Theory of anomalous Landau-Zener tunneling induced by nonlinear coupling
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866908860101427200 |
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| author | Wang, Wen-Yuan Meng, Hong-Juan |
| author_facet | Wang, Wen-Yuan Meng, Hong-Juan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01523 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Theory of anomalous Landau-Zener tunneling induced by nonlinear coupling Wang, Wen-Yuan Meng, Hong-Juan Quantum Physics 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. |
| title | Theory of anomalous Landau-Zener tunneling induced by nonlinear coupling |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.01523 |