1,864 research outputs found
Approximate Selection Rule for Orbital Angular Momentum in Atomic Radiative Transitions
We demonstrate that radiative transitions with \Delta l = - 1 are strongly
dominating for all values of n and l, except small region where l << n.Comment: 5 pages, 1 figur
On the number of cubic orders of bounded discriminant having automorphism group , and related problems
For a binary quadratic form , we consider the action of on
a two-dimensional vector space. This representation yields perhaps the simplest
nontrivial example of a prehomogeneous vector space that is not irreducible,
and of a coregular space whose underlying group is not semisimple. We show that
the nondegenerate integer orbits of this representation are in natural
bijection with orders in cubic fields having a fixed "lattice shape". Moreover,
this correspondence is discriminant-preserving: the value of the invariant
polynomial of an element in this representation agrees with the discriminant of
the corresponding cubic order.
We use this interpretation of the integral orbits to solve three
classical-style counting problems related to cubic orders and fields. First, we
give an asymptotic formula for the number of cubic orders having bounded
discriminant and nontrivial automorphism group. More generally, we give an
asymptotic formula for the number of cubic orders that have bounded
discriminant and any given lattice shape (i.e., reduced trace form, up to
scaling). Via a sieve, we also count cubic fields of bounded discriminant whose
rings of integers have a given lattice shape. We find, in particular, that
among cubic orders (resp. fields) having lattice shape of given discriminant
, the shape is equidistributed in the class group of binary
quadratic forms of discriminant . As a by-product, we also obtain an
asymptotic formula for the number of cubic fields of bounded discriminant
having any given quadratic resolvent field.Comment: 33 page
ac Stark shift and multiphoton-like resonances in low-frequency driven optical lattices
We suggest that Bose-Einstein condensates in optical lattices subjected to ac
forcing with a smooth envelope may provide detailed experimental access to
multiphoton-like transitions between ac-Stark-shifted Bloch bands. Such
transitions correspond to resonances described theoretically by avoided
quasienergy crossings. We show that the width of such anticrossings can be
inferred from measurements involving asymmetric pulses. We also introduce a
pulse tracking strategy for locating the particular driving amplitudes for
which resonances occur. Our numerical calculations refer to a currently
existing experimental set-up [Haller et al., PRL 104, 200403 (2010)].Comment: 5 pages, 6 figure
Analytical solution to the Schrodinger equation of a laser-driven correlated two-particle system
The time-dependent quantum system of two laser-driven electrons in a harmonic
oscillator potential is analysed, taking into account the repulsive Coulomb
interaction between both particles. The Schrodinger equation of the
two-particle system is shown to be analytically soluble in case of arbitrary
laser frequencies and individual oscillator frequencies, defining the system.
Quantum information processing could be a possible field of applicationComment: 5 page
Firm Size and the Characteristics of Computer Use
Although researchers have examined the differences between managing large and small businesses, few studies have explored these differences in terms of managing the use of computers. Nearly all of the important MIS research is being conducted in large organizations. The results of these research efforts may not apply to smaller firms if their MIS environments are indeed different. Thus, the present focus of most MIS research may be missing the needs and problems of thousands of small business users. Several MIS articles suggest that smal I businesses face unique problems in the management of their computer resources, but thus far the evidence cited is anecdotal. Few research efforts have studied this issue scientifically. This study tests the contention that small businesses use computers differently than large businesses by examining a sample of Los Angeles manufacturing firms of various sizes
Unitary theory of laser Carrier-Envelope Phase effects
We consider a quantum state interacting with a short intense linearly
polarized laser pulse. Using the two-dimensional time representation and
Floquet picture we establish a straightforward connection between the laser
carrier-envelope phase (CEP) and the wave function. This connection is revealed
as a unitary transformation in the space of Floquet components. It allows any
CEP effect to be interpreted as an interference between the components and to
put limits on using the CEP in coherent control. A 2-level system is used to
illustrate the theory. On this example we demonstrate strong intensity
sensitivity of the CEP effects and predict an effect for pulses much longer
than the oscillation period of the carrier.Comment: 13 pages, 4 figure
Inverse Landau-Zener-Stuckelberg problem for qubit-resonator systems
We consider theoretically a superconducting qubit - nanomechanical resonator
(NR) system, which was realized by LaHaye et al. [Nature 459, 960 (2009)].
First, we study the problem where the state of the strongly driven qubit is
probed through the frequency shift of the low-frequency NR. In the case where
the coupling is capacitive, the measured quantity can be related to the
so-called quantum capacitance. Our theoretical results agree with the
experimentally observed result that, under resonant driving, the frequency
shift repeatedly changes sign. We then formulate and solve the inverse
Landau-Zener-Stuckelberg problem, where we assume the driven qubit's state to
be known (i.e. measured by some other device) and aim to find the parameters of
the qubit's Hamiltonian. In particular, for our system the qubit's bias is
defined by the NR's displacement. This may provide a tool for monitoring of the
NR's position.Comment: 10 pages, 7 figure
Orbital L-functions for the space of binary cubic forms
We introduce the notion of orbital L-functions for the space of binary cubic
forms and investigate their analytic properties. We study their functional
equations and residue formulas in some detail. Aside from the intrinsic
interest, results from this paper are used to prove the existence of secondary
terms in counting functions for cubic fields. This is worked out in a companion
paper (arXiv:1102.2914).Comment: 49 pages; submitte
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