Spin critical opalescence in zero temperature Bose-Einstein Condensates

Cold atom developments suggest the prospect of measuring scaling properties and long-range fluctuations of continuous phase transitions at zero-temperature. We discuss the conditions for characterizing the phase separation of Bose-Einstein condensates of boson atoms in two distinct hyperfine spin states. The mean-field description breaks down as the system approaches the transition from the miscible side. An effective spin description clarifies the ferromagnetic nature of the transition. We show that a difference in the scattering lengths for the bosons in the same spin state leads to an effective internal magnetic field. The conditions at which the internal magnetic field vanishes (i.e., equal values of the like-boson scattering lengths) is a special point. We show that the long range density fluctuations are suppressed near that point while the effective spin exhibits the long-range fluctuations that characterize critical points. The zero-temperature system exhibits critical opalescence with respect to long wavelength waves of impurity atoms that interact with the bosons in a spin-dependent manner.Comment: 6 pages, 2 figure

Modelling decision tables from data.

On most datasets induction algorithms can generate very accurate classifiers. Sometimes, however, these classifiers are very hard to understand for humans. Therefore, in this paper it is investigated how we can present the extracted knowledge to the user by means of decision tables. Decision tables are very easy to understand. Furthermore, decision tables provide interesting facilities to check the extracted knowledge on consistency and completeness. In this paper, it is demonstrated how a consistent and complete DT can be modelled starting from raw data. The proposed method is empirically validated on several benchmarking datasets. It is shown that the modelling decision tables are sufficiently small. This allows easy consultation of the represented knowledge.Data;

Molecule formation as a diagnostic tool for second order correlations of ultra-cold gases

We calculate the momentum distribution and the second-order correlation function in momentum space, $g^{(2)}({\bf p},{\bf p}',t)$ for molecular dimers that are coherently formed from an ultracold atomic gas by photoassociation or a Feshbach resonance. We investigate using perturbation theory how the quantum statistics of the molecules depend on the initial state of the atoms by considering three different initial states: a Bose-Einstein condensate (BEC), a normal Fermi gas of ultra-cold atoms, and a BCS-type superfluid Fermi gas. The cases of strong and weak coupling to the molecular field are discussed. It is found that BEC and BCS states give rise to an essentially coherent molecular field with a momentum distribution determined by the zero-point motion in the confining potential. On the other hand, a normal Fermi gas and the unpaired atoms in the BCS state give rise to a molecular field with a broad momentum distribution and thermal number statistics. It is shown that the first-order correlations of the molecules can be used to measure second-order correlations of the initial atomic state.Comment: revtex, 15 pages,8 figure

Lorentz violation in neutron and allowed nuclear beta decay

We explore the possibility that the weak interaction violates Lorentz, and in particular rotational, invariance in neutron and allowed nuclear beta decay. A broad class of Lorentz-violating effects is considered, in which the standard propagator of the W-boson acquires an additional Lorentz-violating tensor. The general decay rate for allowed beta decay that incorporates such a modified propagator is derived. The resulting Lorentz-violating signals are discussed for the different types of beta-decay transitions, Fermi, Gamow-Teller, and mixed. We study the implications of our formalism for dedicated beta-decay experiments. We give a short overview of the few relevant experiments that have been performed or are ongoing.Comment: 23 pages; added reference

Limits on Lorentz violation in neutral-Kaon decay

The KLOE collaboration recently reported bounds on the directional dependence of the lifetime of the short-lived neutral kaon K_S with respect to the cosmic microwave background dipole anisotropy. We interpret their results in a general framework developed to probe Lorentz violation in the weak interaction. In this approach a Lorentz-violating tensor \chi_{\mu\nu} is added to the standard propagator of the W boson. We derive the K_S decay rate in a naive tree-level model and calculate the asymmetry for the lifetime. By using the KLOE data the real vector part of \chi_{\mu\nu} is found to be smaller than 10^-2. We briefly discuss the theoretical challenges concerning nonleptonic decays.Comment: Presented at the Sixth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 17-21, 2013

Regression sampling in statistical auditing

Auditing;Regression Analysis;accountancy

Nuclear beta decay with Lorentz violation

We consider the possibility of Lorentz-invariance violation in weak-decay processes. We present a general approach that entails modifying the W-boson propagator by adding a Lorentz-violating tensor to it. We describe the effects of Lorentz violation on nuclear beta decay in this scenario. In particular we show the expression for a first-forbidden transition with a spin change of two. Using data from an old experiment on the rotational invariance of yttrium-90, we derive several bounds on the Lorentz-violating parameters of the order of 10^(-6)-10^(-8).Comment: 4 pages; presented at the Sixth Meeting on CPT and Lorentz Symmetry, Bloomington, Indiana, June 17-21, 2013; Added reference

Symmetry violations in nuclear and neutron β\beta decay

The role of $\beta$ decay as a low-energy probe of physics beyond the Standard Model is reviewed. Traditional searches for deviations from the Standard Model structure of the weak interaction in $\beta$ decay are discussed in the light of constraints from the LHC and the neutrino mass. Limits on the violation of time-reversal symmetry in $\beta$ decay are compared to the strong constraints from electric dipole moments. Novel searches for Lorentz symmetry breaking in the weak interaction in $\beta$ decay are also included, where we discuss the unique sensitivity of $\beta$ decay to test Lorentz invariance. We end with a roadmap for future $\beta$-decay experiments.Comment: Accepted for publication in Rev. Mod. Phys. 86 pages, 13 figure

Testing Lorentz invariance in orbital electron capture

Searches for Lorentz violation were recently extended to the weak sector, in particular neutron and nuclear $\beta$ decay [1]. From experiments on forbidden $\beta$-decay transitions strong limits in the range of $10^{-6}$-$10^{-8}$ were obtained on Lorentz-violating components of the $W$-boson propagator [2]. In order to improve on these limits strong sources have to be considered. In this Brief Report we study isotopes that undergo orbital electron capture and allow experiments at high decay rates and low dose. We derive the expressions for the Lorentz-violating differential decay rate and discuss the options for competitive experiments and their required precision.Comment: accepted for publication as a Brief Report in Physical Review