Natural Nonequilibrium States in Quantum Statistical Mechanics

A quantum spin system is discussed where a heat flow between infinite reservoirs takes place in a finite region. A time-dependent force may also be acting. Our analysis is based on a simple technical assumption concerning the time evolution of infinite quantum spin systems. This assumption, physically natural but currently proved for few specific systems only, says that quantum information diffuses in space-time in such a way that the time integral of the commutator of local observables converges: ⁰ _– dt [B, ^t A]<. In this setup one can define a natural nonequilibrium state. In the time-independent case, this nonequilibrium state retains some of the analyticity which characterizes KMS equilibrium states. A linear response formula is also obtained which remains true far from equilibrium. The formalism presented here does not cover situations where (for time-independent forces) the time-translation invariance and uniqueness of the natural nonequilibrium state are broken.     

Kramers-Wannier dualities via symmetries

Kramers-Wannier dualities in lattice models are intimately connected with symmetries. We show that they can be found directly and explicitly from the symmetry transformations of the boundary states in the underlying conformal field theory. Intriguingly, the only models with a self-duality transformation turn out to be those with an auto-orbifold property.     

Functionalization of MWCNTs with atomic nitrogen

In this study of the changes induced by exposing MWCNTs to a nitrogen plasma, it was found by HRTEM that the atomic nitrogen exposure does not significantly etch the surface of the carbon nanotube (CNT). Nevertheless, the atomic nitrogen generated by a microwave plasma effectively grafts amine, nitrile, amide, and oxime groups onto the CNT surface, as observed by XPS, altering the density of valence electronic states, as seen in UPS.     

Differentiation of SRB States: Correction and Complements

 Taking into account criticism by D. Dolgopyat and M. Jiang, we present here an improved derivation of the formula for the derivative of an SRB measure with respect to parameters.     

A Remark on the Equivalence of Isokinetic and Isoenergetic Thermostats in the Thermodynamic Limit

The Gaussian isokinetic and isoenergetic thermostats of Hoover and Evans are formally equivalent, as remarked by Gallavotti, Rondoni, and Cohen. But outside of equilibrium the fluctuations are uncontrolled and might break the equivalence. We show that equivalence is ensured if we consider an infinite system assumed to be ergodic under space translations.     

Zeros of Graph-Counting Polynomials

Given a finite graph E we define a family of subgraphs F by restricting the number of edges of F with endpoint at any vertex of E. Defining , we can in many cases give precise information on the location of zeros of (zeros all real negative, all imaginary, etc.). Extensions of these results to weighted and infinite graphs are given. Received: 4 May 1998 / Accepted: 12 June 1998     

Locating resonances for AxiomA dynamical systems

For a class of differentiable dynamical systems (called Axiom A systems) it has been shown by Pollicott and the author that correlation functions have Fourier transforms which are meromorphic in a strip. The poles (or resonances) are, however, not easy to locate. This note reviews the results which are known and discusses a simple model where the position of resonances can be estimated. The effect of noise is also discussed.On leave of absence from Institut des Hautes Etudes Scientifiques, 35, route de Chartres, 91440 Buressur-Yvette, France.     

Condensation of lattice gases

Techniques due toR. L. Dobrushin andR. Griffiths are combined to prove the existence of a first order phase transition at low temperature for a class of lattice systems with non nearest-neighbour interaction.     

A theorem on canonical commutation and anticommutation relations

The aim of this note is to characterize representations of the canonical commutation or anticommutation relations which, on a subspace of the space of test-functions, reduce to a sum of copies of the Fock representation.