Quantum Computing for Quantum Tunnelling

Non-Perturbative Renormalization Group and Quantum Tunnelling

The non-perturbative renormalization group (NPRG) is applied to analysis of tunnelling in quantum mechanics. The vacuum energy and the energy gap of anharmonic oscillators are evaluated by solving the local potential approximated Wegner-Houghton equation (LPA W-H eqn.). We find that our results are very good in a strong coupling region, but not in a very weak coupling region, where the dilute gas instanton calculation works very well. So it seems that in analysis of quantum tunnelling, the dilute gas instanton and LPA W-H eqn. play complementary roles to each other. We also analyze the supersy…

氢键上的量子隧穿：基于Cornell型势能模型的质子-氘核同位素效应

Quantum Tunnelling Across Hydrogen Bonds: Proton--Deuteron Isotope Effects from a Cornell-Type Potential Model

本文采用Cornell型势能结合双势井Schrödinger方法研究氢键上的质子与氘核隧穿，通过半解析波函数和隧穿分裂揭示同位素相关的量子效应，为双势井系统隧穿建模提供了通用方法。

关于诺ether电荷存在下的量子隧穿

On quantum tunnelling in the presence of Noether charges

本文提出了一种基于第一性原理的量子隧穿计算方法，针对具有守恒诺ether电荷的初始状态，提供了一种清晰的欧几里得时间预设，以计算隧穿率，并首次处理了具有守恒诺ether电荷和非平凡能量的初始状态。

Quantum tunnelling, real-time dynamics and Picard-Lefschetz thimbles

We follow up the work, where in light of the Picard-Lefschetz thimble approach, we split up the real-time path integral into two parts: the initial density matrix part which can be represented via an ensemble of initial conditions, and the dynamic part of the path integral which corresponds to the integration over field variables at all later times. This turns the path integral into a two-stage problem where, for each initial condition, there exits one and only one critical point and hence a single thimble in the complex space, whose existence and uniqueness are guaranteed by the characteristi…

氢键中量子隧穿的质量标度：解析模型与多维势的比较

Mass-Scaling of Quantum Tunnelling in Hydrogen Bonds: Analytical Model and Comparison with Multidimensional Potentials

本研究提出康奈尔型解析-数值框架，揭示氢键中质子与氘核隧穿劈裂对有效质量平方根的指数标度，并在3D和5D量子模型中验证，为双阱体系提供高效计算方法。

Simulations of "Tunnelling of the 3rd Kind"

We consider the phenomenon of "tunnelling of the 3rd kind", whereby a magnetic field may traverse a classically impenetrable barrier by pair creation of unimpeded quantum fermions. These propagate through the barrier and generate a magnetic field on the other side. We study this numerically using quantum fermions coupled to a classical Higgs-gauge system, where we set up a magnetic field outside a box shielded by two superconducting barriers. We examine the magnitude of the internal magnetic field, and find agreement with existing perturbative results within a factor of two.