2,041 research outputs found
Intertwining Operators And Quantum Homogeneous Spaces
In the present paper the algebras of functions on quantum homogeneous spaces
are studied. The author introduces the algebras of kernels of intertwining
integral operators and constructs quantum analogues of the Poisson and Radon
transforms for some quantum homogeneous spaces. Some applications and the
relation to -special functions are discussed.Comment: 20 pages. The general subject is quantum groups. The paper is written
in LaTe
Density of states of a two-dimensional electron gas in a non-quantizing magnetic field
We study local density of electron states of a two-dimentional conductor with
a smooth disorder potential in a non-quantizing magnetic field, which does not
cause the standart de Haas-van Alphen oscillations. It is found, that despite
the influence of such ``classical'' magnetic field on the average electron
density of states (DOS) is negligibly small, it does produce a significant
effect on the DOS correlations. The corresponding correlation function exhibits
oscillations with the characteristic period of cyclotron quantum
.Comment: 7 pages, including 3 figure
Continuous slice functional calculus in quaternionic Hilbert spaces
The aim of this work is to define a continuous functional calculus in
quaternionic Hilbert spaces, starting from basic issues regarding the notion of
spherical spectrum of a normal operator. As properties of the spherical
spectrum suggest, the class of continuous functions to consider in this setting
is the one of slice quaternionic functions. Slice functions generalize the
concept of slice regular function, which comprises power series with
quaternionic coefficients on one side and that can be seen as an effective
generalization to quaternions of holomorphic functions of one complex variable.
The notion of slice function allows to introduce suitable classes of real,
complex and quaternionic --algebras and to define, on each of these
--algebras, a functional calculus for quaternionic normal operators. In
particular, we establish several versions of the spectral map theorem. Some of
the results are proved also for unbounded operators. However, the mentioned
continuous functional calculi are defined only for bounded normal operators.
Some comments on the physical significance of our work are included.Comment: 71 pages, some references added. Accepted for publication in Reviews
in Mathematical Physic
Algebras generated by two bounded holomorphic functions
We study the closure in the Hardy space or the disk algebra of algebras
generated by two bounded functions, of which one is a finite Blaschke product.
We give necessary and sufficient conditions for density or finite codimension
of such algebras. The conditions are expressed in terms of the inner part of a
function which is explicitly derived from each pair of generators. Our results
are based on identifying z-invariant subspaces included in the closure of the
algebra. Versions of these results for the case of the disk algebra are given.Comment: 22 pages ; a number of minor mistakes have been corrected, and some
points clarified. Conditionally accepted by Journal d'Analyse Mathematiqu
Microscopic Conductivity of Lattice Fermions at Equilibrium - Part I: Non-Interacting Particles
We consider free lattice fermions subjected to a static bounded potential and
a time- and space-dependent electric field. For any bounded convex region
() of space, electric fields
within drive currents. At leading order, uniformly
with respect to the volume of and
the particular choice of the static potential, the dependency on
of the current is linear and described by a conductivity distribution. Because
of the positivity of the heat production, the real part of its Fourier
transform is a positive measure, named here (microscopic) conductivity measure
of , in accordance with Ohm's law in Fourier space. This finite
measure is the Fourier transform of a time-correlation function of current
fluctuations, i.e., the conductivity distribution satisfies Green-Kubo
relations. We additionally show that this measure can also be seen as the
boundary value of the Laplace-Fourier transform of a so-called quantum current
viscosity. The real and imaginary parts of conductivity distributions satisfy
Kramers-Kronig relations. At leading order, uniformly with respect to
parameters, the heat production is the classical work performed by electric
fields on the system in presence of currents. The conductivity measure is
uniformly bounded with respect to parameters of the system and it is never the
trivial measure . Therefore, electric fields generally
produce heat in such systems. In fact, the conductivity measure defines a
quadratic form in the space of Schwartz functions, the Legendre-Fenchel
transform of which describes the resistivity of the system. This leads to
Joule's law, i.e., the heat produced by currents is proportional to the
resistivity and the square of currents
Quantum Separability of the vacuum for Scalar Fields with a Boundary
Using the Green's function approach we investigate separability of the vacuum
state of a massless scalar field with a single Dirichlet boundary. Separability
is demonstrated using the positive partial transpose criterion for effective
two-mode Gaussian states of collective operators. In contrast to the vacuum
energy, entanglement of the vacuum is not modified by the presence of the
boundary.Comment: 4 pages, 1 figure, Revtex, minor corrections. submitted to Phy. Rev.
A topological central point theorem
In this paper a generalized topological central point theorem is proved for
maps of a simplex to finite-dimensional metric spaces. Similar generalizations
of the Tverberg theorem are considered.Comment: In this version some typos were corrected after the official
publicatio
On a conjecture about Dirac's delta representation using q-exponentials
A new representation of Dirac's delta-distribution, based on the so-called
q-exponentials, has been recently conjectured. We prove here that this
conjecture is indeed valid
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