Related papers: Multidimensional Yamada-Watanabe theorem and its a…
We review one dimensional matrix theory and its variations, collective field theory and quantum phase space description. In the planar limit, these theories become classical and can be easily analyzed. With these descriptions, one…
This paper is devoted to the Cauchy problem for the modified multi-component Camassa-Holm system in higher dimensions. On the one hand, we establish an almost complete local well-posedness results for the system in the framework of Besov…
We establish the existence of an optimal partition for the Yamabe equation in the whole space made up of mutually linearly isometric sets, each of them invariant under the action of a group of linear isometries. To do this, we establish the…
We give a review of some recent work on generalization of the Bethe ansatz in the case of $2+1$-dimensional models of quantum field theory. As such a model, we consider one associated with the tetrahedron equation, i.e. the…
Multiple light scattering is widely used to characterize dense colloidal systems as well as in deep tissue imaging; experiments are often interpreted via a theory of diffusion of the light intensity within a sample, neglecting the vector…
We consider a charged particle following the boundary of a two-dimensional domain because a homogeneous magnetic field is applied. We develop the basic scattering theory for the corresponding quantum mechanical edge states. The scattering…
QED theory of multiphoton cascade transitions in atoms and ions is developed. In particular the $ 3s\rightarrow1s+2\gamma $, $ 4s\rightarrow1s+2\gamma $ and $ 3p\rightarrow1s+3\gamma $ processes are considered. Two different approaches…
We prove existence of Yamabe metrics on four-manifolds possessing finitely-many conical points with $\mathbb{Z}_2$-group, using for the first time a min-max scheme in the singular setting. In our variational argument we need to deform…
The one-dimensional scattering of a two body interacting system by an infinite wall is studied in a quantum-mechanical framework. This problem contains some of the dynamical features present in the collision of atomic, molecular and nuclear…
We consider a non-relativistic quantum particle interacting with a singular potential supported by two parallel straight lines in the plane. We locate the essential spectrum under the hypothesis that the interaction asymptotically…
A self-contained discussion of nonrelativistic quantum scattering is presented in the case of central potentials in one space dimension, which will facilitate the understanding of the more complex scattering theory in two and three…
Multidimensional systems are becoming increasingly important as they provide a promising tool for estimation, simulation and control, while going beyond the traditional setting of one-dimensional systems. The analysis of multidimensional…
We study the quantum dissipative dynamics of a particle coupled linearly to a set of two-level systems (the heat bath) via the master equation method which we extract from the path integral formalism independently from the form of the bath…
This paper is devoted to the study of dimension theory, in particular multifractal analysis, for multimodal maps. We describe the Lyapunov spectrum, generalising previous results by Todd. We also study the multifractal spectrum of pointwise…
A piece of the Standard Model presently undergoing intense experimental scrutiny is the Cabibbo Kobayashi Maskawa matrix. Several different measurements are planned to enrich the spectrum of experimental constraints and thus provide one of…
We prove that in conformal classes of metrics near the class of an Einstein metric (other than the standard round metric on a sphere) the Yamabe problem has a unique solution up to scaling. This is a local extension, in the space of…
We extend the planar Markus-Yamabe Jacobian Conjecture to differential systems having jacobian matrix with eigenvalues with negative or zero real parts.
We study Bessel processes on Weyl chambers of types A and B on $\mathbb R^N$. Using elementary symmetric functions, we present several space-time-harmonic functions and thus martingales for these processes $(X_t)_{t\ge0}$ which are…
Whitham modulation theory for the two dimensional Benjamin-Ono (2DBO) equation is presented. A system of five quasi-linear first-order partial differential equations is derived. The system describes modulations of the traveling wave…
Introduced in the field of many-body statistical mechanics, Yang-Baxter equation has become an important tool in a variety fields of physics. In this work, we report the first direct experimental simulation of the Yang-Baxter equation using…