274 research outputs found
Exact Drude weight for the one-dimensional Hubbard model at finite temperatures
The Drude weight for the one-dimensional Hubbard model is investigated at
finite temperatures by using the Bethe ansatz solution. Evaluating finite-size
corrections to the thermodynamic Bethe ansatz equations, we obtain the formula
for the Drude weight as the response of the system to an external gauge
potential. We perform low-temperature expansions of the Drude weight in the
case of half-filling as well as away from half-filling, which clearly
distinguish the Mott-insulating state from the metallic state.Comment: 9 pages, RevTex, To appear in J. Phys.
Quantum Clifford-Hopf Algebras for Even Dimensions
In this paper we study the quantum Clifford-Hopf algebras
for even dimensions and obtain their intertwiner matrices, which are
elliptic solutions to the Yang- Baxter equation. In the trigonometric limit of
these new algebras we find the possibility to connect with extended
supersymmetry. We also analyze the corresponding spin chain hamiltonian, which
leads to Suzuki's generalized model.Comment: 12 pages, LaTeX, IMAFF-12/93 (final version to be published, 2
uuencoded figures added
Singular responses of spin-incoherent Luttinger liquids
When a local potential changes abruptly in time, an electron gas shifts to a
new state which at long times is orthogonal to the one in the absence of the
local potential. This is known as Anderson's orthogonality catastrophe and it
is relevant for the so-called X-ray edge or Fermi edge singularity, and for
tunneling into an interacting one dimensional system of fermions. It often
happens that the finite frequency response of the photon absorption or the
tunneling density of states exhibits a singular behavior as a function of
frequency: where is a
threshold frequency and is an exponent characterizing the singular
response. In this paper singular responses of spin-incoherent Luttinger liquids
are reviewed. Such responses most often do not fall into the familiar form
above, but instead typically exhibit logarithmic corrections and display a much
higher universality in terms of the microscopic interactions in the theory.
Specific predictions are made, the current experimental situation is
summarized, and key outstanding theoretical issues related to spin-incoherent
Luttinger liquids are highlighted.Comment: 21 pages, 3 figures. Invited Topical Review Articl
Correlation Functions of One-Dimensional Lieb-Liniger Anyons
We have investigated the properties of a model of 1D anyons interacting
through a -function repulsive potential. The structure of the
quasi-periodic boundary conditions for the anyonic field operators and the
many-anyon wavefunctions is clarified. The spectrum of the low-lying
excitations including the particle-hole excitations is calculated for periodic
and twisted boundary conditions. Using the ideas of the conformal field theory
we obtain the large-distance asymptotics of the density and field correlation
function at the critical temperature T=0 and at small finite temperatures. Our
expression for the field correlation function extends the results in the
literature obtained for harmonic quantum anyonic fluids.Comment: 19 pages, RevTeX
Theorie de Lubin-Tate non-abelienne et representations elliptiques
Harris and Taylor proved that the supercuspidal part of the cohomology of the
Lubin-Tate tower realizes both the local Langlands and Jacquet-Langlands
correspondences, as conjectured by Carayol. Recently, Boyer computed the
remaining part of the cohomology and exhibited two defects : first, the
representations of GL\_d which appear are of a very particular and restrictive
form ; second, the Langlands correspondence is not realized anymore. In this
paper, we study the cohomology complex in a suitable equivariant derived
category, and show how it encodes Langlands correspondance for all elliptic
representations. Then we transfer this result to the Drinfeld tower via an
enhancement of a theorem of Faltings due to Fargues. We deduce that Deligne's
weight-monodromy conjecture is true for varieties uniformized by Drinfeld's
coverings of his symmetric spaces.Comment: 54 page
Modelling the unfolding pathway of biomolecules: theoretical approach and experimental prospect
We analyse the unfolding pathway of biomolecules comprising several
independent modules in pulling experiments. In a recently proposed model, a
critical velocity has been predicted, such that for pulling speeds
it is the module at the pulled end that opens first, whereas for
it is the weakest. Here, we introduce a variant of the model that is
closer to the experimental setup, and discuss the robustness of the emergence
of the critical velocity and of its dependence on the model parameters. We also
propose a possible experiment to test the theoretical predictions of the model,
which seems feasible with state-of-art molecular engineering techniques.Comment: Accepted contribution for the Springer Book "Coupled Mathematical
Models for Physical and Biological Nanoscale Systems and Their Applications"
(proceedings of the BIRS CMM16 Workshop held in Banff, Canada, August 2016),
16 pages, 6 figure
Superposition rules for higher-order systems and their applications
Superposition rules form a class of functions that describe general solutions
of systems of first-order ordinary differential equations in terms of generic
families of particular solutions and certain constants. In this work we extend
this notion and other related ones to systems of higher-order differential
equations and analyse their properties. Several results concerning the
existence of various types of superposition rules for higher-order systems are
proved and illustrated with examples extracted from the physics and mathematics
literature. In particular, two new superposition rules for second- and
third-order Kummer--Schwarz equations are derived.Comment: (v2) 33 pages, some typos corrected, added some references and minor
commentarie
Local height probabilities in a composite Andrews-Baxter-Forrester model
We study the local height probabilities in a composite height model, derived
from the restricted solid-on-solid model introduced by Andrews, Baxter and
Forrester, and their connection with conformal field theory characters. The
obtained conformal field theories also describe the critical behavior of the
model at two different critical points. In addition, at criticality, the model
is equivalent to a one-dimensional chain of anyons, subject to competing two-
and three-body interactions. The anyonic-chain interpretation provided the
original motivation to introduce the composite height model, and by obtaining
the critical behaviour of the composite height model, the critical behaviour of
the anyonic chains is established as well. Depending on the overall sign of the
hamiltonian, this critical behaviour is described by a diagonal coset-model,
generalizing the minimal models for one sign, and by Fateev-Zamolodchikov
parafermions for the other.Comment: 34 pages, 5 figures; v2: expanded introduction, references added and
other minor change
Macroscopic properties of A-statistics
A-statistics is defined in the context of the Lie algebra sl(n+1). Some
thermal properties of A-statistics are investigated under the assumption that
the particles interact only via statistical interaction imposed by the Pauli
principle of A-statistics. Apart from the general case, three particular
examples are studied in more detail: (a) the particles have one and the same
energy and chemical potential; (b) equidistant energy spectrum; (c) two species
of particles with one and the same energy and chemical potential within each
class. The grand partition functions and the average number of particles are
among the thermodynamical quantities written down explicitly.Comment: 27 pages, 4 figures; to be published in J. Phys.
K-matrices for non-abelian quantum Hall states
Two fundamental aspects of so-called non-abelian quantum Hall states (the
q-pfaffian states and more general) are a (generalized) pairing of the
participating electrons and the non-abelian statistics of the quasi-hole
excitations. In this paper, we show that these two aspects are linked by a
duality relation, which can be made manifest by considering the K-matrices that
describe the exclusion statistics of the fundamental excitations in these
systems.Comment: LaTeX, 12 page
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