广义不确定性原理对MIT袋模型状态方程的影响
Effects of a Generalized Uncertainty Principle on the MIT Bag Model Equation of State
AI总结：
本研究将广义不确定性原理纳入MIT袋模型，通过变形相空间修正热力学量，揭示零温极限下能量密度、压强和重子数密度的饱和及整体下降，增强抗引力坍缩稳定性，为致密星状态方程提供简单量子引力描述。
摘要：
广义不确定性原理（GUP）源于这样的前提：普朗克尺度附近的时空涨落对距离的可分辨精度施加了一个下界，从而导致最小长度的存在。受一种半经典方法的启发，该方法通过变形相空间将GUP纳入配分函数，我们对MIT袋模型的热力学量进行了修正，并提出该修正可作为在具有最小长度的空间中退禁闭夸克物质的有效半经典描述。我们研究了这种变形对零温极限的影响，揭示了能量密度、压强和重子数密度的饱和极限，以及热力学量的整体下降，这表明系统对抗引力坍缩的稳定性增强。这些发现扩展了关于GUP变形的费米气体的现有研究。最终，我们的描述以数学上简单的方式将量子引力效应引入致密星的状态方程，表明其具有扩展到更复杂系统的潜力。
英文摘要：
The Generalized Uncertainty Principle (GUP) is motivated by the premise that spacetime fluctuations near the Planck scale impose a lower bound on the achievable resolution of distances, leading to a minimum length. Inspired by a semiclassical method that integrates the GUP into the partition function by deforming its phase space, we induce a modification on the thermodynamic quantities of the MIT bag model that we propose serves as an effective semiclassical description of deconfined quark matter in a space with minimal length. We investigate the consequences of this deformation on the zero-temperature limit, revealing a saturation limit for the energy density, pressure and baryon number density and an overall decrease of the thermodynamic quantities which suggests an enhanced stability against gravitational collapse. These findings extend existing research on GUP-deformed Fermi gases. Ultimately, our description introduces effects of quantum gravity in the equations of state for compact stars in a mathematically simple manner, suggesting potential for extension to more complex systems.
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