Related papers: A general proof of Landauer-B\"uttiker formula
We study the existence and properties of the non-equilibrium steady state which arises by putting two copies of systems at different temperatures into a thermal contact. We solve the problem for the relativistic systems that are described…
We develop a method of calculating the nonequilibrium steady state (NESS) of an open quantum system that is weakly coupled to reservoirs in different equilibrium states. We describe the system using a Redfield-type quantum master equation…
A novel model of discretized energy cascade generated by Benjamin-Feir instability is presented. Conditions for appearance of direct and inverse cascades are given explicitly, as well as conditions for stabilization of the wave system due…
The general solution of hydrostatic equilibrium equations for a two-component fluid of ions and electrons without a local electroneutrality constraint is found in the framework of Newtonian gravity theory. In agreement with the Poincar\'e…
A simple general theorem is used as a tool that generates nonlocal constants of motion for Lagrangian systems. We review some cases where the constants that we find are useful in the study of the systems: the homogeneous potentials of…
When a thermodynamic system is released from any constraint, after some time its evolution will render it into an equilibrium state. Although the description of this relaxation to thermodynamic equilibrium has been attempted through both…
The purpose of this paper is to study the validity of Stokes' Theorem for singular submanifolds and differential forms with singularities in Euclidean space. The results are presented in the context of Lebesgue Integration, but their proofs…
We study a simplified inertial Ericksen-Leslie system for the nematic liquid crystal flow, which can be viewed as a system coupling Navier-Stokes equations and wave map equations. We prove the global existence of classical solution with…
We revisit the Taub-NUT solution of the Einstein equations without time periodicity condition, showing that the Misner string is still fully transparent for geodesics. In this case, analytic continuation can be carried out through both…
We prove a version of the Poincar\'e-Bendixson theorem for certain classes of curves on the 2-sphere which are not required to be the trajectories of an underlying flow or semiflow on the sphere itself. Using this result we extend the…
In the mathematical modeling of nematic liquid crystals, a practical and physically reliable $\mathbf{Q}$-tensor model can be derived from Onsager's molecular model with the Bingham closure. However, this procedure leads to a singular…
Conventional Non-equilibrium Thermodynamics is mainly concerned with systems in local equilibrium and their entropy production, due to the irreversible processes which take place in these systems. In this paper fluids will be considered in…
The Nelson stochastic mechanics is derived as a consequence of the basic physical principles such as the principle of relativity of observations and the invariance of the action quantum. The unitary group of quantum mechanics is represented…
The pressureless Euler-Navier-Stokes system can be obtained formally from the Vlasov-Navier-Stokes system, under the assumption that the distribution function describing the density of particles is monokinetic. Its study has been the…
We prove global stability for a system of nonlinear wave equations satisfying a generalized null condition. The generalized null condition allows for null forms whose coefficients have bounded $C^k$ norms. We prove both pointwise decay and…
We derive the exact n-point current expectation values in the Landauer-Buttiker non-equilibrium steady state of a multi terminal system with star graph geometry and a point-like defect localised in the vertex. The current cumulants are…
An overview is given of recent advances in the nonequilibrium statistical mechanics of quantum systems and, especially, of time-reversal symmetry relations that have been discovered in this context. The systems considered are driven out of…
In this paper we study equations of magnetic hydrodynamics with a stress tensor. We interpret this system as the generalized Euler equation associated with an abelian extension of the Lie algebra of vector fields with a non-trivial…
For diffusive systems that can be described by fluctuating hydrodynamics and by the Macroscopic Fluctuation Theory of Bertini et al., the total current fluctuations display universal features when the system is closed and in equilibrium.…
Sturm oscillation theorem for second order differential equations was generalized to systems and higher order equations with positive leading coefficient by several authors. What we propose here is a Sturm oscillation theorem for systems of…