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We consider quantum Hamiltonians of the form H(t)=H+V(t) where the spectrum of H is semibounded and discrete, and the eigenvalues behave as E_n~n^alpha, with 0<alpha<1. In particular, the gaps between successive eigenvalues decay as n^{alpha-1}. V(t) is supposed to be periodic, bounded, continuously differentiable in the strong sense and such that the matrix entries with respect to the spectral decomposition of H obey the estimate |V(t)_{m,n}|<=epsilon*|m-n|^{-p}max{m,n}^{-2gamma} for m!=n where epsilon>0, p>=1 and gamma=(1-alpha)/2. We show that the energy diffusion exponent can be arbitrarily small provided p is sufficiently large and epsilon is small enough. More precisely, for any initial condition Psiin Dom(H^{1/2}), the diffusion of energy is bounded from above as <H>_Psi(t)=O(t^sigma) where sigma=alpha/(2ceil{p-1}gamma-1/2). As an application we consider the Hamiltonian H(t)=|p|^alpha+epsilon*v(theta,t) on L^2(S^1,dtheta) which was discussed earlier in the literature by Howland.
The main motivation of this article is to derive sufficient conditions for dynamical stability of periodically driven quantum systems described by a Hamiltonian H(t), i.e., conditions under which it holds sup_{t in R} | (psi(t),H(t) psi(t)) |<infty w
A novel family of exactly solvable quantum systems on curved space is presented. The family is the quantum version of the classical Perlick family, which comprises all maximally superintegrable 3-dimensional Hamiltonian systems with spherical symmetr
A family of discontinuous symplectic maps on the cylinder is considered. This family arises naturally in the study of nonsmooth Hamiltonian dynamics and in switched Hamiltonian systems. The transformation depends on two parameters and is a canonical
Given a 3-dimensional Riemannian manifold (M,g), we investigate the existence of positive solutions of singularly perturbed Klein-Gordon-Maxwell systems and Schroedinger-Maxwell systems on M, with a subcritical nonlinearity. We prove that when the pe
Quantum technology resorts to efficient utilization of quantum resources to realize technique innovation. The systems are controlled such that their states follow the desired manners to realize different quantum protocols. However, the decoherence ca