Bosons Confined in Optical Lattices: the Numerical Renormalization Group revisited

A Bose-Hubbard model, describing bosons in a harmonic trap with a superimposed optical lattice, is studied using a fast and accurate variational technique (MF+NRG): the Gutzwiller mean-field (MF) ansatz is combined with a Numerical Renormalization Group (NRG) procedure in order to improve on both. Results are presented for one, two and three dimensions, with particular attention to the experimentally accessible momentum distribution and possible satellite peaks in this distribution. In one dimension, a comparison is made with exact results obtained using Stochastich Series Expansion.Comment: 10 pages, 15 figure

Ghosts, Strong Coupling and Accidental Symmetries in Massive Gravity

We show that the strong self-interaction of the scalar polarization of a massive graviton can be understood in terms of the propagation of an extra ghost-like degree of freedom, thus relating strong coupling to the sixth degree of freedom discussed by Boulware and Deser in their Hamiltonian analysis of massive gravity. This enables one to understand the Vainshtein recovery of solutions of massless gravity as being due to the effect of the exchange of this ghost which gets frozen at distances larger than the Vainshtein radius. Inside this region, we can trust the two-field Lagrangian perturbatively, while at larger distances one can use the higher derivative formulation. We also compare massive gravity with other models, namely deconstructed theories of gravity, as well as DGP model. In the latter case we argue that the Vainshtein recovery process is of different nature, not involving a ghost degree of freedom.Comment: 21 page

Solving the Richardson equations for Fermions

Forty years ago Richardson showed that the eigenstates of the pairing Hamiltonian with constant interaction strength can be calculated by solving a set of non-linear coupled equations. However, in the case of Fermions these equations lead to singularities which made them very hard to solve. This letter explains how these singularities can be avoided through a change of variables making the Fermionic pairing problem numerically solvable for arbitrary single particle energies and degeneracies.Comment: 5 pages, 4 figures, submitted to Phys.Rev.

A quantum Monte-Carlo method for fermions, free of discretization errors

In this work we present a novel quantum Monte-Carlo method for fermions, based on an exact decomposition of the Boltzmann operator $exp(-\beta H)$. It can be seen as a synthesis of several related methods. It has the advantage that it is free of discretization errors, and applicable to general interactions, both for ground-state and finite-temperature calculations. The decomposition is based on low-rank matrices, which allows faster calculations. As an illustration, the method is applied to an analytically solvable model (pairing in a degenerate shell) and to the Hubbard model.Comment: 5 pages, 4 figures, submitted to Phys. Rev. Let

Optimal Monte Carlo Updating

Based on Peskun's theorem it is shown that optimal transition matrices in Markov chain Monte Carlo should have zero diagonal elements except for the diagonal element corresponding to the largest weight. We will compare the statistical efficiency of this sampler to existing algorithms, such as heat-bath updating and the Metropolis algorithm. We provide numerical results for the Potts model as an application in classical physics. As an application in quantum physics we consider the spin 3/2 XY model and the Bose-Hubbard model which have been simulated by the directed loop algorithm in the stochastic series expansion framework.Comment: 6 pages, 5 figures, replaced with published versio

Naturalness in Cosmological Initial Conditions

We propose a novel approach to the problem of constraining cosmological initial conditions. Within the framework of effective field theory, we classify initial conditions in terms of boundary terms added to the effective action describing the cosmological evolution below Planckian energies. These boundary terms can be thought of as spacelike branes which may support extra instantaneous degrees of freedom and extra operators. Interactions and renormalization of these boundary terms allow us to apply to the boundary terms the field-theoretical requirement of naturalness, i.e. stability under radiative corrections. We apply this requirement to slow-roll inflation with non-adiabatic initial conditions, and to cyclic cosmology. This allows us to define in a precise sense when some of these models are fine-tuned. We also describe how to parametrize in a model-independent way non-Gaussian initial conditions; we show that in some cases they are both potentially observable and pass our naturalness requirement.Comment: 35 pages, 8 figure

Regularization of Brane Induced Gravity

We study the regularization of theories of ``brane induced'' gravity in codimension $N>1$. The brane can be interpreted as a thin dielectric with a large dielectric constant, embedded in a higher dimensional space. The kinetic term for the higher dimensional graviton is enhanced over the brane. A four dimensional gravitation is found on the brane at distances smaller than a critical distance $r<r_c$, and is due to the exchange of a massive resonant graviton. The crossover scale $r_c$ is determined by the mass of the resonance. The suppression of the couplings of light Kaluza-Klein modes to brane matter results in a higher dimensional force law at large distances. We show that the resulting theory is free of ghosts or tachyons.Comment: One reference added. To appear in PRD. 20 pages, 3 figure

When moving faces activate the house area: an fMRI study of object-file retrieval

<p>Abstract</p> <p>Background</p> <p>The visual cortex of the human brain contains specialized modules for processing different visual features of an object. Confronted with multiple objects, the system needs to attribute the correct features to each object (often referred to as 'the binding problem'). The brain is assumed to integrate the features of perceived objects into object files – pointers to the neural representations of these features, which outlive the event they represent in order to maintain stable percepts of objects over time. It has been hypothesized that a new encounter with one of the previously bound features will reactivate the other features in the associated object file according to a kind of pattern-completion process.</p> <p>Methods</p> <p>Fourteen healthy volunteers participated in an fMRI experiment and performed a task designed to measure the aftereffects of binding visual features (houses, faces, motion direction). On each trial, participants viewed a particular combination of features (S1) before carrying out a speeded choice response to a second combination of features (S2). Repetition and alternation of all three features was varied orthogonally.</p> <p>Results</p> <p>The behavioral results showed the standard partial repetition costs: a reaction time increase when one feature was repeated and the other feature alternated between S1 and S2, as compared to complete repetitions or alternations of these features. Importantly, the fMRI results provided evidence that repeating motion direction reactivated the object that previously moved in the same direction. More specifically, perceiving a face moving in the same direction as a just-perceived house increased activation in the parahippocampal place area (PPA). A similar reactivation effect was not observed for faces in the fusiform face area (FFA). Individual differences in the size of the reactivation effects in the PPA and FFA showed a positive correlation with the corresponding partial repetition costs.</p> <p>Conclusion</p> <p>Our study provides the first neural evidence that features are bound together on a single presentation and that reviewing one feature automatically reactivates the features that previously accompanied it.</p