相关论文: An effective and efficient algorithm for the Wigne…

We introduce a new arbitrarily high-order method for the rapid evaluation of hyperbolic potentials (space-time integrals involving the Green's function for the scalar wave equation). With $M$ points in the spatial discretization and $N_t$…

We introduce the Wigner functional representing a quantum field in terms of the field amplitudes and their conjugate momenta. The equation of motion for the functional of a scalar field point out the relevance of solutions of the classical…

Time reversal and spin flip are discrete symmetry operations of substantial import to quantum information and quantum computation. Spin flip arises in the context of separability, quantification of entanglement and the construction of…

In this article, we propose an efficient time-splitting Fourier pseudospectral method for the Wigner(-Poisson)-Fokker-Planck equations. The method achieves second-order accuracy in time and spectral accuracy in phase space, both of which…

A major challenge in single particle reconstruction methods using cryo-electron microscopy is to attain a resolution sufficient to interpret fine details in three-dimensional (3D) macromolecular structures. Obtaining high resolution 3D…

Quantum algorithms are well-suited to calculate estimates of the energy spectra for spin lattice systems. These algorithms are based on the efficient calculation of the discrete Fourier components of the density of states. The efficiency of…

In non-stationary signal processing, prior work has incorporated the quadratic-phase Fourier transform (QPFT) into the ambiguity function (AF) and Wigner distribution (WD) to enhance their performance. This paper introduces an advanced…

A quantum state can be written in phase space, but the resulting object is not generally the probability density of a positive stochastic process on ordinary phase space. We spell this out for Wigner dynamics. If a positive phase-space…

We show that real polarization method can be effectively used to geometrically quantize physical systems with compact phase space, like the spin. Our method enables us to construct a wave function of a qubit in both position and momentum…

In this paper, we introduce an algorithm that provides approximate solutions to semi-linear ordinary differential equations with highly oscillatory solutions, which, after an appropriate change of variables, can be rewritten as…

Tensor regression has attracted significant attention in statistical research. This study tackles the challenge of handling covariates with smooth varying structures. We introduce a novel framework, termed functional tensor regression,…

The coupled dynamics of the scissors mode and the isovector giant quadrupole resonance is studied in a model with separable quadrupole-quadrupole residual interactions. The method of Wigner function moments is applied to derive the…

The Wigner function of quantum systems is an effective instrument to construct the approximate classical description of the systems for which the classical approximation is possible. During the last time, the Wigner function formalism is…

Focusing inversion of potential field data for the recovery of sparse subsurface structures from surface measurement data on a uniform grid is discussed. For the uniform grid the model sensitivity matrices exhibit block Toeplitz Toeplitz…

The double Fourier sphere (DFS) method uses a clever trick to transform a function defined on the unit sphere to the torus and subsequently approximate it by a Fourier series, which can be evaluated efficiently via fast Fourier transforms.…

This work proposes a higher-order iterative framework for solving matrix equations, inspired by the structure and functionality of neural networks. A modification of the classical Jacobi iterative method is introduced to compute…

The Wigner D-matrix is essential in the course of angular momentum techniques. We here derive the new even- and odd-orthogonality properties of the Wigner D-matrix which was yet to be demonstrated in textbooks and also apply them to…

The quantum Fourier transform for discrete variable (dvQFT) is an efficient algorithm for several applications. It is usually considered for the processing of quantum bits (qubits) and its efficient implementation is obtained with two…

Let $\mathbf{K}$ be a field and $\phi$, $\mathbf{f} = (f_1, \ldots, f_s)$ in $\mathbf{K}[x_1, \dots, x_n]$ be multivariate polynomials (with $s < n$) invariant under the action of $\mathcal{S}_n$, the group of permutations of $\{1, \dots,…

Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…