Nonlinear Adiabatic Evolution of Quantum Systems: Geometric Phase and Virtual Magnetic Monopole

We investigate the dynamics of a two-component Bose-Einstein condensate with spin-orbit coupling numerically and analytically. Under the drive of a weak segmented rotational external field, we observe that the system exhibits cyclic soliton motion; however, in contrast to the predictions of quasi-particle theory, the trajectory of the soliton center shows a distinct drift. The underlying mechanism of this anomalous drift is revealed: the moving soliton experiences a Lorentz force induced by a virtual magnetic monopole field in momentum space. We further calculate the phase evolution of the soliton during this cyclic motion and find that its geometric component comprises both an adiabatic Berry phase and a nonadiabatic Aharonov-Anandan phase. Notably, the Berry phase can be expressed in terms of the magnetic flux of the aforementioned virtual monopole field. Our findings hold implications for geometric phase theory and experiments on two-component Bose-Einstein condensates, and may establish a novel link between quantum geometry and soliton dynamics.We investigate the dynamics of a two-component Bose-Einstein condensate with spin-orbit coupling numerically and analytically. Under the drive of a weak segmented rotational external field, we observe that the system exhibits cyclic soliton motion; however, in contrast to the predictions of quasi-particle theory, the trajectory of the soliton center shows a distinct drift. The underlying mechanism of this anomalous drift is revealed: the moving soliton experiences a Lorentz force induced by a virtual magnetic monopole field in momentum space. We further calculate the phase evolution of the soliton during this cyclic motion and find that its geometric component comprises both an adiabatic Berry phase and a nonadiabatic Aharonov-Anandan phase. Notably, the Berry phase can be expressed in terms of the magnetic flux of the aforementioned virtual monopole field. Our findings hold implications for geometric phase theory and experiments on two-component Bose-Einstein condensates, and may establish a novel link between quantum geometry and soliton dynamics.

arXiv:2509.13800Sep 17, 20250 citations

Dirac monopole magnets in non-Hermitian systems

Hou–Yong Yu, Tao Jiang, Li-Chen Zhao

We theoretically establish that non-Hermitian perturbations induce a topological transformation of point-like Dirac monopoles into extended monopole distributions, characterized by distinct charge configurations emergent from three distinct Berry connection forms. Using piecewise adiabatic evolution, we confirm the validity of these configurations through observations of complex geometric phases. Most critically, we find a quantitative relation $Δϕ_d = Δϕ_g$ , which quantifies how cumulative minute energy differences ( $Δϕ_d$ ) manifest as geometric phase shifts ( $Δϕ_g$ ) uniquely in non-Hermitian systems. We further propose a scheme leveraging soliton dynamics in dissipative two-component Bose-Einstein condensates, enabling direct measurement of these topological signatures. These results establish a milestone for understanding Dirac monopole charge distributions and measuring complex geometric phases in non-Hermitian systems, with far-reaching implications for topological quantum computing and non-Hermitian photonics.We theoretically establish that non-Hermitian perturbations induce a topological transformation of point-like Dirac monopoles into extended monopole distributions, characterized by distinct charge configurations emergent from three distinct Berry connection forms. Using piecewise adiabatic evolution, we confirm the validity of these configurations through observations of complex geometric phases. Most critically, we find a quantitative relation $Δϕ_d = Δϕ_g$, which quantifies how cumulative minute energy differences ($Δϕ_d$) manifest as geometric phase shifts ($Δϕ_g$) uniquely in non-Hermitian systems. We further propose a scheme leveraging soliton dynamics in dissipative two-component Bose-Einstein condensates, enabling direct measurement of these topological signatures. These results establish a milestone for understanding Dirac monopole charge distributions and measuring complex geometric phases in non-Hermitian systems, with far-reaching implications for topological quantum computing and non-Hermitian photonics.

arXiv:2508.15186Aug 21, 20250 citations

Nonlinear Adiabatic Evolution of Quantum Systems

Jie Liu, Sheng-Chang Li, Libin Fu +1 more

Springer eBooksJan 1, 20181 citation

Δϕ_d = Δϕ_g

, which quantifies how cumulative minute energy differences (

Δϕ_d

) manifest as geometric phase shifts (

Δϕ_g

) uniquely in non-Hermitian systems. We further propose a scheme leveraging soliton dynamics in dissipative two-component Bose-Einstein condensates, enabling direct measurement of these topological signatures. These results establish a milestone for understanding Dirac monopole charge distributions and measuring complex geometric phases in non-Hermitian systems, with far-reaching implications for topological quantum computing and non-Hermitian photonics.