On the 'Strong-Coupling' Generalization of the Bogoliubov Model

A generalized Bogoliubov model of the Bose gas in the ground state is proposed which properly takes into account both the long-range and short-range spatial boson correlations. It concerns equilibrium characteristics and operates with in-medium Schrodinger equations for the pair wave functions of bosons being the eigenfunctions of the second-order reduced density matrix. The approach developed provides reasonable results for a dilute Bose gas with arbitrary strong interaction between particles (the 'strong-coupling' case) and comes to the canonical Bogoliubov model in the weak-coupling regime.Comment: 6 pages, REVTEX, no figure

Entanglement scaling and spatial correlations of the transverse field Ising model with perturbations

We study numerically the entanglement entropy and spatial correlations of the one dimensional transverse field Ising model with three different perturbations. First, we focus on the out of equilibrium, steady state with an energy current passing through the system. By employing a variety of matrix-product state based methods, we confirm the phase diagram and compute the entanglement entropy. Second, we consider a small perturbation that takes the system away from integrability and calculate the correlations, the central charge and the entanglement entropy. Third, we consider periodically weakened bonds, exploring the phase diagram and entanglement properties first in the situation when the weak and strong bonds alternate (period two-bonds) and then the general situation of a period of n bonds. In the latter case we find a critical weak bond that scales with the transverse field as $J'_c/J$ = $(h/J)^n$, where $J$ is the strength of the strong bond, $J'$ of the weak bond and $h$ the transverse field. We explicitly show that the energy current is not a conserved quantity in this case.Comment: 9 pages, 12 figures, version accepted in PR

Exact master equation for a noncommutative Brownian particle

We derive the Hu-Paz-Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators on the plane with spatial noncommutativity. The results obtained are exact to all orders in the noncommutative parameter. As a by-product we derive some miscellaneous results such as the equilibrium Wigner distribution for the reservoir of noncommutative oscillators, the weak coupling limit of the master equation and a set of sufficient conditions for strict purity decrease of the Brownian particle. Finally, we consider a high-temperature Ohmic model and obtain an estimate for the time scale of the transition from noncommutative to ordinary quantum mechanics. This scale is considerably smaller than the decoherence scale.Comment: Latex file, 28 pages, Published versio

Spatial control of irreversible protein aggregation

Liquid cellular compartments spatially segregate from the cytoplasm and can regulate aberrant protein aggregation, a process linked to several medical conditions, including Alzheimer's and Parkinson's diseases. Yet the mechanisms by which these droplet-like compartments affect protein aggregation remain unknown. Here, we combine kinetic theory of protein aggregation and liquid-liquid phase separation to study the spatial control of irreversible protein aggregation in the presence of liquid compartments. We find that, even for weak interactions between the compartment constituents and the aggregating monomers, aggregates are strongly enriched inside the liquid compartment relative to the surrounding cytoplasm. We show that this enrichment is caused by a positive feedback mechanism of aggregate nucleation and growth which is mediated by a flux maintaining the phase equilibrium between the compartment and the cytoplasm. Our model predicts that the compartment volume that maximizes aggregate enrichment in the compartment is determined by the reaction orders of aggregate nucleation. The underlying mechanism of aggregate enrichment could be used to confine cytotoxic protein aggregates inside droplet-like compartments suggesting potential new avenues against aberrant protein aggregation. Our findings could also represent a common mechanism for the spatial control of irreversible chemical reactions in general

Identification and inference in discrete choice models with imperfect information

We study identification of preferences in a single-agent, static, discrete choice model where the decision maker may be imperfectly informed about the utility generated by the available alternatives. We impose no restrictions on the information frictions the decision maker may face and impose weak assumptions on how the decision maker deals with the uncertainty induced by those frictions. We leverage on the notion of one-player Bayes Correlated Equilibrium in Bergemann and Morris (2013; 2016) to provide a tractable characterisation of the identified set and discuss inference. We use our methodology and data on the 2017 UK general election to estimate a spatial model of voting under weak assumptions on the information that voters have about the returns to voting. We find that the assumptions on the information environment can drive the interpretation of voter preferences. Counterfactual exercises quantify the consequences of imperfect information in politics