Semi-classical Schrödinger equations with harmonic potential and nonlinear perturbation
Semiclassical spectral estimates for Toeplitz operators
Let be a compact Kähler manifold with integral Kähler class and a holomorphic Hermitian line bundle whose curvature is the symplectic form of . Let be a Hamiltonian, and let be the Toeplitz operator with multiplier acting on the space . We obtain estimates on the eigenvalues and eigensections of as , in terms of the classical Hamilton flow of . We study in some detail the case when is an integral coadjoint orbit of a Lie group.
Semiclassical states for weakly coupled nonlinear Schrödinger systems
We consider systems of weakly coupled Schrödinger equations with nonconstant potentials and investigate the existence of nontrivial nonnegative solutions which concentrate around local minima of the potentials. We obtain sufficient and necessary conditions for a sequence of least energy solutions to concentrate.
Semiclassical states of nonlinear Schrödinger equations with bounded potentials
Using some perturbation results in critical point theory, we prove that a class of nonlinear Schrödinger equations possesses semiclassical states that concentrate near the critical points of the potential .
Shape optimization problems for metric graphs
Γ):Γ ∈ 𝒜, ℋ1(Γ) = l}, where ℋ1D1,...,Dk } ⊂ Rd . The cost functional ℰ(Γ) is the Dirichlet energy of Γ defined through the Sobolev functions on Γ vanishing on the points Di. We analyze the existence of a solution in both the families of connected sets and of metric graphs. At the end, several explicit examples are discussed.
Shifted Riccati procedure: application to conformal barotropic FRW cosmologies.
Shoikhet's conjecture and Duflo isomorphism on (co)invariants.
Short waves through thin interfaces and 2-microlocal measures
Sigma models with non-commuting complex structures and extended supersymmetry
We discuss additional supersymmetries for supersymmetric non-linear sigma models described by left and right semichiral superfields.
Singleton independence
Motivated by the central limit problem for algebraic probability spaces arising from the Haagerup states on the free group with countably infinite generators, we introduce a new notion of statistical independence in terms of inequalities rather than of usual algebraic identities. In the case of the Haagerup states the role of the Gaussian law is played by the Ullman distribution. The limit process is realized explicitly on the finite temperature Boltzmannian Fock space. Furthermore, a functional...
Singular Bohr–Sommerfeld rules for 2D integrable systems
Singular eigenfunctions of Calogero-Sutherland type systems and how to transform them into regular ones.
Singular integrals of the time-harmonic relativistic Dirac equation on a piecewise Liapunov surface.
Singular potentials in quantum mechanics and ambiguity in the self-adjoint Hamiltonian.
Skein quantization of Poisson algebras of loops on surfaces
Small global solutions and the nonrelativistic limit for the nonlinear Dirac equation.
In this paper we study the Cauchy problem for the nonlinear Dirac equation in the Sobolev space Hs. We prove the existence and uniqueness of global solutions for small data in Hs with s > 1...
Solitary waves for Maxwell-Dirac and Coulomb-Dirac models
Solitary waves for Maxwell-Schrödinger equations.
Solitons and Gibbs Measures for Nonlinear Schrödinger Equations
We review some recent results concerning Gibbs measures for nonlinear Schrödinger equations (NLS), with implications for the theory of the NLS, including stability and typicality of solitary wave structures. In particular, we discuss the Gibbs measures of the discrete NLS in three dimensions, where there is a striking phase transition to soliton-like behavior.
Solutions globales des systèmes de Dirac-Klein-Gordon