arXiv subjects
Publications and source records attributed to Gavriel Segre.
It is shown that the non-adiabatic Hannay's angle of an integrable non-degenerate classical hamiltonian dynamical system may be related to the Aharonov-Anandan phase it develops when it is looked mathematically as a quantum dynamical system.
I withdraw the previous version of the paper since it contains conceptual and mathematical mistakes. I will soon replace it with a radically revised version.
A bundle theoretic interpretation of the non-adiabatic classical geometric phase is given in the Koopman representation of dynamics
The Mermin-Squires Music Hall inteludium on the Einstein-Podolsky-Rosen affair is analyzed by showing the fallacity of the One-Borel-Normality Criterion and the necessity of replacing it with the more restrictive Algorithmic-Randomness Criterion
Charles Bennett's measure of physical complexity for classical objects, namely logical-depth, is used in order to prove that a chaotic classical dynamical system is not physical complex. The natural measure of physical complexity for quantum objects, quantum logical-depth, is then introduced in order to prove that a chaotic quantum dynamical system is not physical complex too.
Expanding a remark of my PHD-thesis the noncommutative bayesian statistical inference from one wedge of a bifurcate Killing horizon is analyzed looking at its inter-relation with the Unruh effect
Some little step forward is made in the analysis of the mathematical structure of Tonal Harmony, a task begun by Galilei, Euler and the Lagrange of the first two volumes of Miscellania Taurinensia
taking aside the review part, a finite-cardinality's set of new ideas concerning algorithmic information issues in Quantum Mechanics is introduced and analyzed
Some little considerations concerning the application of the Theory of Dirichlet Forms to stocastic variational principle on riemannian manifolds are performed
Asher Peres' proof that a violation of No Cloning Theorem would imply a violation of the Second Law of Thermodynamics is shown not to take into account the algorithmic-information's contribution to the Thermodynamical Entropy of the semi-permeable membranes of Peres' engine.
The gedanken-experiment of Einstein's lift is analyzed in order of determining whether the free-falling observer inside the lift can detect the eventual topological non-triviality of space-time
Giorgio Parisi's recent speculations on the concept of continuous dimension (cond-mat/0207334) are compared with Von Neumann's serious work.
We introduce and analyze a quantum analogue of the Law of Excluded Gambling Strategies of Classical Decision Theory by the definition of different kind of quantum casinos. The necessity of keeping into account entaglement (by the way we give a staightforward generalization of Schmidt's entanglement measure) forces us to adopt the general algebraic language of Quantum Probability Theory whose essential points are reviewed. The Mathematica code of two packages simulating, respectively, classical and quantum gambling is included. The deep link existing between the censorship of winning quantum gambling strategies and the central notion of Quantum Algorithmic Information Theory, namely quantum algorithmic randomness (by the way we introduce and discard the naive noncommutative generalization of the original Kolmogorov definition), is analyzed
The issue of defining a random sequence of qubits is studied in the framework of Algorithmic Free Probability Theory.Its connection with Quantum Algorithmic Information Theory is shown
Martin-Lof's definition of random sequences of cbits as those not belonging to any set of constructive zero Lebesgue measure is reformulated in the language of Algebraic Probability Theory. The adoption of the Pour-El Richards theory of computability structures on Banach spaces allows us to give a natural noncommutative extension of Martin-Lof's definition, characterizing the random elements of a chain Von Neumann algebra. In the particular case of the minimally informative noncommutative alphabet our definition reduces to the definition of a random sequence of qubits.
Unfortunately, after an imprudent sumbission of the paper to the e-print archive, I discovered in it many serious mistakes. So I draw back it .
Paper erroneously re-submitted as duplicte. Readers should look at math-ph/9909004.