Finite size behavior of the asymmetric avalanche process

Variational and diffusion quantum Monte Carlo methods are employed to investigate the zero-temperature phase diagram of the three-dimensional homogeneous electron gas at very low density. Fermi fluid and body-centered cubic Wigner crystal ground state energies are determined using Slater-Jastrow-backflow and Slater-Jastrow many-body wave functions at different densities and spin polarizations in finite simulation cells. Finite-size errors are removed using twist-averaged boundary conditions and extrapolation of the energy per particle to the thermodynamic limit of infinite system size. Unlike previous studies, our results show that the electron gas undergoes a first-order quantum phase transition directly from a paramagnetic fluid to a body-centered cubic crystal at density parameter $r_\text{s} = 86.6(7)$, with no region of stability for an itinerant ferromagnetic fluid. However there is a possible magnetic phase transition from an antiferromagnetic crystal to a ferromagnetic crystal at $r_\text{s}=93(3)$.

A comment on the stationary distribution of the master equation

Existence of only delocalized eigenstates in the electronic spectrum of the Thue–Morse lattice

A new numerical method is introduced that enables a reliable study of disorder‐induced localization of interacting particles. It is based on a quantum mechanical time evolution calculation combined with a finite size scaling analysis. The time evolution of up to four particles in one dimension is studied and localization lengths are defined via the long‐time saturation values of the mean radius, the inverse participation ratio and the center of mass extension. A systematic study of finite size effects using the finite size scaling method is performed in order to extract the localization lengths in the limit of an infinite system size. For a single particle, the well‐known scaling of the localization length λ1 with disorder strength W is observed, λ1 ∝ W—2. For two particles, an interaction‐induced delocalization is found, confirming previous results obtained by numerically calculating matrix elements of the two‐particle Green's function: in the limit of small disorder, the localization length increases with decreasing disorder as λ2 ∝ W—4 and can be much larger than <$>\mitlambda λ1. For three and four particles, delocalization is even stronger. Based on analytical arguments, an upper bound for the n‐particle localization length λn is derived and shown to be in agreement with the numerical data, λn ∝ λ1. Although the localization length increases superexponentially with particle number and can become arbitrarily large for small disorder, it does not diverge for finite λ1 and n. Hence, no extendedstates exist in one dimension, at least for spinless fermions.

Recently, Sá, Ribeiro, and Prosen [Phys. Rev. X 10, 021019 (2020)10.1103/PhysRevX.10.021019] introduced complex spacing ratios to analyze eigenvalue correlations in non-Hermitian systems. At present there are no analytical results for the probability distribution of these ratios in the limit of large system size. We derive an approximation formula for the Ginibre universality class of random matrix theory which converges exponentially fast to the limit of infinite matrix size. We also give results for moments of the distribution in this limit.

Particles with cohesive interactions display a tensile instability in the energy landscape at the Sastry density ρS. The signature of this tensile limit is a minimum in the landscape equation of state, the pressure-density relationship of inherent structures sampled along a liquid isotherm. Our previous work [Y. E. Altabet, F. H. Stillinger, and P. G. Debenedetti, J. Chem. Phys. 145, 211905 (2016)] revisited the phenomenology of Sastry behavior and found that the evolution of the landscape equation of state with system size for particles with interactions typical of molecular liquids indicates the presence of an athermal first-order phase transition between homogeneous and fractured inherent structures, the latter containing several large voids. Here, we study how this tensile limit manifests itself for different interparticle cohesive strengths and identify two distinct regimes. Particles with sufficiently strong cohesion display an athermal first-order phase transition, consistent with our prior characterization. Weak cohesion also displays a tensile instability. However, the landscape equation of state for this regime is independent of system size, suggesting the absence of a first-order phase transition. An analysis of the voids suggests that yielding in the energy landscape of weakly cohesive systems is associated with the emergence of a highly interconnected network of small voids. While strongly cohesive systems transition from exclusively homogeneous to exclusively fractured configurations at ρS in the thermodynamic limit, this interconnected network develops gradually, starting at ρS, even at infinite system size.

In this retrospective study, we compared two systems, continuous flow (CF) (COBE Spectra) versus intermittent flow (IF) (Haemonetics V-50, M-30), in performance of therapeutic plateletapheresis (TP: N = 49 each) and therapeutic leukapheresis (TL: N = 29 each). Pre- and post-procedure cell reductions, specificity of removal, volumes removed, and incidence of adverse reactions were compared. Standard procedures with minor modifications, starch with IF only, and 180 minutes blood processing time were used. The CF system had a significantly lower percent reduction of platelets during TP at 43 +/- 17% than IF at 53 +/- 19%. However, no significant difference was found between CF and IF in percent reduction of white blood cells during TL with 49 +/- 16% and 42 +/- 14%, respectively. The CF system had significantly less hemoglobin reduction (5 +/- 4% vs. 19 +/- 9%, respectively) and white blood cell reduction (13 +/- 15% vs. 27 +/- 17%, respectively) for TP than IF and lower (not significant) hemoglobin reduction (9 +/- 8% vs. 12.4 +/- 8.2%, respectively) as well as platelet reduction (27 +/- 18% vs. 35 +/- 19%, respectively) for TL. CF also had significantly less volume removed than IF during TP (559 +/- 97 vs. 883 +/- 304, respectively) and TL (710 +/- 134 vs. 1405 +/- 421 ml, respectively). Incidence of reactions was lower for CF than IF during TP (8% vs. 10%, respectively) and during TL (14% vs. 21%, respectively).(ABSTRACT TRUNCATED AT 250 WORDS)

The fluctuation-dissipation theorem (FDT) is a hallmark of thermal equilibrium systems in the Gibbs state. We address the question whether the FDT is obeyed by isolated quantum systems in an energy eigenstate. In the framework of the eigenstate thermalization hypothesis, we derive the formal expression for two-time correlation functions in the energy eigenstates or in the diagonal ensemble. They satisfy the Kubo-Martin-Schwinger condition, which is the sufficient and necessary condition for the FDT, in the infinite system size limit. We also obtain the finite size correction to the FDT for finite-sized systems. With extensive numerical works for the XXZ spin chain model, we confirm our theory for the FDT and the finite size correction. Our results can serve as a guide line for an experimental study of the FDT on a finite-sized system.

We analyse the effect of chemical neuro-modulation on collective processes in Ising spin neural networks with separable Hebbian type synaptic interactions. Neuro-modulation is taken into account in the most simple way: a modulator-specific subset of neurons is prevented from transmitting signals. However, the presence of neuro-modulators is taken into account also during the learning stage, which leads to non-symmetric interaction matrices. We derive (in the limit of an infinite system size) the macroscopic laws that determine the system’s evolution in time on the level of order parameters. These laws are very transparant and show that, within the proposed framework, one can understand the functioning of neuro-modulators as follows: their role is to choose from the repertoire of learned behaviour a particular mode of operation. By considering specific examples of learning stages we indicate how neuro-modulation might be used by the brain as an extra degree of freedom for (a) performing selective pattern reconstruction, (b) controlling the reproduction speed of stored pattern sequences or (c) for choosing a particular path from a set of partially overlapping stored trajectories through state space (at points where the trajectories separate).

Visualization experiment of gas–liquid flow pattern downstream of single-orifice plates in horizontal pipes under an intermittent upstream flow

This paper considers decentralized control and optimization methodologies for large populations of systems, consisting of several agents with different individual behaviors, constraints and interests, and affected by the aggregate behavior of the overall population. For such large-scale systems, the theory of aggregative and mean field games has been established and successfully applied in various scientific disciplines. While the existing literature addresses the case of unconstrained agents, we formulate deterministic mean field control problems in the presence of heterogeneous convex constraints for the individual agents, for instance arising from agents with linear dynamics subject to convex state and control constraints. We propose several model-free feedback iterations to compute in a decentralized fashion a mean field Nash equilibrium in the limit of infinite population size. We apply our methods to the constrained linear quadratic deterministic mean field control problem and to the constrained mean field charging control problem for large populations of plug-in electric vehicles.

The modal asymmetry between truth-telling and lying refers to the impossibility of a world in which everyone lies, while on the contrary, a world in which everyone tells the truth is possible. This ethical issue is relevant to modern concerns about epistemic security, or the safety of knowledge. The breakdown of epistemic security leads to the erosion of trust and, hence, to an ‘impossible’ world since a willingness to believe in others is essential for the functioning of society. Here, we examine the threat of disinformation to epistemic security using an individual-based model in which individuals are both senders and receivers of signals and are characterized by their credulity and deceptiveness, which are targets of natural selection. The possible worlds are those favored by natural selection. Lies that significantly harm believers lead to the Kantian scenario: trust is completely eroded and the winners of the evolutionary race are incredulous. However, if the lies are not too harmful, our game evolutionary model predicts a world in which the individuals are both credulous and mildly untruthful. These two possible worlds are separated by a discontinuous phase transition in the limit of infinite population size.

Abstract. One of the most widespread spring-block earthquake models, the Olami-Feder-Christensen model, is investigated without making the assumption that the duration of individual earthquakes is negligible. While the Gutenberg-Richter law for the size distribution of earthquakes is preserved qualitatively for earthquakes of finite duration, the b-value decreases with increasing earthquake duration. The effect decreases with increasing lattice size, although it is not clear whether it completely vanishes in the limit of infinite grid size. For realistic values of earthquake duration, the effect is negligible, so that the original model with zero earthquake duration is appropriate for most applications.

We model networks of identical, all-to-all, pulse-coupled phase oscillators with white noise, in the limit of infinite network size and Dirac pulses, using a Fokker--Planck equation for the phase probability density. We give analytical, constructive existence and uniqueness results for stationary states (i.e., time-independent densities) and derive and study a one-dimensional eigenvalue equation for their linear stability. Our results are supplemented by numerical methods, which are applied to two classes of oscillator response functions. We find that the stationary network activity depends for some response functions monotonically and for others nonmonotonically on the coupling and noise strength. In all cases we find that a sufficiently strong noise locally stabilizes the stationary state, and simulations suggest this stability to be global. For most response functions the stationary state undergoes a supercritical Hopf bifurcation as noise is decreased, and a locally stable limit cycle emerges in its proximity. On that limit cycle, the network splits into groups of approximately synchronized oscillators, while the network's (mean) activity oscillates at frequencies often much higher than the intrinsic oscillator frequency.

We consider an array of lb Cooper pair boxes, each of which is coupled to a superconducting reservoir by acapacitive tunnel junction. We discuss two effects that probe not just the quantumnature of the islands, but also of the superconducting reservoir coupled to them.These are analogues to the well-known quantum optical effects ‘superradiance’ and‘revival’. When revival is extended to multiple systems, we find that ‘entanglementrevival’ can also be observed. In order to study the above effects, we utilize a highlysimplified model for these systems in which all the single-electron energy eigenvaluesare set to be the same (the strong coupling limit), as are the charging energiesof the Cooper pair boxes, allowing the whole system to be represented by twocoupled quantum spins, one finite, which represents the array of boxes, and onerepresenting the reservoir, which we consider in the limit of infinite size. Although thissimplification is drastic, the model retains the main features necessary to capture thephenomena of interest. Given the progress in superconducting box experimentsover recent years, it is possible that experiments to investigate both of theseinteresting quantum coherent phenomena could be performed in the foreseeable future.