41,942 research outputs found
Hidden gauge structure and derivation of microcanonical ensemble theory of bosons from quantum principles
Microcanonical ensemble theory of bosons is derived from quantum mechanics by
making use of a hidden gauge structure. The relative phase interaction
associated with this gauge structure, described by the Pegg-Barnett formalism,
is shown to lead to perfect decoherence in the thermodynamics limit and the
principle of equal a priori probability, simultaneously.Comment: 10 page
Local gauge theory and coarse graining
Within the discrete gauge theory which is the basis of spin foam models, the
problem of macroscopically faithful coarse graining is studied. Macroscopic
data is identified; it contains the holonomy evaluation along a discrete set of
loops and the homotopy classes of certain maps. When two configurations share
this data they are related by a local deformation. The interpretation is that
such configurations differ by "microscopic details". In many cases the homotopy
type of the relevant maps is trivial for every connection; two important cases
in which the homotopy data is composed by a set of integer numbers are: (i) a
two dimensional base manifold and structure group U(1), (ii) a four dimensional
base manifold and structure group SU(2). These cases are relevant for spin foam
models of two dimensional gravity and four dimensional gravity respectively.
This result suggests that if spin foam models for two-dimensional and
four-dimensional gravity are modified to include all the relevant macroscopic
degrees of freedom -the complete collection of macroscopic variables necessary
to ensure faithful coarse graining-, then they could provide appropriate
effective theories at a given scale.Comment: Based on talk given at Loops 11-Madri
Euler-Poincare reduction for discrete field theories
In this note, we develop a theory of Euler-Poincare reduction for discrete
Lagrangian field theories. We introduce the concept of Euler-Poincare equations
for discrete field theories, as well as a natural extension of the
Moser-Veselov scheme, and show that both are equivalent. The resulting discrete
field equations are interpreted in terms of discrete differential geometry. An
application to the theory of discrete harmonic mappings is also briefly
discussed.Comment: 24 pages, 3 figures (v2: simplified treatment
Plane-stress, elastic-plastic states in the vicinity of crack tips
Plane stress analysis of elastic-plastic states in vicinity of straight crack tip in thin plat
An integral formula for L^2-eigenfunctions of a fourth order Bessel-type differential operator
We find an explicit integral formula for the eigenfunctions of a fourth order
differential operator against the kernel involving two Bessel functions. Our
formula establishes the relation between K-types in two different realizations
of the minimal representation of the indefinite orthogonal group, namely the
L^2-model and the conformal model
Superconductivity in an organic insulator at very high magnetic fields
We investigate by electrical transport the field-induced superconducting
state (FISC) in the organic conductor -(BETS)FeCl. Below 4 K,
antiferromagnetic-insulator, metallic, and eventually superconducting (FISC)
ground states are observed with increasing in-plane magnetic field. The FISC
state survives between 18 and 41 T, and can be interpreted in terms of the
Jaccarino-Peter effect, where the external magnetic field {\em compensates} the
exchange field of aligned Fe ions. We further argue that the Fe
moments are essential to stabilize the resulting singlet, two-dimensional
superconducting stateComment: 9 pages 3 figure
On pseudo-hyperk\"ahler prepotentials
An explicit surjection from a set of (locally defined) unconstrained
holomorphic functions on a certain submanifold of (Sp_1(C) \times C^{4n}) onto
the set HK_{p,q} of local isometry classes of real analytic
pseudo-hyperk\"ahler metrics of signature (4p,4q) in dimension 4n is
constructed. The holomorphic functions, called prepotentials, are analogues of
K\"ahler potentials for K\"ahler metrics and provide a complete
parameterisation of HK_{p,q}. In particular, there exists a bijection between
HK_{p,q} and the set of equivalence classes of prepotentials. This affords the
explicit construction of pseudo-hyperk\"ahler metrics from specified
prepotentials. The construction generalises one due to Galperin, Ivanov,
Ogievetsky and Sokatchev. Their work is given a coordinate-free formulation and
complete, self-contained proofs are provided. An appendix provides a vital tool
for this construction: a reformulation of real analytic G-structures in terms
of holomorphic frame fields on complex manifolds.Comment: 53 pages; v2: minor amendments to Def.4.1 and Theorem 4.5; a
paragraph inserted in the proof of the latter; V3: minor changes; V4: minor
changes/ typos corrected for journal versio
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