Related papers: An Error Bound for the Time-Sliced Thawed Gaussian…
This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…
Efficient and accurate numerical propagation of the time dependent Schroedinger equation is a problem with applications across a wide range of physics. This paper develops an efficient, trivially parallelizeable method for relaxing a trial…
We present a space-time ultra-weak discontinuous Galerkin discretization of the linear Schr\"odinger equation with variable potential. The proposed method is well-posed and quasi-optimal in mesh-dependent norms for very general discrete…
The frozen Gaussian approximation, proposed in [Lu and Yang, [15]], is an efficient computational tool for high frequency wave propagation. We continue in this paper the development of frozen Gaussian approximation. The frozen Gaussian…
We consider a version of the stationary phase method in one dimension of A. Erd\'elyi, allowing the phase to have stationary points of non-integer order and the amplitude to have integrable singularities. After having completed the original…
In the present paper we consider the semiclassical magnetic Schr\"odinger equation, which describes the dynamics of particles under the influence of a magnetic field. The solution of the time-dependent Schr\"odinger equation is approximated…
The goal of this paper is to provide an analysis of the "toolkit" method used in the numerical approximation of the time-dependent Schr\"odinger equation. The "toolkit" method is based on precomputation of elementary propagators and was…
The free expansion of a Gaussian wavepacket is a problem commonly discussed in undergraduate quantum classes by directly solving the time-dependent Schrodinger equation as a differential equation. In this work, we provide an alternative way…
In this paper, we present a variational treatment of the linear dependence for a non-orthogonal time-dependent basis set in solving the Schr\"odinger equation. The method is based on: i) the definition of a linearly independent working…
Sparsity properties for phase-space representations of several types of operators have been extensively studied in recent papers, including pseudodifferential, Fourier integral and metaplectic operators, with applications to time-frequency…
The goal of this paper is to provide an analysis of the ``toolkit'' method used in the numerical approximation of the time-dependent Schr\"odinger equation. The ``toolkit'' method is based on precomputation of elementary propagators and was…
Stretched Gaussian distribution is the fundamental solution of the Hausdorff derivative diffusion equation and its corresponding stretched Gaussian noise is a widely encountered non-Gaussian noise in science and engineering. The least…
Propagation of high-frequency wave in periodic media is a challenging problem due to the existence of multiscale characterized by short wavelength, small lattice constant and large physical domain size. Conventional computational methods…
In this paper, we study time decay estimates for the Schr\"odinger propagator on the product cone $(X,g)$, where $X=C(\rho \mathbb{S}^{n-1})=(0,\infty)\times \rho\mathbb{S}^{n-1}$. We prove that the usual dispersive estimate holds when the…
We consider a semiclassical approximation for the time evolution of an originally gaussian wave packet in terms of complex trajectories. We also derive additional approximations replacing the complex trajectories by real ones. These yield…
In this paper, we reformulate the semi-classical Schr\"odinger equation in the presence of electromagnetic field by the Gaussian wave packets transform. With this approach, the highly oscillatory Schr\"odinger equation is equivalently…
We derive dispersion estimates for solutions of the one-dimensional discrete perturbed Schr\"odinger and wave equations. In particular, we improve upon previous works and weaken the conditions on the potentials. To this end we also provide…
Consider the scattering of an acoustic plane wave by a bounded elastic obstacle which is immersed in an open space filled with a homogeneous medium. This paper concerns the mathematical analysis of the coupled two- and three-dimensional…
The L\'evy, jumping process, defined in terms of the jumping size distribution and the waiting time distribution, is considered. The jumping rate depends on the process value. The fractional diffusion equation, which contains the variable…
This work develops an energy-based discontinuous Galerkin (EDG) method for the nonlinear Schr\"odinger equation with the wave operator. The focus of the study is on the energy-conserving or energy-dissipating behavior of the method with…