Critical exponents in metastable decay via quantum activation.

Area of Science:

• Quantum mechanics
• Nonlinear dynamics
• Quantum optics

Background:

• Metastable states in quantum systems can decay over time.
• Bifurcation points represent thresholds where system states disappear.
• Understanding decay mechanisms is crucial for quantum technologies.

Purpose of the Study:

• To investigate the decay of metastable states in a forced quantum oscillator near bifurcation points.
• To analyze the mechanism of decay via quantum activation over a quasienergy barrier.
• To determine the scaling of decay probability with proximity to bifurcation points.

Main Methods:

• Theoretical analysis of a quantum oscillator model.
• Calculation of decay probability W.
• Examination of scaling laws near bifurcation points (eta).

Main Results:

• Decay occurs via quantum activation, distinct from tunneling and thermal activation.
• Decay probability W scales with distance eta to the bifurcation point.
• The exponent xi in the scaling law /ln W/ proportional to eta(xi) was determined for specific driving conditions.

Conclusions:

• Quantum activation is a key decay mechanism for metastable states in driven quantum oscillators near bifurcations.
• The scaling of decay probability provides insights into the stability and lifetime of these states.
• The findings are relevant for understanding and controlling quantum systems in nonlinear regimes.