Riccati and Ermakov equations in time-dependent and time-independent quantum systems.
Rieffel’s pseudodifferential calculus and spectral analysis of quantum Hamiltonians
We use the functorial properties of Rieffel’s pseudodifferential calculus to study families of operators associated to topological dynamical systems acted by a symplectic space. Information about the spectra and the essential spectra are extracted from the quasi-orbit structure of the dynamical system. The semi-classical behavior of the families of spectra is also studied.
Riemannian metrics on 2D-manifolds related to the Euler−Poinsot rigid body motion
The Euler−Poinsot rigid body motion is a standard mechanical system and it is a model for left-invariant Riemannian metrics on SO(3). In this article using the Serret−Andoyer variables we parameterize the solutions and compute the Jacobi fields in relation with the conjugate locus evaluation. Moreover, the metric can be restricted to a 2D-surface, and the conjugate points of this metric are evaluated using recent works on surfaces of revolution. Another related 2D-metric on S2 associated to the...
Riemann-Lebesgue properties of Green's functions with applications to inverse scattering.
Riesz means of bounded states and semi-classical limit connected with a Lieb-Thirring conjecture. II
Ring-like structures with unique symmetric difference related to quantum logic
Ring-like quantum structures generalizing Boolean rings and having the property that the terms corresponding to the two normal forms of the symmetric difference in Boolean algebras coincide are investigated. Subclasses of these structures are algebraically characterized and related to quantum logic. In particular, a physical interpretation of the proposed model following Mackey's approach to axiomatic quantum mechanics is given.
RNA packaging motor: From structure to quantum mechanical modelling and sequential-stochastic mechanism.
Rogers-Ramanujan identities: A century of progress from mathematics to physics.
Root vectors in quantum groups.
Roots of the phase operators.
Rotation-invariant operators on white noise functional.
Rotations in the space of Split octonions.
-linear algebra in economics and physics.
-linear operators in quantum mechanics and in economy.
Sabinin‘s method for classification of local Bol loops
Scale-dependent functions, stochastic quantization and renormalization.
Scaling algebras in local relativistic quantum physics.
Scattering and spectral theory for Stark Hamiltonians in one dimension.
Scattering for a dispersive charge transfer model
Scattering on stratified media: the microlocal properties of the scattering matrix and recovering asymptotics of perturbations
The scattering matrix is defined on a perturbed stratified medium. For a class of perturbations, its main part at fixed energy is a Fourier integral operator on the sphere at infinity. Proving this is facilitated by developing a refined limiting absorption principle. The symbol of the scattering matrix determines the asymptotics of a large class of perturbations.