The Page curve plotted using the typical random state approximation is not applicable to a system with conserved quantities,such as the evaporation process of a charged black hole,during which the electric charge does...The Page curve plotted using the typical random state approximation is not applicable to a system with conserved quantities,such as the evaporation process of a charged black hole,during which the electric charge does not macroscopically radiate out with a uniform rate.In this context,the symmetry-resolved entanglement entropy may play a significant role in describing the entanglement structure of such a system.We attempt to impose constraints on microscopic quantum states to match the macroscopic phenomenon of charge radiation during black hole evaporation.Specifically,we consider a simple qubit system with conserved spin/charge serving as a toy model for the evaporation of charged black holes.We propose refined rules for selecting a random state with conserved quantities to simulate the distribution of charges during the different stages of evaporation and obtain refined Page curves that exhibit distinct features in contrast to the original Page curve.We find that the refined Page curve may have a different Page time and exhibit asymmetric behavior on both sides of the Page time.Such refined Page curves may provide a more realistic description for the entanglement between the charged black hole and radiation during the evaporation process.展开更多
为了研究污泥在低温低湿条件下的干燥规律,获得表征水分迁移过程的有效水分扩散系数(D_(eff))和活化能(E_a),以脱水污泥为研究对象进行了污泥低温低湿干燥试验,探讨了温度(30℃、35℃、40℃、45℃、50℃)和相对湿度(20%、40%、60%)对污...为了研究污泥在低温低湿条件下的干燥规律,获得表征水分迁移过程的有效水分扩散系数(D_(eff))和活化能(E_a),以脱水污泥为研究对象进行了污泥低温低湿干燥试验,探讨了温度(30℃、35℃、40℃、45℃、50℃)和相对湿度(20%、40%、60%)对污泥水分比(MR)和干燥速率(DR)的影响。结果表明,污泥的低温低湿干燥过程属于内部迁移控制,即水分扩散速率决定干燥速率。根据试验数据建立了污泥水分迁移动力学模型,并与6种常用薄层干燥模型进行拟合,通过对决定系数(R^2)、方差(χ~2)和残差平方和(RSS)的比较,得出污泥低温低湿干燥过程可以用Page模型来描述。结合Fick第二定律,得到不同温度(30~50℃)、湿度(20%~60%)条件下污泥有效水分扩散系数的范围为(0.699~1.991)×10^(-9)m^2/s;对传统的Arrhenius公式进行湿度修正,获得了干燥介质温度和湿度对污泥干燥特性影响的数学模型及活化能E_a=23.83 k J/mol。展开更多
基金Supported in part by the Natural Science Foundation of China(12035016,12275275)supported by the Beijing Natural Science Foundation(122031)the Innovative Projects of Science and Technology(E2545BU210)at IHEP.
文摘The Page curve plotted using the typical random state approximation is not applicable to a system with conserved quantities,such as the evaporation process of a charged black hole,during which the electric charge does not macroscopically radiate out with a uniform rate.In this context,the symmetry-resolved entanglement entropy may play a significant role in describing the entanglement structure of such a system.We attempt to impose constraints on microscopic quantum states to match the macroscopic phenomenon of charge radiation during black hole evaporation.Specifically,we consider a simple qubit system with conserved spin/charge serving as a toy model for the evaporation of charged black holes.We propose refined rules for selecting a random state with conserved quantities to simulate the distribution of charges during the different stages of evaporation and obtain refined Page curves that exhibit distinct features in contrast to the original Page curve.We find that the refined Page curve may have a different Page time and exhibit asymmetric behavior on both sides of the Page time.Such refined Page curves may provide a more realistic description for the entanglement between the charged black hole and radiation during the evaporation process.
文摘为了研究污泥在低温低湿条件下的干燥规律,获得表征水分迁移过程的有效水分扩散系数(D_(eff))和活化能(E_a),以脱水污泥为研究对象进行了污泥低温低湿干燥试验,探讨了温度(30℃、35℃、40℃、45℃、50℃)和相对湿度(20%、40%、60%)对污泥水分比(MR)和干燥速率(DR)的影响。结果表明,污泥的低温低湿干燥过程属于内部迁移控制,即水分扩散速率决定干燥速率。根据试验数据建立了污泥水分迁移动力学模型,并与6种常用薄层干燥模型进行拟合,通过对决定系数(R^2)、方差(χ~2)和残差平方和(RSS)的比较,得出污泥低温低湿干燥过程可以用Page模型来描述。结合Fick第二定律,得到不同温度(30~50℃)、湿度(20%~60%)条件下污泥有效水分扩散系数的范围为(0.699~1.991)×10^(-9)m^2/s;对传统的Arrhenius公式进行湿度修正,获得了干燥介质温度和湿度对污泥干燥特性影响的数学模型及活化能E_a=23.83 k J/mol。
