Semiclassical quantization of the periodic Toda chain
| Autor: | F Gohmann, W Pesch, F G Mertens |
|---|---|
| Rok vydání: | 1993 |
| Předmět: |
General Physics and Astronomy
Cnoidal wave Semiclassical physics Statistical and Nonlinear Physics Bethe ansatz Quantization (physics) Nonlinear Sciences::Exactly Solvable and Integrable Systems Chain (algebraic topology) Quantum mechanics Dispersion relation Soliton Toda lattice Mathematical Physics Mathematics |
| Zdroj: | Journal of Physics A: Mathematical and General. 26:7589-7613 |
| ISSN: | 1361-6447 0305-4470 |
| Popis: | Gutzwiller's semiclassical quantization scheme for the trace of Green's function is applied to the periodic Toda chain. We obtain a set of algebraic equations that determine the energy levels arising from a special periodic orbit, namely the single cnoidal wave solution. Our formulae show a simple dependence on the number of particles N in the chain. N merely occurs as a parameter. We perform the soliton limit of our equations and get a semiclassical correction to first order in h to the dispersion relation E=E(p) of a soliton on the infinite chain which is in remarkable agreement with the Bethe ansatz result. The classical data which enter into the semiclassical quantization formula are of interest in their own right. We give a complete treatment of the linear stability analysis of a single cnoidal wave and also some new expressions for its dispersion relation which expresses the frequency v as a function of the wavenumber k. |
| Databáze: | OpenAIRE |
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