1,721,126 research outputs found
Non-trapping magnetic fields and Morrey-Campanato estimates for Schrödinger operators
No full textWe prove some uniform in a priori estimates for solutions of the equation
(∇ −i A)^2u − V (x)u +(λ± i)u = f, λ0, = 0.
The estimates are obtained in terms of Morrey–Campanato norms, and can be used to
prove absence of zero-resonances, in a suitable sense, for electromagnetic Hamiltonians.
Quantitative conditions on the size of the trapping component of the magnetic field and the
non-repulsive component of the electric field are given
Dispersive Equations in Quantum Mechanics
No full textThis article has been selected by the Editors for the prize of the Rendiconti di Matematica
e delle sue Applicazioni for the best PhD Thesis of the Academic Year 2007/2008
Semilinear Schrödinger equation with time dependent coefficients
No full textIn this paper we study local and global well-posedness in L2 and H1 of the Cauchy problem for the following
nonlinear Schr ̈odinger equations
iu_t + a(t)Δu = ±|u|^{γ−1}u,
in the space R^{1+n}, with n ≥ 2. The coefficient a(t) is assumed to be positive, and possibly vanishing with
finite order on a discrete set; we find the relationship between the critical powers γ for the well-posedness and
the order of the zeroes of a
Electromagnetic Schrödinger flow: multiplier methods for dispersion
Full text linkWe show a list of results which have been recently obtained about dispersive properties of the electromagnetic Schrodinger flow. We introduce a general philosophy, based on multiplier techniques, which permits to detect the bad parts of an electromagnetic potential which can possibly affect the dispersion
Spherical Schrödinger hamiltonians: spectral analysis and time decay
No full textIn this survey, we review recent results concerning the canonical dispersive flow e^(itH) led by a Schrödinger Hamiltonian H. We study, in particular, how the time decay of space Lp-norms depends on the frequency localization of the initial datum with respect to the some suitable spherical expansion. A quite complete description of the phenomenon is given in terms of the eigenvalues and eigenfunctions of the restriction of H to the unit sphere, and a comparison with some uncertainty inequality is presented. © Springer International Publishing AG 2017
Carleman estimates and necessary conditions for the existence of waveguides
No full textWe study via Carleman estimates the sharpest possible exponential decay for waveguide solutions to the Laplace equation (partial derivative(2)(t) + Delta)u = Vu + W . (partial derivative(t), del)u and find a necessary quantitative condition On the exponential decay in the spatial-variable of nonzero waveguide solutions which depends on the size of V and W at infinity
Magnetic virial identities, weak dispersion and Strichartz estimates
No full textWe show a family of virial-type identities for the Schrödinger and wave
equations with electromagnetic potentials. As a consequence, some weak dispersive
inequalities in space dimension n ≥ 3, involving Morawetz and smoothing estimates,
are proved; finally,we apply them to prove Strichartz inequalities for thewave equation
with a non-trapping electromagnetic potential with almost Coulomb decay
Misspecification and Expectations Correction in New Keynesian DSGE Models
Full text linkAbstract: This paper focuses on the dynamic misspecification that characterizes the class
of small-scale New-Keynesian models and provides a `natural' remedy for the typical difficulties
these models have in accounting for the rich contemporaneous and dynamic correlation structure
of the data, generally faced with ad hoc shock specifications. We suggest using the `best fitting'
statistical model for the data as a device through which it is possible to adapt the econometric
specification of the New-Keynesian model. The statistical model may feature an autocorrelation
structure that is more involved than the autocorrelation structure implied by the structural
model's reduced form solution under rational expectations, and it is treated as the actual agents'
expectations generating mechanism. A pseudo-structural form is built from the baseline system
of Euler equations by forcing the state vector of the system to have the same dimension as the
state vector characterizing the statistical model. We provide an empirical illustration based on
U.S. quarterly data and a small-scale monetary New Keynesian model
On the blow-up threshold for weakly coupled nonlinear Schrodinger equations
No full textWe study the Cauchy problem for a system of two coupled nonlinear focusing Schrodinger equations arising in nonlinear optics. We discuss when the solutions are global in time or blow-up in finite time. Some results, in dependence of the data of the problem, are proved; in particular we prove, for suitable values of the parameters, that the blow-up threshold (if the nonlinearity has the critical growth) is a universal constant
Quantitative Hardy inequalities for magnetic Hamiltonians
No full textIn this paper we present a new method of proof of Hardy type inequalities for two-dimensional quantum Hamiltonians with a magnetic field of finite flux. Our approach gives a quantitative lower bound on the best constant in these inequalities both for Schrödinger and Pauli operators. Pauli operators with Aharonov-Bohm magnetic field are discussed as well
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