Quantum Blobs

Abstract

Quantum blobs are the smallest phase space units of phase space compatible with the uncertainty principle of quantum mechanics and having the symplectic group as group of symmetries. Quantum blobs are in a bijective correspondence with the squeezed coherent states from standard quantum mechanics, of which they are a phase space picture. This allows us to propose a substitute for phase space in quantum mechanics. We study the relationship between quantum blobs with a certain class of level sets defined by Fermi for the purpose of representing geometrically quantum states.

Prepublication. Dedicated to Basil Hiley

References in corpus (4)

• Delayed Choice Experiments and the Bohm Approach
• On the Use of Minimum Volume Ellipsoids and Symplectic Capacities for Studying Classical Uncertainties for Joint Position-Momentum Measurements
• Gaussian wave packets in phase space: The Fermi g_F function
• Zeno Paradox for Bohmian Trajectories: The Unfolding of the Metatron

Cited by in corpus (13)

• Bohm's Quantum Potential as an Internal Energy
• Short Time Quantum Propagator and Bohmian Trajectories
• Geometric Dynamics of a Harmonic Oscillator, Arbitrary Minimal Uncertainty States and the Smallest Step 3 Nilpotent Lie Group
• Mixed Quantum States with Variable Planck Constant
• Time irreversibility from symplectic non-squeezing
• Entropies from coarse-graining: convex polytopes vs. ellipsoids
• Hydrodynamic interpretation of generic squeezed coherent states: A kinetic theory
• Standard Quantum Mechanics without observers
• Cross-Toeplitz Operators on the Fock--Segal--Bargmann Spaces and Two-Sided Convolutions on the Heisenberg Group
• Irreversibility from staircases in symplectic embeddings
• Pointillisme à la Signac and Construction of a Quantum Fiber Bundle Over Convex Bodies
• Coarse-graining and symplectic non-squeezing
• Toward a relative q-entropy