A generating function for fatgraphs
A geometric derivation of the linear Boltzmann equation for a particle interacting with a Gaussian random field, using a Fock space approach
In this article the linear Boltzmann equation is derived for a particle interacting with a Gaussian random field, in the weak coupling limit, with renewal in time of the random field. The initial data can be chosen arbitrarily. The proof is geometric and involves coherent states and semi-classical calculus.
A geometrical interpretation of the time evolution of the Schrödinger equation for discrete quantum systems
A journey between two curves.
A Lie algebroid on the Wiener space.
A Lieb-Thirring bound for a magnetic Pauli Hamiltonian (II).
We establish a Lieb-Thirring type estimate for Pauli Hamiltonians with non-homogeneous magnetic fields. Besides of depending on the size of the field, the bound also takes into account the size of the field gradient. We then apply the inequality to prove stability of non-relativistic quantum mechanical matter coupled to the quantized ultraviolet-cutoff electromagnetic field for arbitrary values of the fine structure constant.
A low temperature expansion for the pseudoscalar Yukawa model of quantum fields in two space-time dimensions
A mathematical introduction to the Wigner formulation of quantum mechanics
The paper is devoted to review, from a mathematical point of view, some fundamental aspects of the Wigner formulation of quantum mechanics. Starting from the axioms of quantum mechanics and of quantum statistics, we justify the introduction of the Wigner transform and eventually deduce the Wigner equation.
A mathematician's view of the development of physics
A Maxwell-Bloch model with discrete symmetries for wave propagation in nonlinear crystals : an application to KDP
This article presents the derivation of a semi-classical model of electromagnetic-wave propagation in a non centro-symmetric crystal. It consists of Maxwell’s equations for the wave field coupled with a version of Bloch’s equations which takes fully into account the discrete symmetry group of the crystal. The model is specialized in the case of a KDP crystal for which information about the dipolar moments at the Bloch level can be recovered from the macroscopic dispersion properties of the material....
A Maxwell-Bloch model with discrete symmetries for wave propagation in nonlinear crystals: an application to KDP
This article presents the derivation of a semi-classical model of electromagnetic-wave propagation in a non centro-symmetric crystal. It consists of Maxwell's equations for the wave field coupled with a version of Bloch's equations which takes fully into account the discrete symmetry group of the crystal. The model is specialized in the case of a KDP crystal for which information about the dipolar moments at the Bloch level can be recovered from the macroscopic dispersion properties of the material. ...
A measure-theoretic characterization of Boolean algebras among orthomodular lattices
We investigate subadditive measures on orthomodular lattices. We show as the main result that an orthomodular lattice has to be distributive (=Boolean) if it possesses a unital set of subadditive probability measures. This result may find an application in the foundation of quantum theories, mathematical logic, or elsewhere.
A method for weight multiplicity computation based on Berezin quantization.
A minimax principle for eigenvalues in spectral gaps: Dirac operators with Coulomb potentials.
A model of atomic radiation
A model of gauge theory with invariant variables.
A modified Kardar-Parisi-Zhang model.
A monotonicity formula for Yang-Mills Fields.
A multiplicity result for the Schrodinger-Maxwell equations with negative potential
We prove the existence of a sequence of radial solutions with negative energy of the Schrödinger-Maxwell equations under the action of a negative potential.
A new approach to Hom-left-symmetric bialgebras
The main purpose of this paper is to consider a new definition of Hom-left-symmetric bialgebra. The coboundary Hom-left-symmetric bialgebra is also studied. In particular, we give a necessary and sufficient condition that -matrix is a solution of the Hom--equation by a cocycle condition.