We review one of the most versatile theoretical approaches to study time-dependent correlated quantum transport in nano-systems: non-equilibrium Green's function (NEGF) formalism. Within this formalism, can treat, on same footing, inter-particle interactions, external drives and/or perturbations, and coupling baths with a (piece-wise) continuum set degrees freedom. After historical overview the...

Keeping the full quantum nature of the problem, we compute the relaxation time of the Holstein polaron in one dimension after it was driven far from the equilibrium by a strong oscillatory pulse. Just after the pulse, the polaron's kinetic energy increases and subsequently exhibits a relaxation-type decrease with simultaneous emission of phonons. In the weak coupling regime, partial tunneling o...

The paper discusses how the two thermodynamic properties, energy (U) and exergy (E), can be used to solve the problem of quantifying the entropy of non-equilibrium systems. Both energy and exergy are a priori concepts, and their formal dependence on thermodynamic state variables at equilibrium is known. Exploiting the results of a previous study, we first calculate the non-equilibrium exergy En...

We investigate the applicability of the path integral of non-equilibrium statistical mechanics to non-equilibrium damage phenomena. As an example, a fiber-bundle model with a thermal noise and a fiber-bundle model with a decay of fibers are considered. Initially, we develop an analogy with the Gibbs formalism of non-equilibrium states. Later, we switch from the approach of non-equilibrium state...

We consider the shallow water equations with non-flat bottom topography. The smooth solutions of these equations are energy conservative, whereas weak solutions are energy stable. The equations possess interesting steady states of lake at rest as well as moving equilibrium states. We design energy conservative finite volume schemes which preserve (i) the lake at rest steady state in both one an...

Intra-Beam Scattering (IBS) is one of the main limiting processes for the performance of low energy ion storage rings, such as the Extra Low ENergy Antiproton ring (ELENA) that is being constructed at CERN. IBS effects limit the achievable equilibrium 6D beam phase space volume during the cooling process, as well as the stored beam intensity. In this contribution we analyse the IBS effects on t...

We present a general analytic method for understanding how specific motions of a classical bath influence the dynamics of quantum-mechanical observables in mixed quantum-classical molecular dynamics simulations. We apply our method and develop expressions for the special case of quantum solvation, allowing us to examine how specific classical solvent motions couple to the equilibrium energy flu...

Small clusters have a range of unique physical and chemical phenomena that are strongly size dependent. However, analysis of these phenomena often assumes that thermodynamic equilibrium conditions prevail. We compare experimentally measured and ab initio computed photoelectron spectra of bare and deuterated silicon cluster anions produced in a plasma environment. We find that the isomers detect...