Related papers: Quantization of affine bodies. Theory and applicat…
The kinetics of dissolution of an amorphous solid is studied using a simple model of a glass that captures with reasonable accuracy the dynamic heterogeneities associated with the relaxation of an amorphous material at low temperatures. The…
In this work a finite element simulation of the motion of a rigid body in a fluid, with free surface, is described. A completely general referential description (of which both Lagrangian and Eulerian descriptions are special cases) of an…
We develop the general formalism for the study of neutrino propagation in presence of stochastic media. This formalism allows the systematic derivation of evolution equations for averaged quantities as survival probabilities and higher…
The recent experimental progresses in handling microscopic systems have allowed to probe them at levels where fluctuations are prominent, calling for stochastic modeling in a large number of physical, chemical and biological phenomena. This…
The goal of the present account is to review our efforts to obtain and apply a ``collective'' Hamiltonian for a few, approximately decoupled, adiabatic degrees of freedom, starting from a Hamiltonian system with more or many more degrees of…
Integrals of motion and statistical properties of quantized electromagnetic field (e.-m. field) in time-dependent linear dielectric and conductive media are considered, using Choi-Yeon quantization, based on Caldirola-Kanai type…
These lecture notes review the foundations and some applications of light-cone quantization. First I explain how to choose a time in special relativity. Inclusion of Poincare invariance naturally leads to Dirac's forms of relativistic…
In this paper, the massless Schwinger model or two dimensional quantum electrodynamics is exactly solved on a Riemann surface. The partition function and the generating functional of the correlation functions involving the fermionic…
Functionally graded materials (FGMs) are two-phase composites with continuously changing microstructure adapted to performance requirements. Traditionally, the overall behavior of FGMs has been determined using local averaging techniques or…
We study the quantum mechanics of the derivative nonlinear Schrodinger equation which has appeared in many areas of physics and is known to be classically integrable. We find that the N-body quantum problem is exactly solvable with both…
This is the third article in our series of articles exploring connections between dynamical systems of St\"ackel-type and of Painlev\'e-type. In this article we present a method of deforming of minimally quantized quasi-St\"ackel…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
The floating body approach to affine surface area is adapted to a holomorphic context providing an alternate approach to Fefferman's invariant hypersurface measure.
We study a new method - called Schrodingerisation introduced in [Jin, Liu, Yu, arXiv: 2212.13969] - for solving general linear partial differential equations with quantum simulation. This method converts linear partial differential…
The aim of this paper is to perform a deeper geometric analysis of problems appearing in dynamics of affinely rigid bodies. First of all we present a geometric interpretation of the polar and two-polar decomposition of affine motion. Later…
We present a new method for the quantization of totally constrained systems including general relativity. The method consists in constructing discretized theories that have a well defined and controlled continuum limit. The discrete…
We study the deformation quantization of scalar and abelian gauge classical free fields. Stratonovich-Weyl quantizer, star-products and Wigner functionals are obtained in field and oscillator variables. Abelian gauge theory is particularly…
A dynamical theory of hypersurface deformations is presented. It is shown that a (n+1)-dimensional space-time can be always foliated by pure deformations, governed by a non zero Hamiltonian. Quantum deformations states are defined by…
We compute an explicit algebraic deformation quantization for an affine Poisson variety described by an ideal in a polynomial ring, and inheriting its Poisson structure from the ambient space.
In this paper we discuss some aspects of fragmented condensation from a mathematical perspective. We first propose a simple way of characterizing finite fragmentation. Then, inspired by recent results of semiclassical analysis applied to…