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 C3C_3, and related problems

For a binary quadratic form $Q$, we consider the action of $\mathrm{SO}_Q$ 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 $D$, the shape is equidistributed in the class group $\mathrm{Cl}_D$ of binary quadratic forms of discriminant $D$. 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