151,548 research outputs found
Quantum Inozemtsev model, quasi-exact solvability and N-fold supersymmetry
Inozemtsev models are classically integrable multi-particle dynamical systems
related to Calogero-Moser models. Because of the additional q^6 (rational
models) or sin^2(2q) (trigonometric models) potentials, their quantum versions
are not exactly solvable in contrast with Calogero-Moser models. We show that
quantum Inozemtsev models can be deformed to be a widest class of partly
solvable (or quasi-exactly solvable) multi-particle dynamical systems. They
posses N-fold supersymmetry which is equivalent to quasi-exact solvability. A
new method for identifying and solving quasi-exactly solvable systems, the
method of pre-superpotential, is presented.Comment: LaTeX2e 28 pages, no figure
Dynamical Localization in Quasi-Periodic Driven Systems
We investigate how the time dependence of the Hamiltonian determines the
occurrence of Dynamical Localization (DL) in driven quantum systems with two
incommensurate frequencies. If both frequencies are associated to impulsive
terms, DL is permanently destroyed. In this case, we show that the evolution is
similar to a decoherent case. On the other hand, if both frequencies are
associated to smooth driving functions, DL persists although on a time scale
longer than in the periodic case. When the driving function consists of a
series of pulses of duration , we show that the localization time
increases as as the impulsive limit, , is
approached. In the intermediate case, in which only one of the frequencies is
associated to an impulsive term in the Hamiltonian, a transition from a
localized to a delocalized dynamics takes place at a certain critical value of
the strength parameter. We provide an estimate for this critical value, based
on analytical considerations. We show how, in all cases, the frequency spectrum
of the dynamical response can be used to understand the global features of the
motion. All results are numerically checked.Comment: 7 pages, 5 figures included. In this version is that Subsection III.B
and Appendix A on the quasiperiodic Fermi Accelerator has been replaced by a
reference to published wor
Explicit Construction of First Integrals with Quasi-monomial Terms from the Painlev\'{e} Series
The Painlev\'{e} and weak Painlev\'{e} conjectures have been used widely to
identify new integrable nonlinear dynamical systems. For a system which passes
the Painlev\'{e} test, the calculation of the integrals relies on a variety of
methods which are independent from Painlev\'{e} analysis. The present paper
proposes an explicit algorithm to build first integrals of a dynamical system,
expressed as `quasi-polynomial' functions, from the information provided solely
by the Painlev\'{e} - Laurent series solutions of a system of ODEs.
Restrictions on the number and form of quasi-monomial terms appearing in a
quasi-polynomial integral are obtained by an application of a theorem by
Yoshida (1983). The integrals are obtained by a proper balancing of the
coefficients in a quasi-polynomial function selected as initial ansatz for the
integral, so that all dependence on powers of the time is
eliminated. Both right and left Painlev\'{e} series are useful in the method.
Alternatively, the method can be used to show the non-existence of a
quasi-polynomial first integral. Examples from specific dynamical systems are
given.Comment: 16 pages, 0 figure
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