Geometric Representation of Generalized Coherent States and their Symplectic Capacities: A Synthetic Approach

2025/07/25 by de Gosson, Maurice
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2507.19606

Abstract

In this work we review, complete, and synthesize results linking generalized coherent stages (nondegradable Gaussian wavefunctions) to the notions of Fermi ellipsoids, quantum blobs, and microlocal pairs introduced in previous work. These geometric objects are Fermi ellipsoids, quantum blobs, and microlocal pairs. In addition we study various symplectic capacities associated with these objects.

Citations

• Symplectic Coarse-Grained Dynamics: Chalkboard Motion in Classical and Quantum Mechanics
• On the Positivity of Trace Class Operators
• The Symplectic Camel and the Uncertainty Principle: The Tip of an Iceberg?
• Ellipsoids of maximal volume in convex bodies
• Ellipsoids of maximal volume in convex bodies

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• Symplectic Coarse-Grained Classical and Semi-Classical Evolution of Subsystems: New Theoretical Aspects