15,529 research outputs found
Interval structure of the Pieri formula for Grothendieck polynomials
We give a combinatorial interpretation of a Pieri formula for double
Grothendieck polynomials in terms of an interval of the Bruhat order. Another
description had been given by Lenart and Postnikov in terms of chain
enumerations. We use Lascoux's interpretation of a product of Grothendieck
polynomials as a product of two kinds of generators of the 0-Hecke algebra, or
sorting operators. In this way we obtain a direct proof of the result of Lenart
and Postnikov and then prove that the set of permutations occuring in the
result is actually an interval of the Bruhat order.Comment: 27 page
Non-equilibrium Entanglement and Noise in Coupled Qubits
We study charge entanglement in two Coulomb-coupled double quantum dots in
thermal equilibrium and under stationary non-equilibrium transport conditions.
In the transport regime, the entanglement exhibits a clear switching threshold
and various limits due to suppression of tunneling by Quantum Zeno localisation
or by an interaction induced energy gap. We also calculate quantum noise
spectra and discuss the inter-dot current correlation as an indicator of the
entanglement in transport experiments.Comment: 4 pages, 4 figure
Schur Partial Derivative Operators
A lattice diagram is a finite list L=((p_1,q_1),...,(p_n,q_n) of lattice
cells. The corresponding lattice diagram determinant is \Delta_L(X;Y)=\det \|
x_i^{p_j}y_i^{q_j} \|. These lattice diagram determinants are crucial in the
study of the so-called ``n! conjecture'' of A. Garsia and M. Haiman. The space
M_L is the space spanned by all partial derivatives of \Delta_L(X;Y). The
``shift operators'', which are particular partial symmetric derivative
operators are very useful in the comprehension of the structure of the M_L
spaces. We describe here how a Schur function partial derivative operator acts
on lattice diagrams with distinct cells in the positive quadrant.Comment: 8 pages, LaTe
Electromagnetic field near cosmic string
The retarded Green function of the electromagnetic field in spacetime of a
straight thin cosmic string is found. It splits into a geodesic part
(corresponding to the propagation along null rays) and to the field scattered
on the string. With help of the Green function the electric and magnetic fields
of simple sources are constructed. It is shown that these sources are
influenced by the cosmic string through a self-interaction with their field.
The distant field of static sources is studied and it is found that it has a
different multipole structure than in Minkowski spacetime. On the other hand,
the string suppresses the electric and magnetic field of distant sources--the
field is expelled from regions near the string.Comment: 12 pages, 8 figures (low-resolution figures; for the version with
high-resolution figures see http://utf.mff.cuni.cz/~krtous/papers/), v2: two
references added, typos correcte
Current noise of a quantum dot p-i-n junction in a photonic crystal
The shot-noise spectrum of a quantum dot p-i-n junction embedded inside a
three-dimensional photonic crystal is investigated. Radiative decay properties
of quantum dot excitons can be obtained from the observation of the current
noise. The characteristic of the photonic band gap is revealed in the current
noise with discontinuous behavior. Applications of such a device in
entanglement generation and emission of single photons are pointed out, and may
be achieved with current technologies.Comment: 4 pages, 3 figures, to appear in Phys. Rev. B (2005
Observability of counterpropagating modes at fractional-quantum-Hall edges
When the bulk filling factor is equal to 1 - 1/m with m odd, at least one
counterpropagating chiral collective mode occurs simultaneously with
magnetoplasmons at the edge of fractional-quantum-Hall samples. Initial
experimental searches for an additional mode were unsuccessful. In this paper,
we address conditions under which its observation should be expected in
experiments where the electronic system is excited and probed by capacitive
coupling. We derive realistic expressions for the velocity of the slow
counterpropagating mode, starting from a microscopic calculation which is
simplified by a Landau-Silin-like separation between long-range Hartree and
residual interactions. The microscopic calculation determines the stiffness of
the edge to long-wavelength neutral excitations, which fixes the slow-mode
velocity, and the effective width of the edge region, which influences the
magnetoplasmon dispersion.Comment: 18 pages, RevTex, 6 figures, final version to be published in
Physical Review
Noise spectroscopy and interlayer phase-coherence in bilayer quantum Hall systems
Bilayer quantum Hall systems develop strong interlayer phase-coherence when
the distance between layers is comparable to the typical distance between
electrons within a layer. The phase-coherent state has until now been
investigated primarily via transport measurements. We argue here that
interlayer current and charge-imbalance noise studies in these systems will be
able to address some of the key experimental questions. We show that the
characteristic frequency of current-noise is that of the zero wavevector
collective mode, which is sensitive to the degree of order in the system. Local
electric potential noise measured in a plane above the bilayer system on the
other hand is sensitive to finite-wavevector collective modes and hence to the
soft-magnetoroton picture of the order-disorder phase transition.Comment: 5 pages, 2 figure
Ideals of Quasi-Symmetric Functions and Super-Covariant Polynomials for S_n
The aim of this work is to study the quotient ring R_n of the ring
Q[x_1,...,x_n] over the ideal J_n generated by non-constant homogeneous
quasi-symmetric functions. We prove here that the dimension of R_n is given by
C_n, the n-th Catalan number. This is also the dimension of the space SH_n of
super-covariant polynomials, that is defined as the orthogonal complement of
J_n with respect to a given scalar product. We construct a basis for R_n whose
elements are naturally indexed by Dyck paths. This allows us to understand the
Hilbert series of SH_n in terms of number of Dyck paths with a given number of
factors.Comment: LaTeX, 3 figures, 12 page
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