Consistent histories: Description of a world with increasing entropy.
Constant solutions of Yang-Baxter equation for sl(2) and sl(3).
Construction BKW pour l'opérateur de Dirac. Cas d'un potentiel périodique
Construction of coupling-resurgent amplitudes in quantum field theory
Construction of Non-Linear Local Quantum Processes.
Construction of renormalized trajectory.
Construction of the Bethe state for the elliptic quantum group.
Construction of vacuum for the positive-energy representation and its Bose counterpart.
Constructive field theory in zero dimension.
Contact Quantization: Quantum Mechanics = Parallel transport
Quantization together with quantum dynamics can be simultaneously formulated as the problem of finding an appropriate flat connection on a Hilbert bundle over a contact manifold. Contact geometry treats time, generalized positions and momenta as points on an underlying phase-spacetime and reduces classical mechanics to contact topology. Contact quantization describes quantum dynamics in terms of parallel transport for a flat connection; the ultimate goal being to also handle quantum systems in terms...
Contact transformations in Wheeler-Feynman electrodynamics
Continuity and linear extensions of quantum measures on Jordan operator algebras.
Continuous interpolation of solution sets of Lipschitzian quantum stochastic differential inclusions.
Contractions of Lie algebras and algebraic groups
Degenerations, contractions and deformations of various algebraic structures play an important role in mathematics and physics. There are many different definitions and special cases of these notions. We try to give a general definition which unifies these notions and shows the connections among them. Here we focus on contractions of Lie algebras and algebraic groups.
Contractions of Poisson-Lie groups, Lie bialgebras and quantum deformations
Contractions of Poisson-Lie groups are introduced by using Lie bialgebra contractions. As an application, contractions of SL(2,R) Poisson-Lie groups leading to (1+1) Poincaré and Heisenberg structures are analysed. It is shown how the method here introduced allows a systematic construction of the Poisson structures associated to non-coboundary Lie bialgebras. Finally, it is sketched how contractions are also implemented after quantization by using the Lie bialgebra approach.
Contractions of product density operators of systems of identical fermions and bosons.
Contractions of to the Heisenberg group and Berezin calculus. (Contraction de vers le groupe de Heisenberg et calcul de Berezin.)
Controllability of Schrödinger equation with a nonlocal term
This paper is concerned with the internal distributed control problem for the 1D Schrödinger equation, i ut(x,t) = −uxx+α(x) u+m(u) u, that arises in quantum semiconductor models. Here m(u) is a non local Hartree–type nonlinearity stemming from the coupling with the 1D Poisson equation, and α(x) is a regular function with linear growth at infinity, including constant electric fields. By means of both the Hilbert Uniqueness Method and the contraction mapping theorem it is shown that for initial and...
Controllability of Schrödinger equations
One considers a quantum particle in a 1D moving infinite square potential well. It is a nonlinear control system in which the state is the wave function of the particle and the control is the acceleration of the potential well. One proves the local controllability around any eigenstate, and the steady state controllability (controllability between eigenstates) of this control system. In particular, the wave function can be moved from one eigenstate to another one, exactly and in finite time, by...
Convergence of gradient-based algorithms for the Hartree-Fock equations
The numerical solution of the Hartree-Fock equations is a central problem in quantum chemistry for which numerous algorithms exist. Attempts to justify these algorithms mathematically have been made, notably in [E. Cancès and C. Le Bris, Math. Mod. Numer. Anal. 34 (2000) 749–774], but, to our knowledge, no complete convergence proof has been published, except for the large-Z result of [M. Griesemer and F. Hantsch, Arch. Rational Mech. Anal. (2011) 170]. In this paper, we prove the convergence of...