Flow-equation approach to quantum systems driven by an
amplitude-modulated time-periodic force
- URL: http://arxiv.org/abs/2111.15368v2
- Date: Fri, 17 Dec 2021 16:46:21 GMT
- Title: Flow-equation approach to quantum systems driven by an
amplitude-modulated time-periodic force
- Authors: Viktor Novi\v{c}enko and Giedrius \v{Z}labys and Egidijus Anisimovas
- Abstract summary: We apply the method of flow equations to describe quantum systems subject to a time-periodic drive with a time-dependent envelope.
We construct a flow generator that prevents the appearance of additional Fourier harmonics during the flow.
We give several specific examples and discuss the possibility to extend the treatment to cover rapid modulation of the envelope.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We apply the method of flow equations to describe quantum systems subject to
a time-periodic drive with a time-dependent envelope. The driven Hamiltonian is
expressed in terms of its constituent Fourier harmonics with amplitudes that
may vary as a function of time. The time evolution of the system is described
in terms of the phase-independent effective Hamiltonian and the complementary
micromotion operator that are generated by deriving and solving the flow
equations. These equations implement the evolution with respect to an auxiliary
flow variable and facilitate a gradual transformation of the quasienergy matrix
(the Kamiltonian) into a block diagonal form in the extended space. We
construct a flow generator that prevents the appearance of additional Fourier
harmonics during the flow, thus enabling implementation of the flow in a
computer algebra system. Automated generation of otherwise cumbersome
high-frequency expansions (for both the effective Hamiltonian and the
micromotion) to an arbitrary order thus becomes straightforward for driven
Hamiltonians expressible in terms of a finite algebra of Hermitian operators.
We give several specific examples and discuss the possibility to extend the
treatment to cover rapid modulation of the envelope.
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