45 research outputs found
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 of absolutely summable lattice potentials to the optimal class
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 case, it is
proved to occur for both short and long range potentials for Gaussian
distributions, and for potentials of class 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
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 for mechanics
and for relativistic fields. The rank 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
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