By M.-J. Giannoni, A. Voros, J. Zinn-Justin
Within the final decade the certainty of the family among classical and quantum mechanics has complicated drastically and the next extensive topics are handled during this book:-
• random matrices: a resurgence of an outdated concept introduced in from nuclear physics, now the normal for analysing "signatures" of classical chaos in quantum systems;
• the advanced quantum behaviour of pushed Hamiltonian platforms and localization phenomena;
• chaos in scattering platforms and the homes of S -matrices;
• spectra of quantum platforms whose classical analogues are the geodesic flows on negatively curved compact manifolds;
• the wealth of houses of wave capabilities for classically chaotic systems;
• the increase and progress of the concept that of chaos in all sectors of "physics of microscopic media": nuclear, atomic, molecular, solid-state physics.
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Extra info for Chaos and quantum physics = Chaos et physique quantique
The bond energy criterion of Sun and Mackenzie (Sun, 1947, Baldwin, 1981) arises from similar considerations. For systems in which the bonding is at least partially ionic in character, the coordination polyhedra present are to a large extent determined by the relative sizes of their constituent ions, usually expressed as the radius ratio, in which A is the cation and X is the anion. ) For stability, the cation at the center of an AXn polyhedron should fill the cavity defined by the anions, and there exists a critical radius ratio at which the criterion is just fulfilled and below which the cation cannot remain in contact with all the anions and the A X n polyhedron is unstable.
A n d P o u l a i n , M a . (1982a). Mat. Res. Bull. 17, 1035-1043. 34 Marcel Poulain Matecki, M . , P o u l a i n , M i . , and P o u l a i n , M a . (1982b). Mat. Res. Bull. 17, 1275-1281. Matecki, M . , P o u l a i n , M i . , and P o u l a i n , M a . (1983). J. Non-Cryst. Solids 56, 8 1 - 8 6 . Matecki, M . , P o u l a i n , M i . , and P o u l a i n , M a . (1987a). Mat. Res. Bull. 22, 345-350. Matecki, M . , P o u l a i n , M i . , and P o u l a i n , M a . (1987b). Mat. Sei. Forum 19-20, 4 7 - 5 4 .
1986). Numerous other fluoroaluminate glasses have been synthesized in multicomponent 7. Fluoride Glass Composition and Processing 23 F I G . 11. Glass forming area in the (a) A l F 3 - B a F 3 - Y F 3 - C a F 2 , and (b) A l F 3 - B a F 2 - Y F 3 T h F 4 systems. systems including zinc (Matecki and Poulain, 1981), alkali, magnesium, and rare-earths (Poulain and Matecki, 1982). New fluoroaluminate glasses were prepared by Tick (1988) in the A l F 3 - C d F 2 - L i F - P b F 2 system. , 1987).