206 research outputs found
Two-dimensional Time-dependent Point Interactions
We study the time-evolution of a quantum particle subjected to time-dependent
zero-range forces in two dimensions. After establishing a conceivable ansatz
for the solution to the Schr\"{o}dinger equation, we prove that the wave packet
time-evolution is completely specified by the solutions of a system of
Volterra-type equations -- the {\it charge equations} -- involving the
coefficients of the singular part of the wave function, thus extending to the
two-dimensional case known results in one and three dimensions.Comment: 17 pages, AMS-LaTex; presentation of the model changed, small changes
to Lemma 2.1 and Proposition 2.
Decay of a Bound State under a Time-Periodic Perturbation: a Toy Case
We study the time evolution of a three dimensional quantum particle,
initially in a bound state, under the action of a time-periodic zero range
interaction with ``strength'' (\alpha(t)). Under very weak generic conditions
on the Fourier coefficients of (\alpha(t)), we prove complete ionization as (t
\to \infty). We prove also that, under the same conditions, all the states of
the system are scattering states.Comment: LaTeX2e, 15 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
Investigation of asymmetrical shaft power increase during ship maneuvers by means of simulation techniques
Marine propulsion plants can experience large power fluctuations during tight maneuvers, with increases of shaft torque up to and over 100% of the steady values in straight course and considerable asymmetry between internal and external shafts during turning circle. This phenomenon (studied in Viviani et al 2007a and 2007b can be of particular interest for twin screw ships propulsion systems with coupled shaftlines, in which asymmetrical loads can represent a challenge for the whole propulsion system (e.g. unique reduction gear, shaftlines, automation). A joint research has been set up in order to deeply investigate the phenomenon, by means of large scale model testing and related numerical simulations. In the present work, preliminary simulation results with different simplified automation systems and with an automation system more similar to the real one are reported, allowing to get a better insight into this complex problem
On the Asymptotic Dynamics of a Quantum System Composed by Heavy and Light Particles
We consider a non relativistic quantum system consisting of heavy and
light particles in dimension three, where each heavy particle interacts with
the light ones via a two-body potential . No interaction is assumed
among particles of the same kind. Choosing an initial state in a product form
and assuming sufficiently small we characterize the asymptotic
dynamics of the system in the limit of small mass ratio, with an explicit
control of the error. In the case K=1 the result is extended to arbitrary
. The proof relies on a perturbative analysis and exploits a
generalized version of the standard dispersive estimates for the
Schr\"{o}dinger group. Exploiting the asymptotic formula, it is also outlined
an application to the problem of the decoherence effect produced on a heavy
particle by the interaction with the light ones.Comment: 38 page
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
A time-dependent perturbative analysis for a quantum particle in a cloud chamber
We consider a simple model of a cloud chamber consisting of a test particle
(the alpha-particle) interacting with two other particles (the atoms of the
vapour) subject to attractive potentials centered in . At time zero the alpha-particle is described by an outgoing
spherical wave centered in the origin and the atoms are in their ground state.
We show that, under suitable assumptions on the physical parameters of the
system and up to second order in perturbation theory, the probability that both
atoms are ionized is negligible unless lies on the line joining the
origin with . The work is a fully time-dependent version of the original
analysis proposed by Mott in 1929.Comment: 23 page
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