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arXiv · 1810.00193

Effective Hamiltonian theory of the geometric evolution of quantum systems

V. O. Shkolnikov·Guido Burkard
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Abstract

In this work we present an effective Hamiltonian description of the quantum dynamics of a generalized Lambda system undergoing adiabatic evolution. We assume the system to be initialized in the dark subspace and show that its holonomic evolution can be viewed as a conventional Hamiltonian dynamics in an appropriately chosen extended Hilbert space. In contrast to the existing approaches, our method does not require the calculation of the non-Abelian Berry connection and can be applied without any parametrization of the dark subspace, which becomes a challenging problem with increasing system size.

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V. O. Shkolnikov, Guido Burkard. 2019-03-13. Effective Hamiltonian theory of the geometric evolution of quantum systems. https://doi.org/10.1103/physreva.101.042101

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