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## Full-Text Articles in Physics

The Penrose Dodecahedron Revisited, Padmanabhan Aravind, Jordan Massad

#### The Penrose Dodecahedron Revisited, Padmanabhan Aravind, Jordan Massad

*Padmanabhan K. Aravind*

This paper gives an elementary account of the ‘‘Penrose dodecahedron,’’ a set of 40 states of a spin- 3 2 particle used by Zimba and Penrose @Stud. Hist. Phil. Sci. 24, 697–720 ~1993!# to give a proof of Bell’s nonlocality theorem. The Penrose rays are constructed here from the rotation operator of a spin- 3 2 particle and the geometry of a dodecahedron, and their orthogonality properties are derived and illustrated from a couple of different viewpoints. After recalling how the proof of Bell’s theorem can be reduced to a coloring problem on the Penrose rays, a ...

Quantum-Statistical Properties Of Two Coupled Modes Of Electromagnetic Field, Serguei Y. Kalmykov, Mikhail E. Veisman

#### Quantum-Statistical Properties Of Two Coupled Modes Of Electromagnetic Field, Serguei Y. Kalmykov, Mikhail E. Veisman

*Serge Youri Kalmykov*

Squeezing the quantum fluctuations of the two-mode light due to the nonstationary coupling between the quadrature components q_1 and q_2 is examined. The delta-function and step-function mode couplings are considered. The conditions of weak and strong step-function coupling are distinguished, the latter being the condition of the instability for the classical counterpart of the quantum system under study. Under the conditions of weak coupling the quadrature squeezing is established in both a two-mode electromagnetic noise in thermal equilibrium (the thermal state) and a two- mode correlated coherent state (CCS). Squeezing in the thermal state is suppressed at a high temperature ...