2,485 research outputs found
Anderson-like impurity in the one-dimensional t-J model: formation of local states and magnetic behaviour
We consider an integrable model describing an Anderson-like impurity coupled
to an open -- chain. Both the hybridization (i.e. its coupling to bulk
chain) and the local spectrum can be controlled without breaking the
integrability of the model. As the hybridization is varied, holon and spinon
bound states appear in the many body ground state. Based on the exact solution
we study the state of the impurity and its contribution to thermodynamic
quantities as a function of an applied magnetic field. Kondo behaviour in the
magnetic response of the impurity can be observed provided that its parameters
have been adjusted properly to the energy scales of the holon and spinon
excitations of the one-dimensional bulk.Comment: 32 pages, 11 figure
Bounds on set exit times of affine systems, using Linear Matrix Inequalities
Efficient computation of trajectories of switched affine systems becomes possible, if for any such hybrid system, we can manage to efficiently compute the sequence of switching times. Once the switching times have been computed, we can easily compute the trajectories between two successive switches as the solution of an affine ODE. Each switching time can be seen as a positive real root of an analytic function, thereby allowing for efficient computation by using root finding algorithms. These algorithms require a finite interval, within which to search for the switching time. In this paper, we study the problem of computing upper bounds on such switching times, and we restrict our attention to stable time-invariant affine systems. We provide semi-definite programming models to compute upper bounds on the time taken by the trajectories of an affine ODE to exit a set described as the intersection of a few generalized ellipsoids. Through numerical experiments, we show that the resulting bounds are tighter than bounds reported before, while requiring only a modest increase in computation time.publishedVersio
Experimental evidence of accelerated seismic release without critical failure in acoustic emissions of compressed nanoporous materials
The total energy of acoustic emission (AE) events in externally stressed
materials diverges when approaching macroscopic failure. Numerical and
conceptual models explain this accelerated seismic release (ASR) as the
approach to a critical point that coincides with ultimate failure. Here, we
report ASR during soft uniaxial compression of three silica-based (SiO)
nanoporous materials. Instead of a singular critical point, the distribution of
AE energies is stationary and variations in the activity rate are sufficient to
explain the presence of multiple periods of ASR leading to distinct brittle
failure events. We propose that critical failure is suppressed in the AE
statistics by dissipation and transient hardening. Some of the critical
exponents estimated from the experiments are compatible with mean field models,
while others are still open to interpretation in terms of the solution of
frictional and fracture avalanche models.Comment: preprint, Main article: 7 pages, 3 figures. Supplementary material
included in \anc folder: 6 pages, 3 figure
Data-driven control of switched linear systems with probabilistic stability guarantees
This paper tackles state feedback control of switched linear systems under
arbitrary switching. We propose a data-driven control framework that allows to
compute a stabilizing state feedback using only a finite set of observations of
trajectories with quadratic and sum of squares (SOS) Lyapunov functions. We do
not require any knowledge on the dynamics or the switching signal, and as a
consequence, we aim at solving \emph{uniform} stabilization problems in which
the feedback is stabilizing for all possible switching sequences. In order to
generalize the solution obtained from trajectories to the actual system,
probabilistic guarantees on the obtained quadratic or SOS Lyapunov function are
derived in the spirit of scenario optimization. For the quadratic Lyapunov
technique, the generalization relies on a geometric analysis argument, while,
for the SOS Lyapunov technique, we follow a sensitivity analysis argument. In
order to deal with high-dimensional systems, we also develop parallelized
schemes for both techniques. We show that, with some modifications, the
data-driven quadratic Lyapunov technique can be extended to LQR control design.
Finally, the proposed data-driven control framework is demonstrated on several
numerical examples.Comment: This is an extended version to the previous pape
Carrier thermal escape in families of InAs/InP self-assembled quantum dots
We investigate the thermal quenching of the multimodal photoluminescence from
InAs/InP (001) self-assembled quantum dots. The temperature evolution of the
photoluminescence spectra of two samples is followed from 10 K to 300 K. We
develop a coupled rate-equation model that includes the effect of carrier
thermal escape from a quantum dot to the wetting layer and to the InP matrix,
followed by transport, recapture or non-radiative recombination. Our model
reproduces the temperature dependence of the emission of each family of quantum
dots with a single set of parameters. We find that the main escape mechanism of
the carriers confined in the quantum dots is through thermal emission to the
wetting layer. The activation energy for this process is found to be close to
one-half the energy difference between that of a given family of quantum dots
and that of the wetting layer as measured by photoluminescence excitation
experiments. This indicates that electron and holes exit the InAs quantum dots
as correlated pairs
Geometry of Entanglement Sudden Death: Explicit Examples
In open quantum systems, entanglement can vanish faster than coherence. This
phenomenon is usually called sudden death of entanglement. In [M. O. Terra
Cunha, New J. Phys. 9, 237 (2007)] a geometrical explanation was offered and a
classification of all possible scenarios was given. Some classes were
exemplified, but it was still an open question whether there were examples for
the other ones. This was solved in [R.C. Drumond and M.O. Terra Cunha,
arXiv:0809.4445v1]. Here we briefly review the problem, state our results in a
precise way, discuss the generality of the approach, and add some speculative
desirable generalizations.Comment: Contribution written to the Procceedings of 5th Vaxjo Conference on
Foundations of Probability and Physic
- …