Towards the subquantum theory
Transfer matrices and transport for Schrödinger operators
We provide a general lower bound on the dynamics of one dimensional Schrödinger operators in terms of transfer matrices. In particular it yields a non trivial lower bound on the transport exponents as soon as the norm of transfer matrices does not grow faster than polynomially on a set of energies of full Lebesgue measure, and regardless of the nature of the spectrum. Applications to Hamiltonians with a) sparse, b) quasi-periodic, c) random decaying potential are provided....
Transfer of conditions for singular boundary value problems
Numerical solution of linear boundary value problems for ordinary differential equations by the method of transfer of conditions consists in replacing the problem under consideration by a sequence of initial value problems. The method of transfer for systems of equations of the first order with Lebesque integrable coefficients was studied by one of the authors before. The purpose of this paper is to extend the idea of the transfer of conditions to singular boundary value problems for a linear second-order...
Transient phenomena in quantum bound states subjected to a sudden perturbation.
Transitions d’Anderson pour des opérateurs de Schrödinger quasi-périodiques en dimension 1
Transverse evolution operator for the Gross-Pitaevskii equation in semiclassical approximation.
Truncated Infinitesimal Shifts, Spectral Operators and Quantized Universality of the Riemann Zeta Function
We survey some of the universality properties of the Riemann zeta function and then explain how to obtain a natural quantization of Voronin’s universality theorem (and of its various extensions). Our work builds on the theory of complex fractal dimensions for fractal strings developed by the second author and M. van Frankenhuijsen in [60]. It also makes an essential use of the functional analytic framework developed by the authors in [25] for rigorously studying the spectral operator (mapping...
Tunnel effect and symmetries for non-selfadjoint operators
We study low lying eigenvalues for non-selfadjoint semiclassical differential operators, where symmetries play an important role. In the case of the Kramers-Fokker-Planck operator, we show how the presence of certain supersymmetric and -symmetric structures leads to precise results concerning the reality and the size of the exponentially small eigenvalues in the semiclassical (here the low temperature) limit. This analysis also applies sometimes to chains of oscillators coupled to two heat baths,...
Two Hartree-Fock models for the vacuum polarization
We review recent results about the derivation and the analysis of two Hartree-Fock-type models for the polarization of vacuum. We pay particular attention to the variational construction of a self-consistent polarized vacuum, and to the physical agreement between our non-perturbative construction and the perturbative description provided by Quantum Electrodynamics.
Two-dimensional supersymmetric quantum mechanics: two fixed centers of force.