Related papers: Optimal barrier subdivision for Kramers' escape ra…
We show how reaction coordinate path lengths affect the relaxation efficiency of a complex system. To this purpose, we consider the metric contributions to the transition rates. These metric contributions preserve informations about the…
The stationary phase method is applied to diffusion by a potential barrier for an incoming wave packet with energies greater then the barrier height. It is observed that a direct application leads to paradoxical results. The correct…
Controlling the evolution of nonequilibrium systems to minimize dissipated heat or work is a key goal for designing nanodevices, both in nanotechnology and biology. Progress in computing optimal protocols has thus far been limited to either…
Minimum Bayes Risk (MBR) decoding optimizes output selection by maximizing the expected utility value of an underlying human distribution. While prior work has shown the effectiveness of MBR decoding through empirical evaluation, few…
Previous studies have used numerical methods to optimize the hyperpolarizability of a one-dimensional quantum system. These studies were used to suggest properties of one-dimensional organic molecules, such as the degree of modulation of…
Rare transitions between long-lived metastable states underlie a great variety of physical, chemical and biological processes. Our quantitative understanding of reactive mechanisms has been driven forward by the insights of transition state…
We disucss a statistical estimation problem of an optimal dividend barrier when the surplus process follows a L\'{e}vy insurance risk process. The optimal dividend barrier is defined as the level of the barrier that maximizes the…
In this paper, we formulate a novel trajectory optimization scheme that takes into consideration the state uncertainty of the robot and obstacle into its collision avoidance routine. The collision avoidance under uncertainty is modeled here…
The narrow escape problem consists of deriving the asymptotic expansion of the solution of a drift-diffusion equation with the Dirichlet boundary condition on a small absorbing part of the boundary and the Neumann boundary condition on the…
Diffusion of a particle in the N-dimensional external potential which is periodic in one dimension and unbounded in the other N-1 dimensions is investigated. We find an analytical expression for the overdamped diffusion and study…
A schematic model of over-damped motion is presented which permits one to calculate the mean first passage time for nuclear fission. Its asymptotic value may exceed considerably the lifetime suggested by Kramers rate formula, which applies…
The paper is devoted to the relaxation and integral representation in the space of functions of bounded variation for an integral energy arising from optimal design problems. The presence of a perimeter penalization is also considered in…
In this paper escape rates and local escape rates for special flows are sudied. In a general context the first result is that the escape rate depends monotonically on the ceiling function and fulfills certain scaling, invariance, and…
We present a family of algorithms for the fast determination of reaction paths and barriers in phase space and the computation of the corresponding rates. The method requires the reaction times be large compared to the microscopic time,…
Using the random matrix model, we discuss the effect of couplings to non-collective states on the penetrability of a one dimensional potential barrier. We show that these non-collective excitations hinder the penetrability and thus smear…
We consider the problem of tunneling escape of particles from a multiparticle system confined within a potential trap. The process is nonlinear due to the interparticle interaction. Using the hydrodynamic representation for the quantum…
Using a recently developed procedure - multiple wave packet decomposition - here we study the phase time formulation for tunneling/reflecting particles colliding with a potential barrier. To partially overcome the analytical difficulties…
In this paper we study the tunneling using a background independent (polymer) quantization scheme. We show that at low energies, for the tunneling through a single potential barrier, the polymer transmission coefficient and the polymer…
We study the escape rate of a particle in a metastable potential in presence of a dissipative bath coupled to the momentum of the particle. Using the semiclassical bounce technique, we find that this rate is exponentially enhanced. In…
After reexamining the above barrier diffusion problem where we notice that the wave packet collision implies the existence of {\em multiple} reflected and transmitted wave packets, we analyze the way of obtaining phase times for…