相关论文: Discrete phase integral method for five-term recur…

We develop a path integral representation for the dynamics of quantum systems with a finite-dimensional Hilbert space, formulated entirely within a discrete phase space. Starting from the discrete Wigner function defined on $\mathbb{Z}_d…

We present a deep learning approach for computing multi-phase solutions to the semiclassical limit of the Schr\"odinger equation. Traditional methods require deriving a multi-phase ansatz to close the moment system of the Liouville…

We formulate analytically the reflection of a one dimensional, expanding free wave-packet (wp) from an infinite barrier. Three types of wp's are considered, representing an electron, a molecule and a classical object. We derive a threshold…

We introduce topological phases of matter defined by skyrmions in the ground state spin -- or pseudospin -- expectation value textures in the Brillouin zone, the chiral and helical topological skyrmion phases of matter. These phases are…

Several strategies in phase retrieval are unified by an iterative "difference map" constructed from a pair of elementary projections and a single real parameter $\beta$. For the standard application in optics, where the two projections…

We present strongly stable semi-discrete finite difference approximations to the quarter space problem (x>0, t>0) for the first order in time, second order in space wave equation with a shift term. We consider space-like (pure outflow) and…

In transport theory, physical phenomena are well described using the Boltzmann equation, which is efficiently simulated and discretized with the lattice Boltzmann method. The collision step defines the microscopic molecules behavior, and…

We study the problem of recovering the phase from magnitude measurements; specifically, we wish to reconstruct a complex-valued signal x of C^n about which we have phaseless samples of the form y_r = |< a_r,x >|^2, r = 1,2,...,m (knowledge…

Fractional Klein-Kramers equation can well describe subdiffusion in phase space. In this paper, we develop the fully discrete scheme for fractional Klein-Kramers equation based on the backward Euler convolution quadrature and local…

An initial-boundary value problem for the $n$-dimensional ($n\geq 2$) time-dependent Schr\"odinger equation in a semi-infinite (or infinite) parallelepiped is considered. Starting from the Numerov-Crank-Nicolson finite-difference scheme, we…

Interacting quantum spin models are remarkably useful for describing different types of physical, chemical, and biological systems. Significant understanding of their equilibrium properties has been achieved to date, especially for the case…

Phase field modelling offers an extremely general framework to predict microstructural evolutions in complex systems. However, its computational implementation requires a discretisation scheme with a grid spacing small enough to preserve…

We consider the time discretization based on Lie-Trotter splitting, for the nonlinear Schrodinger equation, in the semi-classical limit, with initial data under the form of WKB states. We show that both the exact and the numerical solutions…

Mathematical models of protein-protein dynamics, such as the heterodimer model, play a crucial role in understanding many physical phenomena. This model is a system of two semilinear parabolic partial differential equations describing the…

We have theoretically investigated the time-symmetry breaking phase transition process for two discrete states coupled with a one-dimensional continuum by solving the nonlinear eigenvalue prob- lem for the effective Hamiltonian associated…

We develop time integration methods in low-rank representation that can adaptively adjust approximation ranks to achieve a prescribed accuracy, while ensuring that these ranks remain proportional to the corresponding best approximation…

We investigate nonrelativistic quantum mechanics on the discretized half-line, constructing a one-parameter family of Hamiltonians that are analogous to the Robin family of boundary conditions in continuum half-line quantum mechanics. For…

A simple formula is derived for the maximum squeezing rate which occurs at the initial stages of the squeezing process: the rate only depends on the second partial derivatives of a classical Hamiltonian. Rules for optimum rotation of the…

We point out some problems with the previously-proposed phase diagram of the $Z_6$ spin models. Consideration of the diagram near to the decoupling surface using both exact and approximate arguments suggests a modification which remedies…

We present a simplification of the recursive algorithm for the evaluation of intersection numbers for differential $n$-forms, by combining the advantages emerging from the choice of delta-forms as generators of relative twisted cohomology…