The comprehension of universal thermodynamic behaviors in the supercritical region is crucial for examining the characteristics of black hole systems under high temperature and pressure.This study is devoted to the an...The comprehension of universal thermodynamic behaviors in the supercritical region is crucial for examining the characteristics of black hole systems under high temperature and pressure.This study is devoted to the analysis of characteristic lines and crossover behaviors within the supercritical region.By making use of the free energy,we introduce three key thermodynamic quantities:scaled variance,skewness,and kurtosis.Our results demonstrate that the Widom line,associated with the maximal scaled variance,can effectively differentiate between small and large black hole-like subphases,each displaying distinct thermodynamic behaviors within the supercritical region.Furthermore,by utilizing quasinormal modes,we identify the Frenkel line,offering a dynamic perspective to distinguish between small and large black hole-like subphases.These contribute to a deeper comprehension of black hole subphases in the supercritical region,thus illuminating new facets of black hole thermodynamics.展开更多
In this work,the phase structure of a holographic s+d model with quartic potential terms from 4D Einstein–Gauss–Bonnet gravity is studied in the probe limit.We first show the qd-μphase diagram with a very small val...In this work,the phase structure of a holographic s+d model with quartic potential terms from 4D Einstein–Gauss–Bonnet gravity is studied in the probe limit.We first show the qd-μphase diagram with a very small value of the Gauss–Bonnet coefficientα=1×10-7and in the absence of the quartic terms to locate the suitable choice of the value of qd,where the system admits coexistent s+d solutions.Then we consider the various values of the Gauss–Bonnet coefficientαand present theα-μphase diagram to show the influence of the Gauss–Bonnet term on the phase structure.We also give an example of the re-entrant phase transition which is also realized in the holographic s+s and s+p models.After that we confirm the universality of the influence of the quartic term with coefficientλdon the d-wave solutions,which is similar to the case of s-wave and p-wave solutions previously studied in the s+p model.Finally we give the dependence of the special values of the quartic term coefficientλdon the Gauss–Bonnet coefficientα,below which the d-wave condensate grows to an opposite direction at the(quasi-)critical point,which is useful in realizing first order phase transitions in further studies of the holographic d-wave superfluids.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12473001,11975072,11875102,11835009,and 11965013)the National SKA Program of China(Grant Nos.2022SKA0110200 and 2022SKA0110203)+1 种基金the National 111 Project(Grant No.B16009)supported by Yunnan High-level Talent Training Support Plan Young&Elite Talents Project(Grant No.YNWR-QNBJ-2018-181).
文摘The comprehension of universal thermodynamic behaviors in the supercritical region is crucial for examining the characteristics of black hole systems under high temperature and pressure.This study is devoted to the analysis of characteristic lines and crossover behaviors within the supercritical region.By making use of the free energy,we introduce three key thermodynamic quantities:scaled variance,skewness,and kurtosis.Our results demonstrate that the Widom line,associated with the maximal scaled variance,can effectively differentiate between small and large black hole-like subphases,each displaying distinct thermodynamic behaviors within the supercritical region.Furthermore,by utilizing quasinormal modes,we identify the Frenkel line,offering a dynamic perspective to distinguish between small and large black hole-like subphases.These contribute to a deeper comprehension of black hole subphases in the supercritical region,thus illuminating new facets of black hole thermodynamics.
基金supported by the National Natural Science Foundation of China(Grant No.11965013)supported by Yunnan High-level Talent Training Support Plan Young&Elite Talents Project(Grant No.YNWR-QNBJ-2018-181)。
文摘In this work,the phase structure of a holographic s+d model with quartic potential terms from 4D Einstein–Gauss–Bonnet gravity is studied in the probe limit.We first show the qd-μphase diagram with a very small value of the Gauss–Bonnet coefficientα=1×10-7and in the absence of the quartic terms to locate the suitable choice of the value of qd,where the system admits coexistent s+d solutions.Then we consider the various values of the Gauss–Bonnet coefficientαand present theα-μphase diagram to show the influence of the Gauss–Bonnet term on the phase structure.We also give an example of the re-entrant phase transition which is also realized in the holographic s+s and s+p models.After that we confirm the universality of the influence of the quartic term with coefficientλdon the d-wave solutions,which is similar to the case of s-wave and p-wave solutions previously studied in the s+p model.Finally we give the dependence of the special values of the quartic term coefficientλdon the Gauss–Bonnet coefficientα,below which the d-wave condensate grows to an opposite direction at the(quasi-)critical point,which is useful in realizing first order phase transitions in further studies of the holographic d-wave superfluids.
