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11 papers · 1 filter
Width of Shape Resonances for Non Globally Analytic Potentials
S. Fujiie, A. Lahmar-Benbernou, A. Martinez
We consider the semiclassical Schroedinger operator with a "well in an island" potential, on which we assume smoothness only, except near infinity. We give the asymptotic expansion…
Time-fractional derivatives in relaxation processes: a tutorial survey
Francesco Mainardi, Rudolf Gorenflo
The aim of this tutorial survey is to revisit the basic theory of relaxation processes governed by linear differential equations of fractional order. The fractional derivatives are…
Some aspects of fractional diffusion equations of single and distributed order
Francesco Mainardi, Gianni Pagnini, Rudolf Gorenflo
The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order $β\in (0,…
The role of the Fox-Wright functions in fractional sub-diffusion of distributed order
Francesco Mainardi, Gianni Pagnini
The fundamental solution of the fractional diffusion equation of distributed order in time (usually adopted for modelling sub-diffusion processes) is obtained based on its Mellin-B…
Spectral analysis of transfer operators associated to Farey fractions
Claudio Bonanno, Sandro Graffi, Stefano Isola
The spectrum of a one-parameter family of signed transfer operators associated to the Farey map is studied in detail. We show that when acting on a suitable Hilbert space of analyt…
The Ghirlanda-Guerra Identities
Pierluigi Contucci, Cristian Giardina'
If the variance of a Gaussian spin-glass Hamiltonian grows like the volume the model fulfills the Ghirlanda-Guerra identities in terms of the normalized Hamiltonian covariance.