Theory of anomalous Landau-Zener tunneling induced by nonlinear coupling

• URL: http://arxiv.org/abs/2603.01523v1
• Date: Mon, 02 Mar 2026 06:52:54 GMT
• Title: Theory of anomalous Landau-Zener tunneling induced by nonlinear coupling
• Authors: Wen-Yuan Wang, Hong-Juan Meng,
• Abstract summary: We develop a theory of Landau-Zener tunneling in a two-level system with amplitude-dependent, sign-reversible nonlinear coupling.<n>We show that beyond a critical interaction strength, the nonlinear coupling fundamentally reshapes the adiabatic energy landscape.<n>Our work establishes a paradigmatic framework for nonlinear-coupling-induced anomalous adiabaticity breaking.
• Score: 4.172523258680988
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop a general theory of Landau-Zener (LZ) tunneling in a two-level system with amplitude-dependent, sign-reversible nonlinear coupling, distinguishing it fundamentally from conventional on-site nonlinearity. Through a combination of analytical and phase-space analysis, we show that beyond a critical interaction strength, the nonlinear coupling fundamentally reshapes the adiabatic energy landscape, introducing a topological twisted and knotted structure. This structure leads to a complete breakdown of the standard exponential LZ formula, even in the adiabatic limit. Central to this anomalous behavior is the emergence of a black-hole-like fixed point, which acts as a universal attractor: upon traversing the critical region, all quantum trajectories converge to this fixed point, irreversibly erasing any memory of the initial state. From this fixed-point picture, we derive an exact analytical expression for the adiabatic tunneling probability, revealing a characteristic power-law dependence on both linear and nonlinear coupling strength. Our work establishes a paradigmatic framework for nonlinear-coupling-induced anomalous adiabaticity breaking and offers a universal mechanism for state control in driven quantum and wave systems.

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