On the goodness of "quantum blobs" in phase space quantization

Abstract

We replace the usual notion of quantum cell from statistical mechanics by that of "quantum blob". A quantum blob is the transform, by a linaer symplectic transformation, of a phase space ball with radius equal to the square root of h-bar. The intersection of a quantum blob with any symplectic plane is an ellipse with area one half of h. This very special property, which is closed related to the principle of the symplectic camel, leads to a symplectic invariant statement of the uncertainty principle. We moreover prove that the average of a phase space Gaussian over a quantum blob is the Wigner transform of a minimum uncertainty Gaussian.

References in corpus (5)

• Universal geometric approach to uncertainty, entropy and information
• Congruences and Canonical Forms for a Positive Matrix: Application to the Schweinler-Wigner Extremum Principle
• Generalizations of Heisenberg uncertainty relation
• The "Symplectic Camel Principle" and Semiclassical Mechanics
• Entanglement transformations of pure Gaussian states

Cited by in corpus (1)

• Non-linear Fokker-Planck equations from conformal metrics and scalar curvature