Related papers: Real time quantum dynamics preaveraged over imagin…
Ultrafast chemical reactions are difficult to simulate because they involve entangled, many-body wavefunctions whose computational complexity grows rapidly with molecular size. In photochemistry, the breakdown of the Born-Oppenheimer…
When suitably generalized and interpreted, the path-integral offers an alternative to the more familiar quantal formalism based on state-vectors, selfadjoint operators, and external observers. Mathematically one generalizes the…
We demonstrate that a numerical linked cluster expansion method is a powerful tool to calculate quantum dynamics. We calculate the dynamics of the magnetization and spin correlations in the two-dimensional transverse field Ising and XXZ…
The Feynman path integral representation of quantum theory is used in a non--parametric Bayesian approach to determine quantum potentials from measurements on a canonical ensemble. This representation allows to study explicitly the…
Applicability of Feynman path integral approach to numerical simulations of quantum dynamics in real time domain is examined. Coherent quantum dynamics is demonstrated with one dimensional test cases (quantum dot models) and performance of…
Molecular dynamics is based on solving Newton's equations for many-particle systems that evolve along complex, highly fluctuating trajectories. The orbital instability and short-time complexity of Newtonian orbits is in sharp contrast to…
The dynamics of a wide range of technologically important quantum systems are dominated by their interaction with just a few environmental modes. Such highly structured environments give rise to long-lived bath correlations that induce…
A generalized approach of the Born-Oppenheimer approximation is developed to analytically deal with the influence exercised by the spatial motion of atom's mass-center on a two-level atom in an optical ring cavity with a quantized…
Conventional molecular dynamics simulations macromolecules require long computational times because the most interesting motions are very slow compared with the fast oscillations of bond lengths and bond angles that limit the integration…
Optimally-shaped electromagnetic fields have the capacity to coherently control the dynamics of quantum systems and thus offer a promising means for controlling molecular transformations relevant to chemical, biological, and materials…
Metastability is a common obstacle to performing long molecular dynamics simulations. Many numerical methods have been proposed to overcome it. One method is parallel replica dynamics, which relies on the rapid convergence of the underlying…
We present a new formulation for the emergence of classical dynamics in a quantum world by considering a path integral approach that also incorporates continuous measurements. Our program is conceptually different from the decoherence…
Quantum transition amplitudes are formulated for a model system with local internal time, using path integrals. The amplitudes are shown to be more regular near a turning point of internal time than could be expected based on existing…
We generalize ideas in the recent literature and develop new ones in order to propose a general class of contour integral methods for linear convection-diffusion PDEs and in particular for those arising in finance. These methods aim to…
Dynamical maps describe general transformations of the state of a physical system, and their iteration can be interpreted as generating a discrete time evolution. Prime examples include classical nonlinear systems undergoing transitions to…
We introduce an approach for approximate real-time evolution of quantum systems using Tensor Renormalization Group (TRG) methods originally developed for imaginary time. We use Higher- Order TRG (HOTRG) to generate a coarse-grained time…
Prethermalization has been extensively studied in systems close to integrability. We propose a more general, yet conceptually simpler, setup for this phenomenon. We consider a---possibly nonintegrable---reference dynamics, weakly perturbed…
It is considered, in the framework of constrained systems, the quantum dynamics of non-relativistic particles moving on a d-dimensional Riemannian manifold M isometrically embedded in $R^{d+n}$. This generalizes recent investigations where…
If we use the path integral approach, we can write quantum electrodynamics (QED) in a way that is manifestly relativistic. However the path integrals are confined to paths that are on mass-shell. What happens if we extend QED by computing…
Many interesting physical theories have analytic classical actions. We show how Feynman's path integral may be defined non-perturbatively, for such theories, without a Wick rotation to imaginary time. We start by introducing a class of…