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C. Gruber

Publications and source records attributed to C. Gruber.

16 recordsLinked to original sources
arXiv2011

Lagrange equations coupled to a thermal equation: mechanics as consequence of thermodynamics

Following the analytic approach to thermodynamics developed by Stueckelberg, we study the evolution equations of a closed thermodynamic system consisting of point particles in a fluid. We obtain a system of coupled differential equations describing the mechanical and the thermal evolution of the system. The coupling between these evolution equations is due to the action of a viscous friction term. Finally, we apply our coupled evolution equations to study the thermodynamics of an isolated system consisting of identical point particles interacting through a harmonic potential.

physics.flu-dyn↗
arXiv2003

On the Second Law of thermodynamics and the piston problem

The piston problem is investigated in the case where the length of the cylinder is infinite (on both sides) and the ratio $m/M$ is a very small parameter, where $m$ is the mass of one particle of the gaz and $M$ is the mass of the piston. Introducing initial conditions such that the stochastic motion of the piston remains in the average at the origin (no drift), it is shown that the time evolution of the fluids, analytically derived from Liouville equation, agrees with the Second Law of thermodynamics. We thus have a non equilibrium microscopical model whose evolution can be explicitly shown to obey the two laws of thermodynamics.

cond-mat.stat-mech↗
arXiv2003

Two-time-scale relaxation towards thermal equilibrium of the enigmatic piston

We 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 $M\gg m$. 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 ${\cal O}(M)$, 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 $X_M(t)=L[1/2-ξ(αt)]$ 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.

cond-mat.stat-mech↗
arXiv1996

SU(m|n) supersymmetric Calogero-Sutherland model confined in harmonic potential

In this work, we study a continuous quantum system of a mixture of bosons and fermions with the supersymmetry SU(m|n). The particles are confined in a harmonic well and interact with each other through the 1/r2 interaction. The ground state wavefunction is constructed explicitly for the most general SU(m|n) case, with the ground state energy given explicitly. The full energy spectrum of excitations in the SU(m|n) model is also equal spaced. In the limiting case where there are no bosons in the system, our results reduce to those obtained previously.

cond-mat↗
arXiv1996

A remark on off-diagonal long range order

In this work, we study some general property of a strongly correlated electron system defined on a lattice. Assuming that the lattice system exhibits off-diagonal long range order, we show rigorously that this assumption would lead to Meissner effect. This generalizes previous results of continuous case to a lattice electron system.

cond-mat↗
arXiv1996

Exactly solvable multi-channel Kondo lattice model

In this work, a multichannel Kondo lattice model is studied in the thermodynamic limit. The conduction band is described by a constant hopping amplitude between any pair of lattice sites. For this system, we have obtained the exact thermodynamical properties and the ground state energies. In the limit of strong interaction between the electrons and the impurity spins, the wavefunctions take the Jastrow product form.

cond-mat↗
arXiv1995

On chiral Hubbard model and the chiral Kondo lattice model

The integrability of the one dimensional chiral Hubbard model is discussed in the limit of strong interaction, U=+\infty. The system is shown to be integrable in sense of existence of an infinite number of constants of motion. The system is related to a chiral Kondo lattice model at strong interaction J=+\infty

cond-mat↗
arXiv1995

Exactly solvable Kondo lattice model

In this work, we exactly solve a Kondo lattice model in the thermodynamic limit. The system consists of an electronic conduction band described by unconstrained hopping matrix elements between the lattice sites. The conducting electrons interact with a localized impurity spin at each lattice cell. We have found the exact thermodynamics, the ground state energies of the system. At T=0, we explicitly demonstrate that the system exhibits a metal-insulator phase transition at half-filling. In the limit of strong coupling between the impurity spin and the electrons, J=\infty, we have solved the system on a lattice of any size L. The ground states are the resonating-valence-bond type Jastrow product wavefunctions. Various correlation functions may be computed for the impurity spins, and for the singlets formed by the electrons and impurities.

cond-mat↗
arXiv1995

Stability of insulating phase in the chiral Kondo lattice model

In this work, the stability of the insulating phase of the 1D chiral Kondo lattice model is studied at half-filling, within the framework of self-consistent variational theory. It is found that arbitrarily small interaction would drive the system from a conducting phase to an insulating phase, in spite of the chirality of the conducting band.

cond-mat↗
arXiv1994

Exact Results of the 1D $1/r^2$ Supersymmetric t-J Model without Translational Invariance

In this work, we continue the study of the supersymmetric t-J model with 1/r^2 hopping and exchange without translational invariance. A set of Jastrow wavefunctions are obtained for the system, with eigenenergies explicitly calculated. The ground state of the t-J model is included in this set of wavefunctions. The spectrum of this t-J model consists of equal-distant energy levels which are highly degenerate.

cond-mat↗
arXiv1993

Invariants of the $1/r^2$ Supersymmetric t-J Models

In this work, we have studied the invariants of motion of two SU(N) supersymmetric t-J model of $1/r^2$ hopping and exchange in one dimension. The first model is defined on a lattice of equal spaced sites, and the second on a non-equal spacing lattice. Using the ``exchange operator formalism'', we are able to construct all the invariants for the models, by mapping the systems to mixtures of fermions and bosons. This identification shows that the supersymmetric t-J model on the chain with equal-spaced sites also belongs to Shastry-Sutherland's ``Super-Lax-Pair'' family. (IPT-EPFL 31/10/1993).

cond-mat↗
arXiv1993

Molecule Formation and the Farey Tree in the One-Dimensional Falicov-Kimball Model

The ground state configurations of the one--dimensional Falicov--Kimball model are studied exactly with numerical calculations revealing unexpected effects for small interaction strength. In neutral systems we observe molecular formation, phase separation and changes in the conducting properties; while in non--neutral systems the phase diagram exhibits Farey tree order (Aubry sequence) and a devil's staircase structure. Conjectures are presented for the boundary of the segregated domain and the general structure of the ground states.

cond-mat↗