570 research outputs found
Local Operators in Massive Quantum Field Theories
Contribution to the proceedings of Schladming 1995. A review of the form
factor approach and its utilisation to determine the space of local operators
of integrable massive quantum theories is given. A few applications are
discussed.Comment: 6 pages, late
Cooperative Transport in a Multi-Particle, Multi-Dimensional Flashing Ratchet
Random and undirected forces are rectified in biological and synthetic systems using ratcheting mechanisms, which employ periodic asymmetric potentials and nonequilibrium conditions to produce useful transport. The density of motors or transported particles is known to strongly affect the nature and efficacy of transport in biological systems, as well as in synthetic ratchets and active swimmer systems. While experimental ratchet implementations typically employ potentials varying in two dimensions (2D), the role of the density of interacting particles in such a system has not been modeled. Prompted by experimental observations and building upon previous simulations, this paper describes the ratcheting process of interacting particles in a 2D flashing ratchet, studied using classical simulations. Increased particle density is found to allow effective ratcheting at higher driving frequencies, compared to the low-density or non-interacting case. High densities also produce a new ratcheting mode at low driving frequencies, based on independent trajectories of high kinetic-energy particles, more than doubling transport at low frequencies
Quantum critical origin of the superconducting dome in SrTiO
We investigate the origin of superconductivity in doped SrTiO (STO) using
a combination of density functional and strong coupling theories within the
framework of quantum criticality. Our density functional calculations of the
ferroelectric soft mode frequency as a function of doping reveal a crossover
from quantum paraelectric to ferroelectric behavior at a doping level
coincident with the experimentally observed top of the superconducting dome.
Based on this finding, we explore a model in which the superconductivity in STO
is enabled by its proximity to the ferroelectric quantum critical point and the
soft mode fluctuations provide the pairing interaction on introduction of
carriers. Within our model, the low doping limit of the superconducting dome is
explained by the emergence of the Fermi surface, and the high doping limit by
departure from the quantum critical regime. We predict that the highest
critical temperature will increase and shift to lower carrier doping with
increasing O isotope substitution, a scenario that is experimentally
verifiable.Comment: 4 pages + supplemental, 3 + 2 figure
On the Fermionic Quasi-particle Interpretation in Minimal Models of Conformal Field Theory
The conjecture that the states of the fermionic quasi-particles in minimal
conformal field theories are eigenstates of the integrals of motion to certain
eigenvalues is checked and shown to be correct only for the Ising model.Comment: 5 pages of Late
Q-systems, Heaps, Paths and Cluster Positivity
We consider the cluster algebra associated to the -system for as a
tool for relating -system solutions to all possible sets of initial data. We
show that the conserved quantities of the -system are partition functions
for hard particles on particular target graphs with weights, which are
determined by the choice of initial data. This allows us to interpret the
simplest solutions of the Q-system as generating functions for Viennot's heaps
on these target graphs, and equivalently as generating functions of weighted
paths on suitable dual target graphs. The generating functions take the form of
finite continued fractions. In this setting, the cluster mutations correspond
to local rearrangements of the fractions which leave their final value
unchanged. Finally, the general solutions of the -system are interpreted as
partition functions for strongly non-intersecting families of lattice paths on
target lattices. This expresses all cluster variables as manifestly positive
Laurent polynomials of any initial data, thus proving the cluster positivity
conjecture for the -system. We also give an alternative formulation in
terms of domino tilings of deformed Aztec diamonds with defects.Comment: 106 pages, 38 figure
The Many Faces of a Character
We prove an identity between three infinite families of polynomials which are
defined in terms of `bosonic', `fermionic', and `one-dimensional configuration'
sums. In the limit where the polynomials become infinite series, they give
different-looking expressions for the characters of the two integrable
representations of the affine algebra at level one. We conjecture yet
another fermionic sum representation for the polynomials which is constructed
directly from the Bethe-Ansatz solution of the Heisenberg spin chain.Comment: 14/9 pages in harvmac, Tel-Aviv preprint TAUP 2125-9
Fusion products, Kostka polynomials, and fermionic characters of su(r+1)_k
Using a form factor approach, we define and compute the character of the
fusion product of rectangular representations of \hat{su}(r+1). This character
decomposes into a sum of characters of irreducible representations, but with
q-dependent coefficients. We identify these coefficients as (generalized)
Kostka polynomials. Using this result, we obtain a formula for the characters
of arbitrary integrable highest-weight representations of \hat{su}(r+1) in
terms of the fermionic characters of the rectangular highest weight
representations.Comment: 21 pages; minor changes, typos correcte
Minimal Models of Integrable Lattice Theory and Truncated Functional Equations
We consider the integrable XXZ model with the special open boundary
conditions. We perform Quantum Group reduction of this model in roots of unity
and use it for the definition Minimal Models of Interable lattice theory. It is
shown that after this Quantum Group reduction Sklyanin's transfer-matrices
satisfy the closed system of the truncated functional relations. We solve these
equations for the simplest case.Comment: 9 pages, LaTeX, corrected some typos, added some reference
Conflict-Free Coloring Made Stronger
In FOCS 2002, Even et al. showed that any set of discs in the plane can
be Conflict-Free colored with a total of at most colors. That is,
it can be colored with colors such that for any (covered) point
there is some disc whose color is distinct from all other colors of discs
containing . They also showed that this bound is asymptotically tight. In
this paper we prove the following stronger results:
\begin{enumerate} \item [(i)] Any set of discs in the plane can be
colored with a total of at most colors such that (a) for any
point that is covered by at least discs, there are at least
distinct discs each of which is colored by a color distinct from all other
discs containing and (b) for any point covered by at most discs,
all discs covering are colored distinctively. We call such a coloring a
{\em -Strong Conflict-Free} coloring. We extend this result to pseudo-discs
and arbitrary regions with linear union-complexity.
\item [(ii)] More generally, for families of simple closed Jordan regions
with union-complexity bounded by , we prove that there exists
a -Strong Conflict-Free coloring with at most colors.
\item [(iii)] We prove that any set of axis-parallel rectangles can be
-Strong Conflict-Free colored with at most colors.
\item [(iv)] We provide a general framework for -Strong Conflict-Free
coloring arbitrary hypergraphs. This framework relates the notion of -Strong
Conflict-Free coloring and the recently studied notion of -colorful
coloring. \end{enumerate}
All of our proofs are constructive. That is, there exist polynomial time
algorithms for computing such colorings
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