Related papers: Efficient wavefunction propagation by minimizing a…
On the base of a 1D Shr\"{o}dinger equation the non-linear first-order differential equation (Ricatti type) for a quantum wave impedance function was derived. The advantages of this approach were discussed and demonstrated for a case of a…
The method developed by Van Dijk, Nogami and Toyama for obtaining the time-evolved wave function of a decaying quantum system is generalized to potentials and initial wave functions of non-compact support. The long time asymptotic behavior…
The dimension of the Hilbert space needed for the description of an interacting electron system increases exponentially with electron number $N$. As pointed out by W. Kohn this exponential wall problem (EWP) limits the concept of…
Numerical solutions to fractional differential equations can be extremely computationally intensive due to the effect of non-local derivatives in which all previous time points contribute to the current iteration. In finite difference…
A recently introduced effective quantum potential theory is studied in a low momentum region of phase space. This low momentum approximation is used to show that the new effective quantum potential induces a space-dependent mass and a…
The algorithm of modified wavelet analysis is discussed. It is based on the weighted least squares approximation. Contrary to the Gaussian as a weight function, we propose to use a compact weight function. The accuracy estimates using the…
We present a novel theoretical formulation for performing quantum dynamics in terms of moments within the single-particle description. By expressing the quantum dynamics in terms of increasing orders of moments, instead of single-particle…
We propose a polymer quantization scheme to derive the effective propagation of gravitational waves on a classical Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. These waves, which may originate from a high energy source, are a…
The evolution and propagation of a partially coherent matter wave (PCMW) is investigated theoretically by the correlation function method. The ABCD matrix formalism previously used for a fully coherent matter wave is extended to the PCMW…
We study the coherence in time and space of electromagnetic fields propagated through complex media. Whether for localization, imaging or telecommunication, the development of dedicated numerical techniques is generally based on the…
In this paper, we consider the classical wave equation with time-dependent, spatially multiscale coefficients. We propose a fully discrete computational multiscale method in the spirit of the localized orthogonal decomposition in space with…
We use variable transformation from the real line to finite or semi-infinite spaces where we expand the regular solution of the 1D time-independent Schrodinger equation in terms of square integrable bases. We also require that the basis…
In this paper, a general model of wireless channels is established based on the physics of wave propagation. Then the problems of inverse scattering and channel prediction are formulated as nonlinear filtering problems. The solutions to the…
We present an efficient \textit{ab initio} algorithm for quantum dynamics simulations of interacting systems that is based on the conditional decomposition of the many-body wavefunction [Phys. Rev. Lett. 113, 083003 (2014)]. Starting with…
An integral formulation for acoustic radiation in moving flows is presented. It is based on a potential formulation for acoustic radiation on weakly non-uniform subsonic mean flows. This work is motivated by the absence of suitable kernels…
Solving the wave equation on an infinite domain has been an ongoing challenge in scientific computing. Conventional approaches to this problem only generate numerical solutions on a small subset of the infinite domain. In this paper, we…
The general formulas to calculate the phase shifts of wave function of a particle scattering on a target formed by a pair of non-identical zero-range potentials are derived. It is shown that at asymptotically great distances from the target…
The study addresses the quantum spreading of a localized stationary flow of high energy particles. Results demonstrate that as particle energy increases, the spreading speed of the particle wave packet diminishes rapidly. Concurrently,…
We suggest scattering experiments which implement the concept of ``protective measurements'' allowing the measurement of the complete wave function even when only one quantum system (rather than an ensemble) is available. Such scattering…
We investigate the reconstruction of the transmission matrix of a time-evolving atmospheric channel with an online recursive optimization routine, using wave-optics simulations. We demonstrate that this estimation technique is able to keep…