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A new fast multipole formulation for solving elliptic difference equations on unbounded domains and its parallel implementation are presented. These difference equations can arise directly in the description of physical systems, e.g.…
We establish a general relation between the statistics of the local Green's function for systems with chaotic wave scattering and a uniform energy loss (absorption) and its two-point correlation function for the same system without…
This work provides a unified theoretical treatment of the single and correlated double-electron emission from a general electronic system. Using Feshbach projection method, the states of interest are selected by the projection operator; the…
The method proposed by Inomata and his collaborators allows us to transform a damped Caldiroli-Kanai oscillator with time-dependent frequency to one with constant frequency and no friction by redefining the time variable, obtained by…
Maxwell's equations for electrodynamics of dispersive and absorptive (passive) media are written in the form of the Schr\"odinger equation with a non-Hermitian Hamiltonian. The Lanczos time-propagation scheme is modified to include…
We study low-energy expansion and high-energy expansion of reflection coefficients for one-dimensional Schr\"odinger equation, from which expansions of the Green function can be obtained. Making use of the equivalent Fokker-Planck equation,…
We present an algorithm for measurement of the Green's function in the hybridization expansion continuous-time quantum Monte-Carlo based on continuous estimators. Compared to the standard method, the present algorithm has similar or better…
Nonequilibrium Green's functions represent underutilized means of studying the time evolution of quantum many-body systems. In view of a rising computer power, an effort is underway to apply the Green's functions formalism to the dynamics…
The discretisation of boundary integral equations for the scalar Helmholtz equation leads to large dense linear systems. Efficient boundary element methods (BEM), such as the fast multipole method (FMM) and $\Hmat$ based methods, focus on…
Normal and anomalous diffusion are ubiquitous in many complex systems [1] . Here, we define a time and space generalized diffusion equation (GDE), which uses fractional-time derivatives and transformed d-path Laplacian operators on…
The non-hermitian quantum dynamics of excitonic energy transfer in photosynthetic systems is investigated using a dissipative two-level dimer model. The approach is based on the Green's function formalism which permits consideration of…
Recent advances in attosecond science have made it increasingly important to develop stable, reliable and accurate algorithms and methods to model the time evolution of atoms and molecules in intense laser fields. A key process in…
We show that a pseudospectral representation of the wavefunction using multiple spatial domains of variable size yields a highly accurate, yet efficient method to solve the time-dependent Schr\"odinger equation. The overall spatial domain…
Interacting many-body quantum systems show a rich array of physical phenomena and dynamical properties, but are notoriously difficult to study: they are challenging analytically and exponentially difficult to simulate on classical…
Nonequilibrium quantum mechanics can be solved with the Keldysh formalism, which evolves the quantum mechanical states forward in time in the presence of a time-dependent field, and then evolves them backward in time, undoing the effect of…
Three numerical algorithms are proposed to solve the time-dependent elastodynamic equations in elastic solids. All algorithms are based on approximating the solution of the equations, which can be written as a matrix exponential. By…
We study the long time behavior of second order particle systems interacting through global Lipschitz kernels. Combining hypocoercivity method in [37] and relative entropy method in [25], we are able to overcome the degeneracy of diffusion…
We introduce ECHO, a transformer-operator framework for generating million-point PDE trajectories. While existing neural operators (NOs) have shown promise for solving partial differential equations, they remain limited in practice due to…
We propose an algorithm based on variational quantum imaginary time evolution for solving the Feynman-Kac partial differential equation resulting from a multidimensional system of stochastic differential equations. We utilize the…
A quantum algorithm is developed to calculate decay rates and cross sections using quantum resources that scale polynomially in the system size assuming similar scaling for state preparation and time evolution. This is done by computing…