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Stability of Gabor Frames Under Small Time Hamiltonian Evolutions
We consider Hamiltonian deformations of Gabor systems, where the window evolves according to the action of a Schrödinger propagator and the...
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Subprincipal Symbol for Toeplitz Operators
We establish some subprincipal estimates for Berezin–Toeplitz operators on symplectic compact manifolds. From this, we construct a family of...
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Quantum Unsharpness and Symplectic Rigidity
We discuss a link between “hard” symplectic topology and an unsharpness principle for generalized quantum observables (positive operator valued...
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Infinitesimal Deformations of a Formal Symplectic Groupoid
Given a formal symplectic groupoid G over a Poisson manifold ( M , π 0 ), we define a new object, an infinitesimal deformation of G , which can be...
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A New Approach to the \({\ast}\) -Genvalue Equation
We show that the eigenvalues and eigenfunctions of the star-genvalue equation can be completely expressed in terms of the corresponding eigenvalue...
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Universal Star Products
One defines the notion of universal deformation quantization: given any manifold M , any Poisson structure Λ on M and any torsionfree linear...
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On Two Theorems about Symplectic Reflection Algebras
We give a new proof and an improvement of two Theorems of J. Alev, M.A. Farinati, T. Lambre and A.L. Solotar [1] : the first one about Hochschild...
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Quantum States and Hardy’s Formulation of the Uncertainty Principle: a Symplectic Approach
We express the condition for a phase space Gaussian to be the Wigner distribution of a mixed quantum state in terms of the symplectic capacity of the...
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Infinitesimal Deformation Quantization of Complex Analytic Spaces
The quantization problem for analytic algebras and for complex analytic spaces is discussed. The construction of Hochschild cohomology is modified...
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Quantization on Curves
Deformation quantization on varieties with singularities offers perspectives that are not found on manifolds. The Harrison component of Hochschild...
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Quantization: Deformation and/or Functor?
After a short presentation of the difference in motivation between the Berezin and deformation quantization approaches, we start with a reminder of...
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Ergodic Properties of the Quantum Geodesic Flow on Tori
We study ergodic averages for a class of pseudodifferential operators on the flat N -dimensional torus with respect to the Schrödinger evolution. The...
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A New Cohomology Theory Associated to Deformations of Lie Algebra Morphisms
We introduce a new cohomology theory related to deformations of Lie algebra morphisms. This notion involves simultaneous deformations of two Lie...
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Strict Quantizations of Symplectic Manifolds
We introduce the notion of a strict quantization of a symplectic manifold and show its existence under a topological condition.
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The Landau Problem on the θ-Deformed Two-Torus
We study the Landau problem on the θ-deformed two-torus and use well-known projective modules to obtain perturbed energy spectra. For a strong...
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Convergent Star Product Algebras on ‘ax+b’
We define nontempered (exponential growth) function spaces on the Lie group ax + b which are stable under some left-invariant (convergent) star...
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A Construction of Berezin–Toeplitz Operators via Schrödinger Operators and the Probabilistic Representation of Berezin–Toeplitz Semigroups Based on Planar Brownian Motion
First we discuss the construction of self-adjoint Berezin–Toeplitz operators on weighted Bergman spaces via semibounded quadratic forms. To ensure...