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Related Experiment Video

Updated: Oct 28, 2025

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Measurement of Quantum Interference in a Silicon Ring Resonator Photon Source

Published on: April 4, 2017

Correspondence between classical and quantum resonances.

F J Arranz¹, R M Benito¹, F Borondo^2,3

¹Grupo de Sistemas Complejos, Universidad Politécnica de Madrid, Avenida Puerta de Hierro 2-4, 28040 Madrid, Spain.

Physical Review. E

|July 17, 2021

Summary

This summary is machine-generated.

Quantum resonances in the CN-Li system mirror classical resonances. A correlation diagram reveals quantum manifestations of classical bifurcations, linking them in the semiclassical limit.

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Last Updated: Oct 28, 2025

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Area of Science:

Molecular dynamics
Quantum mechanics
Chemical physics

Background:

Nonlinear molecular systems exhibit bifurcations and classical resonances with increasing excitation energy.
Understanding the quantum behavior of these resonances is crucial for molecular isomerization dynamics.

Purpose of the Study:

To investigate the quantum manifestations of classical resonances in the isomerizing CN-Li system.
To establish a connection between classical bifurcation energies and quantum resonance energies in the semiclassical limit.

Main Methods:

Utilizing a correlation diagram of eigenenergies versus Planck's constant (ℏ).
Analyzing series of avoided crossings to identify quantum resonances.
Developing a semiclassical theory to derive analytical expressions.

Main Results:

Identified distinct series of avoided crossings corresponding to quantum resonances.
Demonstrated that these quantum resonances are the quantum manifestations of classical resonances.
Extrapolated series to ℏ=0, revealing a correspondence between classical bifurcation energies and quantum resonance energies.

Conclusions:

Quantum resonances accurately reflect classical resonances in nonlinear molecular systems.
The semiclassical limit (ℏ→0) provides a bridge between classical and quantum descriptions of resonance phenomena.
The developed semiclassical theory offers analytical insights into these quantum-classical correspondences.