Transport in Quantum Multi-barrier Systems as Random Walks on a Lattice

Journal of Statistical Physics - Coulomb and log-gases are exchangeable singular Boltzmann–Gibbs measures appearing in mathematical physics at many places, in particular in random matrix...     

On the Fluctuation Relation for Nosé-Hoover Boundary Thermostated Systems

We discuss the transient and steady state fluctuation relation for a mechanical system in contact with two deterministic thermostats at different temperatures. The system is a modified Lorentz gas in which the fixed scatterers exchange energy with the gas of particles, and the thermostats are modelled by two Nosé-Hoover thermostats applied at the boundaries of the system. The transient fluctuation relation, which holds only for a precise choice of the initial ensemble, is verified at all times, as expected. Times longer than the mesoscopic scale, needed for local equilibrium to be settled, are required if a different initial ensemble is considered. This shows how the transient fluctuation relation asymptotically leads to the steady state relation when, as explicitly checked in our systems, the condition found in (D.J. Searles, et al., J. Stat. Phys. 128:1337, 2007), for the validity of the steady state fluctuation relation, is verified. For the steady state fluctuations of the phase space contraction rate Λ and of the dissipation function Ω, a similar relaxation regime at shorter averaging times is found. The quantity Ω satisfies with good accuracy the fluctuation relation for times larger than the mesoscopic time scale; the quantity Λ appears to begin a monotonic convergence after such times. This is consistent with the fact that Ω and Λ differ by a total time derivative, and that the tails of the probability distribution function of Λ are Gaussian.     

Time reversal and symmetries of time correlation functions

ABSTRACT

The time reversal invariance of classical dynamics is reconsidered in this paper with specific focus on its consequences for time correlation functions and associated properties such as transport coefficients. We show that, under fairly common assumptions on the interparticle potential, an isolated Hamiltonian system obeys more than one time reversal symmetry and that this entails non trivial consequences. Under an isotropic and homogeneous potential, in particular, eight valid time reversal operations exist. The presence of external fields that reduce the symmetry of space decreases this number, but does not necessarily impair all time reversal symmetries. Thus, analytic predictions of symmetry properties of time correlation functions and, in some cases, even of their null value are still possible. The noteworthy case of a constant external magnetic field, usually assumed to destroy time reversal symmetry, is considered in some detail. We show that, in this case too, some of the new time reversal operations hold, and that this makes it possible to derive relevant properties of correlation functions without the uninteresting inversion of the direction of the magnetic field commonly enforced in the literature.     

Nonlinear Diffusion and Transient Osmosis

We investigate both analytically and numericallythe concentration dynamics of a solution in two containers connected bya narrow and short channel, in which diffusion obeys a porous medium equation.We also consider the variation of the pressure in the containers due tothe flow of matter in the channel.
In particular, we identify a phenomenon, which depends on the transport of matteracross nano-porous membranes, which we call ``transient osmosis'.
We find that nonlinear diffusion of the porous medium equation type allows numerous differentosmotic-like phenomena, which are not present in the case of ordinary Fickian diffusion.Experimental results suggest one possible candidate for transiently osmotic processes.     

Synchronization of spatiotemporal semiconductor lasers and its application in color image encryption

Optical chaos is a topic of current research characterized by high-dimensional nonlinearity which is attributed to the delay-induced dynamics, high bandwidth and easy modular implementation of optical feedback. In light of these facts, which add enough confusion and diffusion properties for secure communications, we explore the synchronization phenomena in spatiotemporal semiconductor laser systems. The novel system is used in a two-phase colored image encryption process. The high-dimensional chaotic attractor generated by the system produces a completely randomized chaotic time series, which is ideal in the secure encoding of messages. The scheme thus illustrated is a two-phase encryption method, which provides sufficiently high confusion and diffusion properties of chaotic cryptosystem employed with unique data sets of processed chaotic sequences. In this novel method of cryptography, the chaotic phase masks are represented as images using the chaotic sequences as the elements of the image. The scheme drastically permutes the positions of the picture elements. The next additional layer of security further alters the statistical information of the original image to a great extent along the three-color planes. The intermediate results during encryption demonstrate the infeasibility for an unauthorized user to decipher the cipher image. Exhaustive statistical tests conducted validate that the scheme is robust against noise and resistant to common attacks due to the double shield of encryption and the infinite dimensionality of the relevant system of partial differential equations.