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International Journal of Theoretical Physics

Time Evolution of Non-Hermitian Systems Driven by a High-Frequency Field

Gong-Ping Zheng, Guangtao Wang

Published Feb 1, 2022• 3 citations
Publisher
DOI
10.1007/s10773-022-04989-z

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The time evolution of a system with a time-dependent non-Hermitian Hamiltonian is in general unstable with exponential growth or decay. A periodic driving field may stabilize the dynamics because the eigenphases of the associated Floquet operator may become all real. This possibility can emerge for a continuous range of system parameters with subtle domain boundaries. It is further shown that the issue of stability of a driven non-Hermitian Rabi model can be mapped onto the band structure problem of a class of lattice Hamiltonians. As a straightforward application, we show how to use the stability of driven non-Hermitian two-level systems (0 dimension in space) to simulate a spectrum analogous to Hofstadter's butterfly that has played a paradigmatic role in quantum Hall physics. The simulation of the band structure of non-Hermitian superlattice potentials with parity--time reversal symmetry is also briefly discussed.
ABSTRACT We investigate Floquet control of a non‐Hermitian Aubry–André–Harper chain with a spatially fluctuating imaginary gauge field of zero mean. Under open boundary conditions, an exact nonunitary transformation maps the driven problem to its Hermitian counterpart, separating the Hermitian‐frame evolution from the gauge‐induced spatial reweighting of right‐state profiles. This structure distinguishes erratic‐gauge collective pinning from AAH localization with eigenstate‐dependent centers. High‐frequency driving tunes their crossover through the renormalized hopping. The real‐time dynamics shows a nonmonotonic response: intermediate driving enables spreading into the bulk followed by gauge‐induced concentration in an interior region, whereas stronger driving suppresses the underlying spreading. Comparison with the similarity‐matched Hermitian evolution directly separates these two contributions. Our results establish Floquet driving as a route to control collective pinning induced by spatially fluctuating imaginary gauge fields, and suggest a general strategy for manipulating erratic non‐Hermitian states.