Krylov construction and complexity for driven quantum systems
- URL: http://arxiv.org/abs/2305.00256v3
- Date: Thu, 21 Dec 2023 03:45:44 GMT
- Title: Krylov construction and complexity for driven quantum systems
- Authors: Amin A. Nizami and Ankit W. Shrestha
- Abstract summary: We study the study of K-complexity in time-dependent (driven) quantum systems.
For periodic time-dependent (Floquet) systems, we develop a method for doing the Krylov construction.
We study the growth of the Krylov subspace dimension as a function of the system coupling constant.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Krylov complexity is an important dynamical quantity with relevance to the
study of operator growth and quantum chaos, and has recently been much studied
for various time-independent systems. We initiate the study of K-complexity in
time-dependent (driven) quantum systems. For periodic time-dependent (Floquet)
systems, we develop a natural method for doing the Krylov construction and then
define (state and operator) K-complexity for such systems. Focusing on kicked
systems, in particular the quantum kicked rotor on a torus, we provide a
detailed numerical study of the time dependence of Arnoldi coefficients as well
as of the K-complexity with the system coupling constant interpolating between
the weak and strong coupling regime. We also study the growth of the Krylov
subspace dimension as a function of the system coupling constant.
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