服从广义不确定原理的量子系统的退相干极限：Tsallis热统计学的新范式
Decoherence limit of quantum systems obeying generalized uncertainty principle: new paradigm for Tsallis thermostatistics
摘要：
广义不确定原理（GUP）是一种现象学模型，其目的是解释最小长度尺度（例如，普朗克尺度或有效量子描述中的特征反质量尺度）。在这封信中，我们研究了GUP系统在退相干域中可能的观测效应。我们首先导出了与GUP相关的相干态，并揭示了在动量表象中它们与Tsallis的概率幅一致，其非扩展性参数$q$随GUP形变参数$β$单调增加.其次，对于$β< 0$（即，$q < 1$），证明了由于Bekner-Babenko不等式，GUP完全等价于基于Tsallis熵幂的信息论测不准关系.最后，我们调用最大熵原理已知的估计理论，以揭示准经典（退相干）之间的联系GUP相关的量子理论和Tsallis的非广泛的热统计极限。这可能会在从量子理论到模拟引力的一系列领域提供一个令人兴奋的范例。例如，在某些量子引力理论中，如共形引力，上述准经典区域具有相关的观测结果。我们讨论了其中的一些含义。
英文摘要：
The generalized uncertainty principle (GUP) is a phenomenological model whose purpose is to account for a minimal length scale (e.g., Planck scale or characteristic inverse-mass scale in effective quantum description) in quantum systems. In this Letter, we study possible observational effects of GUP systems in their decoherence domain. We first derive coherent states associated to GUP and unveil that in the momentum representation they coincide with Tsallis' probability amplitudes, whose non-extensivity parameter $q$ monotonically increases with the GUP deformation parameter $β$. Secondly, for $β< 0$ (i.e., $q < 1$), we show that, due to Bekner-Babenko inequality, the GUP is fully equivalent to information-theoretic uncertainty relations based on Tsallis-entropy-power. Finally, we invoke the Maximal Entropy principle known from estimation theory to reveal connection between the quasi-classical (decoherence) limit of GUP-related quantum theory and non-extensive thermostatistics of Tsallis. This might provide an exciting paradigm in a range of fields from quantum theory to analog gravity. For instance, in some quantum gravity theories, such as conformal gravity, aforementioned quasi-classical regime has relevant observational consequences. We discuss some of the implications.
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