One-dimensional chains, matrix groups and quantization of Poisson structures

• Autorzy: Sławianowski J.
• Języki publikacji: EN

Abstrakty

EN

Suggested are some toy models of one-dimensional multiparticle systems with internal parameters responsible for the interparticle interactions. Classical and quantum formulations are presented. The system consists of n particles moving along the straight-line or circle and of n(n-1) interaction channels, a kind of discretized field medium. Interaction parameters and particles positions satisfy a closed system of equations of motion. The model is essentially nonlinear, exhibits certain realistic features of intermolecular forces, and is, in principle, rigorously solvable. Mathematically, it is based on Hamiltonian systems on the matrix groups GL(n,R),U(n). There are some links with the theory of completely integrable lattices due to Cologero, Moser, Sutherland.

Słowa kluczowe

EN

Hamiltonian systems; matrix groups; one-dimensional chains; quantization of Poisson structures

PL

grupy macierzy; kwantyzacja struktur Poissona; łańcuchy jednowymiarowe; mechanika analityczna; układy hamiltonowskie

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Journal of Technical Physics
• Rocznik: 1998
• Tom: Vol. 39, no 2
• Strony: 163--187
• Opis fizyczny: Bibliogr. 13 poz.,

Twórcy

autor

Sławianowski J.

• Institute of Fundamental Technological Research, Polish Academy of Sciences, Świętokrzyska 21, 00-049 Warsaw, Poland