Dodonov Viktor V, Dodonov Alexandre V
Institute of Physics, University of Brasilia, P.O. Box 04455, Brasilia 70919-970, DF, Brazil.
International Center of Physics, University of Brasilia, Brasilia 70919-970, DF, Brazil.
Entropy (Basel). 2023 Mar 31;25(4):596. doi: 10.3390/e25040596.
We study the evolution of the energy and magnetic moment of a quantum charged particle placed in a homogeneous magnetic field, when this field changes its sign adiabatically. We show that after a single magnetic field passage through zero value, the famous adiabatic invariant ratio of energy to frequency is reestablished again, but with a proportionality coefficient higher than in the initial state. The concrete value of this proportionality coefficient depends on the power index of the frequency dependence on time near zero point. In particular, the adiabatic ratio of the initial ground state (with zero radial and angular quantum numbers) triplicates if the frequency tends to zero linearly as a function of time. If the Larmor frequency attains zero more than once, the adiabatic proportionality coefficient strongly depends on the lengths of the time intervals between zero points, so that the mean energy behavior can be quasi-stochastic after many passages through zero value. The original Born-Fock adiabatic theorem does not work after the frequency passes through zero. However, its generalization is found: the initial Fock state becomes a wide superposition of many instantaneous Fock states, whose weights do not depend on time in the new adiabatic regime.
我们研究了置于均匀磁场中的量子带电粒子的能量和磁矩的演化，当该磁场绝热地改变其符号时。我们表明，在磁场单次穿过零值后，著名的能量与频率的绝热不变比再次重新建立，但比例系数高于初始状态。该比例系数的具体值取决于频率在零点附近对时间的依赖的幂指数。特别地，如果频率作为时间的函数线性趋于零，则初始基态（径向和角向量子数为零）的绝热比会变为三倍。如果拉莫尔频率不止一次达到零，则绝热比例系数强烈依赖于零点之间时间间隔的长度，以至于在多次穿过零值后平均能量行为可能是准随机的。频率穿过零后，原始的玻恩 - 福克绝热定理不再适用。然而，我们找到了它的推广：初始福克态变成了许多瞬时福克态的广泛叠加，在新的绝热 regime 中其权重不依赖于时间。
