Motion of vortex lines in nonlinear wave mechanics

Motion of vortex lines in quantum mechanics

Exact analytic solutions of the time dependent Schrodinger equation are produced that exhibit a variety of vortex structures. The qualitative analysis of the motion of vortex lines is presented and various types of vortex behavior are identified. Vortex creation and annihilation and vortex interactions are illustrated in the special cases of the free motion, the motion in the harmonic potential, and in the constant magnetic field. Similar analysis of the vortex motions is carried out also for a relativistic wave equation.

Effects of entanglement on vortex dynamics in the hydrodynamic representation of quantum mechanics

The hydrodynamic representation of quantum mechanics describes virtual flow as if a quantum system were fluid in motion. This formulation illustrates pointlike vortices when the phase of a wavefunction becomes nonintegrable at nodal points. We study the dynamics of such pointlike vortices in the hydrodynamic representation for a two-particle wavefunction. In particular, we discuss how quantum entanglement influences vortex-vortex dynamics. For this purpose, we employ the time-dependent quantum variational principle combined with the Rayleigh-Ritz method. We analyze the vortex dynamics and esta…

Zero-Energy Flows and Vortex Patterns in Quantum Mechanics

We show that zero-energy flows appear in many particle systems as same as in single particle cases in 2-dimensions. Vortex patterns constructed from the zero-energy flows can be investigated in terms of the eigenstates in conjugate spaces of Gel'fand triplets. Stable patterns are written by the superposition of zero-energy eigenstates. On the other hand vortex creations and annihilations are described by the insertions of unstable eigenstates with complex-energy eigenvalues into the stable patterns. Some concrete examples are presented in the 2-dimensional parabolic potential barrier case. %, …

混合量子-经典算法用于具有吉布斯-兰道尔势能和涡旋运动定律的复杂非线性偏微分方程

Hybrid quantum-classical algorithms for complex nonlinear partial differential equations with Ginzburg-Landau potential and vortex motion laws

本文提出量子算法求解强非线性 regime 下的复值非线性偏微分方程，利用涡旋动态和线性椭圆方程的渐近性质，结合量子 BPX 预conditioning 和 Schrödingerization 提高计算效率。

Emergent Quantum Dynamics of Vortex Line under Linear Local Induction Approximation

Using the linear local induction approximation, we investigated the self-induced motion of a vortex line that corresponds to the motion of a particle in quantum mechanics. Concerning Kelvin waves, the effective Schrödinger equation, physical quantities operators, and the corresponding path-integral formula are obtained. The vortex line-particle mapping may help in understanding particle motion in quantum mechanics.

Multi-valued vortex solutions to the Schrödinger equation and radiation

This paper addresses the single-valued requirement for quantum wave functions when they are analytically continued in the spatial coordinates. This is particularly relevant for de Broglie-Bohm, hydrodynamic, or stochastic models of quantum mechanics where the physical basis for single-valuedness has been questioned. It first constructs a large class of multi-valued wave functions based on knotted vortex filaments familiar in fluid mechanics, and then it argues that for free particles, these systems will likely radiate electromagnetic radiation if they are charged or have multipolar moments, an…