6,492 research outputs found
Application of graph combinatorics to rational identities of type A
To a word , we associate the rational function . The main object, introduced by C. Greene to generalize
identities linked to Murnaghan-Nakayama rule, is a sum of its images by certain
permutations of the variables. The sets of permutations that we consider are
the linear extensions of oriented graphs. We explain how to compute this
rational function, using the combinatorics of the graph . We also establish
a link between an algebraic property of the rational function (the
factorization of the numerator) and a combinatorial property of the graph (the
existence of a disconnecting chain).Comment: This is the complete version of the submitted fpsac paper (2009
On ergodic states, spontaneous symmetry breaking and the Bogoliubov quasi-averages
It is shown that Bogoliubov quasi-averages select the pure or ergodic states
in the ergodic decomposition of the thermal (Gibbs) state. Our examples include
quantum spin systems and many-body boson systems. As a consequence, we
elucidate the problem of equivalence between Bose-Einstein condensation and the
quasi-average spontaneous symmetry breaking (SSB) discussed for continuous
boson systems. The multi-mode extended van den Berg-Lewis-Pul\'{e} condensation
of type III demonstrates that the only physically reliable quantities are those
that defined by Bogoliubov quasi-averages
On Uniformly finitely extensible Banach spaces
We continue the study of Uniformly Finitely Extensible Banach spaces (in
short, UFO) initiated in Moreno-Plichko, \emph{On automorphic Banach spaces},
Israel J. Math. 169 (2009) 29--45 and Castillo-Plichko, \emph{Banach spaces in
various positions.} J. Funct. Anal. 259 (2010) 2098-2138. We show that they
have the Uniform Approximation Property of Pe\l czy\'nski and Rosenthal and are
compactly extensible. We will also consider their connection with the
automorphic space problem of Lindenstrauss and Rosenthal --do there exist
automorphic spaces other than and ?-- showing that a space
all whose subspaces are UFO must be automorphic when it is Hereditarily
Indecomposable (HI), and a Hilbert space when it is either locally minimal or
isomorphic to its square. We will finally show that most HI --among them, the
super-reflexive HI space constructed by Ferenczi-- and asymptotically
spaces in the literature cannot be automorphic.Comment: This paper is to appear in the Journal of Mathematical Analysis and
Application
Hamiltonian structure of thermodynamics with gauge
The state of a thermodynamic system being characterized by its set of
extensive variables we write the associated intensive
variables the partial derivatives of the entropy in the form where
behaves as a gauge factor. When regarded as independent, the variables
define a space having a canonical
symplectic structure where they appear as conjugate. A thermodynamic system is
represented by a -dimensional gauge-invariant Lagrangian submanifold
of Any thermodynamic process, even dissipative,
taking place on is represented by a Hamiltonian trajectory in
governed by a Hamiltonian function which is zero on
A mapping between the equations of state of different systems is likewise
represented by a canonical transformation in Moreover a natural
Riemannian metric exists for any physical system, with the 's as
contravariant variables, the 's as covariant ones. Illustrative examples
are given.Comment: Proofs corrections latex vali.tex, 1 file, 28 pages [SPhT-T00/099],
submitted to Eur. Phys. J.
- …