200,129 research outputs found
Infinite index extensions of local nets and defects
Subfactor theory provides a tool to analyze and construct extensions of
Quantum Field Theories, once the latter are formulated as local nets of von
Neumann algebras. We generalize some of the results of [LR95] to the case of
extensions with infinite Jones index. This case naturally arises in physics,
the canonical examples are given by global gauge theories with respect to a
compact (non-finite) group of internal symmetries. Building on the works of
Izumi, Longo, Popa [ILP98] and Fidaleo, Isola [FI99], we consider generalized
Q-systems (of intertwiners) for a semidiscrete inclusion of properly infinite
von Neumann algebras, which generalize ordinary Q-systems introduced by Longo
[Lon94] to the infinite index case. We characterize inclusions which admit
generalized Q-systems of intertwiners and define a braided product among the
latter, hence we construct examples of QFTs with defects (phase boundaries) of
infinite index, extending the family of boundaries in the grasp of [BKLR16].Comment: 50 page
Mixing properties for toral extensions of slowly mixing dynamical systems with finite and infinite measure
We prove results on mixing and mixing rates for toral extensions of
nonuniformly expanding maps with subexponential decay of correlations. Both the
finite and infinite measure settings are considered. Under a Dolgopyat-type
condition on nonexistence of approximate eigenfunctions, we prove that existing
results for (possibly nonMarkovian) nonuniformly expanding maps hold also for
their toral extensions.Comment: Final version, published in J. Mod. Dy
Geometry of quantum dynamics in infinite dimension
We develop a geometric approach to quantum mechanics based on the concept of
the Tulczyjew triple. Our approach is genuinely infinite-dimensional and
including a Lagrangian formalism in which self-adjoint (Schroedinger) operators
are obtained as Lagrangian submanifolds associated with the Lagrangian. As a
byproduct we obtain also results concerning coadjoint orbits of the unitary
group in infinite dimension, embedding of the Hilbert projective space of pure
states in the unitary group, and an approach to self-adjoint extensions of
symmetric relations.Comment: 32 page
Solvable rational extensions of the isotonic oscillator
Combining recent results on rational solutions of the Riccati-Schr\"odinger
equations for shape invariant potentials to the finite difference B\"acklund
algorithm and specific symmetries of the isotonic potential, we show that it is
possible to generate the three infinite sets (L1, L2 and L3 families) of
regular rational solvable extensions of this potential in a very direct and
transparent way
Homology over trivial extensions of commutative DG algebras
Conditions on the Koszul complex of a noetherian local ring guarantee
that is non-zero for infinitely many , when
and are finitely generated -modules of infinite projective dimension.
These conditions are obtained from results concerning Tor of differential
graded modules over certain trivial extensions of commutative differential
graded algebras.Comment: 14 page
Exact Model Reduction for Damped-Forced Nonlinear Beams: An Infinite-Dimensional Analysis
We use invariant manifold results on Banach spaces to conclude the existence
of spectral submanifolds (SSMs) in a class of nonlinear, externally forced beam
oscillations. SSMs are the smoothest nonlinear extensions of spectral subspaces
of the linearized beam equation. Reduction of the governing PDE to SSMs
provides an explicit low-dimensional model which captures the correct
asymptotics of the full, infinite-dimensional dynamics. Our approach is general
enough to admit extensions to other types of continuum vibrations. The
model-reduction procedure we employ also gives guidelines for a mathematically
self-consistent modeling of damping in PDEs describing structural vibrations
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