Related papers: Time-Dependent Duhamel Renormalization method with…
The spectral renormalization method was introduced by Ablowitz and Musslimani in 2005, [Opt. Lett. 30, pp. 2140-2142] as an effective way to numerically compute (time-independent) bound states for certain nonlinear boundary value problems.…
In this paper, we present a novel spectral renormalization exponential integrator method for solving gradient flow problems. Our method is specifically designed to simultaneously satisfy discrete analogues of the energy dissipation laws and…
Dynamical electronic- and vibrational-structure theories have received a growing interest in the last years due to their ability to simulate spectra recorded with ultrafast experimental techniques. The exact time evolution of a molecular…
We show that the time-dependent variational principle provides a unifying framework for time-evolution methods and optimisation methods in the context of matrix product states. In particular, we introduce a new integration scheme for…
A major advance in density-matrix renormalization group (DMRG) calculations has been achieved by the invention of highly efficient DMRG techniques for the simulation of real-time dynamics of strongly correlated quantum systems in one…
In this paper recent substantial progress in applying the density-matrix renormalization-group (DMRG) to the simulation of the time-evolution of strongly correlated quantum systems in one dimension is reviewed. Various approaches to…
In a recent Letter [Phys. Rev. Lett. 88, 256403(2002), cond-mat/0109158] Cazalilla and Marston proposed a time-dependent density- matrix renormalization group (TdDMRG) algorithm for the accurate evaluation of out-of-equilibrium properties…
We introduce a dispersive regularization of the compressible Euler equations in Lagrangian coordinates, in the one-dimensional torus. We assume a Van der Waals pressure law, which presents both hyperbolic and elliptic zones. The dispersive…
Methods of quantum nuclear wave-function dynamics have become very efficient in simulating large isolated systems using the time-dependent variational principle (TDVP). However, a straightforward extension of the TDVP to the density matrix…
The time-dependent Schr\"odinger equation (TDSE) in real space is fundamental to understanding the dynamics of many-electron quantum systems, with applications ranging from quantum chemistry to condensed matter physics and materials…
All the Doubly Special Relativity (DSR) models studied in literature so far involve a deformation of the energy conservation rule that forces us to release the hypothesis of the additivity of the energy for composite systems. In view of the…
In this paper a novel numerical scheme for finding the sparse self-localized states of a nonlinear system of equations with missing spectral data is introduced. As in the Petviashivili's and the spectral renormalization method, the…
We study the dynamical density matrix renormalization group (DDMRG) and time-dependent density matrix renormalization group (td-DMRG) algorithms in the ab initio context, to compute dynamical correlation functions of correlated systems. We…
We study linear time dispersive and dissipative systems. Very often such systems are not conservative and the standard spectral theory can not be applied. We develop a mathematically consistent framework allowing (i) to constructively…
The time domain linear sampling method (TD-LSM) solves inverse scattering problems using time domain data by creating an indicator function for the support of the unknown scatterer. It involves only solving a linear integral equation called…
We present a new temporal discretization paradigm for developing energy-production-rate preserving numerical approximations to thermodynamically consistent partial differential equation systems, called the supplementary variable method. The…
Electronic and/or vibronic coherence has been found by recent ultrafast spectroscopy experiments in many chemical, biological and material systems. This indicates that there are strong and complicated interactions between electronic states…
Multivariate time-series data in fields like healthcare and industry are informative but challenging due to high dimensionality and lack of labels. Recent self-supervised learning methods excel in learning rich representations without…
We implement and apply time-dependent density matrix renormalization group (TD-DMRG) algorithms at zero and finite temperature to compute the linear absorption and fluorescence spectra of molecular aggregates. Our implementation is within a…
We study a multi-determinant approach to the time evolution of the nuclear wave functions (TDMD). We employ the Dirac variational principle and use as anzatz for the nuclear wave-function a linear combination of Slater determinants and…