A Floquet Operator with Pure Point Spectrum and Energy Instability
نویسنده
چکیده
It is not immediate whether a self-adjoint operator H with purely point spectrum implies absence of transport under the time evolution U(t) = e−iHt; in fact, it is currently known examples of Schrödinger operators with such kind of spectrum and transport. In case of tight-binding models on l2(IN) the transport is usually probed by the moments of order m > 0 of the position operator Xek = kek, that is,
منابع مشابه
Singular Continuous Floquet Operator for Systems with Increasing Gaps
Consider the Floquet operator of a time independent quantum system, periodically perturbed by a rank one kick, acting on a separable Hilbert space: e0 e |φ〉〈φ| where T and κ are the period and the coupling constant respectively. Assume the spectrum of the self adjoint operator H0 is pure point, simple, bounded from below and the gaps between the eigenvalues (λn) grow like: λn+1 − λn ∼ Cn with d...
متن کاملOn the continuous spectral component of the Floquet operatorfor a periodically kicked quantum system
By a straightforward generalisation, we extend the work of Combescure [J. Stat. Phys. 59, 679 (1990)] from rank-1 to rank-N perturbations. The requirement for the Floquet operator to be pure point is established and compared to that in Combescure. The result matches that in McCaw and McKellar [J. Math. Phys. 46, 032108 (2005)]. The method here is an alternative to that work. We show that if the...
متن کاملClassical and Quantum Dynamics of a Periodically Driven Particle in a Triangular Well
We investigate the correspondence between classical and quantum mechanics for periodically time dependent Hamiltonian systems, using the example of a periodically forced particle in a one-dimensional triangular well potential. In particular, we consider quantum mechanical Floquet states associated with resonances in the classical phase space. When the classical motion exhibits subharmonic reson...
متن کاملPerturbation of an Eigen-value from a Dense Point Spectrum: a General Floquet Hamiltonian
We consider a perturbed Floquet Hamiltonian −i∂t + H + βV (ωt) in the Hilbert space L([0, T ],H, dt). Here H is a self-adjoint operator in H with a discrete spectrum obeying a growing gap condition, V (t) is a symmetric bounded operator in H depending on t 2π-periodically, ω = 2π/T is a frequency and β is a coupling constant. The spectrum Spec(−i∂t + H) of the unperturbed part is pure point and...
متن کامل2 v 1 2 1 D ec 1 99 2 GEOMETRICAL PHASE , GENERALIZED QUASIENERGY AND FLOQUET OPERATOR AS INVARIANTS
For time-periodical quantum systems generalized Floquet operator is found to be integral of motion.Spectrum of this invariant is shown to be quasienergy spectrum.Analogs of invariant Flo-quet operators are found for nonperiodical systems with several characteristic times.Generalized quasienergy states are introduced for these systems. Geometrical phase is shown to be integral of motion. Quantum...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007