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.
Über die Existenz von Wellenoperatoren für zeitabhängige Störungen.
Une description semi-classique de la diffusion quantique
Une formule de Landau-Zener pour un croisement générique de codimension 2
Universal forms for one-dimensional quantum Hamiltonians: a comparison of the SUSY and the de la Peña factorization approaches.
Universal low temperature asymptotics of the correlation functions of the Heisenberg chain.
Universal monotonicity of eigenvalue moments and sharp Lieb–Thirring inequalities
We show that phase space bounds on the eigenvalues of Schr¨odinger operators can be derived from universal bounds recently obtained by E. M. Harrell and the author via a monotonicity property with respect to coupling constants. In particular, we provide a new proof of sharp Lieb– Thirring inequalities.
Using supermodels in quantum optics.
Vacuum energy as spectral geometry.
Velocity and Entropy of Motion in Periodic Potentials
This is a report on recent joint work with J. Asch, and with T. Hudetz and F. Benatti.We consider classical, quantum and semiclassical motion in periodic potentials and prove various results on the distribution of asymptotic velocities.The Kolmogorov-Sinai entropy and its quantum generalization, the Connes-Narnhofer-Thirring entropy, of the single particle and of a gas of noninteracting particles are related.
Wave Equation and Causality Violation
Wave Operators for Defocusing Matrix Zakharov-Shabat Systems with Pnonvanishing at Infinity
2000 Mathematics Subject Classification: Primary: 34L25; secondary: 47A40, 81Q10.In this article we prove that the wave operators describing the direct scattering of the defocusing matrix Zakharov-Shabat system with potentials having distinct nonzero values with the same modulus at ± ∞ exist, are asymptotically complete, and lead to a unitary scattering operator. We also prove that the free Hamiltonian operator is absolutely continuous.
Wave operators for pairs of spaces and the Klein-Gordon equation.
Wave packets techniques
Weak interaction limit for nuclear matter and the time-dependent Hartree-Fock equation
We consider an effective model of nuclear matter including spin and isospin degrees of freedom, described by an -body Hamiltonian with suitably renormalized two-body and three-body interaction potentials. We show that the corresponding mean-field theory (the time-dependent Hartree-Fock approximation) is “exact” as tends to infinity.
Weak Limits of Solutions to Semilinear Hyperbolic Sytems.