Low-frequency anomalies in dynamic localization

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 F-0 and frequency omega of the ac force. It is generally believed that in the low-frequency limit (omega -> 0) DL can be achieved for an infinitesimally small value of the force F-0, i.e.at finite values of Gamma. Such normal behavior is found in homogeneous lattices as well as in inhomogeneous lattices of the Glauber-Fock (GF) type. Here we introduce a tight-binding lattice model with inhomogeneous hopping rates, referred to as a pseudo-GF lattice, which shows DL but fails to reproduce the normal low-frequency behavior of homogeneous and GF lattices. In pseudo-GF lattices, DL can be exactly realized; however, at the DL condition the force amplitude F-0 remains finite as omega -> 0. 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.