Generalized Coupling Model Research Articles

Constraining alternatives to a cosmological constant: Generalized couplings and scale invariance

We present a comparative analysis of observational low-redshift background constraints on three candidate models for explaining the low-redshift acceleration of the universe. The generalized coupling model by Feng and Carloni and the scale invariant model by Maeder (both of which can be interpreted as bimetric theories) are compared to the traditional parametrization of Chevallier, Polarski and Linder. In principle the generalized coupling model, which in vacuum is equivalent to General Relativity, contains two types of vacuum energy: the usual cosmological constant plus a second contribution due to the matter fields. We show that the former is necessary for the model to agree with low-redshift observations, while there is no statistically significant evidence for the presence of the second. On the other hand the scale invariant model effectively has a time-dependent cosmological constant. In this case we show that a matter density Ω m ∼ 0 . 3 is a relatively poor fit to the data, and the best-fit model would require a fluid with a much smaller density and a significantly positive equation of state parameter.

Brownian localization: A generalized coupling model yielding a nonergodic Langevin equation description

A minimal system-plus-reservoir model yielding a nonergodic Langevin equation is proposed, which originates from the cubic-spectral density of environmental oscillators and momentum-dependent coupling. This model allows ballistic diffusion and classical localization simultaneously, in which the fluctuation-dissipation relation is still satisfied but the Khinchin theorem is broken. The asymptotical equilibrium for a nonergodic system requires the initial thermal equilibrium, however, when the system starts from nonthermal conditions, it does not approach the equilibration even though a nonlinear potential is used to bound the particle, this can be confirmed by the zeroth law of thermodynamics. In the dynamics of Brownian localization, due to the memory damping function inducing a constant term, our results show that the stationary distribution of the system depends on its initial preparation of coordinate rather than momentum. The coupled oscillator chain with a fixed end boundary acts as a heat bath, which has long been used in studies of collinear atom/solid-surface scattering and lattice vibration, we investigate this problem from the viewpoint of nonergodicity.

Differences in the molecular weight and the temperature dependences of self-diffusion and zero shear viscosity in linear polyethylene and hydrogenated polybutadiene

Within the context of a generalized coupling model we can support the hypothesis that, while the mode of relaxation for self diffusion ( D) and shear flow (η) are the same, the entanglement interactions are different. We assume that there are two distinct coupling parameters n D and n η for self diffusion and shear flow respectively. The model predicts the molecular weight and temperature dependences to be scaled by the relevant coupling parameters as: η∝[M 2 exp(E a /kT)] 1 (1−n η) and D∝M[M 2 exp(E a /kT)] −1 (1−n D) for melts with Arrhenius temperature dependences. We have found that n n =0.43 and 0.42 for polyethylene (PE) and hydrogenated polybutadiene (HPB) which scale η as M 3.5 and M 3.4. Also the apparent flow activation energies E∗ a of 6.35 kcal mole −1 for PE and 7.2 kcal mol −1 for HPB scale to primitive activation energies E a of 3.6 and 4.2 kcal mole −1 for PE and HPB respectively. On the other hand the M −2 dependence of D results in n D =1/3. Then the reported activation energies for self-diffusion in PE and HPB of 5.49 and 6.2 kcal mole −1 scale to primitive activation energies of 3.7 and 4.1 kcal mole −1, respectively.