Vibrational relaxation of a molecule in strong interaction with a reservoir: Nonmonotonic temperature dependence

This theoretical study of the vibrational relaxation of a molecule in interaction with a reservoir uncovers a noteworthy temperature (T) dependence of the time evolution of the relaxation. Its rate increases with T in one interval but decreases in another. The feature arises not for a weak molecule-reservoir interaction but only for coupling strong enough to require polaronic dressing transformations. Our treatment, based on a recent generalization of the well-known Montroll–Shuler equation for relaxation and an explicit calculation of bath correlations from the microscopically specified Hamiltonian, could provide an alternative explanation of an “inverted” T-dependence of relaxation in an experimental report by Fayer and collaborators on W(CO)₆ dissolved in CHCl₃.     

Connection of the velocity autocorrelation function to the mean-square-displacement and to the memory function of generalized master equations

General connections between the velocity autocorrelation function and the mean-square-displacement for a special initial condition are established and shown to reduce in the high-temperature limit to earlier such results obtained by Scher and Lax. A simple and useful relation, which is valid in the high temperature limit, between the velocity autocorrelation function and memory functions in generalized master equations is given.     

Resonance effects in the nonadiabatic nonlinear quantum dimer

In the presence of 1/f ^β noise, we investigate the logical stochastic resonance (LSR) in an asymmetric bistable model driven by various cycling combinations of two logic inputs. The probability of correct logic outputs is calculated according to true table of logic relationships. Two major results are presented. Firstly, it is shown that the LSR effect can be obtained by changing noise strength. Over entire range of noise variance, white noise can be considered to be better than 1/f noise or 1/f ² noise to obtain clean logic operation. At a smaller noise level, 1/f noise can realize higher output probability than white noise or 1/f ² noise. In the sense, 1/f noise can be considered to be better than white noise or 1/f ². On the other hand, the correct probability can evolves nonmonotonically as noise exponent β increases, and a kind of SR-like effect can be obtained as a result of β. At certain intermediate noise variance, the output probability is able to attain its minimum at β = 1. It is also shown that actually some finite β sometime can be better than β = 0 at small range of noise variance. The study might provide some potential complement to LSR effect in the presence of 1/f ^β noise.     

Phase transitions in systems of self-propelled agents and related network models

An important characteristic of flocks of birds, schools of fish, and many similar assemblies of self-propelled particles is the emergence of states of collective order in which the particles move in the same direction. When noise is added into the system, the onset of such collective order occurs through a dynamical phase transition controlled by the noise intensity. While originally thought to be continuous, the phase transition has been claimed to be discontinuous on the basis of recently reported numerical evidence. We address this issue by analyzing two representative network models closely related to systems of self-propelled particles. We present analytical as well as numerical results showing that the nature of the phase transition depends crucially on the way in which noise is introduced into the system.     

Coupling of tunneling and hopping transport interactions in neutron scattering lineshapes

The results of a recently presented formalism for neutron scattering lineshape calculations are used to characterize the observable consequences of the coupling of tunneling and hopping interactions of atoms moving in solids and are compared with those of another development, which treats the two interactions but neglects the coupling.