Méthode fonctionnelle en théorie des champs
Méthodes de noyaux et de symboles en calcul stochastique non commutatif
Metodi variazionali e topologici nello studio delle equazioni di Schrödinger nonlineari agli stati stazionari
In the present paper we survey some recents results concerning existence of semiclassical standing waves solutions for nonlinear Schrödinger equations. Furthermore, from Maxwell's equations we derive a nonlinear Schrödinger equation which represents a model of propagation of an electromagnetic field in optical waveguides.
Microlocalization of resonant states and estimates of the residue of the scattering amplitude
We obtain some microlocal estimates of the resonant states associated to a resonance of an -differential operator. More precisely, we show that the normalized resonant states are
Microscopic description of 2D topological phases, duality, and 3D state sums.
Microscopic irreversibility.
Mild solutions of quantum stochastic differential equations.
Minimal and maximal sets of Bell-type inequalities holding in a logic.
Mirror symmetry and conformal flatness in general relativity.
Mirror symmetry and toric geometry.
Mirror symmetry in dimension 3
Miura opers and critical points of master functions
Critical points of a master function associated to a simple Lie algebra come in families called the populations [11]. We prove that a population is isomorphic to the flag variety of the Langlands dual Lie algebra . The proof is based on the correspondence between critical points and differential operators called the Miura opers. For a Miura oper D, associated with a critical point of a population, we show that all solutions of the differential equation DY=0 can be written explicitly in terms...
Möbius gyrovector spaces in quantum information and computation
Hyperbolic vectors, called gyrovectors, share analogies with vectors in Euclidean geometry. It is emphasized that the Bloch vector of Quantum Information and Computation (QIC) is, in fact, a gyrovector related to Möbius addition rather than a vector. The decomplexification of Möbius addition in the complex open unit disc of a complex plane into an equivalent real Möbius addition in the open unit ball of a Euclidean 2-space is presented. This decomplexification proves useful, enabling the resulting...
Möbius transformations and monogenic functional calculus.
Model selection for quantum homodyne tomography
This paper deals with a non-parametric problem coming from physics, namely quantum tomography. That consists in determining the quantum state of a mode of light through a homodyne measurement. We apply several model selection procedures: penalized projection estimators, where we may use pattern functions or wavelets, and penalized maximum likelihood estimators. In all these cases, we get oracle inequalities. In the former we also have a polynomial rate of convergence for the non-parametric problem....
Modeling a quantum Hall system via elliptic equations.
Models for quadratic algebras associated with second order superintegrable systems in 2D.
Models of quadratic algebras generated by superintegrable systems in 2D.
Modular atomic effect algebras and the existence of subadditive states
Lattice effect algebras generalize orthomodular lattices and -algebras. We describe all complete modular atomic effect algebras. This allows us to prove the existence of ordercontinuous subadditive states (probabilities) on them. For the separable noncomplete ones we show that the existence of a faithful probability is equivalent to the condition that their MacNeille complete modular effect algebra.
Modular covariance, PCT, spin and statistics