相关论文: The Van Vleck Formula on Ehrenfest time scales and…

Using phase-space complexification, an Initial Value Representation (IVR) for the semiclassical propagator in position space is obtained as a composition of inverse Segal-Bargmann (S-B) transforms of the semiclassical coherent state…

Van Roosbroeck's equations constitute a versatile tool to determine the dynamics of electrons under time- and space-dependent perturbations. Extensively utilized in ordinary semiconductors, their potential to model devices made from…

In this note we study the properties of a sequence of approximate propagators for the Schr\"odinger equation, in the spirit of Feynman's path integrals. Precisely, we consider Hamiltonian operators arising as the Weyl quantization of a…

When computing quantum-mechanical observables, the ``curse of dimensionality'' limits the naive approach that uses the quantum-mechanical wavefunction. The semiclassical Herman--Kluk propagator mitigates this curse by employing a grid-free…

We derive an extension of the standard time dependent WKB theory which can be applied to propagate coherent states and other strongly localised states for long times. It allows in particular to give a uniform description of the…

The steady state of the Fokker-Planck equation corresponding to a density dependent one-step process is approximated by a suitable normal distribution. Starting from the master equations of the process, written in terms of the time…

We present a trajectory-based semiclassical calculation of the Ehrenfest-time dependence of the weak localization correction and the universal conductance fluctuations of a ballistic quantum dot with ideal point contacts. While the weak…

We develop a phase-space framework for fractional generalised anharmonic oscillators and their heat semigroups on weighted modulation spaces. We consider operators of the form \[ \mathcal{H}_{k,l}=(-\Delta)^{l}+V(x), \] where $V$ is a…

The Ehrenfest dynamics, representing a quantum-classical mean-field type coupling, is a widely used approximation in quantum molecular dynamics. In this paper, we propose a time-splitting method for an Ehrenfest dynamics, in the form of a…

We study a crossover from classical to quantum picture in the electron energy statistics in a system with broken time-reversal symmetry. The perturbative and nonperturbative parts of the two level correlation function, $R(\omega)$ are…

We present a stochastic method for solving the time-dependent Schr\"odinger equation, generalizing a ground-state full configuration interaction Quantum Monte Carlo method. By performing the time-integration in the complex plane close to…

This paper is devoted to the numerical analysis of the Hermite spectral method proposed in [14], which provides, in the semiclassical limit, an asymptotic preserving approximation of the von Neumann equation. More precisely, it relies on…

We consider the propagation of wave packets for the nonlinear Schrodinger equation, in the semi-classical limit. We establish the existence of a critical size for the initial data, in terms of the Planck constant: if the initial data are…

In this work, we address the problem of approximating the $k$-disc distribution ("frequency vector") of a bounded-degree graph in sublinear-time under the assumption of hyperfiniteness. We revisit the partition-oracle framework of Hassidim,…

We extend our recently developed semiclassical strong-field Herman-Kluk propagator (SFHK) method to calculate high-order harmonic generation (HHG) for atoms in intense lasers. We show that our method, based on a combination of the…

Following Ehrenfest's approach, the problem of quantum-classical correspondence can be treated in the class of trajectory-coherent functions that approximate as $\h\to 0$ a quantum-mechanical state. This idea leads to a family of systems of…

We investigate the asymptotic behaviour of solutions of a class of nonlocal Fokker--Planck equations defined by nonsingular, heavy-tailed convolution kernels and characterised by a scaling parameter $\e\in(0,1]$ and a fractional index…

When the semiclassical Herman-Kluk propagator is used for evaluating quantum-mechanical observables or time-correlation functions, the initial conditions for the guiding trajectories are typically sampled from the Husimi density. Here, we…

For two Coulombically interacting electrons in a quantum dot with harmonic confinement and a constant magnetic field, we show that time-dependent semiclassical calculations using the Herman-Kluk initial value representation of the…

We study the influence of inelastic electron-electron scattering on the temperature variation of the Seebeck coefficient in the normal phase of quasi-one-dimensional organic superconductors. The theory is based on the numerical solution of…