Search results for "manifold"

2016

The wealth of sensory data coming from different modalities has opened numerous opportunities for data analysis. The data are of increasing volume, complexity and dimensionality, thus calling for new methodological innovations towards multimodal data processing. However, multimodal architectures must rely on models able to adapt to changes in the data distribution. Differences in the density functions can be due to changes in acquisition conditions (pose, illumination), sensors characteristics (number of channels, resolution) or different views (e.g. street level vs. aerial views of a same building). We call these different acquisition modes domains, and refer to the adaptation problem as d…

Z2-Regge versus standard Regge calculus in two dimensions

1999

We consider two versions of quantum Regge calculus: the standard Regge calculus where the quadratic link lengths of the simplicial manifold vary continuously and the ${Z}_{2}$ Regge model where they are restricted to two possible values. The goal is to determine whether the computationally more easily accessible ${Z}_{2}$ model still retains the universal characteristics of standard Regge theory in two dimensions. In order to compare observables such as the average curvature or Liouville field susceptibility, we use in both models the same functional integration measure, which is chosen to render the ${Z}_{2}$ Regge model particularly simple. Expectation values are computed numerically and …

Structural similarities and differences among attractors and their intensity maps in the laser-Lorenz model

1995

Abstract Numerical studies of the laser-Lorenz model using parameters reasonably accessible for recent experiments with a single mode homogeneously broadened laser demonstrate that the form of the return map of successive peak values of the intensity changes from a sharply cusped map in resonance to a map with a smoothly rounded maximum as the laser is detuned into the period doubling regime. This transformation appears to be related to the disappearance (with detuning) of the heteroclinic structural basis for the stable manifold which exists in resonance. This is in contrast to the evidence reported by Tang and Weiss (Phys. Rev. A 49 (1994) 1296) of a cusped map for both the period doublin…

Classical and Quantum Nonultralocal Systems on the Lattice

1997

We classify nonultralocal Poisson brackets for 1-dimensional lattice systems and describe the corresponding regularizations of the Poisson bracket relations for the monodromy matrix. A nonultralocal quantum algebras on the lattices for these systems are constructed. For some class of such algebras an ultralocalization procedure is proposed. The technique of the modified Bethe-Anzatz for these algebras is developed and is applied to the nonlinear sigma model problem.

Closedness of Star Products and Cohomologies

1994

We first review the introduction of star products in connection with deformations of Poisson brackets and the various cohomologies that are related to them. Then we concentrate on what we have called “closed star products” and their relations with cyclic cohomology and index theorems. Finally we shall explain how quantum groups, especially in their recent topological form, are in essence examples of star products.

Information geometry of Gaussian channels

2009

We define a local Riemannian metric tensor in the manifold of Gaussian channels and the distance that it induces. We adopt an information-geometric approach and define a metric derived from the Bures-Fisher metric for quantum states. The resulting metric inherits several desirable properties from the Bures-Fisher metric and is operationally motivated from distinguishability considerations: It serves as an upper bound to the attainable quantum Fisher information for the channel parameters using Gaussian states, under generic constraints on the physically available resources. Our approach naturally includes the use of entangled Gaussian probe states. We prove that the metric enjoys some desir…

Robust control of unstable nonlinear quantum systems

2020

Adiabatic passage is a standard tool for achieving robust transfer in quantum systems. We show that, in the context of driven nonlinear Hamiltonian systems, adiabatic passage becomes highly non-robust when the target is unstable. We show this result for a generic (1:2) resonance, for which the complete transfer corresponds to a hyperbolic fixed point in the classical phase space featuring an adiabatic connectivity strongly sensitive to small perturbations of the model. By inverse engineering, we devise high-fidelity and robust partially non-adiabatic trajectories. They localize at the approach of the target near the stable manifold of the separatrix, which drives the dynamics towards the ta…

On the saddle loop bifurcation

1990

It is shown that the set of C∞ (generic) saddle loop bifurcations has a unique modulus of stability γ ≥]0, 1[∪]1, ∞[ for (C0, Cr)-equivalence, with 1≤r≤∞. We mean for an equivalence (x,μ) ↦ (h(x,μ), ϕ(μ)) with h continuous and ϕ of class Cr. The modulus γ is the ratio of hyperbolicity at the saddle point of the connection. Already asking ϕ to be a lipeomorphism forces two saddle loop bifurcations to have the same modulus, while two such bifurcations with the same modulus are (C0,±Identity)-equivalent.

Matter-wave interference versus spontaneous pattern formation in spinor Bose-Einstein condensates

2013

We describe effects of matter-wave interference of spinor states in the $^{87}$Rb Bose-Einstein condensate. The components of the F=2 manifold are populated by forced Majorana transitions and then fall freely due to gravity in an applied magnetic field. Weak inhomogeneities of the magnetic field, present in the experiment, impose relative velocities onto different $m_F$ components, which show up as interference patterns upon measurement of atomic density distributions with a Stern-Gerlach imaging method. We show that interference effects may appear in experiments even if gradients of the magnetic field components are eliminated but higher order inhomogeneity is present and the duration of t…

The Nonlinear σ Model

1989

The nonlinear (principal) σ model has been for a long time a theoretical laboratory to test different approaches for quantizing classical field theories. Here we shall discuss as an application of the current algebra representation theory a construction of the quantized σ model.