/pdf/from-kuramoto-to-crawford-exploring-the-onset-of-3wpvjokr2x.pdf

From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators

Methods of information geometry

Quantum electrodynamical corrections to the fine structure of helium

We show that many coupled oscillator array configurations considered in the literature can be put into a simple form so that determining the stability of the synchronous state can be done by a master stability function, which can be tailored to one's choice of stability requirement. This solves, once and for all, the problem of synchronous stability for any linear coupling of that oscillator.

/pdf/master-stability-functions-for-synchronized-coupled-systems-14x9mo3phi.pdf

Master Stability Functions for Synchronized Coupled Systems

A new proof is given of the positive energy theorem of classical general relativity. Also, a new proof is given that there are no asymptotically Euclidean gravitational instantons. (These theorems have been proved previously, by a different method, by Schoen and Yau.) The relevance of these results to the stability of Minkowski space is discussed.

/pdf/a-new-proof-of-the-positive-energy-theorem-53vkf3vcke.pdf

A new proof of the positive energy theorem

Relative entropy of two states of a von Neumann algebra is defined in terms of the relative modular operator. The strict positivity, lower semicontinuity, convexity and monotonicity of relative entropy are proved. The Wigner-Yanase-Dyson-Lieb concavity is also proved for general von Neumann algebra.

/pdf/relative-entropy-of-states-of-von-neumann-algebras-1bxowshrc4.pdf

Relative Entropy of States of von Neumann Algebras

International Symposium on Mathematical Problems in Theoretical Physics

Mathematical theory of quantum fields

A necessary and sufficient condition for two quasifree states of CAR to be quasiequivalent is obtained. Quasif ree states is characterized as the unique KMS state of a Bogoliubov automorphism of CAR. The structure of the group of all inner Bogoliubov automorphisms of CAR is clarified.

https://www.ems-ph.org/journals/show_pdf.php?issn=0034-5318&vol=6&iss=3&rank=1

On Quasifree States of CAR and Bogoliubov Automorphisms

The limitation on the measurement of an operator imposed by the presence of a conservation law is studied It is shown that an operator which does not commute with a conserved (additive) quantity cannot be measured exactly (in the sense of von Neumann) It is also shown for a simple case that an approximate measurement of such an operator is possible to any desired accuracy

Huzihiro Araki

Papers

Relative Entropy of States of von Neumann Algebras

International Symposium on Mathematical Problems in Theoretical Physics

Mathematical theory of quantum fields

On Quasifree States of CAR and Bogoliubov Automorphisms

Measurement of Quantum Mechanical Operators