Diagonal Matrix Elements Research Articles

Coupled transport in rotor models

Steady nonequilibrium states are investigated in a one-dimensional setup in the presence of two thermodynamic currents. Two paradigmatic nonlinear oscillators models are investigated: an XY chain and the discrete nonlinear Schrödinger equation. Their distinctive feature is that the relevant variable is an angle in both cases. We point out the importance of clearly distinguishing between energy and heat flux. In fact, even in the presence of a vanishing Seebeck coefficient, a coupling between (angular) momentum and energy arises, mediated by the unavoidable presence of a coherent energy flux. Such a contribution is the result of the ‘advection’ induced by the position-dependent angular velocity. As a result, in the XY model, the knowledge of the two diagonal elements of the Onsager matrix suffices to reconstruct its transport properties. The analysis of the nonequilibrium steady states finally allows to strengthen the connection between the two models.

Partially coherent electron transport in terahertz quantum cascade lasers based on a Markovian master equation for the density matrix

We derive a Markovian master equation for the single-electron density matrix, applicable to quantum cascade lasers (QCLs). The equation conserves the positivity of the density matrix, includes off-diagonal elements (coherences) as well as in-plane dynamics, and accounts for electron scattering with phonons and impurities. We use the model to simulate a terahertz-frequency QCL, and compare the results with both experiment and simulation via nonequilibrium Green's functions (NEGF). We obtain very good agreement with both experiment and NEGF when the QCL is biased for optimal lasing. For the considered device, we show that the magnitude of coherences can be a significant fraction of the diagonal matrix elements, which demonstrates their importance when describing THz QCLs. We show that the in-plane energy distribution can deviate far from a heated Maxwellian distribution, which suggests that the assumption of thermalized subbands in simplified density-matrix models is inadequate. We also show that the current density and subband occupations relax toward their steady-state values on very different time scales.

A note on four-particle form factors of operators in the sinh-Gordon model

The diagonal matrix elements between two-particle states in the sinh-Gordon model are computed analytically for all integers . This confirms the proposal [] by Smirnov and Zamolodchikov for these matrix elements and demonstrates the effectiveness of the algebraic approach to form factors.

Non-adiabatic dynamics around a conical intersection with surface-hopping coupled coherent states.

A surface-hopping extension of the coupled coherent states-method [D. Shalashilin and M. Child, Chem. Phys. 304, 103-120 (2004)] for simulating non-adiabatic dynamics with quantum effects of the nuclei is put forward. The time-dependent Schrödinger equation for the motion of the nuclei is solved in a moving basis set. The basis set is guided by classical trajectories, which can hop stochastically between different electronic potential energy surfaces. The non-adiabatic transitions are modelled by a modified version of Tully's fewest switches algorithm. The trajectories consist of Gaussians in the phase space of the nuclei (coherent states) combined with amplitudes for an electronic wave function. The time-dependent matrix elements between different coherent states determine the amplitude of each trajectory in the total multistate wave function; the diagonal matrix elements determine the hopping probabilities and gradients. In this way, both interference effects and non-adiabatic transitions can be described in a very compact fashion, leading to the exact solution if convergence with respect to the number of trajectories is achieved and the potential energy surfaces are known globally. The method is tested on a 2D model for a conical intersection [A. Ferretti, J. Chem. Phys. 104, 5517 (1996)], where a nuclear wavepacket encircles the point of degeneracy between two potential energy surfaces and interferes with itself. These interference effects are absent in classical trajectory-based molecular dynamics but can be fully incorpo rated if trajectories are replaced by surface hopping coupled coherent states.

Time dependence of the orthotropic compression Young’s moduli and Poisson’s ratios of Chinese fir wood

Abstract The time dependency of the orthotropic compliance for Chinese fir wood [Cunninghamia lanceolata (Lamb.) Hook] has been investigated by performing compressive creep experiments in all orthotropic directions. Time evolution of the creep strain in the axial and lateral directions was recorded by means of the digital image correlation (DIC) technique, to determine the diagonal and nondiagonal elements of the viscoelastic compliance matrix. The results reveal the significant influence of time on the mechanical behavior. The orthotropic nature of the viscoelastic compliance is highlighted by the different time dependency of the Young’s moduli and the Poisson’s ratios obtained for the individual directions. Differences among the time-dependent stress-strain relationship determined at the 25, 50, and 75% stress levels indicate that the viscoelastic behavior of wood is also load-dependent. A Poisson’s ratio values, which are increasing with time in ν LR , ν LT , ν RT , ν TR , and decreasing in ν RL and ν TL , demonstrate that the creep strain is influenced by loading directions. The substantially different time dependency of the nondiagonal elements of the compliance matrix further reveals the orthotropic compliance asymmetry and emphasizes the complexity of the viscoelastic character of wood.

Systematically generated two-qubit anyon braids

Fibonacci anyons are non-Abelian particles for which braiding is universal for quantum computation. Reichardt has shown how to systematically generate nontrivial braids for three Fibonacci anyons which yield unitary operations with off-diagonal matrix elements that can be made arbitrarily small in a particular natural basis through a simple and efficient iterative procedure. This procedure does not require brute force search, the Solovay-Kitaev method, or any other numerical technique, but the phases of the resulting diagonal matrix elements cannot be directly controlled. We show that despite this lack of control the resulting braids can be used to systematically construct entangling gates for two qubits encoded by Fibonacci anyons.

Object-oriented fusion of RADARSAT-2 polarimetric synthetic aperture radar and HJ-1A multispectral data for land-cover classification

The contribution of the integration of optical and polarimetric synthetic aperture radar (PolSAR) data to accurate land-cover classification was investigated. For this purpose, an object-oriented classification methodology that consisted of polarimetric decomposition, hybrid feature selection, and a support vector machine (SVM) was proposed. A RADARSAT-2 Fine Quad-Pol image and an HJ-1A CCD2 multispectral image were used as data sources. First, polarimetric decomposition was implemented for the RADARSAT-2 image. Sixty-one polarimetric parameters were extracted using different polarimetric decomposition methods and then merged with the main diagonal elements ( T 11 , T 22 , T 33 ) of the coherency matrix to form a multichannel image with 64 layers. Second, the HJ-1A and the multichannel images were divided into numerous image objects by implementing multiresolution segmentation. Third, 1104 features were extracted from the HJ-1A and the multichannel images for each image object. Fourth, the hybrid feature selection method that combined the ReliefF filter approach and the genetic algorithm (GA) wrapper approach (ReliefF–GA) was used. Finally, land-cover classification was performed by an SVM classifier on the basis of the selected features. Five other classification methodologies were conducted for comparison to verify the contribution of optical and PolSAR data integration and to test the superiority of the proposed object-oriented classification methodology. Comparison results show that HJ-1A data, RADARSAT-2 data, polarimetric decomposition, ReliefF–GA, and SVM have a significant contribution by improving land-cover classification accuracy.

Simulating Replica Exchange: Markov State Models, Proposal Schemes, and the Infinite Swapping Limit.

Replica exchange molecular dynamics is a multicanonical simulation technique commonly used to enhance the sampling of solvated biomolecules on rugged free energy landscapes. While replica exchange is relatively easy to implement, there are many unanswered questions about how to use this technique most efficiently, especially because it is frequently the case in practice that replica exchange simulations are not fully converged. A replica exchange cycle consists of a series of molecular dynamics steps of a set of replicas moving under different Hamiltonians or at different thermodynamic states followed by one or more replica exchange attempts to swap replicas among the different states. How the replica exchange cycle is constructed affects how rapidly the system equilibrates. We have constructed a Markov state model of replica exchange (MSMRE) using long molecular dynamics simulations of a host-guest binding system as an example, in order to study how different implementations of the replica exchange cycle can affect the sampling efficiency. We analyze how the number of replica exchange attempts per cycle, the number of MD steps per cycle, and the interaction between the two parameters affects the largest implied time scale of the MSMRE simulation. The infinite swapping limit is an important concept in replica exchange. We show how to estimate the infinite swapping limit from the diagonal elements of the exchange transition matrix constructed from MSMRE "simulations of simulations" as well as from relatively short runs of the actual replica exchange simulations.

Analytic results for the population dynamics of a driven dipolar molecular system

We theoretically investigate the dipolar molecular system driven by monochromatic periodic, linear, parabolic, and ${\mathrm{sech}}^{2}$ forms external fields, respectively. The two-level Hamiltonian model with nonzero diagonal dipole matrix elements is adopted to describe the population dynamics of the driven dipolar molecule, and the corresponding exact solutions are presented in terms of the confluent Heun equations without the generalized rotating-wave approximation. The analytic solutions derived here are valid in the whole parameter space.

Minimum Entropy as a Measure of Effective Dimensionality

We demonstrate that eigenvalues minimize information entropy of the main diagonal elements of a symmetric matrix over all possible orthogonal transforms. This legitimizes the use of the exponential entropy of standardized eigenvalues as a measure of effective covariance matrix dimensionality. In particular, this provides rigorous justification for the choice of the PCA basis in the construction of Effective Number of Trading Dimensions (ENTD) introduced in Gnedenko and Yelnik (2016).

Sparsity-Aware DOA Estimation Scheme for Noncircular Source in MIMO Radar.

In this paper, a novel sparsity-aware direction of arrival (DOA) estimation scheme for a noncircular source is proposed in multiple-input multiple-output (MIMO) radar. In the proposed method, the reduced-dimensional transformation technique is adopted to eliminate the redundant elements. Then, exploiting the noncircularity of signals, a joint sparsity-aware scheme based on the reweighted norm penalty is formulated for DOA estimation, in which the diagonal elements of the weight matrix are the coefficients of the noncircular MUSIC-like (NC MUSIC-like) spectrum. Compared to the existing norm penalty-based methods, the proposed scheme provides higher angular resolution and better DOA estimation performance. Results from numerical experiments are used to show the effectiveness of our proposed method.

Quantum state tomography via mutually unbiased measurements in driven cavity QED systems

We present a feasible proposal for quantum tomography of qubit and qutrit states via mutually unbiased measurements in dispersively coupled driven cavity QED systems. We first show that measurements in the mutually unbiased bases (MUBs) are practically implemented by projecting the detected states onto the computational basis after performing appropriate unitary transformations. The measurement outcomes can then be determined by detecting the steady-state transmission spectra (SSTS) of the driven cavity. It is found that all the measurement outcomes for each MUB (i.e., all the diagonal elements of the density matrix of each detected state) can be read out directly from only one kind of SSTS. In this way, we numerically demonstrate that the exemplified qubit and qutrit states can be reconstructed with the fidelities 0.952 and 0.961, respectively. Our proposal could be straightforwardly extended to other high-dimensional quantum systems provided that their MUBs exist.

Eigenstate thermalization in the two-dimensional transverse field Ising model.

We study the onset of eigenstate thermalization in the two-dimensional transverse field Ising model (2D-TFIM) in the square lattice. We consider two nonequivalent Hamiltonians: the ferromagnetic 2D-TFIM and the antiferromagnetic 2D-TFIM in the presence of a uniform longitudinal field. We use full exact diagonalization to examine the behavior of quantum chaos indicators and of the diagonal matrix elements of operators of interest in the eigenstates of the Hamiltonian. An analysis of finite size effects reveals that quantum chaos and eigenstate thermalization occur in those systems whenever the fields are nonvanishing and not too large.

Mixed Quantum-Classical Study of Nonadiabatic Curve Crossing in Condensed Phases.

We apply the mixed quantum-classical Liouville (MQCL) equation to investigate the nonadiabatic curve crossing in condensed phases. More specifically, electron transfer rate constants of the spin-Boson model are calculated by employing a rate constant expression using the collective solvent polarization as the reaction coordinate. In the calculation, classical nuclear degrees of freedom are initially sampled at the transition state configuration, and the initial state for the electronic degree of freedom is obtained from a mixed quantum-classical Boltzmann distribution. Different contributions to the electron transfer rate from the diagonal and off-diagonal elements of the initial density matrix, and contributions from trajectories with positive and negative initial velocities are analyzed. It is shown that the off-diagonal elements of the initial density matrix play an important role in the total electron transfer rate. The MQCL results are also compared with those calculated using Ehrenfest dynamics. It is found that, although the Ehrenfest dynamics is inaccurate when the reactive flux rate expression is used directly, it can give reasonably accurate results when individual contributions from the diagonal and off-diagonal elements of the initial density matrix are calculated.

Exact quantum Bayesian rule for qubit measurements in circuit QED.

Developing efficient framework for quantum measurements is of essential importance to quantum science and technology. In this work, for the important superconducting circuit-QED setup, we present a rigorous and analytic solution for the effective quantum trajectory equation (QTE) after polaron transformation and converted to the form of Stratonovich calculus. We find that the solution is a generalization of the elegant quantum Bayesian approach developed in arXiv:1111.4016 by Korotokov and currently applied to circuit-QED measurements. The new result improves both the diagonal and off-diagonal elements of the qubit density matrix, via amending the distribution probabilities of the output currents and several important phase factors. Compared to numerical integration of the QTE, the resultant quantum Bayesian rule promises higher efficiency to update the measured state, and allows more efficient and analytical studies for some interesting problems such as quantum weak values, past quantum state, and quantum state smoothing. The method of this work opens also a new way to obtain quantum Bayesian formulas for other systems and in more complicated cases.

Three Dimensional SRG Evolution of theNNInteractions Using Picard Iteration

The Similarity Renormalization Group (SRG) evolution of nucleon-nucleon (NN ) interactions is calculated directly as function of momentum vectors for realistic potentials. To overcome the stiffness of the SRG flow equations in differential form for far off diagonal matrix elements, the differential equation is transformed to an integral form without employing a partial wave decomposition.

The Calculation of Single-Nucleon Energies of Nuclei by Considering Two-Body Effective Interaction, n(k,ρ), and a Hartree-Fock Inspired Scheme

The nucleon single-particle energies (SPEs) of the selected nuclei, that is, O16, Ca40, and Ni56, are obtained by using the diagonal matrix elements of two-body effective interaction, which generated through the lowest-order constrained variational (LOCV) calculations for the symmetric nuclear matter with the Aυ18 phenomenological nucleon-nucleon potential. The SPEs at the major levels of nuclei are calculated by employing a Hartree-Fock inspired scheme in the spherical harmonic oscillator basis. In the scheme, the correlation influences are taken into account by imposing the nucleon effective mass factor on the radial wave functions of the major levels. Replacing the density-dependent one-body momentum distribution functions of nucleons, n(k,ρ), with the Heaviside functions, the role of n(k,ρ) in the nucleon SPEs at the major levels of the selected closed shell nuclei is investigated. The best fit of spin-orbit splitting is taken into account when correcting the major levels of the nuclei by using the parameterized Wood-Saxon potential and the Aυ18 density-dependent mean field potential which is constructed by the LOCV method. Considering the point-like protons in the spherical Coulomb potential well, the single-proton energies are corrected. The results show the importance of including n(k,ρ), instead of the Heaviside functions, in the calculation of nucleon SPEs at the different levels, particularly the valence levels, of the closed shell nuclei.

A representation-theoretic proof of the branching rule for Macdonald polynomials

We give a new representation-theoretic proof of the branching rule for Macdonald polynomials using the Etingof-Kirillov Jr. expression for Macdonald polynomials as traces of intertwiners of U_q(gl_n). In the Gelfand-Tsetlin basis, we show that diagonal matrix elements of such intertwiners are given by application of Macdonald's operators to a simple kernel. An essential ingredient in the proof is a map between spherical parts of double affine Hecke algebras of different ranks based upon the Dunkl-Kasatani conjecture.

Nonlocality in pure and mixed n-qubit X states

Nonlocality for general multiqubit X states is studied in detail. Pure and mixed states are analyzed as far as their maximum amount of nonlocality is concerned, and analytic results are obtained for important families of these states. The particular form of nonzero diagonal and antidiagonal matrix elements makes the corresponding study easy enough to obtain exact results. We also provide a numerical recipe to randomly generate an important family of X states endowed with a given degree of mixture.

BER Performance Analysis and Comparison for Large Scale MIMO Receiver

Objective: Multiple Input Multiple Output (MIMO) low complexity CHEMP (Channel Hardening Exploiting Message Passing) receiver which utilizes the channel hardening in the large scale MIMO channel to reduce the complexity. Methods: The Channel Hardening refers that the off diagonal elements of HTH matrix become progressively weaker than the diagonal elements because of the channel gain matrix H size increases. It is used for detection and estimation. The proposed receiver uses Message Passing Detection (MPD) algorithm and the estimation HTH matrix. Findings: Hence, the proposed receiver gives better performance than the Minimum Mean Square Error (MMSE) and Subspace Marginalization with Interference Suppression (SUMIS) detectors since the MPD detection algorithm uses only the matrix multiplication and it does not need the matrix inversion. Improvements: The optimized Low Density Parity Check (LDPC) codes are used to provide the considerable improvement than LDPC cods.