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In this paper we study quantum simulation algorithms on the elastic wave equations using the Schr\"odingerisation method. The Schr\"odingerisation method transforms any linear PDEs into a system of Schr\"odinger-type PDEs -with unitary…
The real-time contour formalism for Green's functions provides time-dependent information of quantum many-body systems. In practice, the long-time simulation of systems with a wide range of energy scales is challenging due to both the…
The rogue wave solutions (rational multi-breathers) of the nonlinear Schrodinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5…
We develop an analog classical simulation algorithm of noiseless quantum dynamics. By formulating the Schr\"{o}dinger equation into a linear system of real-valued ordinary differential equations (ODEs), the probability amplitudes of a…
We obtain analytic solution of the time-independent Schrodinger equation in two dimensions for a charged particle moving in the field of an electric quadrupole. The solution is written as a series in terms of special functions that support…
We analyze the two-dimensional photoelectrons momentum distribution of Ar atom ionized by midinfrared laser pulses and mainly concentrate on the energy range below 2Up. By using a generalized quantum trajectory Monte Carlo (GQTMC)…
Time-dependent Partial Differential Equations with given initial conditions are considered in this paper. New differentiation techniques of the unknown solution with respect to time variable are proposed. It is shown that the proposed…
This paper proposes a new non-iterative time-domain simulation approach using Differential Transform Method (DTM) to solve the set of non-linear Differential-Algebraic Equations (DAEs) involved in a DFIG-based wind power system. The DTM is…
We live in an age in which high-performance computing is transforming the way we do science. Previously intractable problems are now becoming accessible by means of increasingly realistic numerical simulations. One of the most enduring and…
Classical simulations of quantum computations are vital for the future development of this emerging technology. To this end, decision diagrams have been proposed as a complementary technique which frequently allows to tackle the inherent…
The curse of dimensionality is ubiquitous in both numerical and data-driven methods. This is particularly severe for space-time methods, which treat the combined space-time domain simultaneously. We investigate the effectiveness of a…
Time-dependent quantum chemical methods coupled to Gaussian basis sets are gaining popularity in modeling the electron dynamics of atoms and molecules interacting with intense laser fields. Two approaches most widely used for this purpose,…
We improve the complex scaling method (CSM) to obtain virtual states, which were previously challenging in the conventional CSM. Our approach solves the Schr\"odinger equation in the momentum space as an eigenvalue problem by choosing the…
An important class of spatio-temporal models is constructed by leveraging the hierarchical structure of dynamical (or, state-space) models. This paper proposes a new statistical dynamical model for spatio-temporal processes motivated by…
We review an explicit approach to obtaining numerical solutions of the Schr\"odinger equation that is conceptionally straightforward and capable of significant accuracy and efficiency. The method and its efficacy are illustrated with…
We develop a novel approach to the coupled motion of electrons and ions that focuses on the dynamics of the electronic subsystem. Usually the description of electron dynamics involves an electronic Schr\"odinger equation where the nuclear…
We present a list of formulas describing classical radiation of the rank s tensor field from an accelerated point-like source in flat space-time of arbitrary even dimension d. This allows straightforward evaluating the total intensity and…
We present an efficient classical algorithm based on the construction of a unitary quantum circuit for simulating the Isotropic Wave Equation (IWE) in one, two, or three dimensions. Using an analogy with the massless Dirac equation, second…
The assisted Schwinger effect, which is predicted to display non-perturbative quantum tunnelling, is expected to be produced in precision lab experiments with electron beams and intense lasers. Indeed, many novel effects predicted by a…
Multi-dimensional direct numerical simulation (DNS) of the Schr\"odinger equation is needed for design and analysis of quantum nanostructures that offer numerous applications in biology, medicine, materials, electronic/photonic devices,…