Low-frequency anomalies in dynamic localization

Stefano Longhi

Quantum mechanical spreading of a particle hopping on tight binding lattices can be suppressed by the application of an external ac force, leading to periodic wave packet reconstruction. Such a phenomenon, referred to as dynamic localization (DL), occurs for certain magic values of the ratio \(\Gamma=F_0/\omega\) between the amplitude F0 and frequency ω of the ac force. It is generally believed that in the low-frequency limit \((\omega\to0)\) DL can be achieved for an infinitesimally small value of the force F0, i.e. at finite values of \(\Gamma\). Such a normal behavior is found in homogeneous lattices as well as in inhomogeneous lattices of Glauber-Fock type. Here we introduce a tight-binding lattice model with inhomogeneous hopping rates, referred to as pseudo Glauber-Fock lattice, which shows DL but fails to reproduce the normal low-frequency behavior of homogeneous and Glauber-Fock lattices. In pseudo Glauber-Fock lattices, DL can be exactly realized, however at the DL condition the force amplitude \(F_0\) remains finite as \(\omega\to0\). Such an anomalous behavior is explained in terms of a PT symmetry breaking transition of an associated two-level non-Hermitian Hamiltonian that effectively describes the dynamics of the Hermitian lattice model.


Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el)

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