Christian Gruber

Thermodynamics of systems with internal adiabatic constraints: time evolution of the adiabatic piston

The equations for the time evolution of the controversial adiabatic piston problem are obtained using a very primitive model of the fluids. It thus shows that the first and second laws of thermodynamics lead to equations of motion which determine uniquely the final equilibrium state, while this state cannot be predicted using only the laws of thermostatics.

Ground States and Flux Configurations of the Two-Dimensional Falicov-Kimball Model

The Falicov-Kimball model is a lattice model of itinerant spinless fermions (“electrons”) interacting by an on-site potential with classical particles (“ions”). We continue the investigations of the crystalline ground states that appear for various filling of electrons and ions for large coupling. We investigate the model for square as well as triangular lattices. New ground states are found and the effects of a magnetic flux on the structure of the phase diagram are studied. The flux phase problem where one has to find the optimal flux configurations and the nuclei configurations is also solved in some cases. Finally we consider a model where the fermions are replaced by hard-core bosons. This model also has crystalline ground states. Therefore their existence does not require the Pauli principle, but only the on-site hard-core constraint for the itinerant particles.

On the properties of inhomogeneous charged systems

We give a proof and an extension of equations previously derived by Wertheim and Lovett, Mou and Buff, relating the gradient of the density to an integral of the external force over the pair correlation function; when the system has boundaries it also involves a surface contribution. These equations are derived and used for systems which may contain free charges, dipoles, and a rigid background (jellium). In particular, we derive an equation for the density profile near a plane electrode and we show that the correlation function has to decay no faster than ‖x‖−N(N=space dimension) parallel to the electode.

On the equivalence between KMS-states and equilibrium states for classical systems

It is shown that for any KMS-state of a classical system of non-coincident particles, the distribution functions are absolutely continuous with respect to Lebesgue measure; the equivalence between KMS states and Canonical Gibbs States is then established.

Two-Time-Scale Relaxation Towards Thermal Equilibrium of the Enigmatic Piston

AbstractWe investigate the evolution of a system composed of N non-interacting point particles of mass m in a container divided into two chambers by a movable adiabatic piston of mass M≫m. Using a two-time-scale perturbation approach in terms of the small parameter α=2m/(M+m), we show that the evolution towards thermal equilibrium proceeds in two stages. The first stage is a fast, deterministic, adiabatic relaxation towards mechanical equilibrium. The second stage, which takes place at times

Berezinskii–Kosterlitz–Thouless Order in Two-Dimensional O(2)-Ferrofluid

\mathcal{O}

On the Second Law of Thermodynamics and the Piston Problem

(M), is a slow fluctuation-driven, diathermic relaxation towards thermal equilibrium. A very simple equation is derived which shows that in the second stage, the position of the piston is given by XM(t)= L[1/2−ξ(αt)] where the function ξ is independent of M. Numerical simulations support the assumptions underlying our analytical derivations and illustrate the large mass range in which the picture holds.

The Hubbard Quantum Wire

We study some mechanical problems in which a friction force is acting on a system. Using the fundamental concepts of state, time evolution and energy conservation, we explain how to extend Newtonian mechanics to thermodynamics. We arrive at the two laws of thermodynamics and then apply them to investigate the time evolution and heat transfer of some significant examples.