Correspondence between classical and quantum resonances

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.