2,552 research outputs found
Comment on "Order parameter of A-like 3He phase in aerogel"
We argue that the inhomogeneous A-phase in aerogel is energetically more
preferable than the "robust" phase suggested by I. A. Fomin, JETP Lett. 77, 240
(2003); cond-mat/0302117 and cond-mat/0401639.Comment: 2 page
Towards Field Theory in Spaces with Multivolume Junctions
We consider a spacetime formed by several pieces having common timelike
boundary which plays the role of a junction between them. We establish junction
conditions for fields of various spin and derive the resulting laws of wave
propagation through the junction, which turn out to be quite similar for fields
of all spins. As an application, we consider the case of multivolume junctions
in four-dimensional spacetime that may arise in the context of the theory of
quantum creation of a closed universe on the background of a big mother
universe. The theory developed can also be applied to braneworld models and to
the superstring theory.Comment: 20 pages, 3 figures, revtex; published 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
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
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