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arXiv 2402.02848cond-mat.quant-gas
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超冷原子系统中量子液滴的信息论测度

Information theoretic measures on quantum droplets in ultracold atomic systems

Sk Siddik, Golam Ali Sekh

AI总结:

该研究利用 Shannon 熵、Fisher 信息、Rényi 熵和 Tsallis 熵刻画超冷 Bose-Einstein 凝聚体中量子液滴概率密度由平顶向尖顶的转变,并识别液滴相起始。

摘要:

我们采用 Shannon 熵、Fisher 信息、Rényi 熵和 Tsallis 熵来研究 Bose-Einstein 凝聚体中的量子液滴相。在超越平均场描述中,带有 Lee-Huang-Yang 修正的 Gross-Pitaevskii 方程给出一族具有不同化学势的量子液滴。当化学势较大时,开始形成具有尖顶概率密度分布的量子液滴;而当化学势较小时,其概率密度分布变为平顶。我们表明,熵测度能够区分概率密度分布的形状变化,因此能够识别液滴相的起始。在液滴相起始期间,Shannon 熵随化学势降低而逐渐减小,并在从平顶 QD 向尖顶 QD 平滑转变的附近达到最小值。在此阶段,Shannon 熵随化学势进一步降低而突然增大。我们在 Fisher 信息的情形中观察到相反趋势。这些结果被发现与 Rényi 和 Tsallis 熵测度相一致。

英文摘要:

We consider Shannon entropy, Fisher information, Rényi entropy, and Tsallis entropy to study the quantum droplet phase in Bose-Einstein condensates. In the beyond mean-field description, the Gross-Pitaevskii equation with Lee-Huang-Yang correction gives a family of quantum droplets with different chemical potentials. At a larger value of chemical potential, quantum droplet with sharp-top probability density distribution starts to form while it becomes flat top for a smaller value of chemical potential. We show that entropic measures can distinguish the shape change of the probability density distributions and thus can identify the onset of the droplet phase. During the onset of droplet phase, the Shannon entropy decreases gradually with the decrease of chemical potential and attains a minimum in the vicinity where a smooth transition from flat-top to sharp-top QDs occurs. At this stage, the Shannon entropy increases abruptly with the lowering of chemical potential. We observe an opposite trend in the case of Fisher information. These results are found to be consistent with the Rényi and Tsallis entropic measures.

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