, in the sense that they are locally
defined by free holomorphic data. In fact, any special complex manifold is
locally realised as the image of a holomorphic 1-form \alpha : C^n \to T^* C^n.
Such a realisation induces a canonical \nabla-parallel symplectic structure on
M and any special symplectic manifold is locally obtained this way. Special
K\"ahler manifolds are realised as complex Lagrangian submanifolds and
correspond to closed forms \alpha. Finally, we discuss the natural geometric
structures on the cotangent bundle of a special symplectic manifold, which
generalise the hyper-K\"ahler structure on the cotangent bundle of a special
K\"ahler manifold.Comment: 24 pages, latex, section 3 revised (v2), modified Abstract and
Introduction, version to appear in J. Geom. Phy
Nilpotent Classical Mechanics
The formalism of nilpotent mechanics is introduced in the Lagrangian and
Hamiltonian form. Systems are described using nilpotent, commuting coordinates
. Necessary geometrical notions and elements of generalized differential
-calculus are introduced. The so called geometry, in a special case
when it is orthogonally related to a traceless symmetric form, shows some
resemblances to the symplectic geometry. As an example of an -system the
nilpotent oscillator is introduced and its supersymmetrization considered. It
is shown that the -symmetry known for the Graded Superfield Oscillator (GSO)
is present also here for the supersymmetric -system. The generalized
Poisson bracket for -variables satisfies modified Leibniz rule and
has nontrivial Jacobiator.Comment: 23 pages, no figures. Corrected version. 2 references adde
T-duality and Differential K-Theory
We give a precise formulation of T-duality for Ramond-Ramond fields. This
gives a canonical isomorphism between the "geometrically invariant" subgroups
of the twisted differential K-theory of certain principal torus bundles. Our
result combines topological T-duality with the Buscher rules found in physics.Comment: 23 pages, typos corrected, submitted to Comm.Math.Phy
M-theory and Characteristic Classes
In this note we show that the Chern-Simons and the one-loop terms in the
M-theory action can be written in terms of new characters involving the
M-theory four-form and the string classes. This sheds a new light on the
topological structure behind M-theory and suggests the construction of a theory
of `higher' characteristic classes.Comment: 8 pages. Error in gravitational term fixed; minor corrections;
reference and acknowledgement adde
Charge Lattices and Consistency of 6D Supergravity
We extend the known consistency conditions on the low-energy theory of
six-dimensional N = 1 supergravity. We review some facts about the theory of
two-form gauge fields and conclude that the charge lattice Gamma for such a
theory has to be self-dual. The Green-Schwarz anomaly cancellation conditions
in the supergravity theory determine a sublattice of Gamma. The condition that
this sublattice can be extended to a self-dual lattice Gamma leads to a strong
constraint on theories that otherwise appear to be self-consistent.Comment: 15 pages. v2: minor changes; references, additional example added;
v3: minor corrections and clarifications added, JHEP versio
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
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