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At least 1,135 records · Page 63

Asymptotic entanglement transformation between W and GHZ states

We investigate entanglement transformations with stochastic local operations and classical communication in an asymptotic setting using the concepts of degeneration and border rank of tensors from algebraic complexity theory. Results well-known in that field imply that GHZ states can be transformed into W states at rate 1 for any number of parties. As a generalization, we find that the asymptotic conversion rate from GHZ states to Dicke states is bounded as the number of subsystems increases and the number of excitations is fixed. By generalizing constructions of Coppersmith and Winograd and by using monotones introduced by Strassen, we also compute the conversion rate from W to GHZ states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Scale-invariant curvature fluctuations from an extended semiclassical gravity

We present an extension of the semiclassical Einstein equations which couple n-point correlation functions of a stochastic Einstein tensor to the n-point functions of the quantum stress-energy tensor. We apply this extension to calculate the quantum fluctuations during an inflationary period, where we take as a model a massive conformally coupled scalar field on a perturbed de Sitter space and describe how a renormalization independent, almost-scale-invariant power spectrum of the scalar metric perturbation is produced. Furthermore, we discuss how this model yields a natural basis for the calculation of non-Gaussianities of the considered metric fluctuations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

On the combined gradient-stochastic plasticity model: Application to Mo-micropillar compression

A formulation for addressing heterogeneous material deformation is proposed. It is based on the use of a stochasticity-enhanced gradient plasticity model implemented through a cellular automaton. The specific application is on Mo-micropillar compression, for which the irregularities of the strain bursts observed have been experimentally measured and theoretically interpreted through Tsallis' q-statistics.

36 MATERIALS SCIENCE↗

Förster resonance energy transfer, absorption and emission spectra in multichromophoric systems. I. Full cumulant expansions and system-bath entanglement

We study the Förster resonant energy transfer rate, absorption and emission spectra in multichromophoric systems. The multichromophoric Förster theory (MCFT) is determined from an overlap integral of generalized matrices related to the donor’s emission and acceptor’s absorption spectra, which are obtained via a full 2nd-order cumulant expansion technique developed in this work. We calculate the spectra and MCFT rate for both localized and delocalized systems, and calibrate the analytical 2nd-order cumulant expansion with the exact stochastic path integral method. We present three essential findings: (i) The role of the initial entanglement between the donor and its bath is found to be crucial in both the emission spectrum and the MCFT rate. (ii) The absorption spectra obtained by the cumulant expansion method are nearly identical to the exact spectra for both localized and delocalized systems, even when the system-bath coupling is far from the perturbative regime. (iii) For the emission spectra, the cumulant expansion can give reliable results for localized systems, but fail to provide reliable spectra of the high-lying excited states of a delocalized system, when the system-bath coupling is large and the thermal energy is small. This paper also provides a simple golden-rule derivation of the MCFT, reviews existing methods, and motivates further developments in the subsequent papers.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Förster resonance energy transfer, absorption and emission spectra in multichromophoric systems. III. Exact stochastic path integral evaluation

A numerically exact path integral treatment of the absorption and emission spectra of open quantum systems is presented that requires only the straightforward solution of a stochastic differential equation. The approach converges rapidly enabling the calculation of spectra of large excitonic systems across the complete range of system parameters and for arbitrary bath spectral densities. With the numerically exact absorption and emission operators, one can also immediately compute energy transfer rates using the multi-chromophoric Förster resonant energy transfer formalism. Benchmark calculations on the emission spectra of two level systems are presented demonstrating the efficacy of the stochastic approach. This is followed by calculations of the energy transfer rates between two weakly coupled dimer systems as a function of temperature and system-bath coupling strength. It is shown that the recently developed hybrid cumulant expansion (see Paper II) is the only perturbative method capable of generating uniformly reliable energy transfer rates and emission spectra across a broad range of system parameters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A multilevel stochastic collocation method for SPDEs

We present a multilevel stochastic collocation method that, as do multilevel Monte Carlo methods, uses a hierarchy of spatial approximations to reduce the overall computational complexity when solving partial differential equations with random inputs. For approximation in parameter space, a hierarchy of multi-dimensional interpolants of increasing fidelity are used. Rigorous convergence and computational cost estimates for the new multilevel stochastic collocation method are derived and used to demonstrate its advantages compared to standard single-level stochastic collocation approximations as well as multilevel Monte Carlo methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Large-eddy simulation of heavy particle dispersion in wall-bounded turbulent flows

Capabilities and accuracy issues in Lagrangian tracking of heavy particles in velocity fields obtained from large-eddy simulations (LES) of wall-bounded turbulent flows are reviewed. In particular, it is shown that, if no subgrid scale (SGS) model is added to the particle motion equations, particle preferential concentration and near-wall accumulation are significantly underestimated. Results obtained with SGS modeling for the particle motion equations based on approximate deconvolution are briefly recalled. Then, the error purely due to filtering in particle tracking in LES flow fields is singled out and analyzed. The statistical properties of filtering errors are characterized in turbulent channel flow both from an Eulerian and a Lagrangian viewpoint. Implications for stochastic SGS modeling in particle motion equations are briefly outlined.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Bounds for the cumulative conditional expectation function

We introduce the concept of cumulative conditional expectation function. This is a quantity that provides statistical support for making decisions in applied problems. The goal of this paper is to find an analytical expression for upper and lower bounds of this function, assuming stochastic dependence types as being the underlying random structure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Bootstrap performance profiles in stochastic algorithms assessment

Optimization with stochastic algorithms has become a relevant research field. Due to its stochastic nature, its assessment is not straightforward and involves integrating accuracy and precision. Performance profiles for the mean do not show the trade-off between accuracy and precision, and parametric stochastic profiles require strong distributional assumptions and are limited to the mean performance for a large number of runs. In this work, bootstrap performance profiles are used to compare stochastic algorithms for different statistics. This technique allows the estimation of the sampling distribution of almost any statistic even with small samples. Multiple comparison profiles are presented for more than two algorithms. The advantages and drawbacks of each assessment methodology are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A simplified model for dynamics of cell rolling and cell-surface adhesion

We propose a three dimensional model for the adhesion and rolling of biological cells on surfaces. We study cells moving in shear flow above a wall to which they can adhere via specific receptor-ligand bonds based on receptors from selectin as well as integrin family. The computational fluid dynamics are governed by the lattice-Boltzmann method. The movement and the deformation of the cells is described by the immersed boundary method. Both methods are fully coupled by implementing a two-way fluid-structure interaction. The adhesion mechanism is modelled by adhesive bonds including stochastic rules for their creation and rupture. We explore a simplified model with dissociation rate independent of the length of the bonds. We demonstrate that this model is able to resemble the mesoscopic properties, such as velocity of rolling cells.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Organic memristive device as key element for neuromorphic networks

Organic memristive device has three important properties allowing to consider it as a key element of neuromorphic systems. First, its electrical properties are somehow similar to those of synapses. Second, it can be easily transferred into an oscillator. Third, organic nature of the devices allow to assemble them into stochastic 3D networks capable to learning and adaptations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Criticism of generally accepted fundamentals and methodologies of traffic and transportation theory

It is explained why the set of the fundamental empirical features of traffic breakdown (a transition from free flow to congested traffic) should be the empirical basis for any traffic and transportation theory that can be reliable used for control and optimization in traffic networks. It is shown that generally accepted fundamentals and methodologies of traffic and transportation theory are not consistent with the set of the fundamental empirical features of traffic breakdown at a highway bottleneck. To these fundamentals and methodologies of traffic and transportation theory belong (i) Lighthill-Whitham-Richards (LWR) theory, (ii) the General Motors (GM) model class (for example, Herman, Gazis et al. GM model, Gipps’s model, Payne’s model, Newell’s optimal velocity (OV) model, Wiedemann’s model, Bando et al. OV model, Treiber’s IDM, Krauß’s model), (iii) the understanding of highway capacity as a particular stochastic value, and (iv) principles for traffic and transportation network optimization and control (for example, Wardrop’s user equilibrium (UE) and system optimum (SO) principles). Alternatively to these generally accepted fundamentals and methodologies of traffic and transportation theory, we discuss three-phase traffic theory as the basis for traffic flow modeling as well as briefly consider the network breakdown minimization (BM) principle for the optimization of traffic and transportation networks with road bottlenecks.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A queuing model for road traffic simulation

We present in this article a stochastic queuing model for the raod traffic. The model is based on the M/G/c/c state dependent queuing model, and is inspired from the deterministic Godunov scheme for the road traffic simulation. We first propose a variant of M/G/c/c state dependent model that works with density-flow fundamental diagrams rather than density-speed relationships. We then extend this model in order to consider upstream traffic demand as well as downstream traffic supply. Finally, we show how to model a whole raod by concatenating raod sections as in the deterministic Godunov scheme.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Using stochastic activity networks to study the energy feasibility of automatic weather stations

Automatic Weather Stations (AWSs) are systems equipped with a number of environmental sensors and communication interfaces used to monitor harsh environments, such as glaciers and deserts. Designing such systems is challenging, since designers have to maximize the amount of sampled and transmitted data while considering the energy needs of the system that, in most cases, is powered by rechargeable batteries and exploits energy harvesting, e.g., solar cells and wind turbines. To support designers of AWSs in the definition of the software tasks and of the hardware configuration of the AWS we designed and implemented an energy-aware simulator of such systems. The simulator relies on the Stochastic Activity Networks (SANs) formalism and has been developed using the Möbius tool. In this paper we first show how we used the SAN formalism to model the various components of an AWS, we then report results from an experiment carried out to validate the simulator against a real-world AWS and we finally show some examples of usage of the proposed simulator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Modelling of volatility in monetary transmission mechanism

The aim of this paper is to compare different approaches to modeling of volatility in monetary transmission mechanism. For this purpose we built time-varying parameter VAR (TVP-VAR) model with stochastic volatility and VAR-DCC-GARCH model with conditional variance. The data from three European countries are included in the analysis: the Czech Republic, Germany and Slovakia. Results show that VAR-DCC-GARCH system captures higher volatility of observed variables but main trends and detected breaks are generally identical in both approaches.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Notes on power of normality tests of error terms in regression models

Normality is one of the basic assumptions in applying statistical procedures. For example in linear regression most of the inferential procedures are based on the assumption of normality, i.e. the disturbance vector is assumed to be normally distributed. Failure to assess non-normality of the error terms may lead to incorrect results of usual statistical inference techniques such as t-test or F-test. Thus, error terms should be normally distributed in order to allow us to make exact inferences. As a consequence, normally distributed stochastic errors are necessary in order to make a not misleading inferences which explains a necessity and importance of robust tests of normality. Therefore, the aim of this contribution is to discuss normality testing of error terms in regression models. In this contribution, we introduce the general RT class of robust tests for normality, and present and discuss the trade-off between power and robustness of selected classical and robust normality tests of error terms in regression models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗