Metastable States in Driven Nonlinear Systems

This repository contains research and documentation on the study of switching dynamics in driven nonlinear oscillators, with a particular focus on quantum activation in the bistable regime at zero temperature.

Core Concepts

1. Overview - Introduction to switching dynamics and transition mechanisms
2. Keldysh Lagrangian - Development of the Keldysh field theory approach
3. Auxiliary Hamiltonian - Analysis of the auxiliary Hamiltonian system
4. Original Equations of Motion - Derivation and analysis of the system’s equations of motion
5. Fixed Points - Analysis of the fixed points of the auxiliary Hamiltonian
6. Stability Analysis - Analysis of the boundary conditions for the switching trajectories
7. Paths - Analysis of the paths for the switching trajectories

About

This documentation accompanies the research paper “A Real-time Instanton Approach to Quantum Activation” (arXiv:2409.00681) by Chang-Woo Lee, Paul Brookes, Kee-Su Park, Marzena H. Szymańska, and Eran Ginossar.

This work covers research into quantum activation in driven dissipative systems far from equilibrium. The paper and this documentation focus on understanding how quantum noise associated with relaxation can lead to transitions between metastable states, even at zero temperature.

Key areas of investigation include:

• Analysis of fixed points in the bistable regime
• Comparison of different transition mechanisms (thermal activation, quantum tunneling, quantum activation)
• Development of Keldysh field theory approach
• Study of quantum fluctuations and their role in state transitions

The documentation is automatically synchronized with interactive Jupyter notebooks for each section, allowing for both theoretical study and computational exploration of the concepts.