Related papers: Complex Trajectories in a Classical Periodic Poten…
Understanding the crossover from quantum to classical transport phenomena has become of fundamental importance not only for technological applications due to the creation of sub-10nm transistors - an important building block of our modern…
Recently it has been shown that the evolution of open quantum systems may be ``unraveled'' into individual ``trajectories,'' providing powerful numerical and conceptual tools. In this letter we use quantum trajectories to study mesoscopic…
For zero energy, $E=0$, we derive exact, classical solutions for {\em all} power-law potentials, $V(r)=-\gamma/r^\nu$, with $\gamma>0$ and $-\infty <\nu<\infty$. When the angular momentum is non-zero, these solutions lead to the orbits…
We study the stability in finite times of the trajectories of interacting particles. Our aim is to show that in average and uniformly in the number of particles, two trajectories whose initial positions in phase space are close, remain…
A classical mechanics of two Coulomb charges on a plane $(e_1, m_1)$ and $(e_2, m_2)$ subject to a constant magnetic field perpendicular to a plane is considered. Special "superintegrable" trajectories (circular and linear) for which the…
We study the quantum transport through entropic barriers induced by hardwall constrictions of hyperboloidal shape in two and three spatial dimensions. Using the separability of the Schrodinger equation and the classical equations of motion…
We consider the possibility that classical dynamical systems display motion in their lowest energy state, forming a time analogue of crystalline spatial order. Challenges facing that idea are identified and overcome. We display arbitrary…
Trajectories in logarithmic potentials are investigated by taking as example the motion of an electron within a cylindrical capacitor. The solution of the equation of motion in plane polar coordinates, (r,{\phi}) is attained by forming a…
We investigate the quantum recurrence phenomena in periodically driven systems. We calculate the classical period and the quantum recurrence time and develop their interdependence. We further predict the behavior of the recurrence phenomena…
The fragmentation of diatomic molecules under a stochastic force is investigated both classically and quantum mechanically, focussing on their dissociation probabilities. It is found that the quantum system is more robust than the classical…
We extract the information of a quantum motion and decode it into a certain orbit via a single measurable quantity. Such that a quantum chaotic system can be reconstructed as a chaotic attractor. Two configurations for reconstructing this…
Reaction paths and classical and quantum trajectories are studied within a generalized Hamilton-Jacobi framework, which allows to put on equal footing topology and dynamics in chemical reactivity problems. In doing so, we show how…
We describe a semiclassical method to calculate universal transport properties of chaotic cavities. While the energy-averaged conductance turns out governed by pairs of entrance-to-exit trajectories, the conductance variance, shot noise and…
The dynamics of a particle interacting with random classical field in a two-well potential is studied by the functional integration method. The probability of particle localization in either of the wells is studied in detail. Certain…
It is generally accepted that the dynamics of relativistic particles in the lab frame can be described by taking into account the relativistic dependence of the particles momenta on the velocity, with no reference to Lorentz…
According to the correspondence principle, classical mechanics and quantum mechanics agree in the semiclassical limit, although presently it has become more and more clear how intriguing would be to try to fix a boundary between them. Here…
I outline the theory of relativistic charged-particle motion in the magnetosphere in a way suitable for undergraduate courses. I discuss particle and guiding center motion, derive the three adiabatic invariants associated with them, and…
We consider a run-and-tumble particle on a half-line with an absorbing target at the origin. The particle has an internal velocity state that switches between two opposite values at Poisson-distributed times. The position of the particle…
Trajectories are a central concept in our understanding of classical phenomena and also in rationalizing quantum mechanical effects. In this work we provide a way to determine semiclassical paths, approximations to quantum averages in phase…
We analyze the motion of an overdamped classical particle in a multidimensional periodic potential, driven by a weak external noise. We demonstrate that in steady-state, the presence of temporal correlations in the noise and spatial…