科研之友
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摘要
Examples of many-body Hamiltonians are identified which yield time-evolutions, having the property that the projection of an arbitrary orbit in phase space onto configuration space is periodic with a period independent of initial data ("isochrony"), while the evolution in phase space is not periodic. These include a variation on the harmonic oscillator as well as a Hamiltonian yielding the "goldfish" equations of motion. We then investigate a one-body version in the complex plane of this goldfish Hamiltonian. Its quantization is studied, and it is shown that the spectrum is continuous and infinitely degenerate; the general solution of the time-dependent Schrodinger equation in the position representation is not time-periodic, but its square modulus does evolve isochronously. Published by AIP Publishing.
- 出版日期2018-6
