Parameter differentiation and quantum state decomposition for time varying Schroedinger equations

A Stern-Gerlach Experiment in Time

In non-relativistic quantum mechanics, path integrals are normally derived from the Schroedinger equation. This assumes the two formalisms are equivalent. Since time plays a very different role in the Schroedinger equation and in path integrals, this may not be the case. We here derive path integrals directly by imposing two requirements: correct behavior in the classical limit and the most complete practicable symmetry between time and space. With these requirements, the path integral formalism predicts quantum fluctuations over the time dimension analogous to the quantum fluctuations seen ov…

Modes transformation for a Schroedinger type equation: avoided and unavoidable level crossings

An asymptotic approach for a Schroedinger type equation with a non selfadjoint slowly varying Hamiltonian of a special type is developed. The Hamiltonian is assumed to be the result of a small perturbation of an operator with a twofold degeneracy (turning) point, which can be diagonalized at this point. The non-adiabatic transformation of modes is studied in the case where two small parameters are dependent: the parameter characterizing an order of the perturbation is a square root of the adiabatic parameter. The perturbation of the Hamiltonian produces a close pair of simple degeneracy points…

Electron conduction in solid state via time varying wavevectors

In this paper, we study electron wavepacket dynamics in electric and magnetic fields. We rigorously derive the semiclassical equations of electron dynamics in electric and magnetic fields. We do it both for free electron and electron in a periodic potential. We do this by introducing time varying wavevectors $k(t)$. In the presence of magnetic field, our wavepacket reproduces the classical cyclotron orbits once the origin of the Schröedinger equation is correctly chosen to be center of cyclotron orbit. In the presence of both electric and magnetic fields, our equations for wavepacket dynamics …

利用纠缠对偏振物体进行非局域量子区分

Nonlocal quantum differentiation between polarization objects using entanglement

本文实验实现了一种基于偏振纠缠光子对和远程态制备的非局域量子测量方案，仅需两次符合测量即可区分80多个具有不同穆勒矩阵的透明及双折射样品，显著少于全面检测所需的至少8次测量，展示了其在生物医学诊断和遥感等分类检测任务中的高效潜力。

Quantum fields, cosmological constant and symmetry doubling

Energy-parity has been introduced by Kaplan and Sundrum as a protective symmetry that suppresses matter contributions to the cosmological constant [KS05]. It is shown here that this symmetry, schematically Energy --> - Energy, arises in the Hilbert space representation of the classical phase space dynamics of matter. Consistently with energy-parity and gauge symmetry, we generalize the Liouville operator and allow a varying gauge coupling, as in "varying alpha" or dilaton models. In this model, classical matter fields can dynamically turn into quantum fields (Schroedinger picture), accompanied…

非线性势的量子波函数的精确计算

Exact computation of quantum wave functions for nonlinear potentials

本文提出一种基于经典最小作用量精确求解非线性势薛定谔方程的方法，通过调和坐标变换与时间缩放，将非线性势转化为线性振子，从而直接构造精确量子波函数，替代微扰近似。