466 research outputs found
Perturbations of eigenvalues embedded at threshold: one, two and three dimensional solvable models
We examine perturbations of eigenvalues and resonances for a class of
multi-channel quantum mechanical model-Hamiltonians describing a particle
interacting with a localized spin in dimension . We consider
unperturbed Hamiltonians showing eigenvalues and resonances at the threshold of
the continuous spectrum and we analyze the effect of various type of
perturbations on the spectral singularities. We provide algorithms to obtain
convergent series expansions for the coordinates of the singularities.Comment: 20 page
Point interactions in acoustics: one dimensional models
A one dimensional system made up of a compressible fluid and several
mechanical oscillators, coupled to the acoustic field in the fluid, is analyzed
for different settings of the oscillators array. The dynamical models are
formulated in terms of singular perturbations of the decoupled dynamics of the
acoustic field and the mechanical oscillators. Detailed spectral properties of
the generators of the dynamics are given for each model we consider. In the
case of a periodic array of mechanical oscillators it is shown that the energy
spectrum presents a band structure.Comment: revised version, 30 pages, 2 figure
Valutazione dell'efficacia di un coadiuvante topico a base di argento micronizzato, zinco acetato e acido laurico nel trattamento dell'acne lieve-moderata
L'acne è una dermatosi ad eziopatogenesi multifattoriale in cui differenti fattori contribuiscono al mantenimento del processo infiammatorio. Il ruolo del P. acnes è stato, infatti, rideterminato in quanto trigger principale della risposta infiammatoria, essendo in grado di attivare la liberazione di numerose citochine proinfiammatorie. Non a caso, gli antibiotici sono tra i farmaci cardine della terapia topica dell'acne. Il loro uso è, tuttavia, limitato dallo sviluppo di resistenze batteriche. Ne deriva la necessità di utilizzare nuove molecole, le cui proprietà antibatteriche non siano suscettibili di fenomeni di resistenza. Tra le molecole che hanno destato maggiore interesse, per l'azione antibatterica non antibiotico-dipendente, e, pertanto, non soggetta allo sviluppo di resistenze, annoveriamo l'acido laurico, l'argento micronizzato e lo zinco acetato. Il nostro studio si propone di valutare l'efficacia nel trattamenti dell'acne lieve-moderata di una terapia topica a base di argento micronizzato, acido laurico e zinco acetato attraverso una valutazione sia oggettiva, mediante GAGS e Sebutape, che soggettiva, mediante l'ausilio di un nuovo strumento di valutazione della componente psicologica del paziente acneico: l'acne radar
Spin dependent point potentials in one and three dimensions
We consider a system realized with one spinless quantum particle and an array
of spins 1/2 in dimension one and three. We characterize all the
Hamiltonians obtained as point perturbations of an assigned free dynamics in
terms of some ``generalized boundary conditions''. For every boundary condition
we give the explicit formula for the resolvent of the corresponding
Hamiltonian. We discuss the problem of locality and give two examples of spin
dependent point potentials that could be of interest as multi-component
solvable models.Comment: 15 pages, some misprints corrected, one example added, some
references modified or adde
Fast solitons on star graphs
We define the Schr\"odinger equation with focusing, cubic nonlinearity on
one-vertex graphs. We prove global well-posedness in the energy domain and
conservation laws for some self-adjoint boundary conditions at the vertex, i.e.
Kirchhoff boundary condition and the so called and boundary
conditions. Moreover, in the same setting we study the collision of a fast
solitary wave with the vertex and we show that it splits in reflected and
transmitted components. The outgoing waves preserve a soliton character over a
time which depends on the logarithm of the velocity of the ingoing solitary
wave. Over the same timescale the reflection and transmission coefficients of
the outgoing waves coincide with the corresponding coefficients of the linear
problem. In the analysis of the problem we follow ideas borrowed from the
seminal paper \cite{[HMZ07]} about scattering of fast solitons by a delta
interaction on the line, by Holmer, Marzuola and Zworski; the present paper
represents an extension of their work to the case of graphs and, as a
byproduct, it shows how to extend the analysis of soliton scattering by other
point interactions on the line, interpreted as a degenerate graph.Comment: Sec. 2 revised; several misprints corrected; added references; 32
page
Dynamics of F=2 Spinor Bose-Einstein Condensates
We experimentally investigate and analyze the rich dynamics in F=2 spinor
Bose-Einstein condensates of Rb87. An interplay between mean-field driven spin
dynamics and hyperfine-changing losses in addition to interactions with the
thermal component is observed. In particular we measure conversion rates in the
range of 10^-12 cm^3/s for spin changing collisions within the F=2 manifold and
spin-dependent loss rates in the range of 10^-13 cm^3/s for hyperfine-changing
collisions. From our data we observe a polar behavior in the F=2 ground state
of Rb87, while we measure the F=1 ground state to be ferromagnetic. Furthermore
we see a magnetization for condensates prepared with non-zero total spin.Comment: 4 pages, 2 figures, RevTe
On the spectrum of a bent chain graph
We study Schr\"odinger operators on an infinite quantum graph of a chain form
which consists of identical rings connected at the touching points by
-couplings with a parameter . If the graph is "straight",
i.e. periodic with respect to ring shifts, its Hamiltonian has a band spectrum
with all the gaps open whenever . We consider a "bending"
deformation of the chain consisting of changing one position at a single ring
and show that it gives rise to eigenvalues in the open spectral gaps. We
analyze dependence of these eigenvalues on the coupling and the
"bending angle" as well as resonances of the system coming from the bending. We
also discuss the behaviour of the eigenvalues and resonances at the edges of
the spectral bands.Comment: LaTeX, 23 pages with 7 figures; minor changes, references added; to
appear in J. Phys. A: Math. Theo
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