Quantum critical temperature of a modulated oscillator

TL;DR

This paper investigates the quantum critical temperature in a modulated nonlinear oscillator, revealing a temperature-dependent switching rate behavior and highlighting limitations of instanton theory in non-equilibrium systems.

Contribution

It introduces the concept of a quantum critical temperature $T_c$ proportional to $^2$, showing a transition in switching dynamics and challenging existing instanton-based models.

Findings

Switching rate is temperature-independent below $T_c$

Above $T_c$, a quantum crossover with a kink in the distribution slope occurs

Switching rate follows Arrhenius law with temperature-independent activation energy

Abstract

We show that the rate of switching between the vibrational states of a modulated nonlinear oscillator is characterized by a quantum critical temperature $T_c\propto\hbar^2$. The rate is independent of $T$ for $T<T_c$. Above $T_c$ there emerges a quantum crossover region where the slope of the logarithm of the distribution over the oscillator states displays a kink and the switching rate has the Arrhenius form with the activation energy independent of the modulation. The results demonstrate the limitations of the real-time instanton theory of switching in systems lacking detailed balance.