Coherent oscillations and incoherent tunnelling in one - dimensional asymmetric double - well potential

For a model 1d asymmetric double-well potential we calculated so-called survival probability (i.e. the probability for a particle initially localised in one well to remain there). We use a semiclassical (WKB) solution of Schroedinger equation. It is shown that behaviour essentially depends on transition probability, and on dimensionless parameter which is a ratio of characteristic frequencies for low energy non-linear in-well oscillations and inter wells tunnelling. For the potential describing a finite motion (double-well) one has always a regular behaviour. For the small value of the parameter there is well defined resonance pairs of levels and the survival probability has coherent oscillations related to resonance splitting. However for the large value of the parameter no oscillations at all for the survival probability, and there is almost an exponential decay with the characteristic time determined by Fermi golden rule. In this case one may not restrict oneself to only resonance pair levels. The number of perturbed by tunnelling levels grows proportionally to the value of this parameter (by other words instead of isolated pairs there appear the resonance regions containing the sets of strongly coupled levels). In the region of intermediate values of the parameter one has a crossover between both limiting cases, namely the exponential decay with subsequent long period recurrent behaviour.Comment: 19 pages, 7 figures, Revtex, revised version. Accepted to Phys. Rev.

Cooperative surmounting of bottlenecks

The physics of activated escape of objects out of a metastable state plays a key role in diverse scientific areas involving chemical kinetics, diffusion and dislocation motion in solids, nucleation, electrical transport, motion of flux lines superconductors, charge density waves, and transport processes of macromolecules, to name but a few. The underlying activated processes present the multidimensional extension of the Kramers problem of a single Brownian particle. In comparison to the latter case, however, the dynamics ensuing from the interactions of many coupled units can lead to intriguing novel phenomena that are not present when only a single degree of freedom is involved. In this review we report on a variety of such phenomena that are exhibited by systems consisting of chains of interacting units in the presence of potential barriers. In the first part we consider recent developments in the case of a deterministic dynamics driving cooperative escape processes of coupled nonlinear units out of metastable states. The ability of chains of coupled units to undergo spontaneous conformational transitions can lead to a self-organised escape. The mechanism at work is that the energies of the units become re-arranged, while keeping the total energy conserved, in forming localised energy modes that in turn trigger the cooperative escape. We present scenarios of significantly enhanced noise-free escape rates if compared to the noise-assisted case. The second part deals with the collective directed transport of systems of interacting particles overcoming energetic barriers in periodic potential landscapes. Escape processes in both time-homogeneous and time-dependent driven systems are considered for the emergence of directed motion. It is shown that ballistic channels immersed in the associated high-dimensional phase space are the source for the directed long-range transport

A boundary integral formalism for stochastic ray tracing in billiards

Determining the flow of rays or non-interacting particles driven by a force or velocity field is fundamental to modelling many physical processes. These include particle flows arising in fluid mechanics and ray flows arising in the geometrical optics limit of linear wave equations. In many practical applications, the driving field is not known exactly and the dynamics are determined only up to a degree of uncertainty. This paper presents a boundary integral framework for propagating flows including uncertainties, which is shown to systematically interpolate between a deterministic and a completely random description of the trajectory propagation. A simple but efficient discretisation approach is applied to model uncertain billiard dynamics in an integrable rectangular domain

Periodic orbit analysis of an elastodynamic resonator using shape deformation

We report the first definitive experimental observation of periodic orbits (POs) in the spectral properties of an elastodynamic system. The Fourier transform of the density of flexural modes show peaks that correspond to stable and unstable POs of a clover shaped quartz plate. We change the shape of the plate and find that the peaks corresponding to the POs that hit only the unperturbed sides are unchanged proving the correspondence. However, an exact match to the length of the main POs could be made only after a small rescaling of the experimental results. Statistical analysis of the level dynamics also shows the effect of the stable POs.Comment: submitted to Europhysics Letter