Resonant Processes in a Frozen Gas

We present a theory of resonant processes in a frozen gas of atoms interacting via dipole-dipole potentials that vary as $r^{-3}$, where $r$ is the interatomic separation. We supply an exact result for a single atom in a given state interacting resonantly with a random gas of atoms in a different state. The time development of the transition process is calculated both on- and off-resonance, and the linewidth with respect to detuning is obtained as a function of time $t$. We introduce a random spin Hamiltonian to model a dense system of resonators and show how it reduces to the previous model in the limit of a sparse system. We derive approximate equations for the average effective spin, and we use them to model the behavior seen in the experiments of Anderson et al. and Lowell et al. The approach to equilibrium is found to be proportional to $\exp (-\sqrt{\gamma_{eq}t}$), where the constant $\gamma _{eq}$ is explicitly related to the system's parameters.Comment: 30 pages, 6 figure

Monomial Testing and Applications

In this paper, we devise two algorithms for the problem of testing $q$-monomials of degree $k$ in any multivariate polynomial represented by a circuit, regardless of the primality of $q$. One is an $O^*(2^k)$ time randomized algorithm. The other is an $O^*(12.8^k)$ time deterministic algorithm for the same $q$-monomial testing problem but requiring the polynomials to be represented by tree-like circuits. Several applications of $q$-monomial testing are also given, including a deterministic $O^*(12.8^{mk})$ upper bound for the $m$-set $k$-packing problem.Comment: 17 pages, 4 figures, submitted FAW-AAIM 2013. arXiv admin note: substantial text overlap with arXiv:1302.5898; and text overlap with arXiv:1007.2675, arXiv:1007.2678, arXiv:1007.2673 by other author

Polarization dependent photoionization cross-sections and radiative lifetimes of atomic states in Ba

The photoionization cross-sections of two even-parity excited states, $5d6d ^3D_1$ and $6s7d ^3D_{2}$, of atomic Ba at the ionization-laser wavelength of 556.6 nm were measured. We found that the total cross-section depends on the relative polarization of the atoms and the ionization-laser light. With density-matrix algebra, we show that, in general, there are at most three parameters in the photoionization cross-section. Some of these parameters are determined in this work. We also present the measurement of the radiative lifetime of five even-parity excited states of barium.Comment: 11 pages, 7 figure

Transport properties of double-walled carbon nanotube quantum dots

The transport properties of quantum dot (QD) systems based on double-walled carbon nanotube (DWCNT) are investigated. The interplay between microscopic structure and strong Coulomb interaction is treated within a bosonization framework. The linear and nonlinear G-V-V_g characteristics of the QD system is calculated by starting from the Liouville equation for the reduced density matrix. Depending on the intershell couplings, an 8-electron periodicity of the Coulomb blockade peak spacing in the case of commensurate DWCNT QDs and a 4-electron periodicity in the incommensurate case are predicted. The contribution of excited states of DWCNTs to the nonlinear transport is investigated as well.Comment: 18 pages, 7 figure

Testing formula satisfaction

We study the query complexity of testing for properties defined by read once formulae, as instances of massively parametrized properties, and prove several testability and non-testability results. First we prove the testability of any property accepted by a Boolean read-once formula involving any bounded arity gates, with a number of queries exponential in \epsilon and independent of all other parameters. When the gates are limited to being monotone, we prove that there is an estimation algorithm, that outputs an approximation of the distance of the input from satisfying the property. For formulae only involving And/Or gates, we provide a more efficient test whose query complexity is only quasi-polynomial in \epsilon. On the other hand we show that such testability results do not hold in general for formulae over non-Boolean alphabets; specifically we construct a property defined by a read-once arity 2 (non-Boolean) formula over alphabets of size 4, such that any 1/4-test for it requires a number of queries depending on the formula size

Mutual independence of critical temperature and superfluid density under pressure in optimally electron-doped superconducting LaFeAsO1−x_{1-x}Fx_{x}

The superconducting properties of LaFeAsO$_{1-x}$F$_{x}$ in conditions of optimal electron-doping are investigated upon the application of external pressure up to $\sim 23$ kbar. Measurements of muon-spin spectroscopy and dc magnetometry evidence a clear mutual independence between the critical temperature $T_{c}$ and the low-temperature saturation value for the ratio $n_{s}/m^{*}$ (superfluid density over effective band mass of Cooper pairs). Remarkably, a dramatic increase of $\sim 30$ % is reported for $n_{s}/m^{*}$ at the maximum pressure value while $T_{c}$ is substantially unaffected in the whole accessed experimental window. We argue and demonstrate that the explanation for the observed results must take the effect of non-magnetic impurities on multi-band superconductivity into account. In particular, the unique possibility to modify the ratio between intra-band and inter-bands scattering rates by acting on structural parameters while keeping the amount of chemical disorder constant is a striking result of our proposed model.Comment: 8 pages (Main text: 5 pages. Paper merged with supplemental information), 5 figure

Tight bounds for classical and quantum coin flipping

Coin flipping is a cryptographic primitive for which strictly better protocols exist if the players are not only allowed to exchange classical, but also quantum messages. During the past few years, several results have appeared which give a tight bound on the range of implementable unconditionally secure coin flips, both in the classical as well as in the quantum setting and for both weak as well as strong coin flipping. But the picture is still incomplete: in the quantum setting, all results consider only protocols with perfect correctness, and in the classical setting tight bounds for strong coin flipping are still missing. We give a general definition of coin flipping which unifies the notion of strong and weak coin flipping (it contains both of them as special cases) and allows the honest players to abort with a certain probability. We give tight bounds on the achievable range of parameters both in the classical and in the quantum setting.Comment: 18 pages, 2 figures; v2: published versio

Aspects of Type 0 String Theory

A construction of compact tachyon-free orientifolds of the non-supersymmetric Type 0B string theory is presented. Moreover, we study effective non-supersymmetric gauge theories arising on self-dual D3-branes in Type 0B orbifolds and orientifolds.Comment: 9 pages, LATEX; submitted to Proceedings of Strings '9