51 research outputs found
On Pauli Pairs
The state of a system in classical mechanics can be uniquely reconstructed if
we know the positions and the momenta of all its parts. In 1958 Pauli has
conjectured that the same holds for quantum mechanical systems. The conjecture
turned out to be wrong. In this paper we provide a new set of examples of Pauli
pairs, being the pairs of quantum states indistinguishable by measuring the
spatial location and momentum. In particular, we construct a new set of
spatially localized Pauli pairs.Comment: submitted to JM
Measurement of the motional sidebands of a nanogram-scale oscillator in the quantum regime
We describe measurements of the motional sidebands produced by a mechanical oscillator (with effective
mass 43 ng and resonant frequency 705 kHz) that is placed in an optical cavity and cooled close to its quantum
ground state. The red and blue sidebands (corresponding to Stokes and anti-Stokes scattering) from a single laser
beam are recorded simultaneously via a heterodyne measurement. The oscillator’s mean phonon number ¯n is
inferred from the ratio of the sidebands, and reaches a minimum value of 0.84 ± 0.22 (corresponding to a mode
temperature T = 28 ± 7μK). We also infer ¯n from the calibrated area of each of the two sidebands, and from the
oscillator’s total damping. The values of ¯n inferred from these four methods are in close agreement. The behavior
of the sidebands as a function of the oscillator’s temperature agrees well with theory that includes the quantum
fluctuations of both the cavity field and the mechanical oscillator
Rotated multifractal network generator
The recently introduced multifractal network generator (MFNG), has been shown
to provide a simple and flexible tool for creating random graphs with very
diverse features. The MFNG is based on multifractal measures embedded in 2d,
leading also to isolated nodes, whose number is relatively low for realistic
cases, but may become dominant in the limiting case of infinitely large network
sizes. Here we discuss the relation between this effect and the information
dimension for the 1d projection of the link probability measure (LPM), and
argue that the node isolation can be avoided by a simple transformation of the
LPM based on rotation.Comment: Accepted for publication in JSTA
Hypercyclic algebras for convolution and composition operators
[EN] We provide an alternative proof to those by Shkarin and by Bayart and Matheron that the operator D of complex differentiation supports a hypercyclic algebra on the space of entire functions. In particular we obtain hypercyclic algebras for many convolution operators not induced by polynomials, such as , , or , where . In contrast, weighted composition operators on function algebras of analytic functions on a plane domain fail to support supercyclic algebras.This work is supported in part by MEC, Project MTM 2016-7963-P. We also thank Angeles Prieto for comments and suggestions.Bès, J.; Conejero, JA.; Papathanasiou, D. (2018). Hypercyclic algebras for convolution and composition operators. Journal of Functional Analysis. 274(10):2884-2905. https://doi.org/10.1016/j.jfa.2018.02.003S288429052741
Subdifferential rolle’s and mean value inequality theorems
Two main results presented by the authors include a mean-value inequality for a class of Gateaux subdifferentiable functions and a subdifferential Rolle’s theorem in a Banach space. For the second part, if a (Gateaux/Fréchet)subdifferentiable function f is bounded by " on the boundary of a unit ball, then there exists a Gateaux/Fréchet) subgradient of f at an interior point of the ball which is bounded by 2"
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