A Fulling–Kuchment theorem for the 1D harmonic oscillator http://dx.doi.org/10.1088/0266-5611/28/4/045009 by Guillemin, Victor; Hezari, Hamid (Department of Mathematics, Massachusetts Institute
of Technology, Cambridge, MA 02139-4397 (United States)), E-mail: vwg@math.mit.edu,
E-mail: hezari@math.mit.edu Read MoreCollapse
[en]
We prove that there exists a pair of non-isospectral 1D semiclassical Schrödinger
operators whose spectra agree up to O(h^{∞}). In particular, all their semiclassical
trace invariants are the same. Our proof is based on an idea of Fulling–Kuchment and
Hadamard’s variational formula applied to suitable perturbations of the harmonic oscillator.
(paper)$$$$
An inverse problem for a wave equation with arbitrary initial values and a finite
time of observations http://dx.doi.org/10.1088/0266-5611/27/9/095006 by Cipolatti, Rolci (Departamento de Métodos Matemáticos, Instituto de Matemática, Universidade
Federal do Rio de Janeiro, Ilha do Fundão, Caixa Postal 68530, CEP 21941-972, Rio
de Janeiro (Brazil)); Yamamoto, Masahiro (Department of Mathematical Sciences, The
University of Tokyo, Komaba Meguro, Tokyo 153-8914 (Japan)), E-mail: cipolatti@im.ufrj.br,
E-mail: myama@ms.u-tokyo.ac.jp Read MoreCollapse
[en]
We consider a solution u(p, g, a, b) to an initial value–boundary value problem for
a wave equation and we discuss an inverse problem of determining a coefficient p(x)
and a, b by observations of u(p, g, a, b)(x, t) in a neighbourhood ω of ∂Ω over a
time interval (0, T) and ∂^{i}_{t}u(p, g, a, b)(x, T_{0}),
x in Ω, i = 0, 1, with T_{0} < T. We prove that if T − T_{0} and T_{0}
are larger than the diameter of Ω, then we can choose a finite number of Dirichlet
boundary inputs g_{1}, ..., g_{N}, so that the mapping is uniformly
Lipschitz continuous with suitable Sobolev norms provided that {p, a_{j},
b_{j}}_{1≤j≤N} remains in some bounded set in a suitable Sobolev space.
In our inverse problem, initial values are also unknown, and we do not assume any
positivity of the initial values. Our key is a Carleman estimate and the exact controllability
in a Sobolev space of higher order$$$$
Recent developments in the theory of plasma-based collisionally excited x-ray lasers
(XRL) have shown an optimization potential based on the dependence of the absorption
region of the pumping laser on its angle of incidence on the plasma. For the experimental
proof of this idea, a number of diagnostic schemes were developed, tested, qualified
and applied. A high-resolution imaging system, yielding the keV emission profile perpendicular
to the target surface, provided positions of the hottest plasma regions, interesting
for the benchmarking of plasma simulation codes. The implementation of a highly efficient
spectrometer for the plasma emission made it possible to gain information about the
abundance of the ionization states necessary for the laser action in the plasma. The
intensity distribution and deflection angle of the pump laser beam could be imaged
for single XRL shots, giving access to its refraction process within the plasma. During
a European collaboration campaign at the Lund Laser Center, Sweden, the optimization
of the pumping laser incidence angle resulted in a reduction of the required pumping
energy for a Ni-like Mo XRL, which enabled the operation at a repetition rate of 10
Hz. Using the experiences gained there, the XRL performance at the PHELIX facility,
GSI Darmstadt with respect to achievable repetition rate and at wavelengths below
20 nm was significantly improved, and also important information for the development
towards multi-100 eV plasma XRLs was acquired. Due to the setup improvements achieved
during the work for this thesis, the PHELIX XRL system now has reached a degree of
reproducibility and versatility which is sufficient for demanding applications like
the XRL spectroscopy of heavy ions. In addition, a European research campaign, aiming
towards plasma XRLs approaching the water-window (wavelengths below 5 nm) was initiated.
(orig.)$$$$
Computing estimates of material properties from transmission eigenvalues http://dx.doi.org/10.1088/0266-5611/28/5/055009 by Giorgi, Giovanni (DIMA, Università degli Studi di Genova, via Dodecaneso 35, 16146
Genova (Italy)); Haddar, Houssem (INRIA, Saclay, Ile de France/CMAP, Ecole Polytechnique,
Route de Saclay, 91128 Palaiseau Cedex (France)), E-mail: giorgi@dima.unige.it, E-mail:
haddar@cmap.polytechnique.fr Read MoreCollapse
[en]
This work is motivated by inverse scattering problems, those problems where one is
interested in reconstructing the shape and the material properties of an inclusion
from electromagnetic farfield measurements. More precisely, we are interested in complementing
the so-called sampling methods by providing an estimate of the material properties
of the sought inclusion. We use for this purpose a measure of the first transmission
eigenvalue. Our method is then based on computing the desired estimate by reformulating
the so-called interior transmission eigenvalue problem as an eigenvalue problem for
the material coefficients. We will restrict ourselves to the two-dimensional setting
of the problem and treat the cases of both transverse electric and transverse magnetic
polarizations. We present a number of numerical experiments that validate our methodology
for homogeneous and inhomogeneous inclusions and backgrounds. We also treat the case
of a background with absorption and the case of scatterers with multiple connected
components of different refractive indices. (paper)$$$$
The aim of the presented experiment was to investigate the feasibility of satellite-based
global quantum key distribution. In this context, a free-space quantum key distribution
experiment over a real distance of 144 km was performed. The transmitter and the receiver
were situated in 2500 m altitude on the Canary Islands of La Palma and Tenerife, respectively.
The small and compact transmitter unit generated attenuated laser pulses, that were
sent to the receiver via a 15-cm optical telescope. The receiver unit for polarisation
analysis and detection of the sent pulses was integrated into an existing mirror telescope
designed for classical optical satellite communications. To ensure the required stability
and efficiency of the optical link in the presence of atmospheric turbulence, the
two telescopes were equipped with a bi-directional automatic tracking system. Still,
due to stray light and high optical attenuation, secure key exchange would not be
possible using attenuated pulses in connection with the standard BB84 protocol. The
photon number statistics of attenuated pulses follows a Poissonian distribution. Hence,
by removing a photon from all pulses containing two or more photons, an eavesdropper
could measure its polarisation without disturbing the polarisation state of the remaining
pulse. In this way, he can gain information about the key without introducing detectable
errors. To protect against such attacks, the presented experiment employed the recently
developed method of using additional ''decoy'' states, i.e., the the intensity of
the pulses created by the transmitter were varied in a random manner. By analysing
the detection probabilities of the different pulses individually, a photon-number-splitting
attack can be detected. Thanks to the decoy-state analysis, the secrecy of the resulting
quantum key could be ensured despite the Poissonian nature of the emitted pulses.
For a channel attenuation as high as 35 dB, a secret key rate of up to 250 bit/s was
achieved. Our outdoor experiment was carried out under real atmospheric conditions
and with a channel attenuation comparable to an optical link from ground to a satellite
in low earth orbit. Hence, it definitely shows the feasibility of satellite-based
quantum key distribution using a technologically comparatively simple system. (orig.)$$$$
Study of plasma polarization spectroscopy 93 KB - http://www.iaea.org/inis/collection/NCLCollectionStore/_Public/36/116/36116173.pdf - Text Version by Iwamae, Atsushi; Fujimoto, Takashi (Kyoto Univ., Dept. of Engineering Physics and
Mechanics, Kyoto (Japan)); Kawachi, Tetsuya; Hasegawa, Noboru (Japan Atomic Energy
Research Inst., Kansai Research Establishment, Kizu, Kyoto (Japan)) fromProceedings of the fourth symposium on advanced photon research Read MoreCollapse
[en]
Nitrogen gas target was irradiated by a linearly polarized ultra-short pulse of Ti:Sapphire
laser light with duration of 50 fs and energy of 150 mJ. We changed the direction
of the polarization of the incident laser light and observed the emission of the resonance
series lines of the lithiumlike ions and radiative recombination spectrum from recombining
helium-like ions. (author)$$$$
A remarkable variety of particle acceleration occurs in the solar system, from lightning-related
acceleration of electrons to tens of MeV energy in less than a millisecond in planetary
atmospheres; to acceleration of auroral and radiation belt particles in planetary
magnetospheres; to acceleration at planetary bow shocks, co-rotating interplanetary
region shocks, shocks driven by fast coronal mass ejections, and at the heliospheric
termination shock; to acceleration in magnetic reconnection regions in solar flares
and at planetary magnetopause and magnetotail current sheets. These acceleration processes
often occur in conjunction with transient energy releases, and some are very efficient,
with the accelerated particles containing ∼ 10-50% of the total energy released. Others
are highly selective; for example, the acceleration in ^{3}He-rich solar particle
events enriches ^{3}He by a factor of up to 10,000 or more relative to ^{4}He.
Unlike acceleration processes outside the solar system, the accelerated particles
and the physical conditions in the acceleration region can be studied through direct
in situ measurements, and/or through detailed imaging and spectroscopy. Here I review
recent observations of these acceleration phenomena, our current understanding of
the physics involved, and the applicability to particle acceleration elsewhere in
the universe. (author)$$$$
The equations of fluid mechanics, coupled with those that describe matter transportation
at the molecular level must be handled effectively. Putting the fluid into equations,
we model the Bloch NMR flow equations into the harmonic wave equation for the analysis
of general fluid flow. We derived the solution of the modelled harmonic equation in
non relativistic quantum mechanics and discuss its semi classical application to illustrate
its potential wide-ranging usefulness in the search for the best possible data obtainable
for general fluid flow analysis. Representing the solution of the derived harmonic
wave equation by a normalized state function is quite useful in generating the properly
normalized wave functions and in the efficient evaluation of expectation values of
many operators that can be fundamental to the analysis of fluid flow especially at
the microscopic level. (author)$$$$
Wigner's dynamical transition state theory in phase space: classical and quantum http://dx.doi.org/10.1088/0951-7715/21/1/R01 by Waalkens, Holger; Schubert, Roman; Wiggins, Stephen (School of Mathematics, University
of Bristol, University Walk, Bristol BS8 1TW (United Kingdom)), E-mail: h.waalkens@math.rug.nl,
E-mail: roman.schubert@bristol.ac.uk, E-mail: s.wiggins@bristol.ac.uk Read MoreCollapse
[en]
We develop Wigner's approach to a dynamical transition state theory in phase space
in both the classical and quantum mechanical settings. The key to our development
is the construction of a normal form for describing the dynamics in the neighbourhood
of a specific type of saddle point that governs the evolution from reactants to products
in high dimensional systems. In the classical case this is the standard Poincaré–Birkhoff
normal form. In the quantum case we develop a normal form based on the Weyl calculus
and an explicit algorithm for computing this quantum normal form. The classical normal
form allows us to discover and compute the phase space structures that govern classical
reaction dynamics. From this knowledge we are able to provide a direct construction
of an energy dependent dividing surface in phase space having the properties that
trajectories do not locally 're-cross' the surface and the directional flux across
the surface is minimal. Using this, we are able to give a formula for the directional
flux through the dividing surface that goes beyond the harmonic approximation. We
relate this construction to the flux–flux autocorrelation function which is a standard
ingredient in the expression for the reaction rate in the chemistry community. We
also give a classical mechanical interpretation of the activated complex as a normally
hyperbolic invariant manifold (NHIM), and further describe the structure of the NHIM.
TIM. The quantum normal form provides us with an efficient algorithm to compute quantum
reaction rates and we relate this algorithm to the quantum version of the flux–flux
autocorrelation function formalism. The significance of the classical phase space
structures for the quantum mechanics of reactions is elucidated by studying the phase
space distribution of scattering states. The quantum normal form also provides an
efficient way of computing Gamov–Siegert resonances. We relate these resonances to
the lifetimes of the quantum activated complex. We consider several one, two and three
degree-of-freedom systems and show explicitly how calculations of the above quantities
can be carried out. Our theoretical framework is valid for Hamiltonian systems with
an arbitrary number of degrees of freedom and we demonstrate that in several situations
it gives rise to algorithms that are computationally more efficient than existing
methods. (invited article)$$$$
A direct sampling method to an inverse medium scattering problem http://dx.doi.org/10.1088/0266-5611/28/2/025003 by Ito, Kazufumi (Department of Mathematics and Center for Research in Scientific Computation,
North Carolina State University, Raleigh, NC (United States)); Jin, Bangti (Department
of Mathematics and Institute for Applied Mathematics and Computational Science, Texas
A and M University, College Station, TX 77843-3368 (United States)); Zou, Jun (Department
of Mathematics, The Chinese University of Hong Kong, Shatin, NT (Hong Kong)), E-mail:
kito@unity.ncsu.edu, E-mail: btjin@math.tamu.edu, E-mail: zou@math.cuhk.edu.hk Read MoreCollapse
[en]
In this work we present a novel sampling method for time harmonic inverse medium scattering
problems. It provides a simple tool to directly estimate the shape of the unknown
scatterers (inhomogeneous media), and it is applicable even when the measured data
are only available for one or two incident directions. A mathematical derivation is
provided for its validation. Two- and three-dimensional numerical simulations are
presented, which show that the method is accurate even with a few sets of scattered
field data, computationally efficient, and very robust with respect to noises in the
data. (paper)$$$$