Quantum Tunnelling and Thermally Driven Transitions in a Double Well Potential at Finite Temperature
arXiv:2312.12101 · doi:10.1088/1751-8121/ad4b7b
Abstract
We explore dissipative quantum tunnelling, a phenomenon central to various physical and chemical processes, using a double-well potential model. This paper aims to bridge gaps in understanding the crossover from thermal activation to quantum tunnelling, a domain still shrouded in mystery despite extensive research. We study a Caldeira-Leggett-derived model of quantum Brownian motion and investigate the Lindblad and stochastic Schrödinger dynamics numerically, seeking to offer new insights into the transition states in the crossover region. Our study has implications for quantum computing and understanding fundamental natural processes, highlighting the significance of quantum effects on transition rates and temperature influences on tunnelling. Additionally, we introduce a new model for quantum Brownian motion which takes Lindblad form and is formulated as a modification of the widely known model found in Breuer and Petruccione. In our approach, we remove the zero-temperature singularity resulting in a better description of low-temperature quantum Brownian motion near a potential minima.
arXiv comment20 pages, 14 figures. J. Phys. A: Math. Theor (2024)
References in corpus (8)
- Negativity of the Wigner function as an indicator of nonclassicality
- Convolutionless Non-Markovian master equations and quantum trajectories: Brownian motion revisited
- Quantum Anti-Zeno Effect
- A Lindblad Model of Quantum Brownian Motion
- Lindblad dynamics of Gaussian states and their superpositions in the semiclassical limit
- Quantum-jump vs stochastic Schrödinger dynamics for Gaussian states with quadratic Hamiltonians and linear Lindbladians
- Quantum measurement and thermally assisted proton tunnelling
- The two lowest eigenvalues of the harmonic oscillator in the presence of a Gaussian perturbation