TY - JOUR
T1 - Classical analog of the quantum metric tensor
AU - Gonzalez, Diego
AU - Gutiérrez-Ruiz, Daniel
AU - Vergara, J. David
N1 - Publisher Copyright:
© 2019 American Physical Society.
PY - 2019/3/29
Y1 - 2019/3/29
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85064068931&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.99.032144
DO - 10.1103/PhysRevE.99.032144
M3 - Artículo
C2 - 30999496
AN - SCOPUS:85064068931
SN - 2470-0045
VL - 99
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 3
M1 - 032144
ER -