State Decomposition Research Articles

The negative-parity spin-1/2 Λ baryon spectrum from lattice QCD and effective theory

The spectrum of the negative-parity spin-1/2 Λ baryons is studied using lattice QCD and hadronic effective theory in a unitarized coupled-channel framework. A direct comparison between the two approaches is possible by considering the hadronic effective theory in a finite volume and with hadron masses and mesonic decay constants that correspond to the situation studied on the lattice. Comparing the energy level spectrum and SU(3) flavor decompositions of the individual states, it is found that the lowest two states extracted from lattice QCD can be associated with one of the two Λ(1405)-poles and the Λ(1670) resonance. The quark mass dependences of these two lattice QCD levels are in good agreement with their effective theory counterparts. However, as current lattice QCD studies still rely on three-quark operators to generate the physical states, clear signals corresponding to the meson-baryon scattering states, that appear in the finite volume effective theory calculation, are not yet seen.

An Evolutionary Metaheuristic Based on State Decomposition for Domain-Independent Satisficing Planning

DAEX is a metaheuristic designed to improve the plan quality and the scalability of an encapsulated planning system. DAEX is based on a state decomposition strategy, driven by an evolutionary algorithm, which benefits from the use of a classical planning heuristic to maintain an ordering of atoms within the individuals. The proof of concept is achieved by embedding the domain-independent satisficing YAHSP planner and using the critical path h1 heuristic. Experiments with the resulting algorithm are performed on a selection of IPC benchmarks from classical, cost-based and temporal domains. Under the experimental conditions of the IPC, and in particular with a universal parameter setting common to all domains, DAEYAHSP is compared to the best planner for each type of domain. Results show that DAEYAHSP performs very well both on coverage and quality metrics. It is particularly noticeable that DAEX improves a lot on plan quality when compared to YAHSP, which is known to provide largely suboptimal solutions; making it competitive with state-of-the-art planners. This article gives a full account of the algorithm, reports on the experiments and provides some insights on the algorithm behavior.

Many-body entanglement in fermion systems

We introduce a general bipartite-like representation and Schmidt decomposition of an arbitrary pure state of $N$ indistinguishable fermions, based on states of $M<N$ and $(N-M)$ fermions. It is directly connected with the reduced $M$- and $(N-M)$-body density matrices (DMs), which have the same spectrum in such states. The concept of $M$-body entanglement emerges naturally in this scenario, generalizing that of one-body entanglement. Rigorous majorization relations satisfied by the normalized $M$-body DM are then derived, which imply that the associated entropy will not increase, on average, under a class of operations which have these DMs as post-measurement states. Moreover, such entropy is an upper bound to the average bipartite entanglement entropy generated by a class of operations which map the original state to a bipartite state of $M$ and $N-M$ effectively distinguishable fermions. Analytic evaluation of the spectrum of $M$-body DMs in some strongly correlated fermionic states is also provided.

Asynchronous [formula omitted] control for hidden singular Markov jump systems with incomplete transition probabilities via state decomposition approach

This paper addresses the asynchronous H∞ control problem for hidden singular Markov jump systems (HSMJSs) with incomplete transition probabilities. By employing the state decomposition approach, a novel augmented Lyapunov-Krasovkii functional (LKF) with the components of state vectors is designed to reduce the redundant decision variables. Meanwhile, a parameter-dependent reciprocally convex matrix inequality (PDRCMI) is introduced to decrease conservatism. To handle the non-synchronization phenomenon of the system mode and the controller mode, an asynchronous state feedback controller based on hidden Markov model (HMM) is developed. In addition, the incomplete transition probabilities are considered so that a more practical potential strategy is addressed. Finally, numerical examples are provided to illustrate the superiority and practicability of the presented results.

Average quantum coherence of pure-state decomposition

We study the average quantum coherence over the pure state decompositions of a mixed quantum state. An upper bound of the average quantum coherence is provided and sufficient conditions for the saturation of the upper bound are shown. These sufficient conditions always hold for two and three dimensional systems. This provides a tool to estimate the average coherence experimentally by measuring only the diagonal elements, which remarkably requires less measurements compared with state tomography. We then describe the pure state decompositions of qubit state in Bloch sphere geometrically. For any given qubit state, the optimal pure state decomposition achieving the maximal average quantum coherence as well as three other pure state decompositions are shown in the Bloch sphere. The order relations among their average quantum coherence are invariant for any coherence measure. The results presented in this paper are universal and suitable for all coherence measures.

The Bloch vectors formalism for a finite-dimensional quantum system

In the present article, we consistently develop the main issues of the Bloch vectors formalism for an arbitrary finite-dimensional quantum system. In the frame of this formalism, qudit states and their evolution in time, qudit observables and their expectations, entanglement and nonlocality, etc are expressed in terms of the Bloch vectors—the vectors in the Euclidean space , arising under decompositions of observables and states in different operator bases. Within this formalism, we specify for all d ⩾ 2 the set of Bloch vectors of traceless qudit observables and describe its properties; also, find for the sets of the Bloch vectors of qudit states, pure and mixed, the new compact expressions in terms of the operator norms that explicitly reveal the general properties of these sets and have the unified form for all d ⩾ 2. For the sets of the Bloch vectors of qudit states under the generalized Gell‐Mann representation, these general properties cannot be analytically extracted from the known equivalent specifications of these sets via the system of algebraic equations. We derive the general equations describing the time evolution of the Bloch vector of a qudit state if a qudit system is isolated and if it is open and find for both cases the main properties of the Bloch vector evolution in time. For a pure bipartite state of a dimension d 1 × d 2, we quantify its entanglement via the characteristics of the Bloch vectors for its reduced states. The introduced general formalism is important both for the theoretical analysis of quantum system properties and for quantum applications, in particular, for optimal quantum control, since, for systems where states are described by vectors in the Euclidean space, the methods of optimal control, analytical and numerical, are well developed.

Stabilization mechanisms of three novel full-nitrogen molecules

Full-nitrogen energetic materials have excellent performance in the quest for higher-energy and greener explosive materials. Herein, the structure, properties under electric field, transition state, and unimolecular decomposition of octaazapentalene (o-N8), azidopentazole (a-N8), and bispentazole (N10) are studied in detail using density functional theory methods. The results show that three molecules are aromatic and each N atom is in the molecular plane. Applied electric field will change the bond length, atomic charge, and rate constant of thermal decomposition. The two pentazole rings of N10 immediately change from being in a plane (180°) to being perpendicular to each other (90.64°–91.81°) when the absolute value of the electric field intensity is greater than 40 × 10–4 a.u. The stability order of the three molecules is o-N8 > a-N8 > N10 judged by the activation energy of the initial decompostion. In addition to decompose to N2 in the azole ring, o-N8 was found to have a new pathway to eliminate N2 in the azide group. Moreover, ab initio molecular dynamics simulations were performed to further reveal the effect of different temperatures on the cleavage of single molecules.

New reliableH∞filter design for singular Markovian jump time‐delay systems with sensor failures

AbstractThe issue of the reliable exponentialH∞filtering (HF) is revisited for singular Markovian jump time‐delay systems (SMJTSs) accompanied by sensor failures and interval time‐varying delays. By a new mode‐dependent Lyapunov–Krasovskii functional (LKF) containing three augmented nonintegral terms, some mean‐square exponentially admissible (MSEA) conditions satisfying anH∞performance are derived subject to state decomposition method. On this basis, a novel reliable filter design approach is first proposed for SMJTSs by means of the idea of the state decomposition and recombining. And the filter parameters we want can be obtained. Worth noting that the results presented are not only related to interval time‐varying delay and sensor failure but also to interval delay‐change‐rate. Meanwhile, the sufficient conditions established have less conservatism and lower computational complexity in comparison with the existing results. The effectiveness and superiority of the proposed methods are verified by two numerical examples derived from some existing papers.

Further results on delay‐dependent H∞ filtering for singular systems with interval time‐varying delays

AbstractThis paper revisits the problem of H∞ filter design for singular systems with interval time‐varying delays. Firstly, by state decomposition method (SDM), a novel Lyapunov–Krasovskii functional (LKF) including two augmented nonintegral terms is presented. Secondly, via the constructed LKF and the linear matrix inequality (LMI) technique, sufficient stability conditions with lower conservatism are achieved such that the considered singular system is admissible with specified H∞ performance level. Thirdly, a state decomposition‐recombination approach is first introduced to obtain a desired H∞ filter in terms of matrix component transformation technology. Finally, the validity and superiority of the results obtained are verified via two numerical examples.

Everettian relative states in the Heisenberg picture.

Everett's relative-state construction in quantum theory has never been satisfactorily expressed in the Heisenberg picture. What one might have expected to be a straightforward process was impeded by conceptual and technical problems that we solve here. The result is a construction which, unlike Everett's one in the Schrödinger picture, makes manifest the locality of Everettian multiplicity, its inherently approximative nature and its origin in certain kinds of entanglement and locally inaccessible information. (By Everettian, we are referring not only to Everett's own work, but also to versions of quantum theory that elaborate and refine his. The notion of relative states first appeared in Everett (Everett 1973 In The many worlds interpretation of quantum mechanics (eds BS DeWitt, N Graham)). We are proposing a formalism for relative states that is more detailed and more illuminating than Everett's.) Our construction also allows us to give a more precise definition of an Everett ‘universe’, under which it is fully quantum, not quasi-classical, and we compare the Everettian decomposition of a quantum state with the foliation of a space–time.

Improving the efficiency and safety of operation of underground tunnel escalators. Forecasting model

The subways of Moscow and St. Petersburg are the oldest in Russia. Its infrastructure includes a diverse fleet of equipment. The fleet of rolling stock in the last decade was mainly renewed, while due to the peculiarities of operation and mainly for financial reasons, the escalator fleet will not be replaced for a long time. In this connection, the main task of the departments responsible for the operation of escalators is to maintain the rapidly aging fleet in good condition. Thus, a situation, when the escalator economy is a source of costs to meet the constantly increasing demand for resources is formed. At the same time, the limited allocation of all types of resources only aggravates the current situation. The above circumstances contribute to the actualization of the issue of selection of tools, which makes it possible to increase the efficiency and safety of operation of underground tunnel escalators. According to the authors of the paper, one of such tools can be the forecasting of the technical state of the elements of the escalator subsystems, made on the basis of special routing of information flows, designed for the optimal distribution of allocated resources. Since an escalator is a complex technical object of increased danger, the routing of information flows for it characterizing its technical condition is possible only on the basis of a preliminary decomposition into information levels. For this reason, the beginning of the paper is devoted to the decomposition of the technical state of the escalator into four information levels, covering all aspects of the technical state from the micro-level of the state of materials from which the elements of the escalator subsystems are made, ending with the functional state of the entire escalator. The purpose of the work is further revealed. It consists in describing a general mathematical model for predicting the technical state of the elements of the escalator subsystems and the requirements for its construction. The work describes the main task that solves the proposed forecast model. In conclusion, the options for using the proposed model are considered. The scientific novelty of the proposed approach lies in the use of the modern mathematical apparatus of the fuzzy set theory for processing parametric information, elements of artificial intelligence, as well as a precedent approach in analyzing the operational situation, which, in combination, are necessary to build a predictive model of the technical state as applied to the escalator facilities of the subway. From a practical point of view, it should be noted that the proposed mathematical model, implemented on the basis of modern information technologies, will make it possible to more rationally adjust the mechanisms for allocating resources, while ensuring the necessary level of safety for passenger transportation.

Lifted Bayesian Filtering in Multiset Rewriting Systems

We present a model for Bayesian filtering (BF) in discrete dynamic systems where multiple entities (inter)-act, i.e. where the system dynamics is naturally described by a Multiset rewriting system (MRS). Typically, BF in such situations is computationally expensive due to the high number of discrete states that need to be maintained explicitly.&#x0D; We devise a lifted state representation, based on a suitable decomposition of multiset states, such that some factors of the distribution are exchangeable and thus afford an efficient representation. Intuitively, this representation groups together similar entities whose properties follow an exchangeable joint distribution. Subsequently, we introduce a BF algorithm that works directly on lifted states, without resorting to the original, much larger ground representation.&#x0D; This algorithm directly lends itself to approximate versions by limiting the number of explicitly represented lifted states in the posterior. We show empirically that the lifted representation can lead to a factorial reduction in the representational complexity of the distribution, and in the approximate cases can lead to a lower variance of the estimate and a lower estimation error compared to the original, ground representation.

Detection of degenerate Stokes index states

Stokes phase is the phase difference between orthogonal component states in the decomposition of any polarization state. Phase singularities in the Stokes phase distribution are Stokes singularities of an inhomogeneous polarization distribution. Under circular decomposition, Stokes phase distribution (phi _{12}) represents polarization azimuth (gamma ) distribution and the singularities present in it are polarization singularities. Therefore, the charge of the Stokes vortices depicted as Stokes index sigma _{12} is an important parameter associated with the polarization singularity. The Hybrid order Poincaré sphere (HyOPS)/Higher order Poincaré sphere (HOPS) beams, all having same Stokes index, contain a Stokes singularity at the center of the beam as these beams are constructed by vortex superposition. These beams, being superposition of orthogonal orbital angular momentum (OAM) states in orthogonal spin angular momentum (SAM) states can offer great multiplexing capabilities in communication. In this article, we identify these degenerate Stokes index states and discuss the ways and means of lifting this degeneracy. Otherwise, there are limitations on intensity based detection techniques, where demultiplexing or segregation of different HOPS/HyOPS beams is warranted. The method adduced here uses the diffraction of these beams through an equilateral triangular aperture in combination with polarization transformation as a probe to lift the Stokes index/Stokes phase degeneracy. Successively, the novelty of the detection scheme is discussed in the context of beams with alike polarization distributions where even the technique of Stokes polarimetry fails to predict the OAM and SAM content of the beam.

Elucidation of Thermal Degradation Model for Low and High Density Polyethylene by Statistical Parameters

AbstractSolid state decomposition studies of Low and High Density Polyethylene (LDPE and HDPE) have been carried out in the present work. Thermo‐gravimetric analysis (TGA) is utilized to determine the degradation kinetics for pure plastic samples at different heating rates. The distribution of activation energy values and rates estimated using various Iso‐conversional methods have been selected on basis of correlation coefficients. For LDPE, isoconversional method of Friedman and for HDPE Flynn Wall Ozawa methods are used to estimate the distribution of activation energies having their mean values as 256.5 and 257.2 kJ/mol respectively. The inputs from Isoconversional methods are used to determine decomposition behavior with Criado method. Model based studies performed with Criado method identifies the solid‐state degradation follows contracting volume‐sphere (R3) model based on lower statistical parameter values. The identified decomposition model is validated by Coats Redfern method which also results in lower statistical parameter values. This is further validated through a best fit of extent of reaction profile against temperature, substantiating the solid‐state decomposition model followed by given plastic fractions.

Further results on delay-dependent stability for neutral singular systems via state decomposition method

Abstract This paper studies the delay-dependent stability for neutral singular systems. In the light of state decomposition method, a novel augmented Lyapunov-Krasovskii functional including less decision variables is developed. Then by means of zero-value equations technology, some sufficient stability conditions in the form of linear matrix inequalities are acquired, which guarantees the non-impulsiveness, regularity and stability for the proposed neutral singular systems. The obtained stability criterion takes the sizes of both the discrete- and neutral- delays into account. They are less conservative than those presented by previous analytical approaches. Numerical examples are given to show the feasibility of our method and the interrelation between the discrete- and neutral- delays.

Band gap modified zinc oxide nanoparticles: an efficient visible light active catalyst for wastewater treatment

The use of photocatalysis in wastewater treatment using low cost photocatalyst plays a vital role in thwarting the enigma of water pollution. In this work, we report synthesis of metal- and non-metal-doped zinc oxide (ZnO) nanostructures via solid state, solvent and surfactant-free microwave-assisted thermal decomposition method. HRTEM images confirm the formation of highly crystalline nanorod morphology in the case of sodium-doped ZnO. The photocatalytic activity of the synthesized samples initially assessed by the degradation of methylene blue under visible light illumination suggests that SZO-3 (15wt% Na-doped) with admirable degradation rate (95% in 180 min with apparent rate constant of 1.69 × 10–2 min−1) and tenacious photostability envisages its potential applications in water treatment processes. The coalescence of ultrasound, visible light and catalyst resulted in augmented degradation (99.5%) in 60 min.

Characteristics of the Stability and Decomposition of Metastable Gas Hydrates

Results are presented from studying the metastable states of Freon-12 gas hydrate via pulsed NMR in the range of thermodynamic parameters limited by the line of ice–hydrate–gas and supercooled water–hydrate–gas equilibrium in the P–T phase diagram. The dependence is found for the lifetime of metastable Freon-12 gas hydrate on a sample’s temperature and degree of hydrate formation. New data on the conditions of the stability and decomposition of the metastable states of the given gas hydrate are obtained using samples with 100% conversion of water to the former. It is found that the crystallization of water formed upon the dissociation of Freon-12 gas hydrate into supercooled water and gas alters the mechanism of dissociation. A scheme for the formation of water/ice upon the dissociation of gas hydrates is proposed to explain the experimental data.

Dissipativity Analysis for Singular Time-Delay Systems Via State Decomposition Method

This paper studies the dissipativity of singular time-delay systems. The objective is to derive a less conservative criterion with less computational demand. Throughout this paper, the augmented Lyapunov–Krasovskii functional (LKF) and the free-matrix-based integral inequality are used to realize less conservativeness. On the basis of these techniques, a less conservative criterion is first given. Then, by decomposing singular time-delay systems into differential equations and algebraic ones, state vectors of the systems are divided into two parts. To reduce redundant decision variables, each part of the state vectors is considered independently to construct a special augmented LKF with less decision variables. As a result, an improved criterion is deduced, and thus less conservativeness and less computational demand are achieved at the same time. Moreover, the presented state decomposition method provides a new research idea for singular time-delay systems not yet reported in the literatures. Finally, the above statements are demonstrated by a numerical example.

Separability discrimination and decomposition of m -partite quantum mixed states

The separability detecting problem of mixed states is one of the fundamental problems in quantum information theory. In the last 20 years, almost all methods are based on the sufficient or necessary conditions for entanglement. However, in this paper, we only need one algorithm to solve the problem. We propose a tensor optimization method to check whether an $m$-partite quantum mixed state is separable or not and give a decomposition for it if it is. We first convert the separability discrimination problem of mixed states to the positive Hermitian decomposition problem of Hermitian tensors. Then, employing the $E$-truncated $K$-moment method, we obtain an optimization model for discriminating separability. Moreover, applying semidefinite relaxation method, we get a hierarchy of semidefinite relaxation optimization models and propose an $E$-truncated $K$-moment and semidefinite relaxations (ETKM-SDR) algorithm for detecting the separability of mixed states. The algorithm can also be used for symmetric and non-symmetric decomposition of separable mixed states. By numerical examples, we find that not all symmetric separable states have symmetric decompositions. The algorithm can be used for studying properties of mixed states in the future.

Uncoupled Majorana fermions in open quantum systems: on the efficient simulation of non-equilibrium stationary states of quadratic Fermi models

A decomposition of the non-equilibrium stationary state of a quadratic Fermi system influenced by linear baths is obtained and used to establish a simulation protocol in terms of tensor states. The scheme is then applied to examine the occurrence of uncoupled Majorana fermions in Kitaev chains subject to baths on the ends. The resulting phase diagram is compared against the topological characterization of the equilibrium chain and the protocol efficiency is studied with respect to this model.