Related papers: Relaxation time approximation revisited and non-an…
The general scheme for the treatment of relaxation processes and temporal autocorrelations of dynamical variables for many particle systems is presented in framework of the recurrence relations approach. The time autocorrelation functions…
The dynamic response of an interacting electron system is determined by an extension of the relaxation-time approximation forced to obey local conservation laws for number, momentum and energy. A consequence of these imposed constraints is…
When relaxation towards an equilibrium or steady state is exponential at large times, one usually considers that the associated relaxation time $\tau$, i.e., the inverse of that decay rate, is the longest characteristic time in the system.…
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…
Lattice relaxation profoundly reshapes electronic structures in twisted materials. Prevailing treatments, however, typically rely on large-scale density functional theory (DFT), which is computationally costly and mechanistically opaque.…
We extend the Boltzmann equation in the relaxation time approximation to explicitly include transitions between particles forming an interacting mixture. Using the detailed balance condition as well as conditions of energy-momentum and…
Relaxation rates in nearly integrable systems usually increase quadratically with the strength of the perturbation that breaks integrability. We show that the relaxation rates can be significantly smaller in systems that are integrable…
A non-linear conjugate gradient optimization scheme is used to obtain excitation energies within the Random Phase Approximation (RPA). The solutions to the RPA eigenvalue equation are located through a variational characterization using a…
We introduce a residence-time approach (RTA) for determining position-dependent diffusivities from biased molecular dynamics simulations. The method is formulated for trajectory segments in which the effective drift along the transport…
Relaxation processes in supercooled liquids are known to exhibit interesting as well as complex behavior. One of the hallmarks of this relaxation process observed in the measured auto correlation function is occurrence of multiple steps of…
We study stability of interacting nonlinear systems with time-delayed communications, using contraction theory and a simplified wave variable design inspired by robotic teleoperation. We show that contraction is preserved through specific…
Usually, the relaxation times of a gas are estimated in the frame of the Boltzmann equation. In this paper, instead, we deal with the relaxation problem in the frame of the dynamical theory of Hamiltonian systems, in which the definition…
Correlators at finite density and temperature encode important information about a physical system, such as transport and causality. For a massive gas of particles in the relaxation time approximation of kinetic theory, we provide complete…
The attention mechanism is an important reason for the success of transformers. It relies on computing pairwise relations between tokens. To reduce the high computational cost of standard quadratic attention, linear attention has been…
I present a simple model of the time dependence of the contact area between solid bodies, assuming either a totally uncorrelated surface topography, or a self affine surface roughness. The existence of relaxation effects (that I incorporate…
Recovering properties of correlation functions is typically challenging. On one hand, experimentally, it requires measurements with a temporal resolution finer than the system's dynamics. On the other hand, analytical or numerical analysis…
In this article a correspondence has been established between the out of equilibrium system dissipation and the thermodynamic field redefinition of the macroscopic variables through the momentum dependent relaxation time approximation…
Sometimes the dynamics of a physical system is described by non-Hamiltonian equations of motion, and additionally, the system is characterized by long-range interactions. A concrete example is that of particles interacting with light as…
We reformulate the Boltzmann equation in the relaxation time approximation undergoing Bjorken flow in terms of a novel partial differential equation for the generating function of the moments of the distribution function. This is used to…
Many experimentally relevant systems are quasi-one-dimensional, consisting of nearly decoupled chains. In these systems, there is a natural separation of scales between the strong intra-chain interactions and the weak interchain coupling.…