Research on Hawking Radiation as Tunneling from Schwarzshild-anti-de Sitter Black Hole

After taking into account energy conservation and the particle’s self-gravitation interaction, Hawking radiation of the massive particle as tunneling from Schwarzshild-anti-de Sitter black hole is studied by using Parikh-Wilczek’s semi-classical quantum tunneling approach. Meanwhile, Hawking radiation as tunneling from the black hole is reexamined by developing Angheben–Nadalini–Vanzo–Zerbini (ANVZ) covariant method to cover energy conservation and the particle’s self-gravitation interaction. Both the results perfectly generalize those obtained by Parikh and Wilczek, and show that the tunneling rate is related to the change of Bekenstein-Hawking entropy, and the factual emission spectrum is not exactly thermal, but satisfies the underlying unitary theory. PACS: 04.70-s, 9760. Lf.     

核的巨单极激发的求和规则和核物质的不可压缩性系数

采用近来在研究核基态中极为成功的相对论模型研究有限核的同位旋巨单极共振 ,从而给出核物质的不可压缩性系数 .讨论了建立在相对论平均场基态上的相对论无规位相近似的自洽处理 .自洽要求基态和巨共振激发态的研究从同一个有效拉氏量出发 .与相对论平均场的无海近似自洽 ,相对论无规位相近似不仅要包含正能态的粒子 -空穴激发 ,还必须考虑 Fermi海核子态和 Dirac海核子态激发的贡献 .用约束的相对论平均场方法得到核的巨单极共振的能量逆权重的求和规则 ,验证 Dirac海核子态的贡献 .比较理论计算和实验测量的巨单极共振的能量得到核物质的不可压缩性系数为 2 5 0 - 2 70 MeV. The isoscalar giant monopole resonance for finite nuclei and the nuclear matter incompressibility are studied in a consistent relativistic approach, which achieves a great success in describing the properties of nuclear ground states. The consistency in the relativistic random phase approximation (RRPA) built on the relativistic mean field (RMF) ground states are investigated. The RMF wave function of nucleus and the particle-hole residual interactions in RRPA are calculated from...     

Impact of the phonon coupling on the radiative neutron capture

Inclusion of the coupling of quasiparticle degrees of freedom with phonon degrees is a natural extention of the standard QRPA approach. The paper presents the quantitative impact of this phonon coupling on the dipole strength and radiative neutron capture for the stable ¹²⁴Sn and very exotic ¹⁵⁰Sn isotopes, as an illustration, using the self-consistent version of the Extended Theory of Finite Fermi Systems. It was found that the phonon contribution to the pygmy-dipole resonance and radiative neutron capture cross section is increased with the (N − Z) difference growth. The results show that the self-consistent nuclear structure calculations are important for unstable nuclei, where phenomenological approaches do not work.     

Radiative strength function and the pygmy dipole resonance in <Superscript>208</Superscript>Pb and <Superscript>70</Superscript>Ni

The pygmy-resonance parameters and the E1 strength function are derived for ²⁰⁸Pb using a fully self-consistent microscopic formalism recently developed for magic nuclei, which takes into account quasiparticle phonon interactions (or coupling to phonons) in addition to the random phase approximation. For the radiative strength function of ²⁰⁸Pb at energies above 5 MeV, the experimental data of the Oslo group are adequately described by our predictions, whereby the important role of coupling to phonons is confirmed. By comparing the measurements based on the (³He, ³He′γ) and (γ, γ′) reactions, we discuss the physical properties of the radiative strength function measured for ²⁰⁸Pb. For the neutron-rich ⁷⁰Ni nucleus, predictions for the radiative strength function and the pygmy resonance are obtained using a partially self-consistent approach, which invokes the Skyrme forces in deriving the mean field, effective nucleon–nucleon interaction, and phonon characteristics.     

Phonons in a magnon superfluid and symmetry-breaking field

Recent experiments [1,2] on the measurement of the spectrum of the Goldstone collective mode of a coherently precessing state in ³He-B are discussed using the presentation of the coherent-spin precession in terms of the Bose-Einstein condensation of magnons. The mass in the spectrum of the Goldstone boson—a phonon in the superfluid magnon liquid—is induced by the symmetry-breaking field, which is played by the RF magnetic field. The text was submitted by the author in English.     

Study of the Gamow-Teller resonance in 90Nb and 208Bi

An approach is proposed for studying the spreading properties of the Gamow-Teller resonance (GTR) in heavy nuclei including the coupling to 2p2h configurations and the ground-state correlations beyond RPA. The GTR is generated by a proton p-neutron h (πp-νh) phonon within the renormalized RPA. The second-order configuration mixing beyond RPA is realized by constructing two-phonon configurations, in which one of two intermediate phonon states is a πp-νh phonon. The numerical calculations are performed in the parent nuclei ⁹⁰Zr and ²⁰⁸Pb making use of M3Y nucleon-nucleon interaction and the single-particle wave functions obtained in the standard harmonic oscillator potential. The single-particle energies around the Fermi surface are substituted with the empirical values or those given by a Woods-Saxon potential. The results obtained provide a reasonable account for recent experimental findings on the GTR in these nuclei. The extension of the present approach to highly excited (hot) nuclei is also provided. The GTR is found to be stable against temperatures up to T = 6 MeV.     

Excitonic polaron in the molecular crystal model: Nonlocal dynamic coherent-potential approximation

A nonlocal dynamic coherent-potential approximation is formulated as a further development of the dynamic coherent-potential method. The nonlocal dynamic coherent-potential approximation is an efficient method of determining the one-exciton Green’s function in a model with the Hamiltonian in the strong-coupling approximation, where a spectrum of optical phonons is assumed, and the exciton-phonon interaction operator is linear or quadratic in the phonon operators. A system of recursion equations is derived, from which the coherent potential is found as a function of the energy E and the wave vector k. An analytical expression is derived for the one-exciton Green’s function in the case of narrow (in comparison with the phonon energy) exciton bands and exciton-phonon interaction linear in the phonon operators. For broader exciton bands and more complex exciton-phonon interaction the system of equations determining the coherent potential represents a recursion algorithm, which can be effectively implemented by numerical means. Fiz. Tverd. Tela (St. Petersburg) 39, 1560–1563 (September 1997)     

On the mechanisms of superfluidity in atomic nuclei

A system of equations is obtained for the Cooper gap in nuclei. The system takes two mechanisms of superfluidity into account in an approximation quadratic in the phonon-production amplitude: a Bardeen-Cooper-Schrieffer (BCS)-type mechanism and a quasiparticle-phonon mechanism. These equations are solved for ¹²⁰Sn in a realistic approximation. If the simple procedures proposed are used to determine the new particle-particle interaction and to estimate the average effect, then the contribution of the quasiparticle-phonon mechanism to the observed width of the pairing gap is 26% and the BCS-type contribution is 74%. This means that at least in semimagic nuclei pairing is of a mixed nature — it is due to the two indicated mechanisms, the first being mainly a surface mechanism and the second mainly a volume mechanism. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 10, 669–674 (25 May 1999)     

Collective states of odd nuclei in a model with quadrupole-octupole degrees of freedom

We apply the collective axial quadrupole—octupole Hamiltonian to describe the rotation—vibration motion of odd nuclei with Coriolis coupling between the even-even core and the unpaired nucleon.We consider that the core oscillates coherently with respect to the quadrupole and octupole axialdeformation variables. The coupling between the core and the unpaired nucleon provides a split paritydoublet structure of the spectrum. The formalism successfully reproduces the parity-doublet splitting in a wide range of odd-A nuclei. It provides model estimations for the third angular-momentum projection K on the intrinsic symmetry axis and the related intrinsic nuclear structure. The text was submitted by the authors in English.     

Phonon–particle coupling effects in the single-particle energies of semi-magic nuclei

A method is presented to evaluate the particle–phonon coupling (PC) corrections to the single-particle energies in semi-magic nuclei. In such nuclei, always there is a collective low-lying 2⁺ phonon, and a strong mixture of single-particle and particle–phonon states often occurs. As in magic nuclei the so-called g _L ² approximation, where g _L is the vertex of the L-phonon creation, can be used for finding the PC correction δΣ^PC(ε) to the initial mass operator Σ₀. In addition to the usual pole diagram, the phonon “tadpole” diagram is also taken into account. In semi-magic nuclei, the perturbation theory in δΣ^PC(ε) with respect to Σ₀ is often invalid for finding the PC-corrected single-particle energies. Instead, the Dyson equation with the mass operator Σ(ε) = Σ₀ + δΣ^PC(ε) is solved directly, without any use of the perturbation theory. Results for a chain of semi-magic Pb isotopes are presented.     

Is Hawking temperature modified by the quantum tunneling beyond semiclassical approximation

Hawking temperature of a static and spherically symmetric black hole beyond semiclassical approximation is studied. The calculations show us that different definition of the particle’s energy gives different Hawking temperature. However, we argue that the result obtained using the standard definition of the particle energy is reasonable because it keeps the validity of the first law of the thermodynamics, i.e., both the Hawking temperature and entropy are not modified by the quantum tunneling beyond semiclassical approximation. The result shows us that any hypothetical (^h/_2p){\hbar} corrections to the tunneling rate are to be interpreted not as quantum corrections to the Hawking temperature but as fluctuations about a thermal background.     

Properties of the absorption spectrum due to the Gamma;1+ → Γ4− transition

We present results for the absorption spectrum due to a localized Γ₁⁺ → Γ₄^? transition that take into account the properties of the linear electron- phonon (e-p) interactions transforming as Γ₁⁺, Γ₃⁺ and Γ₅⁺ in the excited electronic state, in the cases of strong and weak e-p interaction coupling. We show that in the strong e-p interaction coupling limit the asymmetric shape of the structured band is due to the commutation relations of the e-p interaction matrices. Moreover, in the weak coupling limit we present an expression for the spectrum line shape obtained by taking into account the time ordering of the e-p interaction matrices and the phonon propagators at all times. It is shown in the latter case that the densities of phonon states corresponding to the electronic excited state are different from those corresponding to the ground state, and the e-p coupling constants are redefined due to the Jahn-Teller interactions.     

O17和F17低能反宇称态的相干结构

应用壳模型方法计算了O¹⁷和F¹⁷的低能反宇称态。核子间剩余相互作用取为δ型核力。第一步在L-S耦合近似下求解方程。结果表明,低能态具有“配对”的相干结构。第二步用一种近似办法加进了自旋轨道耦合力,得到了可以和实验进行比较的能谱。计算了已有实验数据的跃迁几率。     

A numerical comparison of three different approaches to the weak or intermediate coupling model for 2 particle — 1 hole states

The secular equation of the usual shell-model approach to 2 particle (p) — 1 hole (h) states is transcribed in such a way that it can be viewed as the simultaneous coupling of a hole to a (pp) vibrationand a particle to a particle-hole vibration. The resulting diagonalisation problem is built up by the subsolutions of the (ph) and (pp) TDA, i.e. no matrix elements of the bare two-body interaction enter the equations. We discuss the mathematical properties of the new equations and compare them to the usually applied formulation of the weak or intermediate coupling model. Finally we give a numerical study for the low-lying states of negative parity of O¹⁷.     

On the microscopic theory of electronic contributions to lattice dynamics of anharmonic crystals

A formalism is set up to study the electronic contribution to the phonon dynamics in an arbitrary crystal, conducting or insulating, without assuming small ionic oscillations. Therefore, in contrast to a harmonic Born-Oppenheimer approximation, such an approach allows for renormalization effects due to phonon-phonon interaction over the complete temperature range of the solid phase. The “weak coupling” approximation between nuclei and electrons is shown to be sufficient in order to obtain the dynamical matrix microscopically in terms of the complete inverse dielectric function of the electrons.     

Logarithmic corrections to $${\mathcal{N} = 2}$$ black hole entropy: an infrared window into the microstates

Logarithmic corrections to the extremal black hole entropy can be computed purely in terms of the low energy data—the spectrum of massless fields and their interaction. The demand of reproducing these corrections provides a strong constraint on any microscopic theory of quantum gravity that attempts to explain the black hole entropy. Using quantum entropy function formalism we compute logarithmic corrections to the entropy of half BPS black holes in N=2{{\mathcal N}=2} supersymmetric string theories. Our results allow us to test various proposals for the measure in the OSV formula, and we find agreement with the measure proposed by Denef and Moore if we assume their result to be valid at weak topological string coupling. Our analysis also gives the logarithmic corrections to the entropy of extremal Reissner–Nordstrom black holes in ordinary Einstein–Maxwell theory.     

Self-consistent treatment of superconducting hole systems and anharmonic lattices in oxides

An extention of Hirsch's Hamiltonian describing the hole system is proposed by including a coupling to the anharmonic lattice and a modulation of the hopping interaction due to lattice displacements. The model is discussed within the variational Bogoliubov's approach, assuming a BCS-like trial Hamiltonian for the hole-like subsystem and a self-consistent phonon approximation for the lattice. The model allows in general to discuss an interplay between superconductivity and ferroelectricity. The results for the critical temperature and the isotope effect coefficient in the superconducting paraelectric phase in one dimension are presented. In particular, the strong influence of the phonon softening on the superconducting transition is widely discussed.