Low-frequency anomalies in dynamic localization.

Area of Science:

• Quantum mechanics
• Condensed matter physics
• Solid-state physics

Background:

• Quantum mechanical spreading of particles in tight-binding lattices is typically suppressed by external AC forces, a phenomenon known as dynamic localization (DL).
• DL occurs at specific force amplitude (F0) to frequency (ω) ratios (Γ), with standard models predicting DL at infinitesimally small F0 in the low-frequency limit (ω → 0).

Purpose of the Study:

• Introduce and investigate a novel tight-binding lattice model with inhomogeneous hopping rates, termed a pseudo-Galuber-Fock (pseudo-GF) lattice.
• Analyze the low-frequency behavior of dynamic localization in this pseudo-GF lattice and compare it to homogeneous and standard GF lattices.

Main Methods:

• Development of a pseudo-GF lattice model with inhomogeneous hopping rates.
• Analysis of the conditions for dynamic localization (DL) in the low-frequency limit (ω → 0).
• Employing a PT symmetry-breaking transition analysis of an associated two-level non-Hermitian Hamiltonian to explain the observed anomalous behavior.

Main Results:

• The pseudo-GF lattice exhibits dynamic localization (DL), but deviates from the normal low-frequency behavior observed in homogeneous and GF lattices.
• In pseudo-GF lattices, DL is achieved at finite force amplitude (F0) even as the frequency (ω) approaches zero.
• This anomalous low-frequency behavior is linked to a PT symmetry-breaking transition in the effective non-Hermitian Hamiltonian.

Conclusions:

• Pseudo-GF lattices present a unique system for studying dynamic localization with anomalous low-frequency characteristics.
• The findings challenge the conventional understanding of DL in the low-frequency regime and highlight the role of lattice inhomogeneity.
• The connection to PT symmetry provides a new theoretical framework for understanding dynamic localization in complex lattice structures.