9,013 research outputs found
The decoherence and interference of cosmological arrows of time for a de Sitter universe with quantum fluctuations
We consider the superposition of two semiclassical solutions of the
Wheeler-DeWitt equation for a de Sitter universe, describing a quantized scalar
vacuum propagating in a universe that is contracting in one case and expanding
in the other, each identifying a opposite cosmological arrow of time. We
discuss the suppression of the interference terms between the two arrows of
time due to environment-induced decoherence caused by modes of the scalar
vacuum crossing the Hubble horizon. Furthermore, we quantify the effect of the
interference on the expectation value of the observable field mode
correlations, with respect to an observer that we identify with the spatial
geometry
Analysis and design of quadratically bounded QPV control systems
© 2019. ElsevierA nonlinear system is said to be quadratically bounded (QB) if all its solutions are bounded and this is guaranteed using a quadratic Lyapunov function. This paper considers the QB analysis and state-feedback controller design problems for quadratic parameter varying (QPV) systems. The developed approach, which relies on a linear matrix inequality (LMIs) feasibility problem, ensures that the QB property holds for an invariant ellipsoid which contains a predefined polytopic region of the state space. An example is used to illustrate the main characteristics of the proposed approach and to confirm the validity of the theoretical results.Peer ReviewedPostprint (author's final draft
The recurrence function of a random Sturmian word
This paper describes the probabilistic behaviour of a random Sturmian word.
It performs the probabilistic analysis of the recurrence function which can be
viewed as a waiting time to discover all the factors of length of the
Sturmian word. This parameter is central to combinatorics of words. Having
fixed a possible length for the factors, we let to be drawn
uniformly from the unit interval , thus defining a random Sturmian word
of slope . Thus the waiting time for these factors becomes a random
variable, for which we study the limit distribution and the limit density.Comment: Submitted to ANALCO 201
Quantum Cramer-Rao bound for a Massless Scalar Field in de Sitter Space
How precisely can we estimate cosmological parameters by performing a quantum
measurement on a cosmological quantum state? In quantum estimation theory the
variance of an unbiased parameter estimator is bounded from below by the
inverse of measurement-dependent Fisher information and ultimately by quantum
Fisher information, which is the maximization of the former over all positive
operator valued measurements. Such bound is known as the quantum Cramer-Rao
bound. We consider the evolution of a massless scalar field with Bunch-Davies
vacuum in a spatially flat FLRW spacetime, which results in a two-mode squeezed
vacuum out-state for each field wave number mode. We obtain the expressions of
the quantum Fisher information as well as the Fisher informations associated to
occupation number measurement and power spectrum measurement, and show the
specific results of their evoluation for pure de Sitter expansion and de Sitter
expansion followed by a radiation-dominated phase as examples. We will discuss
these results from the point of view of the quantum-to-classical transition of
cosmological perturbations and show quantitatively how this transition and the
residual quantum correlations affect the bound on the precision.Comment: 16 pages, published versio
Replica Symmetry Breaking in Cold Atoms and Spin Glasses
We consider a system composed by N atoms trapped within a multimode cavity,
whose theoretical description is captured by a disordered multimode Dicke
model. We show that in the resonant, zero field limit the system exactly
realizes the Sherrington-Kirkpatrick model. Upon a redefinition of the
temperature, the same dynamics is realized in the dispersive, strong field
limit. This regime also gives access to spin-glass observables which can be
used to detect Replica Symmetry Breaking.Comment: 6 pages, 3 figure
Beyond the storage capacity: data driven satisfiability transition
Data structure has a dramatic impact on the properties of neural networks,
yet its significance in the established theoretical frameworks is poorly
understood. Here we compute the Vapnik-Chervonenkis entropy of a kernel machine
operating on data grouped into equally labelled subsets. At variance with the
unstructured scenario, entropy is non-monotonic in the size of the training
set, and displays an additional critical point besides the storage capacity.
Remarkably, the same behavior occurs in margin classifiers even with randomly
labelled data, as is elucidated by identifying the synaptic volume encoding the
transition. These findings reveal aspects of expressivity lying beyond the
condensed description provided by the storage capacity, and they indicate the
path towards more realistic bounds for the generalization error of neural
networks.Comment: 5 pages, 2 figure
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