5,456 research outputs found
Improved energy estimates for a class of time-dependent perturbed Hamiltonians
We consider time-dependent perturbations which are relatively bounded with
respect to the square root of an unperturbed Hamiltonian operator, and whose
commutator with the latter is controlled by the full perturbed Hamiltonian. The
perturbation is modulated by two auxiliary parameters, one regulates its
intensity as a prefactor and the other controls its time-scale via a regular
function, whose derivative is compactly supported in a finite interval. We
introduce a natural generalization of energy conservation in the case of
time-dependent Hamiltonians: the boundness of the two-parameter unitary
propagator for the physical evolution with respect to -th power energy
norm for all . We provide bounds of the -th power energy
norms, uniformly in time and the time-scale parameter, for the unitary
propagators, generated by the time-dependent perturbed Hamiltonian and by the
unperturbed Hamiltonian in the interaction picture. The physically interesting
model of Landau-type Hamiltonians with an additional weak and
time-slowly-varying electric potential of unit drop is included in this
framework.Comment: 20 page
SR-FTiR microscopy and FTIR imaging in the earth sciences
During the last decades, several books have been devoted to the application
of spectroscopic methods in mineralogy. Several short courses and meetings have
addressed particular aspects of spectroscopy, such as the analysis of hydrous
components in minerals and Earth materials. In these books, complete treatment
of the infrared theory and practical aspects of instrumentation and methods,
along with an exhaustive list of references, can be found. The present chapter
is intended to cover those aspects of infrared spectroscopy that have been
developed in the past decade and are not included in earlier reviews such as
Volume 18 of Reviews in Mineralogy. These new topics involve primarily: (1) the
use of synchrotron radiation (SR), which, although not a routine method, is now
rather extensively applied in infrared studies, in particular those requiring
ultimate spatial and time resolution and the analysis of extremely small
samples (a few tens of micrometers); (2) the development of imaging techniques
also for foreseen time resolved studies of geo-mineralogical processes and
environmental studies.Comment: 36 pages, 24 figures - Reviews in Mineralogy & Geochemistry - Vol. 78
(2013) in pres
Observation of Scissors Modes in solid state systems with a SQUID
The occurrence of scissors modes in crystals that have deformed ions in their
cells has been predicted some time ago. The theoretical value of their energy
is rather uncertain, however, ranging between 10 and a few tenths of eV, with
the corresponding widths of 10^-7, 10^-6 eV. Their observation by resonance
fluorescence experiments therefore requires a photon spectrometer covering a
wide energy range with a very high resolving power. We propose and discuss a
new experiment in which such difficulties are overcome by measuring with a
SQUID the variation of the magnetic field associated with the excitation of
scissors modes.Comment: 8 pages, 2 figure
The Haldane model and its localization dichotomy
Gapped periodic quantum systems exhibit an interesting Localization Dichotomy, which emerges when one looks at the localization of the optimally localized Wannier functions associated to the Bloch bands below the gap. As recently proved, either these Wannier functions are exponentially localized, as it happens whenever the Hamiltonian operator is time-reversal symmetric, or they are delocalized in the sense that the expectation value of |x| 2 diverges. Intermediate regimes are forbidden. Following the lesson of our Maestro, to whom this contribution is gratefully dedicated, we find useful to explain this subtle mathematical phenomenon in the simplest possible model, namely the discrete model proposed by Haldane [10]. We include a pedagogical introduction to the model and we explain its Localization Dichotomy by explicit analytical arguments. We then introduce the reader to the more general, model-independent version of the dichotomy proved in [19]
Molecular simulation of the phase behavior of noble gases using accurate two-body and three-body intermolecular potentials
Gibbs ensemble Monte Carlo simulations are reported for the vapor- liquid phase coexistence of argon, krypton, and xenon. The calculations employ accurate two-body potentials in addition to contributions from three-body dispersion interactions resulting from third-order triple-dipole, dipole-dipole-quadrupole, dipole- quadrupole-quadrupole, quadrupole-quadrupole-quadrupole, and fourth- order triple- dipole terms. It is shown that vapor-liquid equilibria are affected substantially by three-body interactions. The addition of three-body interactions results in good overall agreement of theory with experimental data. In particular, the subcritical liquid- phase densities are predicted accurately. (C) 1999 American Institute of Physics. S0021- 9606(99)50728-9
Diffusion-aggregation processes with mono-stable reaction terms
This paper analyses front propagation of the equation
where is a monostable (ie Fisher-type) nonlinear reaction term and changes its sign once, from positive to negative values,in the interval where the process is studied. This model equation accounts for simultaneous diffusive and aggregative behaviors of a population dynamic depending on the population density at time and position . The existence of infinitely many travelling wave solutions is proven. These fronts are parametrized by their wave speed and monotonically connect the stationary states u = 0 and v = 1. In the degenerate case, i.e. when D(0) and/or D(1) = 0, sharp profiles appear, corresponding to the minimum wave speed. They also have new behaviors, in addition to those already observed in diffusive models, since they can be right compactly supported, left compactly supported, or both. The dynamics can exhibit, respectively, the phenomena of finite speed of propagation, finite speed of saturation, or both
Aggregative movement and front propagation for bi-stable population models
Front propagation for the aggregation-diffusion-reaction equation is investigated, where f is a bi-stable reaction-term and D(v) is a diffusion coefficient with changing sign, modeling aggregating-diffusing processes. We provide necessary and sufficient conditions for the existence of traveling wave solutions and classify them according to how or if they attain their equilibria at finite times. We also show that the dynamics can exhibit the phenomena of finite speed of propagation and/or finite speed of saturation
- …