2,641 research outputs found
Robust superfluid phases of 3He in aerogel
Within a phenomenological approach possible forms of the order parameter of
the superfluid phases of 3He in a vicinity of the transition temperature are
discussed. Effect of aerogel is described by a random tensor field interacting
with the orbital part of the order parameter. With respect to their interaction
with the random tensor field a group of "robust" order parameters which can
maintain long-range order in a presence of the random field is specified.
Robust order parameters, corresponding to Equal Spin Pairing (ESP) states are
found and proposed as candidates for the observed A-like superfluid phase of
liquid 3He in aerogel.Comment: 5 pages, prepared for QFS 200
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
Applications of BGP-reflection functors: isomorphisms of cluster algebras
Given a symmetrizable generalized Cartan matrix , for any index , one
can define an automorphism associated with of the field of rational functions of independent indeterminates It is an isomorphism between two cluster algebras associated to the
matrix (see section 4 for precise meaning). When is of finite type,
these isomorphisms behave nicely, they are compatible with the BGP-reflection
functors of cluster categories defined in [Z1, Z2] if we identify the
indecomposable objects in the categories with cluster variables of the
corresponding cluster algebras, and they are also compatible with the
"truncated simple reflections" defined in [FZ2, FZ3]. Using the construction of
preprojective or preinjective modules of hereditary algebras by Dlab-Ringel
[DR] and the Coxeter automorphisms (i.e., a product of these isomorphisms), we
construct infinitely many cluster variables for cluster algebras of infinite
type and all cluster variables for finite types.Comment: revised versio
Discrete integrable systems, positivity, and continued fraction rearrangements
In this review article, we present a unified approach to solving discrete,
integrable, possibly non-commutative, dynamical systems, including the - and
-systems based on . The initial data of the systems are seen as cluster
variables in a suitable cluster algebra, and may evolve by local mutations. We
show that the solutions are always expressed as Laurent polynomials of the
initial data with non-negative integer coefficients. This is done by
reformulating the mutations of initial data as local rearrangements of
continued fractions generating some particular solutions, that preserve
manifest positivity. We also show how these techniques apply as well to
non-commutative settings.Comment: 24 pages, 2 figure
Cluster algebras in algebraic Lie theory
We survey some recent constructions of cluster algebra structures on
coordinate rings of unipotent subgroups and unipotent cells of Kac-Moody
groups. We also review a quantized version of these results.Comment: Invited survey; to appear in Transformation Group
The HeH Reaction with Full Final--State Interaction
An {\it ab initio} calculation of the HeH longitudinal
response is presented. The use of the integral transform method with a Lorentz
kernel has allowed to take into account the full four--body final state
interaction (FSI). The semirealistic nucleon-nucleon potential MTI--III and the
Coulomb force are the only ingredients of the calculation. The reliability of
the direct knock--out hypothesis is discussed both in parallel and in non
parallel kinematics. In the former case it is found that lower missing momenta
and higher momentum transfers are preferable to minimize effects beyond the
plane wave impulse approximation (PWIA). Also for non parallel kinematics the
role of antisymmetrization and final state interaction become very important
with increasing missing momentum, raising doubts about the possibility of
extracting momentum distributions and spectroscopic factors. The comparison
with experimental results in parallel kinematics, where the Rosenbluth
separation has been possible, is discussed.Comment: 17 pages, 5 figure
Preliminary results of the Cerenkov EAS flashes the Crimean Astrophysical Observatory
The facility designed for the study of angular resolution of light in the extensive air showers EAS flashes is described. The threshold energy of the facility is about 3 x 10 to the 12h power eV. The data on the angular distribution of light in a flash and the ratio of the flux in the UV and visual region as a function of the distance to the axis of a shower are given. Obtained results are compared to the published computations
Search for the gamma-ray fluxes with energies above 10915) eV from various objects
Considerable interest has developed in the search for local sources of superhigh-energy gamma-rays. The experimental data obtained with the extensive air showers (EAS) array of the Moscow State University are analyzed with a view to searching for the superhigh-energy gamma-rays from various objects and regions of the Galaxy
The solution of the quantum T-system for arbitrary boundary
We solve the quantum version of the -system by use of quantum
networks. The system is interpreted as a particular set of mutations of a
suitable (infinite-rank) quantum cluster algebra, and Laurent positivity
follows from our solution. As an application we re-derive the corresponding
quantum network solution to the quantum -system and generalize it to
the fully non-commutative case. We give the relation between the quantum
-system and the quantum lattice Liouville equation, which is the quantized
-system.Comment: 24 pages, 18 figure
Constraint on the QED Vertex from the Mass Anomalous Dimension
We discuss the structure of the non-perturbative fermion-boson vertex in
quenched QED. We show that it is possible to construct a vertex which not only
ensures that the fermion propagator is multiplicatively renormalizable, obeys
the appropriate Ward-Takahashi identity, reproduces perturbation theory for
weak couplings and guarantees that the critical coupling at which the mass is
dynamically generated is gauge independent but also makes sure that the value
for the anomalous dimension for the mass function is strictly 1, as Holdom and
Mahanta have proposed.Comment: 8 pages, LaTeX, October 199
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