Fractional Floquet theory
نویسندگان
چکیده
A fractional generalization of the Floquet theorem is suggested for Schr\"odinger equations (FTSE)s with time-dependent periodic Hamiltonians. The obtained result, called (fFT), formulated in form Mittag-Leffler function, which considered as eigenfunction Caputo derivative. formula makes it possible to reduce FTSE standard quantum mechanics Hamiltonian, where valid. Two examples related resonances are well support result.
منابع مشابه
Floquet fractional Chern insulators.
We show theoretically that periodically driven systems with short range Hubbard interactions offer a feasible platform to experimentally realize fractional Chern insulator states. We exemplify the procedure for both the driven honeycomb and the square lattice, where we derive the effective steady state band structure of the driven system by using the Floquet theory and subsequently study the in...
متن کاملFloquet Theory
Lemma 8.4 If C is a n n × matrix with 0 det ≠ C , then, there exists a n n × (complex) matrix B such that C e = . Proof: For any matrix C , there exists an invertible matrix P , s.t. 1 P CP J − = , where J is a Jordan matrix. If C e = , then, 1 1 1 P B P B e P e P P CP J − − − = = = . Therefore, it is suffice to prove the result when C is in a canonical form. Suppose that 1 ( , , ) s C diag C C...
متن کاملFloquet Theory for Mimo Sampled-data Systems
The paper transfers some classical results by Floquet from the theory of linear differential equations with periodically varying coefficients to MIMO sampleddata systems. The problem of modal control is formulated for sampled-data systems, and the general solution is given in a polynomial form.
متن کاملFloquet Boundary Value Problem of Fractional Functional Differential Equations∗
In this paper, we prove the existence of positive solutions for Floquet boundary value problem concerning fractional functional differential equations with bounded delay. The results are obtained by using two fixed point theorems on appropriate cones.
متن کاملFloquet Theory as a Computational Tool
We describe how classical Floquet theory may be utilized, in a continuation framework, to construct an efficient Fourier spectral algorithm for approximating periodic orbits. At each continuation step, only a single square matrix, whose size equals the dimension of the phasespace, needs to be factorized; the rest of the required numerical linear algebra just consists of backsubstitutions with t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Chaos Solitons & Fractals
سال: 2023
ISSN: ['1873-2887', '0960-0779']
DOI: https://doi.org/10.1016/j.chaos.2023.113196