Displaying similar documents to “Quantum ergodicity of C*-dynamical systems”

Index and dynamics of quantized contact transformations

Steven Zelditch (1997)

Annales de l'institut Fourier

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Quantized contact transformations are Toeplitz operators over a contact manifold ( X , α ) of the form U χ = Π A χ Π , where Π : H 2 ( X ) → L 2 ( X ) is a Szegö projector, where χ is a contact transformation and where A is a pseudodifferential operator over X . They provide a flexible alternative to the Kähler quantization of symplectic maps, and encompass many of the examples in the physics literature, e.g. quantized cat maps and kicked rotors. The index problem is to determine ind ( U χ ) when the principal symbol is unitary, or equivalently...

Ergodic Dilation of a Quantum Dynamical System

Carlo Pandiscia (2014)

Confluentes Mathematici

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Using the Nagy dilation of linear contractions on Hilbert space and the Stinespring’s theorem for completely positive maps, we prove that any quantum dynamical system admits a dilation in the sense of Muhly and Solel which satisfies the same ergodic properties of the original quantum dynamical system.

Isospectrality for quantum toric integrable systems

Laurent Charles, Álvaro Pelayo, San Vũ Ngoc (2013)

Annales scientifiques de l'École Normale Supérieure

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We give a full description of the semiclassical spectral theory of quantum toric integrable systems using microlocal analysis for Toeplitz operators. This allows us to settle affirmatively the isospectral problem for quantum toric integrable systems: the semiclassical joint spectrum of the system, given by a sequence of commuting Toeplitz operators on a sequence of Hilbert spaces, determines the classical integrable system given by the symplectic manifold and commuting Hamiltonians....

Quantum ergodicity and quantum limits for sub-Riemannian Laplacians

Yves Colin de Verdière, Luc Hillairet, Emmanuel Trélat (2014-2015)

Séminaire Laurent Schwartz — EDP et applications

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This paper is a proceedings version of [6], in which we state a Quantum Ergodicity (QE) theorem on a 3D contact manifold, and in which we establish some properties of the Quantum Limits (QL). We consider a sub-Riemannian (sR) metric on a compact 3D manifold with an oriented contact distribution. There exists a privileged choice of the contact form, with an associated Reeb vector field and a canonical volume form that coincides with the Popp measure. We state a QE theorem...