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 $\eta$. Necessary geometrical notions and elements of generalized differential $\eta$-calculus are introduced. The so called $s-$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 $\eta$-system the nilpotent oscillator is introduced and its supersymmetrization considered. It is shown that the $R$-symmetry known for the Graded Superfield Oscillator (GSO) is present also here for the supersymmetric $\eta$-system. The generalized Poisson bracket for $(\eta,p)$-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