Uncertainty relation and quantitative condition of inversion symmetry of time in many-particle system

A quantitative aspect of the Heisenberg uncertainty

Minimization of the expectation value of energy under the constraints imposed by the uncertainty principle can be a convenient method of solving quantum-mechanical problems.

谐波反演有助于击败时间-能量不确定关系

Harmonic inversion helps to beat time-energy uncertainty relations

提出一种从量子系统的极短时间信号中高精度提取能量的实用方法，其时间-精度乘积远低于时间-能量不确定关系的极限。

Adiabatic Conditions and the Uncertainty Relation

The condition for adiabatic approximation are of basic importance for the applications of the adiabatic theorem. The traditional quantitative condition was found to be necessary but not sufficient, but we do not know its physical meaning and the reason why it is necessary from the physical point of view. In this work, we relate the adiabatic theorem to the uncertainty relation, and present a clear physical picture of the traditional quantitative condition. It is shown that the quantitative condition is just the amplitude of the probability of transition between two levels in the time interval …

Quantitative Determination of the Adiabatic Condition Using Force-Detected Nuclear Magnetic Resonance

The adiabatic condition governing cyclic adiabatic inversion of proton spins in a micron-sized ammonium chloride crystal was studied using room temperature nuclear magnetic resonance force microscopy. A systematic degradation of signal-to-noise was observed as the adiabatic condition became violated. A theory of adiabatic following applicable to cyclic adiabatic inversion is reviewed and implemented to quantitatively determine an adiabaticity threshold $(γH_1)^2/(ω_{osc}Ω) = 6.0$ from our experimental results.