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Adsorption of Hg on lunar samples
Understanding the presence, migration mechanisms and trapping of indigneous gases and volatiles on the moon is the objective of this study. The rare gases Ar and Xe and highly volatile Hg/sup 0/ and Br/sup 0/ (and/or their compounds) have been determined to be present in the lunar regolith. Evidence for these elements in the moon was recently reviewed. Studies of the sorption behavior of Xe on lunar material have been carried out. We report here preliminary results of a study designed to rationalize the behavior of Hg in lunar material
Quantum mechanics on manifolds and topological effects
A unique classification of the topological effects associated to quantum
mechanics on manifolds is obtained on the basis of the invariance under
diffeomorphisms and the realization of the Lie-Rinehart relations between the
generators of the diffeomorphism group and the algebra of infinitely
differentiable functions on the manifold. This leads to a unique
("Lie-Rinehart") C* algebra as observable algebra; its regular representations
are shown to be locally Schroedinger and in one to one correspondence with the
unitary representations of the fundamental group of the manifold. Therefore, in
the absence of spin degrees of freedom and external fields, the first homotopy
group of the manifold appears as the only source of topological effects.Comment: A few comments have been added to the Introduction, together with
related references; a few words have been changed in the Abstract and a Note
added to the Titl
Fluctuations of Matrix Entries of Regular Functions of Wigner Matrices
We study the fluctuations of the matrix entries of regular functions of
Wigner random matrices in the limit when the matrix size goes to infinity. In
the case of the Gaussian ensembles (GOE and GUE) this problem was considered by
A.Lytova and L.Pastur in J. Stat. Phys., v.134, 147-159 (2009). Our results are
valid provided the off-diagonal matrix entries have finite fourth moment, the
diagonal matrix entries have finite second moment, and the test functions have
four continuous derivatives in a neighborhood of the support of the Wigner
semicircle law.Comment: minor corrections; the manuscript will appear in the Journal of
Statistical Physic
Molecular materials from 1,3,2-dithiazolyls. Solid-state structures and magnetic properties of 2,3-naphthalene and quinoxaline derivatives
Edge Currents in Non-commutative Chern-Simons Theory from a New Matrix Model
This paper discusses the formulation of the non-commutative Chern-Simons (CS)
theory where the spatial slice, an infinite strip, is a manifold with
boundaries. As standard star products are not correct for such manifolds, the
standard non-commutative CS theory is not also appropriate here. Instead we
formulate a new finite-dimensional matrix CS model as an approximation to the
CS theory on the strip. A work which has points of contact with ours is due to
Lizzi, Vitale and Zampini where the authors obtain a description for the fuzzy
disc. The gauge fields in our approach are operators supported on a subspace of
finite dimension N+\eta of the Hilbert space of eigenstates of a simple
harmonic oscillator with N, \eta \in Z^+ and N \neq 0. This oscillator is
associated with the underlying Moyal plane. The resultant matrix CS theory has
a fuzzy edge. It becomes the required sharp edge when N and \eta goes to
infinity in a suitable sense. The non-commutative CS theory on the strip is
defined by this limiting procedure. After performing the canonical constraint
analysis of the matrix theory, we find that there are edge observables in the
theory generating a Lie algebra with properties similar to that of a
non-abelian Kac-Moody algebra. Our study shows that there are (\eta+1)^2
abelian charges (observables) given by the matrix elements (\cal A_i)_{N-1 N-1}
and (\cal A_i)_{nm} (where n or m \geq N) of the gauge fields, that obey
certain standard canonical commutation relations. In addition, the theory
contains three unique non-abelian charges, localized near the N^th level. We
show that all non-abelian edge observables except these three can be
constructed from the abelian charges above. Using the results of this analysis
we discuss the large N and \eta limit.Comment: LaTeX, 16 pages and 2 figures. Comments added in sections 4 and 5. A
minor error corrected in section 4. Figures replaced for clarity. Typos
correcte
Imprints of the Quantum World in Classical Mechanics
The imprints left by quantum mechanics in classical (Hamiltonian) mechanics
are much more numerous than is usually believed. We show Using no physical
hypotheses) that the Schroedinger equation for a nonrelativistic system of
spinless particles is a classical equation which is equivalent to Hamilton's
equations.Comment: Paper submitted to Foundations of Physic
Convergence to SPDEs in Stratonovich form
We consider the perturbation of parabolic operators of the form
by large-amplitude highly oscillatory spatially dependent
potentials modeled as Gaussian random fields. The amplitude of the potential is
chosen so that the solution to the random equation is affected by the
randomness at the leading order. We show that, when the dimension is smaller
than the order of the elliptic pseudo-differential operator , the
perturbed parabolic equation admits a solution given by a Duhamel expansion.
Moreover, as the correlation length of the potential vanishes, we show that the
latter solution converges in distribution to the solution of a stochastic
parabolic equation with a multiplicative term that should be interpreted in the
Stratonovich sense. The theory of mild solutions for such stochastic partial
differential equations is developed. The behavior described above should be
contrasted to the case of dimensions that are larger than or equal to the order
of the elliptic pseudo-differential operator . In the latter case, the
solution to the random equation converges strongly to the solution of a
homogenized (deterministic) parabolic equation as is shown in the companion
paper [2]. The stochastic model is therefore valid only for sufficiently small
space dimensions in this class of parabolic problems.Comment: 21 page
Bessel Process and Conformal Quantum Mechanics
Different aspects of the connection between the Bessel process and the
conformal quantum mechanics (CQM) are discussed. The meaning of the possible
generalizations of both models is investigated with respect to the other model,
including self adjoint extension of the CQM. Some other generalizations such as
the Bessel process in the wide sense and radial Ornstein- Uhlenbeck process are
discussed with respect to the underlying conformal group structure.Comment: 28 Page
Composite Fermion Description of Correlated Electrons in Quantum Dots: Low Zeeman Energy Limit
We study the applicability of composite fermion theory to electrons in
two-dimensional parabolically-confined quantum dots in a strong perpendicular
magnetic field in the limit of low Zeeman energy. The non-interacting composite
fermion spectrum correctly specifies the primary features of this system.
Additional features are relatively small, indicating that the residual
interaction between the composite fermions is weak. \footnote{Published in
Phys. Rev. B {\bf 52}, 2798 (1995).}Comment: 15 pages, 7 postscript figure
On the lattice structure of probability spaces in quantum mechanics
Let C be the set of all possible quantum states. We study the convex subsets
of C with attention focused on the lattice theoretical structure of these
convex subsets and, as a result, find a framework capable of unifying several
aspects of quantum mechanics, including entanglement and Jaynes' Max-Ent
principle. We also encounter links with entanglement witnesses, which leads to
a new separability criteria expressed in lattice language. We also provide an
extension of a separability criteria based on convex polytopes to the infinite
dimensional case and show that it reveals interesting facets concerning the
geometrical structure of the convex subsets. It is seen that the above
mentioned framework is also capable of generalization to any statistical theory
via the so-called convex operational models' approach. In particular, we show
how to extend the geometrical structure underlying entanglement to any
statistical model, an extension which may be useful for studying correlations
in different generalizations of quantum mechanics.Comment: arXiv admin note: substantial text overlap with arXiv:1008.416
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