12,433 research outputs found
Sheaf Logic, Quantum Set Theory and the Interpretation of Quantum Mechanics
Based on the Sheaf Logic approach to set theoretic forcing, a hierarchy of
Quantum Variable Sets is constructed which generalizes and simplifies the
analogous construction developed by Takeuti on boolean valued models of set
theory. Over this model two alternative proofs of Takeuti's correspondence,
between self adjoint operators and the real numbers of the model, are given.
This approach results to be more constructive showing a direct relation with
the Gelfand representation theorem, revealing also the importance of these
results with respect to the interpretation of Quantum Mechanics in close
connection with the Deutsch-Everett multiversal interpretation. Finally, it is
shown how in this context the notion of genericity and the corresponding
generic model theorem can help to explain the emergence of classicality also in
connection with the Deutsch- Everett perspective.Comment: 34 pages, 2 figure
Contextual logic for quantum systems
In this work we build a quantum logic that allows us to refer to physical
magnitudes pertaining to different contexts from a fixed one without the
contradictions with quantum mechanics expressed in no-go theorems. This logic
arises from considering a sheaf over a topological space associated to the
Boolean sublattices of the ortholattice of closed subspaces of the Hilbert
space of the physical system. Differently to standard quantum logics, the
contextual logic maintains a distributive lattice structure and a good
definition of implication as a residue of the conjunction.Comment: 16 pages, no figure
Analytic solution of nonlinear fractional Burgers-type equation by invariant subspace method
In this paper we study the analytic solutions of Burgers-type nonlinear
fractional equations by means of the Invariant Subspace Method. We first study
a class of nonlinear equations directly related to the time-fractional Burgers
equation. Some generalizations linked to the forced time-fractional Burgers
equations and variable-coefficient diffusion are also considered. Finally we
study a Burgers-type equation involving both space and time-fractional
derivatives
Coarse-grained distributions and superstatistics
We show an interesting connexion between the coarse-grained distribution
function arising in the theory of violent relaxation for collisionless stellar
systems (Lynden-Bell 1967) and the notion of superstatistics introduced
recently by Beck & Cohen (2003). We also discuss the analogies and differences
between the statistical equilibrium state of a multi-components
self-gravitating system and the metaequilibrium state of a collisionless
stellar system. Finally, we stress the important distinction between mixing
entropies, generalized entropies, H-functions, generalized mixing entropies and
relative entropies
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