Classical analog of the quantum metric tensor

Abstract

We present a classical analog of the quantum metric tensor, which is defined for classical integrable systems that undergo an adiabatic evolution governed by slowly varying parameters. This classical metric measures the distance, on the parameter space, between two infinitesimally different points in phase space, whereas the quantum metric tensor measures the distance between two infinitesimally different quantum states. We discuss the properties of this metric and calculate its components, exactly in the cases of the generalized harmonic oscillator, the generalized harmonic oscillator with a linear term, and perturbatively for the quartic anharmonic oscillator. Finally, we propose alternative expressions for the quantum metric tensor and Berry's connection in terms of quantum operators.

arXiv comment13 pages

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Cited by in corpus (6)

• Phase space formulation of the Abelian and non-Abelian quantum geometric tensor
• Geometry of the parameter space of a quantum system: Classical point of view
• Classical description of the parameter space geometry in the Dicke and Lipkin-Meshkov-Glick models
• Classical analogs of generalized purities, entropies, and logarithmic negativity
• Generalized quantum geometric tensor for excited states using the path integral approach
• Classical analogs of the covariance matrix, purity, linear entropy, and von Neumann entropy