The structure of strongly additive states and Markov triplets on the CAR algebra

We find a characterization of states satisfying equality in strong subadditivity of entropy and of Markov triplets on the CAR algebra. For even states, a more detailed structure of the density matrix is given.Comment: 11 page

On the optical properties of carbon nanotubes--Part I. A general formula for the dynamical optical conductivity

This paper is the first one of a series of two articles in which we revisit the optical properties of single-walled carbon nanotubes (SWNT). Produced by rolling up a graphene sheet, SWNT owe their intriguing properties to their cylindrical quasi-one-dimensional (quasi-1D) structure (the ratio length/radius is experimentally of order of 10^3). We model SWNT by circular cylinders of small diameters on the surface of which the conduction electron gas is confined by the electric field generated by the fixed carbon ions. The pair-interaction potential considered is the 3D Coulomb potential restricted to the cylinder. To reflect the quasi-1D structure, we introduce a 1D effective many-body Hamiltonian which is the starting-point of our analysis. To investigate the optical properties, we consider a perturbation by a uniform time-dependent electric field modeling an incident light beam along the longitudinal direction. By using Kubo's method, we derive within the linear response theory an asymptotic expansion in the low-temperature regime for the dynamical optical conductivity at fixed density of particles. The leading term only involves the eigenvalues and associated eigenfunctions of the (unperturbed) 1D effective many-body Hamiltonian, and allows us to account for the sharp peaks observed in the optical absorption spectrum of SWNT.Comment: Comments: 24 pages. Revised version. Accepted for publication in J.M.

A partition-free approach to transient and steady-state charge currents

We construct a non-equilibrium steady state and calculate the corresponding current for a mesoscopic Fermi system in the partition-free setting. To this end we study a small sample coupled to a finite number of semi-infinite leads. Initially, the whole system of quasi-free fermions is in a grand canonical equilibrium state. At t = 0 we turn on a potential bias on the leads and let the system evolve. We study how the charge current behaves in time and how it stabilizes itself around a steady state value, which is given by a Landauer-type formula.Comment: 14 pages, submitte

Comment on: Modular Theory and Geometry

In this note we comment on part of a recent article by B. Schroer and H.-W. Wiesbrock. Therein they calculate some new modular structure for the U(1)-current-algebra (Weyl-algebra). We point out that their findings are true in a more general setting. The split-property allows an extension to doubly-localized algebras.Comment: 13 pages, corrected versio

Wavelet Methods in the Relativistic Three-Body Problem

In this paper we discuss the use of wavelet bases to solve the relativistic three-body problem. Wavelet bases can be used to transform momentum-space scattering integral equations into an approximate system of linear equations with a sparse matrix. This has the potential to reduce the size of realistic three-body calculations with minimal loss of accuracy. The wavelet method leads to a clean, interaction independent treatment of the scattering singularities which does not require any subtractions.Comment: 14 pages, 3 figures, corrected referenc

Adaiabtic theorems and reversible isothermal processes

Isothermal processes of a finitely extended, driven quantum system in contact with an infinite heat bath are studied from the point of view of quantum statistical mechanics. Notions like heat flux, work and entropy are defined for trajectories of states close to, but distinct from states of joint thermal equilibrium. A theorem characterizing reversible isothermal processes as quasi-static processes (''isothermal theorem'') is described. Corollaries concerning the changes of entropy and free energy in reversible isothermal processes and on the 0th law of thermodynamics are outlined

Quantum Kinetic Evolution of Marginal Observables

We develop a rigorous formalism for the description of the evolution of observables of quantum systems of particles in the mean-field scaling limit. The corresponding asymptotics of a solution of the initial-value problem of the dual quantum BBGKY hierarchy is constructed. Moreover, links of the evolution of marginal observables and the evolution of quantum states described in terms of a one-particle marginal density operator are established. Such approach gives the alternative description of the kinetic evolution of quantum many-particle systems to generally accepted approach on basis of kinetic equations.Comment: 18 page

Approach to equilibrium for a class of random quantum models of infinite range

We consider random generalizations of a quantum model of infinite range introduced by Emch and Radin. The generalization allows a neat extension from the class $l_1$ of absolutely summable lattice potentials to the optimal class $l_2$ of square summable potentials first considered by Khanin and Sinai and generalised by van Enter and van Hemmen. The approach to equilibrium in the case of a Gaussian distribution is proved to be faster than for a Bernoulli distribution for both short-range and long-range lattice potentials. While exponential decay to equilibrium is excluded in the nonrandom $l_1$ case, it is proved to occur for both short and long range potentials for Gaussian distributions, and for potentials of class $l_2$ in the Bernoulli case. Open problems are discussed.Comment: 10 pages, no figures. This last version, to appear in J. Stat. Phys., corrects some minor errors and includes additional references and comments on the relation to experiment

Towards Rigorous Derivation of Quantum Kinetic Equations

We develop a rigorous formalism for the description of the evolution of states of quantum many-particle systems in terms of a one-particle density operator. For initial states which are specified in terms of a one-particle density operator the equivalence of the description of the evolution of quantum many-particle states by the Cauchy problem of the quantum BBGKY hierarchy and by the Cauchy problem of the generalized quantum kinetic equation together with a sequence of explicitly defined functionals of a solution of stated kinetic equation is established in the space of trace class operators. The links of the specific quantum kinetic equations with the generalized quantum kinetic equation are discussed.Comment: 25 page

Realizations of Causal Manifolds by Quantum Fields

Quantum mechanical operators and quantum fields are interpreted as realizations of timespace manifolds. Such causal manifolds are parametrized by the classes of the positive unitary operations in all complex operations, i.e. by the homogenous spaces \D(n)=\GL(\C^n_\R)/\U(n) with $n=1$ for mechanics and $n=2$ for relativistic fields. The rank $n$ gives the number of both the discrete and continuous invariants used in the harmonic analysis, i.e. two characteristic masses in the relativistic case. 'Canonical' field theories with the familiar divergencies are inappropriate realizations of the real 4-dimensional causal manifold \D(2). Faithful timespace realizations do not lead to divergencies. In general they are reducible, but nondecomposable - in addition to representations with eigenvectors (states, particle) they incorporate principal vectors without a particle (eigenvector) basis as exemplified by the Coulomb field.Comment: 36 pages, latex, macros include