829 research outputs found
Upper quantum Lyapunov Exponent and Anosov relations for quantum systems driven by a classical flow
We generalize the definition of quantum Anosov properties and the related
Lyapunov exponents to the case of quantum systems driven by a classical flow,
i.e. skew-product systems. We show that the skew Anosov properties can be
interpreted as regular Anosov properties in an enlarged Hilbert space, in the
framework of a generalized Floquet theory. This extension allows us to describe
the hyperbolicity properties of almost-periodic quantum parametric oscillators
and we show that their upper Lyapunov exponents are positive and equal to the
Lyapunov exponent of the corresponding classical parametric oscillators. As
second example, we show that the configurational quantum cat system satisfies
quantum Anosov properties.Comment: 17 pages, no figur
On the Impossibility to Extend Triples of Mutually Unbiased Product Bases in Dimension Six
An analytic proof is given which shows that it is impossible to extend any
triple of mutually unbiased (MU) product bases in dimension six by a single MU
vector. Furthermore, the 16 states obtained by removing two orthogonal states
from any MU product triple cannot figure in a (hypothetical) complete set of
seven MU bases. These results follow from exploiting the structure of MU
product bases in a novel fashion, and they are among the strongest ones
obtained for MU bases in dimension six without recourse to computer algebra.Comment: 12 pages, identical to published versio
Chaos and quantum-nondemolition measurements
The problem of chaotic behavior in quantum mechanics is investigated against the background of the theory of quantum-nondemolition (QND) measurements. The analysis is based on two relevant features: The outcomes of a sequence of QND measurements are unambiguously predictable, and these measurements actually can be performed on one single system without perturbing its time evolution. Consequently, QND measurements represent an appropriate framework to analyze the conditions for the occurrence of ‘‘deterministic randomness’’ in quantum systems. The general arguments are illustrated by a discussion of a quantum system with a time evolution that possesses nonvanishing algorithmic complexity
Semantic filtering through deep source separation on microscopy images
By their very nature microscopy images of cells and tissues consist of a
limited number of object types or components. In contrast to most natural
scenes, the composition is known a priori. Decomposing biological images into
semantically meaningful objects and layers is the aim of this paper. Building
on recent approaches to image de-noising we present a framework that achieves
state-of-the-art segmentation results requiring little or no manual
annotations. Here, synthetic images generated by adding cell crops are
sufficient to train the model. Extensive experiments on cellular images, a
histology data set, and small animal videos demonstrate that our approach
generalizes to a broad range of experimental settings. As the proposed
methodology does not require densely labelled training images and is capable of
resolving the partially overlapping objects it holds the promise of being of
use in a number of different applications
Reconstruction of the spin state
System of 1/2 spin particles is observed repeatedly using Stern-Gerlach
apparatuses with rotated orientations. Synthesis of such non-commuting
observables is analyzed using maximum likelihood estimation as an example of
quantum state reconstruction. Repeated incompatible observations represent a
new generalized measurement. This idealized scheme will serve for analysis of
future experiments in neutron and quantum optics.Comment: 4 pages, 1 figur
How to determine a quantum state by measurements: The Pauli problem for a particle with arbitrary potential
The problem of reconstructing a pure quantum state ¿¿> from measurable quantities is considered for a particle moving in a one-dimensional potential V(x). Suppose that the position probability distribution ¿¿(x,t)¿2 has been measured at time t, and let it have M nodes. It is shown that after measuring the time evolved distribution at a short-time interval ¿t later, ¿¿(x,t+¿t)¿2, the set of wave functions compatible with these distributions is given by a smooth manifold M in Hilbert space. The manifold M is isomorphic to an M-dimensional torus, TM. Finally, M additional expectation values of appropriately chosen nonlocal operators fix the quantum state uniquely. The method used here is the analog of an approach that has been applied successfully to the corresponding problem for a spin system
Constructing Mutually Unbiased Bases in Dimension Six
The density matrix of a qudit may be reconstructed with optimal efficiency if
the expectation values of a specific set of observables are known. In dimension
six, the required observables only exist if it is possible to identify six
mutually unbiased complex 6x6 Hadamard matrices. Prescribing a first Hadamard
matrix, we construct all others mutually unbiased to it, using algebraic
computations performed by a computer program. We repeat this calculation many
times, sampling all known complex Hadamard matrices, and we never find more
than two that are mutually unbiased. This result adds considerable support to
the conjecture that no seven mutually unbiased bases exist in dimension six.Comment: As published version. Added discussion of the impact of numerical
approximations and corrected the number of triples existing for non-affine
families (cf Table 3
Small denominators, frequency operators, and Lie transforms for nearly integrable quantum spin systems
Based on the previously proposed notions of action operators and of quantum integrability, frequency operators are introduced in a fully quantum-mechanical setting. They are conceptually useful because another formulation can be given to unitary perturbation theory. When worked out for quantum spin systems, this variant is found to be formally equivalent to canonical perturbation theory applied to nearly integrable systems consisting of classical spins. In particular, it becomes possible to locate the quantum-mechanical operator-valued equivalent of the frequency denominators that may cause divergence of the classical perturbation series. The results that are established here link the concept of quantum-mechanical integrability to a technical question, namely, the behavior of specific perturbation series
The 13C Pocket in Low Mass AGB Stars
It is well known that thermally pulsing Asymptotic Giant Branch stars with
low mass play a relevant role in the chemical evolution. They have synthesized
about 30% of the galactic carbon and provide an important contribution to the
nucleosynthesis of heavy elements (A>80). The relevant nucleosynthesis site is
the He-rich intermediate zone (less than 10^{-2} Msun), where
alpha(2alpha,gamma)12C reactions and slow neutron captures on seed nuclei
essentially iron) take place. A key ingredient is the interplay between nuclear
processes and convective mixing. It is the partial overlap of internal and
external convective zones that allows the dredge-up of the material enriched in
C and heavy elements. We review the progresses made in the last 50 years in the
comprehension of the s process in AGB stars, with special attention to the
identification of the main neutron sources and to the particular physical
conditions allowing this important nucleosynthesis.Comment: Accepted for Publication on PAS
Chaotic Evolution in Quantum Mechanics
A quantum system is described, whose wave function has a complexity which
increases exponentially with time. Namely, for any fixed orthonormal basis, the
number of components required for an accurate representation of the wave
function increases exponentially.Comment: 8 pages (LaTeX 16 kB, followed by PostScript 2 kB for figure
- …