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Quantum Geometric Tensor (Fubini-Study Metric) in Simple Quantum System: A pedagogical Introduction

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arxiv 1012.1337 v2 pith:6T5ZTSWW submitted 2010-12-06 quant-ph math-phmath.MP

Quantum Geometric Tensor (Fubini-Study Metric) in Simple Quantum System: A pedagogical Introduction

classification quant-ph math-phmath.MP
keywords quantumgeometricmetrictensorfubini-studyintroductionpartphysical
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Geometric Quantum Mechanics is a novel and prospecting approach motivated by the belief that our world is ultimately geometrical. At the heart of that is a quantity called Quantum Geometric Tensor (or Fubini-Study metric), which is a complex tensor with the real part serving as the Riemannian metric that measures the `quantum distance', and the imaginary part being the Berry curvature. Following a physical introduction of the basic formalism, we illustrate its physical significance in both the adiabatic and non-adiabatic systems.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Geometric curvature driven by many-body collective fluctuations

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    Collective fluctuations generate dynamical Berry curvature via non-commutative transverse quantum fluctuations and non-local-time interactions, distinguishable from bare band geometry in antisymmetric inelastic scatte...

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    The Bures metric near rank-changing points is a coordinate artifact for N=2 but reduces to a conical metric with genuine curvature singularities for N>=3, illustrated by specific Lindblad processes.

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    This thesis explores geometric and dynamical properties of entanglement in two- and many-body spin systems under XXZ and Ising interactions using phase space and Fubini-Study geometry.