Related papers: Numerical approaches to time evolution of complex …
The combined quantum electron-nuclear dynamics is often associated with the Born-Huang expansion of the molecular wave function and the appearance of nonadiabatic effects as a perturbation. On the other hand, native multicomponent…
We investigate how dynamical decoupling methods may be used to manipulate the time evolution of quantum many-body systems. These methods consist of sequences of external control operations designed to induce a desired dynamics. The systems…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
In this work simple and effective quantization procedure of classical dynamical systems is proposed and illustrated by a number of examples. The procedure is based entirely on differential equations which describe time evolution of systems.
In view of the current availability and variety of measured data, there is an increasing demand for powerful signal processing tools that can cope successfully with the associated problems that often arise when data are being analysed. In…
We characterize good clocks, which are naturally subject to fluctuations, in statistical terms. We also obtain the master equation that governs the evolution of quantum systems according to these clocks and find its general solution. This…
We introduce the concept of numerical Gaussian processes, which we define as Gaussian processes with covariance functions resulting from temporal discretization of time-dependent partial differential equations. Numerical Gaussian processes,…
Switching dynamical systems are an expressive model class for the analysis of time-series data. As in many fields within the natural and engineering sciences, the systems under study typically evolve continuously in time, it is natural to…
A quantum walk is the quantum analogue of a random walk. While it is relatively well understood how quantum walks can speed up random walk hitting times, it is a long-standing open question to what extent quantum walks can speed up the…
There is a growing interest in methods for detecting and interpreting changes in experimental time evolution data. Based on measured time series, the quantitative characterization of dynamical phase transitions at bifurcation points of the…
We propose quantum methods for solving differential equations that are based on a gradual improvement of the solution via an iterative process, and are targeted at applications in fluid dynamics. First, we implement the Jacobi iteration on…
Biharmonic wave equations are of importance to various applications including thin plate analyses. In this work, the numerical approximation of their solutions by a $C^1$-conforming in space and time finite element approach is proposed and…
We investigate what a snapshot of a quantum evolution - a quantum channel reflecting open system dynamics - reveals about the underlying continuous time evolution. Remarkably, from such a snapshot, and without imposing additional…
The theoretical analysis of the Adiabatic Quantum Computation protocol presents several challenges resulting from the difficulty of simulating, with classical resources, the unitary dynamics of a large quantum device. We present here a…
Variational quantum algorithms offer a promising new paradigm for solving partial differential equations on near-term quantum computers. Here, we propose a variational quantum algorithm for solving a general evolution equation through…
We study a homogenisation problem for problems of mixed type in the framework of evolutionary equations. The change of type is highly oscillatory. The numerical treatment is done by a discontinuous Galerkin method in time and a continuous…
Time evolution of quantum systems is of interest in physics, in chemistry, and, more recently, in computer science. Quantum computers are suggested as one route to propagating quantum systems far more efficiently than ordinary numerical…
A time-stepping scheme with adaptivity in both the step size and the integration order is presented in the context of non-equilibrium dynamics described via Kadanoff-Baym equations. The accuracy and effectiveness of the algorithm are…
We present a new high-order accurate computational fluid dynamics model based on the incompressible Navier-Stokes equations with a free surface for the accurate simulation of nonlinear and dispersive water waves in the time domain. The…
Evolution in imaginary time is a prominent technique for finding the ground state of quantum many-body systems, and the heart of a number of numerical methods that have been used with great success in quantum chemistry, condensed matter and…