Quantum and classical correlations for a two-qubit X structure density matrix

We derive explicit expressions for quantum discord and classical correlation for an X structure density matrix. Based on the characteristics of the expressions, the quantum discord and the classical correlation are easily obtained and compared under different initial conditions using a novel analytical method. We explain the relationships among quantum discord, classical correlation, and entanglement, and further find that the quantum discord is not always larger than the entanglement measured by concurrence in a general two-qubit X state. The new method, which is different from previous approaches, has certain guiding significance for analysing quantum discord and classical correlation of a two-qubit X state, such as a mixed state.

Data Gathering in Wireless Sensor Networks Via Regular Low Density Parity Check Matrix

A great challenge faced by wireless sensor networks(WSNs) is to reduce energy consumption of sensor nodes. Fortunately, the data gathering via random sensing can save energy of sensor nodes. Nevertheless, its randomness and density usually result in difficult implementations, high computation complexity and large storage spaces in practical settings. So the deterministic sparse sensing matrices are desired in some situations. However,it is difficult to guarantee the performance of deterministic sensing matrix by the acknowledged metrics. In this paper, we construct a class of deterministic sparse sensing matrices with statistical versions of restricted isometry property(St RIP) via regular low density parity check(RLDPC) matrices. The key idea of our construction is to achieve small mutual coherence of the matrices by confining the column weights of RLDPC matrices such that St RIP is satisfied. Besides, we prove that the constructed sensing matrices have the same scale of measurement numbers as the dense measurements. We also propose a data gathering method based on RLDPC matrix. Experimental results verify that the constructed sensing matrices have better reconstruction performance, compared to the Gaussian, Bernoulli, and CSLDPC matrices. And we also verify that the data gathering via RLDPC matrix can reduce energy consumption of WSNs.

Improved hybrid parallel strategy for density matrix renormalization group method

We propose a new heterogeneous parallel strategy for the density matrix renormalization group(DMRG)method in the hybrid architecture with both central processing unit(CPU)and graphics processing unit(GPU).Focusing on the two most time-consuming sections in the finite DMRG sweeps,i.e.,the diagonalization of superblock and the truncation of subblock,we optimize our previous hybrid algorithm to achieve better performance.For the former,we adopt OpenMP application programming interface on CPU and use our own subroutines with higher bandwidth on GPU.For the later,we use GPU to accelerate matrix and vector operations involving the reduced density matrix.Applying the parallel scheme to the Hubbard model with next-nearest hopping on the 4-leg ladder,we compute the ground state of the system and obtain the charge stripe pattern which is usually observed in high temperature superconductors.Based on simulations with different numbers of DMRG kept states,we show significant performance improvement and computational time reduction with the optimized parallel algorithm.Our hybrid parallel strategy with superiority in solving the ground state of quasi-two dimensional lattices is also expected to be useful for other DMRG applications with large numbers of kept states,e.g.,the time dependent DMRG algorithms.

Real-space parallel density matrix renormalization group with adaptive boundaries

We propose an improved real-space parallel strategy for the density matrix renormalization group(DMRG)method,where boundaries of separate regions are adaptively distributed during DMRG sweeps.Our scheme greatly improves the parallel efficiency with shorter waiting time between two adjacent tasks,compared with the original real-space parallel DMRG with fixed boundaries.We implement our new strategy based on the message passing interface(MPI),and dynamically control the number of kept states according to the truncation error in each DMRG step.We study the performance of the new parallel strategy by calculating the ground state of a spin-cluster chain and a quantum chemical Hamiltonian of the water molecule.The maximum parallel efficiencies for these two models are 91%and 76%in 4 nodes,which are much higher than the real-space parallel DMRG with fixed boundaries.

Density matrix for an electron confined in quantum dots under uniform magnetic field and static electrical field

Using unitary transformations, this paper obtains the eigenvalues and the common eigenvector of Hamiltonian and a new-defined generalized angular momentum （Lz） for an electron confined in quantum dots under a uniform magnetic field （UMF） and a static electric field （SEF）. It finds that the eigenvalue of Lz just stands for the expectation value of a usual angular momentum lz in the eigen-state. It first obtains the matrix density for this system via directly calculating a transfer matrix element of operator exp（-βH） in some representations with the technique of integral within an ordered products （IWOP） of operators, rather than via solving a Bloch equation. Because the quadratic homogeneity of potential energy is broken due to the existence of SEF, the virial theorem in statistical physics is not satisfactory for this system, which is confirmed through the calculation of thermal averages of physical quantities.

An optimized cluster density matrix embedding theory

We propose an optimized cluster density matrix embedding theory(CDMET).It reduces the computational cost of CDMET with simpler bath states.And the result is as accurate as the original one.As a demonstration,we study the distant correlations of the Heisenberg J_(1)-J_(2)model on the square lattice.We find that the intermediate phase(0.43≤sssim J_(2)≤sssim 0.62)is divided into two parts.One part is a near-critical region(0.43≤J_(2)≤0.50).The other part is the plaquette valence bond solid(PVB)state(0.51≤J_(2)≤0.62).The spin correlations decay exponentially as a function of distance in the PVB.

Optimizing the Computation of Many-Pair Density Matrix in VDPC

Recently an algorithm that acts the variational principle directly to a coherent-pair condensate (VDPC) has been proposed. This algorithm can avoid time-consuming projection while maintaining particle number conservation. Quickly computation of many-pair density matrix (MPDM) is one of the keys to improve the computational efficiency of VDPC algorithm. In this work, we propose a scheme that limits the energy range of block particles to the vicinity of the Fermi surface, which reduces the time complexity of computing the MPDM without losing physical details. The results show that by appropriately limiting the energy range, we can greatly reduce the number of matrix elements that need to be computed, and reducing the time required for the computation.

Reduced one-body density matrix of Tonks-Girardeau gas at finite temperature

With thermal Bose–Fermi mapping method, we investigate the Tonks–Girardeau gas at finite temperature. It is shown that at low temperature, the Tonks gas displays the Fermi-like density profiles, and with the increase in temperature, the Tonks gas distributes in wider region. The reduced one-body density matrix is diagonal dominant in the whole temperature region, and the off-diagonal elements shall vanish rapidly with the deviation from the diagonal part at high temperature.

Influence of matrix physical properties on flow characteristics in dual network model

The tight oil formation develops with microfractures and matrix pores,it is important to study the influence of matrix physical properties on flow characteristics.At first,the representative fracture and matrix samples are selected respectively in the dual media,the fracture and matrix digital rocks are constructed with micro-CT scanning at different resolutions,and the corresponding fracture and matrix pore networks are extracted,respectively.Then,the modified integration method is proposed to build the dual network model containing both fracture and matrix pore-throat elements,while the geometric-topological structure equivalent matrix pores are generated to fill in the skeleton domain of fracture network,the constructed dual network could describe the geometric-topological structure characteristics of fracture and matrix pore-throat simultaneously.At last,by adjusting the matrix pore density and the matrix filling domain factor,a series of dual network models are obtained to analyze the influence of matrix physical properties on flow characteristics in dual-media.It can be seen that the matrix system contributes more to the porosity of the dual media and less to the permeability.With the decrease in matrix pore density,the porosity/permeability contributions of matrix system to dual media keep decreasing,but the decrease is not significant,the oil-water co-flow zone decreases and the irreducible water saturation increases,and the saturation interval dominated by the fluid flow in the fracture keeps increasing.With the decrease in matrix filling domain factor,the porosity/permeability contributions of matrix system to dual media decreases,the oil-water co-flow zone increases and the irreducible water saturation decreases,and the saturation interval dominated by the fluid flow in the fracture keeps increasing.The results can be used to explain the dual-media flow pattern under different matrix types and different fracture control volumes during tight oil production.

How Kieffer Density Matrix Formalism Aids Different Initial Time Steps, Leading to Lorentz Violations, and Breakup of Primordial Black Holes for GW Generation

A result from Kieffer, as outlined at the beginning of the article identifies two different candidates for initial time steps, delta t. We assert that this difference in time steps may be related to a specific early universe Lorentz Violation. The author asserts that the existence of early universe Lorentz violation in turn is assisting in a breakup of primordial black holes. And that also has a tie into Kieffer different time steps as outlined. And the wrap up is given in the final part of this document.

Effect of sintering on the relative density of Cr-coated diamond/Cu composites prepared by spark plasma sintering

Cr-coated diamond/Cu composites were prepared by spark plasma sintering. The effects of sintering pressure, sintering temperature, sintering duration, and Cu powder particle size on the relative density and thermal conductivity of the composites were investigated in this paper. The influence of these parameters on the properties and microstructures of the composites was also discussed. The results show that the relative density of Cr-coated diamond/Cu reaches ~100% when the composite is gradually compressed to 30 MPa during the heating process. The densification temperature increases from 880 to 915℃ when the diamond content is increased from 45vol% to 60vol%. The densification temperature does not increase further when the content reaches 65vol%. Cu powder particles in larger size are beneficial for increasing the relative density of the composite.

Multiple extended target tracking algorithm based on Gaussian surface matrix

In this paper, we consider the problem of irregular shapes tracking for multiple extended targets by introducing the Gaussian surface matrix（GSM） into the framework of the random finite set（RFS） theory. The Gaussian surface function is constructed first by the measurements, and it is used to define the GSM via a mapping function. We then integrate the GSM with the probability hypothesis density（PHD） filter, the Bayesian recursion formulas of GSM-PHD are derived and the Gaussian mixture implementation is employed to obtain the closed-form solutions. Moreover, the estimated shapes are designed to guide the measurement set sub-partition, which can cope with the problem of the spatially close target tracking. Simulation results show that the proposed algorithm can effectively estimate irregular target shapes and exhibit good robustness in cross extended target tracking.

Spectral Density Estimation of Continuous Time Series

This paper studies spectral density estimation of a strictly stationary r-vector valued continuous time series including missing observations. The finite Fourier transform is constructed in L-joint segments of observations. The modified periodogram is defined and smoothed to estimate the spectral density matrix. We explore the properties of the proposed estimator. Asymptotic distribution is discussed.

A Combined Heterotic String and Kähler Manifold Elucidation of Ordinary Energy,Dark Matter,Olbers’s Paradox and Pure Dark Energy Density of the Cosmos

We utilize the topological-geometrical structure imposed by the Heterotic superstring theory on spacetime in conjunction with the K3 Kähler manifold to explain the mysterious nature of dark matter and its coupling to the pure dark energy density of the cosmos. The analogous situations in the case of a Kerr black hole as well as the redundant components of the Riemannian tensor are pointed out and the final result was found to be in complete agreement with all previous theoretical ones as well as all recent accurate measurements and cosmic observations. We conclude by commenting briefly on the Cantorian model of Zitterbewegung and the connection between Olbers’s paradox and dark energy.

Spin density matrix forΩ−and its polarization alignment in ψ(3686)→Ω−Ω¯^(+)

We investigate the spin density matrix of Ω− in the Cartesian coordinate system of baryon-antibaryon pairs produced in e+e−annihilation.Using the helicity formalism of Jacob and Wick,we derive the expression for the spin-3/2 density matrices.Our analysis is based on the angular distribution of the process e+e−→ψ(3686)→Ω−Ω¯^(+ )in the BESIII experiment.By decomposing the polarization state of Ω− particles along different coordinate axes,we examine the polarization dependence of the cross-section.Our results demonstrate that Ω− particles exhibit varying degrees of tensor polarization along the x-,y-,and z-axes,as well as weak vector polarization and rank-3 tensor polarization along the y-axis.To the best of our knowledge,this is the first study to calculate the polarization dependence of the cross-section distributions for the annihilation process e+e−→Ω−Ω¯^(+).Our theoretical predictions are in good agreement with the experimental measurements.

THE ERGODICITY FOR BI-IMMIGRATION BIRTH AND DEATH PROCESSES IN RANDOM ENVIRONMENT

The concepts of bi-immigration birth and death density matrix in random environment and bi-immigration birth and death process in random environment are introduced. For any bi-immigration birth and death matrix in random environment Q（θ） with birth rate λ 〈 death rate μ, the following results are proved, （1） there is an unique q-process in random environment, P^-（θ＊（0）;t） = （p^-（θ^＊（0）;t,i,j）,i,j ≥ 0）, which is ergodic, that is, lim t→∞（θ^＊（0）;t,i,j） = π^-（θ^＊（0）;j） ≥0 does not depend on i ≥ 0 and ∑j≥0π （θ＊（0）;j） = 1, （2） there is a bi-immigration birth and death process in random enjvironment （X^＊ = {X^＊,t ≥ 0},ε^＊ = {εt,t ∈ （-∞, ∞）}） with random transition matrix P^-（θ^＊ （0）;t） such that X^＊ is a strictly stationary process.

Electromagnetically induced transparency and electromagnetically induced absorption in Y-type system

The propagation of a probe field through a four-level Y-type atomic system is described in the presence of two additional coherent radiation fields,namely,the control field and the coupling field.An expression for the probe response is derived analytically from the optical Bloch equations under steady state condition to study the absorptive properties of the system under probe field propagation through an ensemble of stationary atoms as well as in a Doppler broadened atomic vapor medium.The most striking result is the conversion of electromagnetically induced transparency(EIT)into electromagnetically induced absorption(EIA)as we start switching from weak probe regime to strong probe regime.The dependence of this conversion on residual Doppler averaging due to wavelength mismatch is also shown by choosing the coupling transition as a Rydberg transition.

A RIGOROUS DERIVATION OF THE GROSS-PITAEVSKII HIERARCHY FOR WEAKLY COUPLED TWO-DIMENSIONAL BOSONS

In this article, we consider the dynamics of N two-dimensional boson systems interacting through a pair potential N-1Va（xi -xj） where Va（x） = a^-2V（x/a）. It is well known that the Cross-Pitaevskii （GP） equation is a nonlinear SchrSdinger equation and the GP hierarchy is an infinite BBGKY hierarchy of equations so that if ut solves the GP equation, then the family of k-particle density matrices { k ut, k≥1} solves the GP hierarchy. Denote by ψN,t the solution to the N-particle Schrodinger equation. Under the assumption that a = N^-ε for 0 〈 ε 〈 3/4, we prove that as N→∞ the limit points of the k-particle density matrices of CN,t are solutions of the GP hierarchy with the coupling constant in the nonlinear term of the GP equation given by f V（x） dx.

Intraband dynamics and terahertz emission in biased semiconductor superlattices coupled to double far-infrared pulses

This paper studies both the intraband polarization and terahertz emission of a semiconductor superlattice in combined dc and ac electric fields by using the superposition of two identical time delayed and phase shifted optical pulses. By adjusting the delay between these two optical pulses, our results show that the intraband polarization is sensitive to the time delay. The peak values appear again for the terahertz emission intensity due to the superposition of two optical pulses. The emission lines of terahertz blueshift and redshift in different ac electric fields and dynamic localization appears. The emission lines of THz only appear to blueshift when the biased superlattice is driven by a single optical pulse. Due to excitonic dynamic localization, the terahertz emission intensity decays with time in different dc and ac electric fields. These are features of this superlattice which distinguish it from a supertattice generated by a single optical pulse to drive it.

Ground-state phase diagram of the dimerizedspin-1/2 two-leg ladder

Dimerized spin-1/2 ladders exhibit a variety of phase structures,which depend on the intra-chain and inter-chain spin exchange energies as well as on the dimerization pattern of the ladder.Using the density matrix renormalization group(DMRG)algorithm,we study critical properties of the bond-alternating two-leg Heisenberg spin ladder with diagonal interaction J_(×).Two types of spin systems,staggered dimerized antiferromagnetic ladder and columnar dimerized ferro-antiferromagnetic couplings ladder,are investigated.To clarify the phase transition behaviors,we simultaneously analyze the string order parameter(SOP),the twisted order parameter(TOP),as well as a measurement of the quantum information analysis.Based on measuring this different observables,we establish the phase diagram accurately and give the fitting functions of the phase boundaries.In addition,the phase transition of cross-coupled spin ladder(in the absence of intrinsic dimerization)is also discussed.