Mott insulator to superfluid transition in the Bose-Hubbard model: a strong-coupling approach

We present a strong-coupling expansion of the Bose-Hubbard model which describes both the superfluid and the Mott phases of ultracold bosonic atoms in an optical lattice. By performing two successive Hubbard-Stratonovich transformations of the intersite hopping term, we derive an effective action which provides a suitable starting point to study the strong-coupling limit of the Bose-Hubbard model. This action can be analyzed by taking into account Gaussian fluctuations about the mean-field approximation as in the Bogoliubov theory of the weakly interacting Bose gas. In the Mott phase, we reproduce results of previous mean-field theories and also calculate the momentum distribution function. In the superfluid phase, we find a gapless spectrum and compare our results with the Bogoliubov theory.Comment: 8 pages, 6 figures; (v2) Two references adde

A New Scale to Measure War Attitudes: Construction and Predictors

Attitudes people have toward war in general have been of recent interest due to the war on terrorism and the war in Iraq. The purpose of this research was to develop a scale to measure war attitudes and to investigate factors that may influence these attitudes. In the first study, a scale was developed that measured war attitudes. Three factors emerging from the War Attitude Scale were labeled ethics of war, support for war, and affect about war. Patriotism-nationalism, authoritarianism, social criticism, belief in war outcomes, support of the president, and gender were found to be significant predictors of war attitudes. In the second study, the scale was administered to a community sample. A confirmatory factor analysis was conducted with three similar factors emerging. Additionally, the community sample results allowed further generalization of the findings. Implications for the construction of the War Attitude Scale and its predictors are discussed

Quantum criticality of a Bose gas in an optical lattice near the Mott transition

We derive the equation of state of bosons in an optical lattice in the framework of the Bose-Hubbard model. Near the density-driven Mott transition, the expression of the pressure P({\mu},T) versus chemical potential and temperature is similar to that of a dilute Bose gas but with renormalized mass m^* and scattering length a^*. m^* is the mass of the elementary excitations at the quantum critical point governing the transition from the superfluid phase to the Mott insulating phase, while a^* is related to their effective interaction at low energy. We use a nonperturbative renormalization-group approach to compute these parameters as a function of the ratio t/U between hopping amplitude and on-site repulsion.Comment: v1) 4 pages, 6 figures. v2) Significant rewriting (new title) with more emphasis on the quantum critical behavior near the Mott transitio

Importance Sampling for Multiscale Diffusions

We construct importance sampling schemes for stochastic differential equations with small noise and fast oscillating coefficients. Standard Monte Carlo methods perform poorly for these problems in the small noise limit. With multiscale processes there are additional complications, and indeed the straightforward adaptation of methods for standard small noise diffusions will not produce efficient schemes. Using the subsolution approach we construct schemes and identify conditions under which the schemes will be asymptotically optimal. Examples and simulation results are provided

Quantum non-malleability and authentication

In encryption, non-malleability is a highly desirable property: it ensures that adversaries cannot manipulate the plaintext by acting on the ciphertext. Ambainis, Bouda and Winter gave a definition of non-malleability for the encryption of quantum data. In this work, we show that this definition is too weak, as it allows adversaries to "inject" plaintexts of their choice into the ciphertext. We give a new definition of quantum non-malleability which resolves this problem. Our definition is expressed in terms of entropic quantities, considers stronger adversaries, and does not assume secrecy. Rather, we prove that quantum non-malleability implies secrecy; this is in stark contrast to the classical setting, where the two properties are completely independent. For unitary schemes, our notion of non-malleability is equivalent to encryption with a two-design (and hence also to the definition of Ambainis et al.). Our techniques also yield new results regarding the closely-related task of quantum authentication. We show that "total authentication" (a notion recently proposed by Garg, Yuen and Zhandry) can be satisfied with two-designs, a significant improvement over the eight-design construction of Garg et al. We also show that, under a mild adaptation of the rejection procedure, both total authentication and our notion of non-malleability yield quantum authentication as defined by Dupuis, Nielsen and Salvail.Comment: 20+13 pages, one figure. v2: published version plus extra material. v3: references added and update

Infrared behavior of interacting bosons at zero temperature

We review the infrared behavior of interacting bosons at zero temperature. After a brief discussion of the Bogoliubov approximation and the breakdown of perturbation theory due to infrared divergences, we present two approaches that are free of infrared divergences -- Popov's hydrodynamic theory and the non-perturbative renormalization group -- and allow us to obtain the exact infrared behavior of the correlation functions. We also point out the connection between the infrared behavior in the superfluid phase and the critical behavior at the superfluid--Mott-insulator transition in the Bose-Hubbard model.Comment: 8 pages, 4 figures. Proceedings of the 19th International Laser Physics Workshop, LPHYS'10 (Foz do Iguacu, Brazil, July 5-9, 2010

A Renormalization group approach for highly anisotropic 2D Fermion systems: application to coupled Hubbard chains

I apply a two-step density-matrix renormalization group method to the anisotropic two-dimensional Hubbard model. As a prelude to this study, I compare the numerical results to the exact one for the tight-binding model. I find a ground-state energy which agrees with the exact value up to four digits for systems as large as $24 \times 25$. I then apply the method to the interacting case. I find that for strong Hubbard interaction, the ground-state is dominated by magnetic correlations. These correlations are robust even in the presence of strong frustration. Interchain pair tunneling is negligible in the singlet and triplet channels and it is not enhanced by frustration. For weak Hubbard couplings, interchain non-local singlet pair tunneling is enhanced and magnetic correlations are strongly reduced. This suggests a possible superconductive ground state.Comment: 8 pages, 11 figures, expanded version of cond-mat/060856

Genome-Wide Association to Body Mass Index and Waist Circumference: The Framingham Heart Study 100K Project

BACKGROUND: Obesity is related to multiple cardiovascular disease (CVD) risk factors as well as CVD and has a strong familial component. We tested for association between SNPs on the Affymetrix 100K SNP GeneChip and measures of adiposity in the Framingham Heart Study. METHODS: A total of 1341 Framingham Heart Study participants in 310 families genotyped with the Affymetrix 100K SNP GeneChip had adiposity traits measured over 30 years of follow up. Body mass index (BMI), waist circumference (WC), weight change, height, and radiographic measures of adiposity (subcutaneous adipose tissue, visceral adipose tissue, waist circumference, sagittal height) were measured at multiple examination cycles. Multivariable-adjusted residuals, adjusting for age, age-squared, sex, smoking, and menopausal status, were evaluated in association with the genotype data using additive Generalized Estimating Equations (GEE) and Family Based Association Test (FBAT) models. We prioritized mean BMI over offspring examinations (1–7) and cohort examinations (10, 16, 18, 20, 22, 24, 26) and mean WC over offspring examinations (4–7) for presentation. We evaluated associations with 70,987 SNPs on autosomes with minor allele frequencies of at least 0.10, Hardy-Weinberg equilibrium p ≥ 0.001, and call rates of at least 80%. RESULTS: The top SNPs to be associated with mean BMI and mean WC by GEE were rs110683 (p-value 1.22*10-7) and rs4471028 (p-values 1.96*10-7). Please see for the complete set of results. We were able to validate SNPs in known genes that have been related to BMI or other adiposity traits, including the ESR1 Xba1 SNP, PPARG, and ADIPOQ. CONCLUSION: Adiposity traits are associated with SNPs on the Affymetrix 100K SNP GeneChip. Replication of these initial findings is necessary. These data will serve as a resource for replication as more genes become identified with BMI and WC.National Heart, Lung, and Blood Institute's Framingham Heart Study (N01-HC-25195); Atwood (R01 DK066241); National Institutes of Health National Center for Research Resources Shared Instrumentation grant (1S10RR163736-01A1

Coupling Lattice Boltzmann and Molecular Dynamics models for dense fluids

We propose a hybrid model, coupling Lattice Boltzmann and Molecular Dynamics models, for the simulation of dense fluids. Time and length scales are decoupled by using an iterative Schwarz domain decomposition algorithm. The MD and LB formulations communicate via the exchange of velocities and velocity gradients at the interface. We validate the present LB-MD model in simulations of flows of liquid argon past and through a carbon nanotube. Comparisons with existing hybrid algorithms and with reference MD solutions demonstrate the validity of the present approach.Comment: 14 pages, 5 figure