Related papers: The time-dependent Born-Oppenheimer approximation
We present a time-dependent extension of logarithmic perturbation theory for nonrelativistic quantum dynamics governed by the Schr\"odinger equation, in which the logarithm of the wave function is expanded in powers of a coupling constant.…
We prove strong small deviations results for Brownian motion under independent time-changes satisfying their own asymptotic criteria. We then apply these results to certain stochastic integrals which are elements of second-order homogeneous…
A four dimensional treatment of nonrelativistic space-time gives a natural frame to deal with objective time derivatives. In this framework some well known objective time derivatives of continuum mechanics appear as Lie-derivatives. Their…
We propose a new approximation-technique to deal with the exact macroscopic integro-differential evolution equations of statistical systems which self-consistently accounts for dissipative effects. Concentrating on one and two point…
Emergence of one-time-direction macroscopic evolution of a classical system of two mixed gases having different temperatures is derived and explained. The analysis performed at the microscopic level, where the time-symmetric laws of…
We consider a time-fractional subdiffusion equation with a Caputo derivative in time, a general second-order elliptic spatial operator, and a right-hand side that is non-smooth in time. The presence of the latter may lead to locking…
Inconsistencies are pointed out in a recent proposal [L. Diosi, Phys. Rev. A 80, 064104 (2009); arXiv:0905.3908v1] for a quantum version of the classical linear Boltzmann equation.
The energy-dependent frame transformation theory of Gao and Greene 1990 [Phys. Rev. A {\bf 42}, 6946 (1990)] is extended to yield quantitatively accurate description of the dissociative recombination process. Evidence is presented to show…
Linear-time invariant (LTI) oscillation systems such as forced mechanical vibration, series RLC and parallel RLC circuits can be solved by using simplest initial conditions or employing of Green's function of which knowledge of initial…
Network interactions between dynamical units are often subject to time delay. We develop a phase reduction method for delay-coupled oscillator networks. The method is based on rewriting the delay-differential equation as an ordinary…
Conventional lattice Boltzmann models only satisfy moment isotropy up to fourth order. In order to accurately describe improtant physical effects beyond the isothermal Navier-Stokes fluid regime, higher order isotropy is required. In this…
This work explores Boltzmann's time hypothesis, which associates the perceived direction of "time flow" with the second law of thermodynamics. We discuss mechanisms that can be responsible for the action of the second law, for directional…
We study an ordinary differential equation controlled by a stochastic process. We present results on existence and uniqueness of solutions, on associated local times (Trotter and Ray-Knight theorems), and on time and direction of…
The global many-electron wave function overlap matrix accounts for all effects beyond the Born-Oppenheimer approximation in the discrete variable local diabatic representation, a numerically exact framework for modeling nonadiabatic conical…
Various methods have been proposed to approximate a solution to the truncated Hausdorff moment problem. In this paper, we establish a method of comparison for the performance of the approximations. Three ways of producing random moment…
We present some novel results indicating that time's description in present-day physics is deficient. We use Hawking's information-erasure hypothesis to counter his own claim that time's arrow depends only on initial conditions. Next, we…
The existence of small amounts of advanced radiation, or a tilt in the arrow of time, makes the basic equations of physics mixed-type functional differential equations. The novel features of such equations point to a microphysical structure…
We construct local solutions to the Benjamin-Ono equation for quasi-periodic initial data. The solution is unique among limits of smooth solutions and depends continuously on the data. Our result applies to a richer class of quasi-periodic…
Using the Mott exact cross section for moderate relativistic energies, we calculated the corrections to the first-order Born higher moments of the energy-loss distribution of charged particles in a wide range of the particle charge numbers.
It is shown that the justification of the Boltzman H-theorem needs more than just the assumption of molecular chaos and the picture of time irreversibility related to it should be reinvestigated.