Temporal and spatial chaos in the Kerr-AdS black hole in an extended phase space

Based on the Melnikov method, we investigate chaotic behaviors in the extended thermodynamic phase space for a slowly rotating Kerr-AdS black hole under temporal and spatial perturbations. Our results show that the temporal perturbation coming from a thermal quench of the spinodal region in the phase diagram may cause temporal chaos only when the perturbation amplitude is above a critical value, which involves the angular momentum J. Under the spatial perturbation, however, it is found that spatial chaos always occurs, independent of the perturbation amplitude.     

On thermodynamics of RN-dS black hole surrounded by the quintessence

De Sitter black holes have the black hole horizon and the cosmological horizon, and the thermodynamic quantities on the two horizons all satisfy the first law of thermodynamics. The thermodynamic quantities on the two horizons are not independent but are correlated to each other. Taking de Sitter space-time as thermodynamic system, we investigated the effective thermodynamic quantities of Reissner–Nordström de Sitter black hole surrounded by the quintessence (RN-DSQ). We obtained the effective temperature and entropy of the system by considering the corrections between the black hole horizon and the cosmological horizon. We found that the entropy of the RN-DSQ is in agreement with that of Reissner–Nordström de Sitter black hole. It offers a basis for further studying of the thermodynamic properties of de Sitter space-time.     

正则黑洞熵与相变

应用隧道效应对黑洞Hawking辐射研究得到的辐射谱,对非旋转黑洞的正则熵进行讨论.所得熵遵守Bekenstein-Hawking 面积定律,并带有修正项,主要修正项与面积的对数成正比,另有与黑洞热容量有关的修正项.利用所给出的正则熵,对黑洞的相变进行讨论,得到当黑洞的热容量出现发散时,正则熵在该处并不出现复数,由此认为此相变为二级相变. 关键词： 正则系综 量子修正 黑洞相变     

Quantum corrections to the spectroscopy of a BTZ black hole via periodicity

Quantum corrections to the area spectrum and the entropy spectrum of a BTZ black hole are calculated by equaling the motion period of an outgoing wave coming from the quantum corrections of the semiclassical action to the period of gravitational system with respect to the Euclidean time. We find that the area spectrum and the entropy spectrum are independent of the properties of particles. Furthermore, in the presence of higher-order quantum corrections, the area spectrum is found to be corrected by inverse area terms while the entropy spectrum is found to have a universal form, $\varDelta S_{BH}=2\pi $ . Both results show that the entropy spectrum is independent of not only the BTZ black hole parameters but also the higher-order quantum corrections, which implies that the entropy spectrum is more natural than the area spectrum in quantum gravity theory.     

The shadow and observation appearance of black hole surrounded by the dust field in Rastall theory

In the context of Rastall gravity, the shadow and observation intensity casted by the new Kiselev-like black hole with dust field have been numerically investigated. In this system, the Rastall parameter and surrounding dust field structure parameter have considerable consequences on the geometric structure of spacetime. Considering the photon trajectories near the black hole, we investigate the variation of the radii of photon sphere, event horizon and black hole shadow under the different related parameters. Furthermore, taking into account two different spherically symmetric accretion models as the only background light source, we also studied the observed luminosity and intensity of black holes. For the both spherical accretions background, the results show that the decrease or increase of the observed luminosity depends on the value range of relevant parameters, and the promotion effect is far less obvious than the attenuation effect on the observed intensity. One can find that the inner shadow region and outer bright region of the black hole wrapped by infalling accretion are significantly darker than those of the static model, which is closely related to the Doppler effect. In addition, the size of the shadow and the position of the photon sphere are always the same in the two accretion models, which means that the black hole shadow depend only on the geometry of spacetime, while the observation luminosity is affected by the form of accretion material and the related spacetime structure.     

Quantum phase transition by employing trace distance along with the density matrix renormalization group

We use an alternative method to investigate the quantum criticality at zero and finite temperature using trace distance along with the density matrix renormalization group. It is shown that the average correlation measured by the trace distance between the system block and environment block in a DMRG sweep is able to detect the critical points of quantum phase transitions at finite temperature. As illustrative examples, we study spin-1 XXZ chains with uniaxial single-ion-type anisotropy and the Heisenberg spin chain with staggered coupling and external magnetic field. It is found that the trace distance shows discontinuity at the critical points of quantum phase transition and can be used as an indicator of QPTs.     

Is the percolation transition of hard spheres a thermodynamic phase transition?

In hard-sphere systems, there is a fluid-solid transition, but no gas-liquid transition. In the fluid region, however, one can find a purely geometric percolation transition, which is studied in detail. The van der Waals model of hard spheres is treated. In this model, a uniform negative background potential is added. This modification does not change the structure, but induces a gas-liquid transition. In fact, percolation and the gas-liquid transition can be related to each other.     

激光驱动下腔与玻色-爱因斯坦凝聚中的量子相变

Dicke模型中的量子相变在三十多年前已被预言,该模型描述的是N个二能级原子与单模腔场集体耦合的系统.在标准Dicke模型的基础上加入原子光的非线性相互作用和含时外场驱动,使用含时幺正变换和Holstein-Primafoff变换方法从理论上推导出基态能量表达式.并且给出了丰富的相图,而且这些性质最近已有文献从实验上验证.本文主要呈现了非线性相互作用和外场驱动对量子相变的影响.     

Quantum phase transition in the generalized single-mode superradiant model

In this paper we reveal a zero-temperature quantum phase transition for the single-mode superradiant model with the form A² from the normal to superradiant phase by mean of the Holstein-Primakoff transformation. In the thermodynamic limit, in which the numbers of atoms becomes infinite, the ground state energy and corresponding wavefunctions of both the normal and superradiant phases are obtained and therefore the scaling behavior near the critical transition point is derived.     

Entropy of higher-dimensional charged Gauss–Bonnet black hole in de Sitter space

The fundamental equation of the thermodynamic system gives the relation between the internal energy, entropy and volume of two adjacent equilibrium states. Taking a higher-dimensional charged Gauss–Bonnet black hole in de Sitter space as a thermodynamic system, the state parameters have to meet the fundamental equation of thermodynamics. We introduce the effective thermodynamic quantities to describe the black hole in de Sitter space. Considering that in the lukewarm case the temperature of the black hole horizon is equal to that of the cosmological horizon, we conjecture that the effective temperature has the same value. In this way, we can obtain the entropy formula of spacetime by solving the differential equation. We find that the total entropy contains an extra term besides the sum of the entropies of the two horizons. The corrected term of the entropy is a function of the ratio of the black hole horizon radius to the cosmological horizon radius, and is independent of the charge of the spacetime.     

High dimensional AdS-like black hole and phase transition in Einstein-bumblebee gravity

In this study, we obtained an exact high dimensional anti-de Sitter (AdS) black hole solution in Einstein-bumblebee gravity theory. This AdS-like black hole can only exist with a linear functional potential of the bumblebee field. We found that the Smarr formula and the first law of black hole thermodynamics can still be constructed in this Lorentz symmetry breaking black hole spacetime, but the conceptions of the black hole horizon area/entropy and the volume inside the horizon should be renewed due to its anisotropy. We also found that two types of phase transition exist: small-large black hole phase transition and Hawking-Page phase transition, like those of the Schwarzschild AdS black hole. After Lorentz symmetry breaking, the black hole mass at the divergent point of heat capacity becomes small, and the Gibbs free energy of the meta-stable large black hole is also smaller, showing that the large stable black hole can be more easily formed.     

Thermodynamics of black holes in the quintessential phase space

Considering that the negative pressure of the accelerated expansion of the universe results from the cosmological constant or the dark energy quintessence, we use the dark energy quintessence to construct the "quintessential" phase space. In contrast to the previous discussion in which the cosmological constant is considered as the black hole (BH) phase transition pressure, in this analysis, we believe that the pressure results from quintessence. The characteristics of critical behavior, Gibbs free energy, and temperature behavior in quintessential phase space are investigated. We observe that the phase transition belongs to van der Waals phase transition within\begin{document}$ -1 <\omega_{\rm q}<-2/3 $\end{document}. If \begin{document}$ \omega_{\rm q} $\end{document}is within (–2/3, –1/3), the phase transition loses the large BH phase transition characteristics, which is caused by the later stage of the phase transition being completely dominated by quintessence dark energy with negative pressure. These results suggest that the quintessential phase space can be constructed with the pressure from the thermal quintessence, and it can be used as a new probe to explore the thermodynamics of BHs.     

自旋场对Barriola-vilenkin黑洞熵的量子修正

用砖墙模型的方法，讨论了无源引力场对Barriola-Vilenkin黑洞熵的量子修正.计算表明， 量子修正应该包含两部分：其中一部分与视界面积成正比，在视界附近与紫外截断因子是 平方反比发散的；另一部分是两个对数发散项，这部分除了与黑洞的本身特征性质(M，η) 有关以外，还与自旋场的自旋有关.结果与标量场引起的量子修正具有完全不同的形式. 关键词： 砖墙模型 量子修正 黑洞熵     

Quantum phase transition of alkaline-earth fermionic atoms confined in an optical superlattice

Using the density matrix renormalization group method, we evaluate the spin and charge gaps of alkaline-earth fermionic atoms in a periodic one-dimensional optical superlattice. The number of delocalized atoms is equal to the lattice size and we consider an antiferromagnetic coupling between delocalized and localized atoms. We found a quantum phase transition from a Kondo insulator spin liquid state without confining potential to a charge-gapped antiferromagnetic state with nonzero potential. For each on-site coupling, there is a critical potential point for which the spin gap vanishes and its value increases linearly with the local interaction.     

A first-order phase transition in a three-dimensional vertex model

For a specific three-dimensional vertex model, it is proven that it will show a first-order phase transition. The critical temperature is given in terms of the energy of some local vertex configurations. The approach used is similar to the Nagle approach. Some classes of compounds are considered which may be related to this model.     

包围有暗能量黑洞的Hawking辐射修正

运用由Banerjee和Majhi所发展的非半经典近似的Hamiliton-Jacobi方法,计算了被暗能量包围的黑洞温度和熵,得到了修正后的温度和熵.在修正后的熵中,面积定理包含面积对数修正和面积幂的倒数。     

应用多尺度纠缠重整化算法研究量子自旋系统的量子相变和基态纠缠

应用多尺度纠缠重整化算法模拟自旋为1/2的一维量子XYX模型,通过计算局域序参量和度量纠缠的单缠节(one-tangle)、并发纠缠(concurrence)和纠缠比率R,确定系统的基态相图和纠缠相图.发现系统的纠缠相图比基态相图包含更多的物理信息.另外,从局域序参量和能隙与外磁场的标度关系,萃取出与磁化率和关联长度有关的临界指数β和v.     

Analytic phase structures and thermodynamic curvature for the charged AdS black hole in alternative phase space

In this paper, we visit the thermodynamic criticality and thermodynamic curvature of the charged AdS black hole in a new phase space. It is shown that when the square of the total charge of the charged black hole is considered as a thermodynamic quantity, the charged AdS black hole also admits a van der Waals-type critical behavior without the help of thermodynamic pressure and thermodynamic volume. Based on this, we study the fine phase structures of the charged AdS black hole with fixed AdS background in the new framework. On the one hand, we give the phase diagram structures of the charged AdS black hole accurately and analytically, which fills up the gap in dealing with the phase transition of the charged AdS black holes by taking the square of the charge as a thermodynamic quantity. On the other hand, we analyse the thermodynamic curvature of the black hole in two coordinate spaces. The thermodynamic curvatures obtained in two different coordinate spaces are equivalent to each other and are also positive. Based on an empirical conclusion under the framework of thermodynamic geometry, we speculate that when the square of charge is treated as an independent thermodynamic quantity, the charged AdS black hole is likely to present a repulsive between its molecules. More importantly, based on the thermodynamic curvature, we obtain a universal exponent at the critical point of phase transition.     

Mining a charged black hole and the third law of black hole thermodynamics

We consider the rate at which energy can be extracted from a charged black hole using the mining process developed by Unruh and Wald. It is shown that for a Reissner-Nordström black hole the mining rate depends on the mass of the hole (unlike in the Schwarzschild case) and goes to zero asT ^BH 0. We also argue that it is impossible to achieveT _BH=0 in a finite time by mining.     

Thermodynamics and weak cosmic censorship conjecture of an AdS black hole with a monopole in the extended phase space

The first law of black hole thermodynamics has been shown to be valid in the extended phase space.However,the second law and the weak cosmic censorship conjecture have not been investigated extensively.We investigate the laws of thermodynamics and the weak cosmic censorship conjecture of an AdS black hole with a global monopole in the extended phase space in the case of charged particle absorption.It is shown that the first law of thermodynamics is valid,while the second law is violated for the extremal and near-extremal black holes.Moreover,we find that the weak cosmic censorship conjecture is valid only for the extremal black hole,and that it can be violated for the near-extremal black holes,which is different from the previous results.