An approximate exchange-correlation hole density as a functional of the natural orbitals

The Fermi and Coulomb holes that can be used to describe the physics of electron correlation are calculated and analysed for a number of typical cases, ranging from prototype dynamical correlation to purely nondynamical correlation. Their behaviour as a function of the position of the reference electron and of the nuclear positions is exhibited. The notion that the hole can be written as the square of a hole amplitude, which is exactly true for the exchange hole, is generalized to the total holes, including the correlation part. An Ansatz is made for an approximate yet accurate expression for the hole amplitude in terms of the natural orbitals. employing the local (at the reference position) values of the natural orbitals and the density. This expression for the hole amplitude leads to an approximate two-electron density matrix that: (a) obeys correct permutation symmetry in the electron coordinates; (b) integrates to the exact one-matrix; and (c) yields exact correlation energies in the limiting cases of predominant dynamical correlation (high Z two-electron ions) and pure nondynamical correlation (dissociated H₂).     

Asymptotically FRW black holes

Special solutions of the LTB family representing collapsing over-dense regions corresponding to asymptotically closed, open, or flat FRW models are found. These solutions may be considered as representing dynamical mass condensations leading to black holes immersed in a FRW universe. We study the dynamics of the collapsing region, and its density profile. The question of the strength of the central singularity and its nakedness, as well as the existence of an apparent horizon and an event horizon is dealt with in detail, shedding light to the notion of cosmological black holes. Differences to the Schwarzschild black hole are addressed.     

Escape of black holes from the brane

TeV-scale gravity theories allow the possibility of producing small black holes at energies that soon will be explored at the CERN LHC or at the Auger observatory. One of the expected signatures is the detection of Hawking radiation that might eventually terminate if the black hole, once perturbed, leaves the brane. Here, we study how the "black hole plus brane" system evolves once the black hole is given an initial velocity that mimics, for instance, the recoil due to the emission of a graviton. The results of our dynamical analysis show that the brane bends around the black hole, suggesting that the black hole eventually escapes into the extra dimensions once two portions of the brane come in contact and reconnect. This gives a dynamical mechanism for the creation of baby branes.     

Regular Black Holes with Cosmological Constant

We present a class of regular black holes with cosmological constant A in nonlinear electrodynamics. Instead of usual singularity behind black hole horizon, all fields and curvature invariants are regular everywhere for the regular black holes. Through gauge invariant approach, the linearly dynamical stability of the regular black hole is studied. In odd-parity sector, we find that the A term does not appear in the master equations of perturbations, which shows that the regular black hole is stable under odd-parity perturbations. On the other hand, for the even-parity sector, the master equations are more complicated than the case without the cosmological constant. We obtain the sufficient conditions for stability of the regular black hole. We also investigate the thermodynamic properties of the regular black hole. and find that those thermodynamic quantities do not satisfy the differential form of first law of black hole thermodynamics. The reason for violating the first law is revealed.     

Black Holes in Bose–Einstein Condensates

It is shown that there exist both dynamically stable and unstable dilute-gas Bose–Einstein condensates that, in the hydrodynamic limit, exhibit a behavior completely analogous to that of gravitational black holes. The dynamical instabilities involve creation of quasiparticle pairs in positive and negative energy states. We illustrate these features in two qualitatively different one-dimensional models. We have also simulated the creation of a stable sonic black hole by solving the Gross–Pitaevskii equation numerically for a condensate subject to a trapping potential that is adiabatically deformed. A sonic black hole could in this way be created experimentally with state-of-the-art or planned technology.     

Clarification of the bootstrap percolation paradox

We study the onset of the bootstrap percolation transition as a model of generalized dynamical arrest. Our results apply to two dimensions, but there is no significant barrier to extending them to higher dimensionality. We develop a new importance-sampling procedure in simulation, based on rare events around "holes", that enables us to access bootstrap lengths beyond those previously studied. By framing a new theory in terms of paths or processes that lead to emptying of the lattice we are able to develop systematic corrections to the existing theory and compare them to simulations. Thereby, for the first time in the literature, it is possible to obtain credible comparisons between theory and simulation in the accessible density range.     

动态球对称Einstein-Yang-Mills-Chern-Simons黑洞的霍金辐射

用Hamilton-Jacobi方法研究了动态球对称Einstein-Yang-Mills-Chern-Simons 黑洞事件视界处的隧穿辐射特征及其黑洞事件视界处的温度. 其结果表明,黑洞温度及隧穿率与黑洞的固有性质及其动态特征有关. 这对于进一步研究动态黑洞的热力学性质及其相关问题是有意义的. 其方法的重要意义在于研究这类动态黑洞的霍金辐射时, 不仅适用于标量场隧穿辐射的情形, 同时也适用于研究旋量场、矢量场以及引力波的隧穿辐射. 关键词： Einstein-Yang-Mills-Chern-Simons黑洞 霍金隧穿辐射 Hamilton-Jacobi方程     

Spin waves and static susceptibility in the weakly doped t-J model

We investigate the spin dynamics in weakly doped high-temperature superconductors. The system is described by the two-dimensional t-J model. Our focus is on the interaction between mobile holes and spin waves. The calculations are based on a recently introduced cumulant method for computing the ground state energy of correlated electronic systems. Contrary to previous works using dynamical quantities like correlation functions or spectral densities our approach contains a static view to the system. This new method treats spin and hole dynamics on the same basis and allows for the calculation of static and dynamical quantities. We present results for spin-wave energies and transverse static susceptibilities for small hole concentrations and various values of t/J. We find a strong renor-malization of the spin-wave energies due to the spin-hole interaction. In agreement with neutron scattering experiments the spin-wave velocity vanishes at a critical hole density of a few percent which is equivalent to the instability of the antiferromagnetic order.     

Kaluza—Klein Black-Hole Entropy by Quantum Statistics

By using the method of quantum statistics, we directly derive the partition functions of bosonic and fermionic field in Kaluza—Klein black hole with axial symmetry. Then via the improved brick-wall method, membrane model, we obtain that the entropy of bosonic and fermionic field in black hole is proportional to the area of horizon. In our result, the stripped term and the divergent logarithmic term no longer exist. The problem that the state density is divergent around the horizon doesn't exist either. We also give the influence of the spining degeneracy of particles on the entropy of black hole. We offer a new, simple, and direct way of calculating the entropy of different complicated black holes.     

Accretion onto Charged Black Holes in Einstein and Massive Theories of Gravity *

The accretion process is being investigated onto some important black holes such as Born-Infeld-AdS black hole, non-linear charged black hole solution in AdS space-time and Einstein-Yang-Mills massive gravity in the presence of Born-Infeld nonlinear electrodynamics. We find out the relations of radial velocity, energy density and change of mass for mention black holes and analyze their behavior graphically for different values of equation of state parameters $\omega$. We also examine the relations for critical speed for these black holes. It is observed that for different state parameters different fluids exhibit different evolutions in black holes backgrounds. The energy density of some fluids is negative or positive near the black hole while other fluids become cause to increase or decrease in black hole mass.     

Towers of gravitational theories

In this essay we introduce a theoretical framework designed to describe black hole dynamics. The difficulties in understanding such dynamics stems from the proliferation of scales involved when one attempts to simultaneously describe all of the relevant dynamical degrees of freedom. These range from the modes that describe the black hole horizon, which are responsible for dissipative effects, to the long wavelength gravitational radiation that drains mechanical energy from macroscopic black hole bound states. We approach the problem from a Wilsonian point of view, by building a tower of theories of gravity each of which is valid at different scales. The methodology leads to multiple new results in diverse topics including phase transitions of Kaluza-Klein black holes and the interactions of spinning black hole in non-relativistic orbits. Moreover, our methods tie together speculative ideas regarding dualities for black hole horizons to real physical measurements in gravitational wave detectors.     

InAs quantum dots in GaAs holes: island number dependence on hole diameter and conduction-band coupling estimates

We studied the formation of InAs islands in holes defined by electron-beam lithography on GaAs substrates. The islands grew selectively in the holes, with one to nine islands per hole. The number of islands depends simply on the hole diameter, filling the holes at a constant effective two-dimensional density. We define the ratio of this effective density to the density on an unpatterned control sample to be the selectivity ratio, and we find a selectivity ratio of greater than 1000 for the present samples. We estimated the lateral conduction-band coupling for closely spaced islands and conclude them to be plausible candidates for weakly coupled device building blocks.     

Transmission processes in random patterns of subwavelength holes

The optical transmission of random patterns of holes is believed to depend on the transmission of the independent holes only. By comparing the transmission spectra of random patterns with different densities, we show that the quasi-cylindrical wave plays an important role in the transmission of samples with large hole densities. Furthermore, we report on a speckle pattern seen in the transmission of these arrays. By studying the degree of depolarization in this speckle pattern, as a function of hole density, we are able to quantify the role of surface plasmons to the transmission.     

Thermodynamics,phase transitions and Ruppeiner geometry for Einstein–dilaton–Lifshitz black holes in the presence of Maxwell and Born–Infeld electrodynamics

In this paper, we first obtain the higher-dimen-sional dilaton–Lifshitz black hole solutions in the presence of Born–Infeld (BI) electrodynamics. We find that there are two different solutions for the cases of \(z=n+1\) and \(z\ne n+1\) where z is the dynamical critical exponent and n is the number of spatial dimensions. Calculating the conserved and thermodynamical quantities, we show that the first law of thermodynamics is satisfied for both cases. Then we turn to the study of different phase transitions for our Lifshitz black holes. We start with the Hawking–Page phase transition and explore the effects of different parameters of our model on it for both linearly and BI charged cases. After that, we discuss the phase transitions inside the black holes. We present the improved Davies quantities and prove that the phase transition points shown by them are coincident with the Ruppeiner ones. We show that the zero temperature phase transitions are transitions in the radiance properties of black holes by using the Landau–Lifshitz theory of thermodynamic fluctuations. Next, we turn to the study of the Ruppeiner geometry (thermodynamic geometry) for our solutions. We investigate thermal stability, interaction type of possible black hole molecules and phase transitions of our solutions for linearly and BI charged cases separately. For the linearly charged case, we show that there are no phase transitions at finite temperature for the case \( z\ge 2\). For \(z<2\), it is found that the number of finite temperature phase transition points depends on the value of the black hole charge and there are not more than two. When we have two finite temperature phase transition points, there is no thermally stable black hole between these two points and we have discontinuous small/large black hole phase transitions. As expected, for small black holes, we observe finite magnitude for the Ruppeiner invariant, which shows the finite correlation between possible black hole molecules, while for large black holes, the correlation is very small. Finally, we study the Ruppeiner geometry and thermal stability of BI charged Lifshtiz black holes for different values of z. We observe that small black holes are thermally unstable in some situations. Also, the behavior of the correlation between possible black hole molecules for large black holes is the same as for the linearly charged case. In both the linearly and the BI charged cases, for some choices of the parameters, the black hole system behaves like a Van der Waals gas near the transition point.     

Gauss-bonnet black holes and possibilities for their experimental search

Corollaries of gravity models with second-order curvature corrections in the form of a Gauss-Bonnet term and possibilities (or impossibilities) for their experimental search or observations are discussed. The full version of the four-dimensional Schwarzschild-Gauss-Bonnet black hole solution and the constraint on the possible minimal black hole mass following from this model are considered. Using our solution as a model for the final stages of Hawking evaporation of black holes with a low initial mass (up to 10¹⁵ g) whose lifetime is comparable to that of our Universe, we have revealed differences in the patterns of evaporation: we have obtained high values of the emitted energy and showed the impossibility of an experimental search for primordial black holes by their evaporation products. Scenarios for the evaporation of Gauss-Bonnet black holes in multidimensional gravity models and possibilities for their experimental search are also discussed.     

Minimum black hole mass from colliding Gaussian packets

We study the formation of a black hole in the collision of two Gaussian packets. Rather than following their dynamical evolution in detail, we assume a horizon forms when the mass function for the two packets becomes larger than half the flat areal radius, as it would occur in a spherically symmetric geometry. This simple approximation allows us to determine the existence of a minimum black hole mass solely related to the width of the packets. We then comment on the possible physical implications, both in classical and quantum physics, and models with extra spatial dimensions.     

Strongly enhanced hole-phonon coupling in the metallic state of the dilute two-dimensional hole gas

We have studied the temperature dependent phonon emission rate P(T) of a strongly interacting (r(s) > or =22) dilute 2D GaAs hole system using a standard carrier heating technique. In the still poorly understood metallic state, we observe that P(T) changes from P(T) approximately T5 to P(T) approximately T7 above 100 mK, indicating a crossover from screened piezoelectric (PZ) coupling to screened deformation potential (DP) coupling for hole-phonon scattering. Quantitative comparison with theory shows that the long range PZ coupling between holes and phonons has the expected magnitude; however, in the metallic state, the short range DP coupling between holes and phonons is almost 20 times stronger than expected from theory. The density dependence of P(T) shows that it is easier to cool low-density 2D holes in GaAs than higher density 2D hole systems.     

Interaction potential and thermo-correction to the equation of state for thermally stable Schwarzschild anti-de Sitter black holes

The microscopic structure of black holes remains a challenging subject. In this paper, based on the well-accepted fact that black holes can be mapped to thermodynamic systems, we make a preliminary exploration of the microscopic structure of the thermodynamically stable Schwarzschild anti-de-Sitter(SAdS) black hole. In accordance with the number density and thermodynamic scalar curvature, we give the interaction potential among the molecules of thermodynamically stable SAdS black holes and analyze its effectiveness. Moreover, we derive the thermo-correction to the equation of state for such black holes that arises from interactions among black-hole molecules using virial coefficients.     

Thermodynamics of Gauss–Bonnet black holes revisited

We investigate the Gauss–Bonnet black hole in five dimensional anti-de Sitter spacetimes (GBAdS). We analyze all thermodynamic quantities of the GBAdS, which is characterized by the Gauss–Bonnet coupling c and mass M, comparing with those of the Born–Infeld-AdS (BIAdS), Reissner–Norstr?m-AdS black holes (RNAdS), Schwarzschild-AdS (SAdS), and BTZ black holes. For c<0 we cannot obtain the black hole with positively definite thermodynamic quantities of mass, temperature, and entropy, because the entropy does not satisfy the area law. On the other hand, for c>0, we find the BIAdS-like black hole, showing that the coupling c plays the role of a pseudo-charge. Importantly, we could not obtain the SAdS in the limit of c→0, which means that the GBAdS is basically different from the SAdS. In addition, we clarify the connections between thermodynamic and dynamical stability. Finally, we also conjecture that if a black hole is big and thus globally stable, its quasi-normal modes may take on analytic expressions.