The Geometric Phase in Quantum Systems

By S Pascazio. 2003

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Anomalous hall effect (2009, background): “…anomalous velocity is dependent only on the perfect crystal Hamiltonian and can be related to changes in the phase of Bloch state wavepackets when an electric field causes them to evolve in crystal momentum space (Bohm et al., 2003; Chang and Niu, 1996; Sundaram and Niu, 1999; Xiao and Niu, 2009).”
Semiconductor Probes of Light Dark Matter (2012, background): “For an electron in any periodic potential, the delocalized eigenfunctions of the Hamiltonian can be expressed in terms of localized wavefunctions, in the form [30, 31]”
Topological invariance and global Berry phase in non-Hermitian systems (2013, background): “Since the wave function is periodic for k, the wave vector k can be regarded as a parameter inducing the Berry phase.[16] The complex geometric phases in two bands can be expressed as γ ± = ∮”
Geometry of quantum phase transitions (2019, methodology): “We will illustrate how the use of the geometric methods, such as geometric phase [30, 27], and in particular its mixed state generalisation, the Uhlmann geometric phase [156], may provide a novel perspective in the investigation of NESS-QPTs.”
Pseudo-Hermitian Representation of Quantum Mechanics (2008, background): “This is a compact manifold for finite N and a well-known infinite-dimensional manifold with very special and useful mathematical properties for infinite N , [54].”