Mariza Stefanello Simsen

Quantum Energy Expectation in Periodic Time-Dependent Hamiltonians via Green Functions

Let be the Floquet operator of a time periodic Hamiltonian . For each positive and discrete observable (which we call a probe energy), we derive a formula for the Laplace time average of its expectation value up to time in terms of its eigenvalues and Green functions at the circle of radius . Some simple applications are provided which support its usefulness.

On

In this work we prove continuity of solutions with respect to initial conditions and exponent parameters and we prove upper semicontinuity of a family of global attractors for problems of the form ∂us ∂t − div(|∇us|s∇us) + f(x, us) = g, where f : Ω×R→ R is a non-globally Lispchitz Carathéodory mapping, g ∈ L2(Ω), Ω is a bounded smooth domain in Rn, n ≥ 1 and ps(·)→ p in L∞(Ω) (p > 2 constant) as s goes to infinity.

p_s(x)

We study the asymptotic behavior of parabolic p(x)-Laplacian problems of the form ∂uλ ∂t − div(D|∇uλ|∇uλ) + a|uλ|uλ = B(uλ) in L(R), where n ≥ 1, p ∈ L∞(Rn) such that 2 M ≥ D(x) ≥ σ > 0 a.e. in R, λ ∈ [0,∞), B : L(R) → L(R) is a globally Lipschitz map and a : R → R is a non-negative continuous function such that there exists R1 > 0 with {x ∈ R; a(x) = 0} ⊂ BR1(0), infx∈Rn\BR1 (0) a(x) > 0, and ∫ R\BR1 (0) 1 a(x)2/(p(x)−2) dx < +∞. We also study the sensitivity of the problem according to the variation of the diffusion coefficients.

-Laplacian Parabolic Problems with Non-Globally Lipschitz Forcing Term

In this work we improve the result presented by Kloeden-Simsen-Stefanello Simsen in [ 8 ] by reducing uniform conditions. We prove theoretical results in order to establish convergence in the Hausdorff semi-distance of the component subsets of the pullback attractor of a non-autonomous multivalued problem to the global attractor of the corresponding autonomous multivalued problem.

Parabolic problems in R n with spatially variable exponents

We study almost periodic orbits of quantum systems and prove that for periodic time-dependent Hamiltonians an orbit is almost periodic if, and only if, it is precompact. In the case of quasiperiodic time-dependence we present an example of a precompact orbit that is not almost periodic. Finally we discuss some simple conditions assuring dynamical stability for nonautonomous quantum system.