Relationship between the wave function and space

Relationship between the ground-state wave function of a magnet and its static structure factor

We state and prove two theorems about the ground state of magnetic systems described by very general Heisenberg-type models and discuss their implications for magnetic neutron scattering. The first theorem states that two models cannot have the same correlator without sharing the corresponding ground states. According to the second theorem, an $N$-qubit wave function cannot reproduce the correlators of a given system unless it represents a true ground state of that system. We discuss the implications for neutron scattering inverse problems. We argue that the first theorem provides a framework …

广义波粒二象性的相干性与熵互补关系

Coherence and entropy complementarity relations of generalized wave-particle duality

本文针对量子高维系统，构建了n路径干涉条纹可预测性与可见性的广义度量，利用Morozova-Chentsov函数确立平均相干性描述的波粒关系，并建立了可见性、可预测性与量子f熵间的互补关系，揭示了波粒二象性与其它物理量的深刻联系。

Schwinger, Pegg and Barnett approaches and a relationship between angular and Cartesian quantum descriptions II: Phase Spaces

Following the discussion -- in state space language -- presented in a preceding paper, we work on the passage from the phase space description of a degree of freedom described by a finite number of states (without classical counterpart) to one described by an infinite (and continuously labeled) number of states. With that it is possible to relate an original Schwinger idea to the Pegg and Barnett approach to the phase problem. In phase space language, this discussion shows that one can obtain the Weyl-Wigner formalism, for both Cartesian {\em and} angular coordinates, as limiting elements of t…

Metrics for two electron random potential systems

Metrics have been used to investigate the relationship between wavefunction distances and density distances for families of specific systems. We extend this research to look at random potentials for time-dependent single electron systems, and for ground-state two electron systems. We find that Fourier series are a good basis for generating random potentials. These random potentials also yield quasi-linear relationships between the distances of ground-state densities and wavefunctions, providing a framework in which Density Functional Theory can be explored.

The Loschmidt Index

We study the nodes of the wavefunction overlap between ground states of a parameter-dependent Hamiltonian. These nodes are topological, and we can use them to analyze in a unifying way both equilibrium and dynamical quantum phase transitions in multi-band systems. We define the Loschmidt index as the number of nodes in this overlap and discuss the relationship between this index and the wrapping number of a closed auxiliary hypersurface. This relationship allows us to compute this index systematically, using an integral representation of the wrapping number. We comment on the relationship betw…

Quantum Hydrodynamics: Kirchhoff Equations

In this paper, we show that the Kirchhoff equations are derived from the Schrödinger equation by assuming the wave function to be a polynomial like solution. These Kirchhoff equations describe the evolution of $n$ point vortices in hydrodynamics. In two dimensions, Kirchhoff equations are used to demonstrate the solution to single particle Laughlin wave function as complex Hermite polynomials. We also show that the equation for optical vortices, a two dimentional system, is derived from Kirchhoff equation by using paraxial wave approximation. These Kirchhoff equations satisfy a Poisson bracket…

Hagedorn–Hermite对应关系

The Hagedorn--Hermite Correspondence

本研究建立Hagedorn半经典波包与厄米函数的阶梯算符对应关系，揭示其代数结构，推广最小不确定乘积至多维，并推导两类波包生成函数、多项式的关联。