A review of Monte Carlo simulations for the Bose-Hubbard model with diagonal disorder

We review the physics of the Bose-Hubbard model with disorder in the chemical potential focusing on recently published analytical arguments in combination with quantum Monte Carlo simulations. Apart from the superfluid and Mott insulator phases that can occur in this system without disorder, disorder allows for an additional phase, called the Bose glass phase. The topology of the phase diagram is subject to strong theorems proving that the Bose Glass phase must intervene between the superfluid and the Mott insulator and implying a Griffiths transition between the Mott insulator and the Bose glass. The full phase diagrams in 3d and 2d are discussed, and we zoom in on the insensitivity of the transition line between the superfluid and the Bose glass in the close vicinity of the tip of the Mott insulator lobe. We briefly comment on the established and remaining questions in the 1d case, and give a short overview of numerical work on related models.Comment: 30 pages, 8 figure

Recent developments in Quantum Monte-Carlo simulations with applications for cold gases

This is a review of recent developments in Monte Carlo methods in the field of ultra cold gases. For bosonic atoms in an optical lattice we discuss path integral Monte Carlo simulations with worm updates and show the excellent agreement with cold atom experiments. We also review recent progress in simulating bosonic systems with long-range interactions, disordered bosons, mixtures of bosons, and spinful bosonic systems. For repulsive fermionic systems determinantal methods at half filling are sign free, but in general no sign-free method exists. We review the developments in diagrammatic Monte Carlo for the Fermi polaron problem and the Hubbard model, and show the connection with dynamical mean-field theory. We end the review with diffusion Monte Carlo for the Stoner problem in cold gases.Comment: 68 pages, 22 figures, review article; replaced with published versio

The EU-Korea FTA and its implications for the future EU-Singapore FTA. EU Centre Background Brief No. 4, June 2011

Summary. In 2006, the European Union (EU) announced its intention to conclude a new generation of free trade agreements (FTAs) with strategic partners. These FTAs, primarily motivated by economic considerations, would aim at a high level of trade liberalisation. In particular, they would cover the areas which are crucial to the EU’s competitiveness, such as services liberalisation and investment promotion and protection, and include strong provisions to tackle non-tariff barriers in areas such as intellectual property rights, public procurement, regulatory barriers and unfair competition. The EU also identified key partners that would offer significant opportunities for EU companies. ASEAN, Korea and Mercosur emerged as priorities in view of their market potential and the current level of protection against EU export interests. The first FTA that EU has concluded in Asia is the EU-Korea FTA, which will provisionally enter into force on 1st July 2011. The EU considers it the most “ambitious” EU FTA and is presented as a “benchmark” for future ones. An overview of the main elements of the FTA illustrates the level of ambition of the EU in concluding its new generation of FTAs. In particular, it provides interesting insights into what a future EU-Singapore FTA may look like. After negotiations between the EU and ASEAN were put on hold, the EU decided to enter into negotiations with individual ASEAN member states, starting with Singapore in December 2009. Both partners are currently entering the last phase of negotiations and the FTA may be concluded over the next few months. The final shape of the EU-Singapore FTA would provide a reference point for a 21st century FTA and for EU’s negotiations with other ASEAN member states, laying the foundation for the future of a comprehensive EU-ASEAN economic partnership

Measuring the equation of state of trapped ultracold bosonic systems in an optical lattice with in-situ density imaging

We analyze quantitatively how imaging techniques with single-site resolution allow to measure thermodynamical properties that cannot be inferred from time-of-light images for the trapped Bose-Hubbard model. If the normal state extends over a sufficiently large range, the chemical potential and the temperature can be extracted from a single shot, provided the sample is in thermodynamic equilibrium. When the normal state is too narrow, temperature is low but can still be extracted using the fluctuation-dissipation theorem over the entire trap range as long as the local density approximation remains valid, as was recently suggested by Qi Zhou and Tin-Lun Ho [arXiv:0908.3015]. However, for typical present-day experiments, the number of samples needed is of the order of 1000 in order to get the temperature at least $10 \%$ accurate, but it is possible to reduce the variance by 2 orders of magnitude if the density-density correlation length is short, which is the case for the Bose-Hubbard model. Our results provide further evidence that cold gases in an optical lattices can be viewed as quantum analog computers.Comment: 8 pages, 10 figure

Absence of a Direct Superfluid to Mott Insulator Transition in Disordered Bose Systems

We prove the absence of a direct quantum phase transition between a superfluid and a Mott insulator in a bosonic system with generic, bounded disorder. We also prove compressibility of the system on the superfluid--insulator critical line and in its neighborhood. These conclusions follow from a general {\it theorem of inclusions} which states that for any transition in a disordered system one can always find rare regions of the competing phase on either side of the transition line. Quantum Monte Carlo simulations for the disordered Bose-Hubbard model show an even stronger result, important for the nature of the Mott insulator to Bose glass phase transition: The critical disorder bound, $\Delta_c$, corresponding to the onset of disorder-induced superfluidity, satisfies the relation $\Delta_c > E_{\rm g/2}$, with $E_{\rm g/2}$ the half-width of the Mott gap in the pure system.Comment: 4 pages, 3 figures; replaced with resubmitted versio

Jealousy as a Function of Rival Characteristics: Two large replication studies and meta-analyses support gender differences in reactions to rival attractiveness but not dominance

Jealousy is a key emotion studied in the context of romantic relationships. One seminal study (Dijkstra, P., & Buunk, B. (1998). Jealousy as a function of rival characteristics: An evolutionary perspective. Personality and Social Psychology Bulletin, 24 (11), 1158–1166. https://doi.org/10.1177/01461672982411003) investigated the interactions between a participant’s gender and their reactions to the attractiveness or dominance of a romantic rival. In a vignette-based study, it was found that women’s jealousy was more responsive than men’s to a rival’s attractiveness, whereas in contrast, the rival’s dominance evoked more jealousy from men than from women. Here, we attempt to replicate these interactions in two samples (N = 339 and N = 456) and present subsequent meta-analyses (combined Ns = 5,899 and 4,038, respectively). These meta-analyses showed a small, significant effect of gender on jealousy provoked by rival attractiveness, but no such response to rival dominance. We discuss the potential reasons for these findings and future directions for research on jealousy and rival characteristics