论文标题

量子流体动力学的路径积分方法

A Path Integral approach to Quantum Fluid Dynamics

论文作者

Ghosh, Sagnik, Ghosh, Swapan K.

论文摘要

在这项工作中,我们开发了使用路径积分方法解决量子轨迹的替代方法。该领域的最新技术是同时解决一组非线性的,耦合的部分微分方程(PDE)。我们选择一条根本不同的路线。我们首先为路径积分传播器得出一般的闭合形式表达式,有效作为相应经典路径功能的任何一般电位。该方法是精确的,并且适用于许多维度以及多粒子病例。然后,将其用于计算量子电位(QP),而量子电位(QP)又可以生成量子轨迹。对于不可能进行封闭形式解决方案的情况,该问题被正式沸腾以将经典路径作为边界值问题解决。该工作正式将路径积分方法与量子流体动力学桥接。作为说明该方法的模型应用程序,我们可以制定玩具模型。双孔电势,其中经典路径的边界值问题被扰动地计算出来,但量子部分是精确的。利用这一点,我们深入研究了关于量子隧道的长期辩论之一。

In this work we develop an alternative approach for solution of Quantum Trajectories using the Path Integral method. The state-of-the-art technique in the field is to solve a set of non-linear, coupled partial differential equations (PDEs) simultaneously. We opt for a fundamentally different route. We first derive a general closed form expression for the Path Integral propagator valid for any general potential as a functional of the corresponding classical path. The method is exact and is applicable in many dimensions as well as multi-particle cases. This, then, is used to compute the Quantum Potential (QP), which, in turn, can generate the Quantum Trajectories. For cases, where closed form solution is not possible, the problem is formally boiled down to solving the classical path as a boundary value problem. The work formally bridges the Path Integral approach with Quantum Fluid Dynamics. As a model application to illustrate the method, we work out a toy model viz. the double-well potential, where the boundary value problem for the classical path has been computed perturbatively, but the Quantum part is left exact. Using this we delve into seeking insight in one of the long standing debates with regard to Quantum Tunneling.

扫码加入交流群

加入微信交流群

微信交流群二维码

扫码加入学术交流群,获取更多资源