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Updated: Jul 12, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Geometry and dynamics of squeezing in finite systems
Kurt Bernardo Wolf1, Guillermo Krötzsch
1Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Morelos, México. bwolf@fis.unam.mx
Summary
This study introduces finite Hamiltonian systems and Wigner functions to model squeezing and magnification. These methods complete the finite counterparts of linear canonical transformations in optics.
Area of Science:
- Optics
- Quantum mechanics
- Signal processing
Background:
- Squeezing and magnification are linear canonical transformations for continuous signals in paraxial optics.
- Finite Hamiltonian systems and discrete phase space representations are key areas in theoretical physics.
Purpose of the Study:
- To find unitary matrices for squeezing and magnification in N-point finite Hamiltonian systems.
- To extend the analysis to discrete phase space representations using Wigner quasi-probability distribution functions.
- To complete the finite counterparts of the group of linear canonical transformations.
Main Methods:
- Analysis of squeezing and magnification as a one-parameter group of linear canonical transformations.
- Application of unitary matrices to signal vectors in N-point finite Hamiltonian systems.
- Extension to phase space representation using Wigner quasi-probability distribution functions on discrete torus and sphere.
Main Results:
- Established the connection between continuous optical transformations and discrete Hamiltonian systems.
- Developed finite counterparts for squeezing and magnification operations.
- Completed the finite analogues of the group of linear canonical transformations, including fractional Fourier and Fresnel transforms.
Conclusions:
- The study successfully provides finite analogues for continuous optical linear canonical transformations.
- The methods used are applicable to discrete systems and phase space representations.
- This work unifies concepts from optics, quantum mechanics, and signal processing in a discrete framework.
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