63,793 research outputs found
Atom Lithography with Near-Resonant Light Masks: Quantum Optimization Analysis
We study the optimal focusing of two-level atoms with a near resonant
standing wave light, using both classical and quantum treatments of the
problem. Operation of the focusing setup is considered as a nonlinear spatial
squeezing of atoms in the thin- and thick-lens regimes. It is found that the
near-resonant standing wave focuses the atoms with a reduced background in
comparison with far-detuned light fields. For some parameters, the quantum
atomic distribution shows even better localization than the classical one.
Spontaneous emission effects are included via the technique of quantum Monte
Carlo wave function simulations. We investigate the extent to which
non-adiabatic and spontaneous emission effects limit the achievable minimal
size of the deposited structures.Comment: 10 pages including 11 figures in Revte
Translated tori in the characteristic varieties of complex hyperplane arrangements
We give examples of complex hyperplane arrangements for which the top
characteristic variety contains positive-dimensional irreducible components
that do not pass through the origin of the character torus. These examples
answer several questions of Libgober and Yuzvinsky. As an application, we
exhibit a pair of arrangements for which the resonance varieties of the
Orlik-Solomon algebra are (abstractly) isomorphic, yet whose characteristic
varieties are not isomorphic. The difference comes from translated components,
which are not detected by the tangent cone at the origin.Comment: Revised and expanded; 16 pages, 10 figures; to appear in Topology and
its Application
Characteristic varieties of arrangements
The k-th Fitting ideal of the Alexander invariant B of an arrangement A of n
complex hyperplanes defines a characteristic subvariety, V_k(A), of the complex
algebraic n-torus. In the combinatorially determined case where B decomposes as
a direct sum of local Alexander invariants, we obtain a complete description of
V_k(A). For any arrangement A, we show that the tangent cone at the identity of
this variety coincides with R^1_k(A), one of the cohomology support loci of the
Orlik-Solomon algebra. Using work of Arapura and Libgober, we conclude that all
positive-dimensional components of V_k(A) are combinatorially determined, and
that R^1_k(A) is the union of a subspace arrangement in C^n, thereby resolving
a conjecture of Falk. We use these results to study the reflection arrangements
associated to monomial groups.Comment: LaTeX2e, 20 pages. A reference to Libgober's recent work in
math.AG/9801070 is added. Several points are clarified, a new example is
include
- …