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

Metastable gravity on classical defects

We discuss the realization of metastable gravity on classical defects in infinite-volume extra dimensions. In dilatonic Einstein gravity, it is found that the existence of metastable gravity on the defect core requires violation of the Dominant Energy Condition for codimension Nc = 2 defects. This is illustrated with a detailed analysis of a six-dimensional hyperstring minimally coupled to dilaton gravity. We present the general conditions under which a codimension Nc > 2 defect admits metastable modes, and find that they differ from lower codimensional models in that, under certain conditions, they do not require violation of energy conditions to support quasi-localized gravity.Comment: 10 pages, 3 figures, uses RevTeX, typos corrected, matches published versio

Better than Expected or as Bad as You Thought? The Neurocognitive Development of Probabilistic Feedback Processing

Learning from feedback lies at the foundation of adaptive behavior. Two prior neuroimaging studies have suggested that there are qualitative differences in how children and adults use feedback by demonstrating that dorsolateral prefrontal cortex (DLPFC) and parietal cortex were more active after negative feedback for adults, but after positive feedback for children. In the current study we used functional magnetic resonance imaging (fMRI) to test whether this difference is related to valence or informative value of the feedback by examining neural responses to negative and positive feedback while applying probabilistic rules. In total, 67 healthy volunteers between ages 8 and 22 participated in the study (8–11 years, n = 18; 13–16 years, n = 27; 18–22 years, n = 22). Behavioral comparisons showed that all participants were able to learn probabilistic rules equally well. DLPFC and dorsal anterior cingulate cortex were more active in younger children following positive feedback and in adults following negative feedback, but only when exploring alternative rules, not when applying the most advantageous rules. These findings suggest that developmental differences in neural responses to feedback are not related to valence per se, but that there is an age-related change in processing learning signals with different informative value

Neural mechanisms underlying the induction and relief of perceptual curiosity

Curiosity is one of the most basic biological drives in both animals and humans, and has been identified as a key motive for learning and discovery. Despite the importance of curiosity and related behaviors, the topic has been largely neglected in human neuroscience; hence little is known about the neurobiological mechanisms underlying curiosity. We used functional magnetic resonance imaging (fMRI) to investigate what happens in our brain during the induction and subsequent relief of perceptual curiosity. Our core findings were that (1) the induction of perceptual curiosity, through the presentation of ambiguous visual input, activated the anterior insula and anterior cingulate cortex (ACC), brain regions sensitive to conflict and arousal; (2) the relief of perceptual curiosity, through visual disambiguation, activated regions of the striatum that have been related to reward processing; and (3) the relief of perceptual curiosity was associated with hippocampal activation and enhanced incidental memory. These findings provide the first demonstration of the neural basis of human perceptual curiosity. Our results provide neurobiological support for a classic psychological theory of curiosity, which holds that curiosity is an aversive condition of increased arousal whose termination is rewarding and facilitates memory

The multilevel pairing Hamiltonian versus the degenerate case

We study the pairing Hamiltonian in a set of non degenerate levels. First, we review in the path integral framework the spontaneous breaking of the U(1) symmetry occurring in such a system for the degenerate situation. Then the behaviors with the coupling constant of the ground state energy in the multilevel and in the degenerate case are compared. Next we discuss, in the multilevel case, an exact strong coupling expansion for the ground state energy which introduces the moments of the single particle level distribution. The domain of validity of the expansion, which is known in the macroscopic limit, is explored for finite systems and its implications for the energy of the latter is discussed. Finally the seniority and Gaudin excitations of the pairing Hamiltonian are addressed and shown to display the same gap in leading order.Comment: 20 pages, 4 figure

Exactly-Solvable Models Derived from a Generalized Gaudin Algebra

We introduce a generalized Gaudin Lie algebra and a complete set of mutually commuting quantum invariants allowing the derivation of several families of exactly solvable Hamiltonians. Different Hamiltonians correspond to different representations of the generators of the algebra. The derived exactly-solvable generalized Gaudin models include the Bardeen-Cooper-Schrieffer, Suhl-Matthias-Walker, the Lipkin-Meshkov-Glick, generalized Dicke, the Nuclear Interacting Boson Model, a new exactly-solvable Kondo-like impurity model, and many more that have not been exploited in the physics literature yet