相关论文: Initial wave packets and the various power-law dec…
The behavior of both the survival S(t) and nonescape P(t) probabilities at long times for the one-dimensional free particle system is shown to be closely connected to that of the initial wave packet at small momentum. We prove that both…
The dynamics of an initially localized wavepacket is studied for the generalized nonlinear Schroedinger Equation with a random potential, where the nonlinearity term is |\psi|^p*\psi and "p" is arbitrary. Mainly short times for which the…
A family of wave packets with power law tails are employed to analyze the long time dependence of the corresponding probability density. The densities, associated to packets for free particles in the one-dimensional space, with sufficiently…
In this study, potential scatterings are formulated in experimental setups with Gaussian wave packets in accordance with a probability principle and associativity of products. A breaking of an associativity is observed in scalar products…
Wave-packet scattering from a stationary potential is significantly modified when the wave-packet is subject to an external time-dependent force during the interaction. In the semiclassical limit, wave--packet motion is simply described by…
We study the asymptotic behavior of Bohmian trajectories in a scattering situation with short range potential and for wave functions with a scattering and a bound part. It is shown that the set of possible trajectories splits into…
Normalized wave packets express particles in nature. Their sizes are determined by their interactions with matter, and depend on environments. Nevertheless, these characterize scatterings processes in realistic situations, and govern the…
Conditions are established for the existence of a scattering length and an effective range in the low-energy expansion of the S-wave phase-shift of a central potential in two and three dimensions. The behavior of the phase-shift as a…
Nonlinear initial-boundary value problem on deep-water gravity waves of finite amplitude is solved approximately (up to small terms of higher order) assuming that the waves are generated by an initial disturbance to the water and the…
We consider the long-time behavior of solutions to the short-pulse equation. Using the method of testing by wave packets, we prove small data global existence and modified scattering.
The short-time behavior of quantum decay of an unstable state initially located within an interaction region of finite range is investigated using a resonant expansion of the survival amplitude. It is shown that in general the short-time…
We investigate the long time behavior of a wavepacket initially localized at a single site $n_0$ in translationally invariant harmonic and anharmonic chains with random interactions. In the harmonic case, the energy profile $ \bar{<…
We investigate the short-time dynamics of a delta-function potential barrier on an initially confined wave-packet. There are mainly two conclusions: A) At short times the probability density of the first particles that passed through the…
The long time behaviour of the survival probability of initial state and its dependence on the initial states are considered, for the one dimensional free quantum particle. We derive the asymptotic expansion of the time evolution operator…
The variation of the size of two-body objects is investigated, as the separation energy approaches zero, with both long range potentials and short range potentials having a repulsive core. It is shown that long range potentials can also…
Internal waves are believed to be of primary importance as they affect ocean mixing and energy transport. Several processes can lead to the breaking of internal waves and they usually involve non linear interactions between waves. In this…
In this work we present a general derivation of the non-Fickian behavior for the self-diffusion of identically interacting particle systems with excluded mutual passage. We show that the conditional probability distribution of finding a…
According to Bohmian dynamics, the particles of a quantum system move along trajectories, following a velocity field determined by the wave-function Psi(x,t). We show that for simple one-dimensional systems any initial probability…
We introduce power-law tail quantum wave packets. We show that they can be seen as eigenfunctions of a Hamiltonian with a physical potential. We prove that the free evolution of these packets presents an asymptotic decay of the maximum of…
Modified scattering phenomena are encountered in the study of global properties for nonlinear dispersive partial differential equations in situations where the decay of solutions at infinity is borderline and scattering fails just barely.…