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.     

Universal canonical entropy for gravitating systems

The thermodynamics of general relativistic systems with boundary, obeying a Hamiltonian constraint in the bulk, is determined solely by the boundary quantum dynamics, and hence by the area spectrum. Assuming, for large area of the boundary, (a) an area spectrum as determined by non-perturbative canonical quantum general relativity (NCQGR), (b) an energy spectrum that bears a power law relation to the area spectrum, (c) an area law for the leading order microcanonical entropy, leading thermal fluctuation corrections to the canonical entropy are shown to be logarithmic in area with a universal coefficient. Since the microcanonical entropy also has universal logarithmic corrections to the area law (from quantum space-time fluctuations, as found earlier) the canonical entropy then has a universal form including logarithmic corrections to the area law. This form is shown to be independent of the index appearing in assumption (b). The index, however, is crucial in ascertaining the domain of validity of our approach based on thermal equilibrium.     

Finite-size corrections for logarithmic representations in critical dense polymers

We study (analytic) finite-size corrections in the dense polymer model on the strip by perturbing the critical Hamiltonian with irrelevant operators belonging to the tower of the identity. We generalize the perturbation expansion to include Jordan cells, and examine whether the finite-size corrections are sensitive to the properties of indecomposable representations appearing in the conformal spectrum, in particular their indecomposability parameters. We find, at first order, that the corrections do not depend on these parameters nor even on the presence of Jordan cells. Though the corrections themselves are not universal, the ratios are universal and correctly reproduced by the conformal perturbative approach, to first order.     

Area Spectrum of Black Holes with Quantum Corrections via Periodicity

Using the Heisenberg uncertainty principle, Bekenstein once claimed that the horizon area of a black hole is quantized with uniform spacing $8\pi l_{p}^{2}$ . This spacing is shown to be corrected with inverse area terms from the perspective of periodicity, which indicates that the area spectrum in this case is no longer evenly spaced. Concretely we study the corrected area spectrum by equaling the motion period of an outgoing wave to the period of gravitational system in Kruskal coordinate with respect to the Euclidean time with consideration of quantum corrections to the semiclassical action. To check our result, we also study the corrected area spectrum in the framework of Generalized Uncertainty Principle. We find the area spectrum produced from the perspective of periodicity takes the same form as the one obtained by the Generalized Uncertainty Principle. As examples, area spectrum with quantum corrections of a Schwarzschild black hole and a Kerr black hole are studied. Our result shows that the formula for area spectrum with quantum corrections is universal though it is not independent of the black hole parameters. In addition, we also discuss the motion period of fermions and find that the area spectrum of a black hole is independent of particle statistics when the black hole is perturbed by an outgoing fermion.     

Quantum gravitational contributions to the cosmic microwave background anisotropy spectrum

We derive the primordial power spectrum of density fluctuations in the framework of quantum cosmology. For this purpose we perform a Born-Oppenheimer approximation to the Wheeler-DeWitt equation for an inflationary universe with a scalar field. In this way, we first recover the scale-invariant power spectrum that is found as an approximation in the simplest inflationary models. We then obtain quantum gravitational corrections to this spectrum and discuss whether they lead to measurable signatures in the cosmic microwave background anisotropy spectrum. The nonobservation so far of such corrections translates into an upper bound on the energy scale of inflation.     

Towards the bounce inflationary gravitational wave

In the bounce inflation scenario, the inflation is singularity-free, while the advantages of inflation are preserved. We analytically calculate the power spectrum of its primordial gravitational waves (GWs), and show a universal result including the physics of the bounce phase. The spectrum acquires a cutoff at large scale, while the oscillation around the cutoff scale is quite drastic, which is determined by the details of bounce. Our work highlights that the primordial GWs at large scale may encode the physics of the bounce ever happened at about \({\sim }60\) efolds before inflation.     

Universal spectral statistics in quantum graphs

We prove that the spectrum of an individual chaotic quantum graph shows universal spectral correlations, as predicted by random-matrix theory. The stability of these correlations with regard to nonuniversal corrections is analyzed in terms of the linear operator governing the classical dynamics on the graph.     

The density perturbation power spectrum to second-order corrections in the slow-roll expansion

We set up a formalism that can be used to calculate the power spectrum of the curvature perturbations produced during inflation up to arbitrary order in the slow-roll expansion, and explicitly calculate the power spectrum and spectral index up to second-order corrections.     

Exact asymptotic behavior of correlation functions for disordered spin-1/2 XXZ chains

We consider an XXZ spin-1/2 chain in the presence of several types of disorder that do not break the XY symmetry of the system. We calculate the complete asymptotic form of the spin-correlation functions at zero temperature at the transition between liquid and disordered phase that occurs for a special value of anisotropy in the limit of small disorder. Apart from a universal power law decay of correlations, we find additional logarithmic corrections due to marginally irrelevant operator of disorder.     

Non-markovian resonance fluorescence

The power spectrum of a strong field resonance fluorescence is derived from non-markovian Bloch equations. It is shown that the Mollow spectrum is modified by non-markovian corrections. The main feature of the non-markovian behavior is a nonsymmetric power spectrum even at exact resonance. The magnitude of the non-markovian asymmetry depends on the power of the driving light.     

Anomalies in universal intensity scaling in ultrarelativistic laser-plasma interactions

Laser light incident on targets at intensities such that the electron dynamics is ultrarelativistic gives rise to a harmonic power spectrum extending to high orders and characterized by a relatively slow decay with the harmonic number m that follows a power law dependence, m(-p). Relativistic similarity theory predicts a universal value for p=8/3 up to some cutoff m=m*. The results presented in this Letter suggest that under conditions in which plasma effects contribute to the emission spectrum, the extent of this contribution may invalidate the concept of universal decay. We report a decay with the harmonic number in the ultrarelativistic range characterized by an index 5/3 < or approximately p < or approximately 7/3, significantly weaker than that predicted by the similarity model.     

New approach to quantum corrections in synchrotron radiation

Owing to a recent controversy over the importance of the second-order quantum corrections to the power spectrum of synchrotron radiation, we here reexamine this question by using a proper time method to calculate the forward Compton scattering of a real photon on a spin-0 charged particle in external magnetic fields. This approach, aside from being the simplest method found so far, has the feature that it resembles the classical procedure so that the quantum corrections can be identified at every stage of the computation. The option of being able to perform first the angular integration before doing the proper time integral enables us to simplify the calculation and to obtain the quantum corrections unambiguously. We find that the criterion for the quantum corrections to be important is the same as that found more than two decades ago.     

On the modification of the Efimov spectrum in a finite cubic box

Three particles with large scattering length display a universal spectrum of three-body bound states called “Efimov trimers”. We calculate the modification of the Efimov trimers of three identical bosons in a finite cubic box and compute the dependence of their energies on the box size using effective field theory. Previous calculations for positive scattering length that were perturbative in the finite-volume energy shift are extended to arbitrarily large shifts and negative scattering lengths. The renormalization of the effective field theory in the finite volume is explicitly verified. We investigate the effects of partial-wave mixing and study the behavior of shallow trimers near the dimer energy. Moreover, we provide numerical evidence for universal scaling of the finite-volume corrections.     

Photoionization of the Bound Systems at High Energies

We consider photoionization of a system bound by the central potential V(r). We demonstrate that the high energy nonrelativistic asymptotics of the photoionization cross section can be obtained without solving the wave equation. The asymptotics can be expressed in terms of the Fourier transform of the potential by employing the Lippmann–Schwinger equation. We find the asymptotics for the screened Coulomb field. We demonstrate that the leading corrections to this asymptotics are described by the universal factor. The high energy nonrelativistic asymptotics is found to be determined by the analytic properties of the potential V(r). We show that the energy dependence of the asymptotics of photoionization cross sections of fullerenes is to large extent model-dependent. We demonstrate that if the fullerene field V(r) is approximated by the function with singularities in the complex plane, the power drop of the asymptotics is reached at the energies which are so high that the cross section becomes unobservably small. The preasymptotic behavior with a faster decrease of the cross sections becomes important in these cases.     

Lattice cut-off effects and their reduction in studies of QCD thermodynamics at non-zero temperature and chemical potential

We clarify the relation between the improvement of dispersion relations in the fermion sector of lattice regularized QCD and the improvement of bulk thermodynamic observables. We show that in the infinite temperature limit the cut-off dependence in dispersion relations can be eliminated up to (aⁿ) corrections, if the quark propagator is chosen to be rotationally invariant up to this order. In bulk thermodynamic observables this eliminates cut-off effects up to the same order at vanishing as well as non-vanishing chemical potential. We furthermore show that in the infinite temperature, ideal gas limit the dependence of finite cut-off corrections on the chemical potential is given by Bernoulli polynomials which are universal as they do not depend on a particular discretization scheme. We explicitly calculate leading and next-to-leading order cut-off corrections for some staggered and Wilson fermion type actions and compare these with exact evaluations of the free fermion partition functions. This also includes the chirally invariant overlap and domain wall fermion formulations. PACS  11.15.Ha; 11.10.Wx; 12.38.Gc; 12.38.Mh     

Fluctuations in a lévy flight gas

We consider the density fluctuations of an ideal Brownian gas of particles performing Lévy flìghts characterized by the indexf. We find that the fluctuations scale as N(t) t^H, where the Hurst exponentH locks onto the universal value 1/4 for Lévy flights with a finite root-mean-square range (f>2). For Lévy flights with a finite mean range but infinite root-mean-square range (1相似文献   

On the difficulty of computing higher-twist corrections

We discuss the evaluation of power corrections to hard scattering and decay processes for which an operator product expansion is applicable. The Wilson coefficient of the leading-twist operator is the difference of two perturbative series, each of which has a renirmalon ambiguity of the same order as the power corrections themselves, but which cancel in the difference. We stress the necessity of calculating this coefficient function to sufficiently high orders in perturbation theory so as to make the uncertainty of the same order of or smaller than the relevant power corrections. We investigate in some simple examples whether this can be achieved. Our conclusion is that in most of the theoretical calculations which include power corrections, the uncertainties are at least comparable to the power corrections themselves, and that it will be a very difficult task to improve the situation.     

Higher-curvature corrections to holographic entanglement with momentum dissipation

We study the effects of Gauss–Bonnet corrections on some nonlocal probes (entanglement entropy, n-partite information and Wilson loop) in the holographic model with momentum relaxation. Higher-curvature terms as well as scalar fields make in fact nontrivial corrections to the coefficient of the universal term in entanglement entropy. We use holographic methods to study such corrections. Moreover, holographic calculation indicates that mutual and tripartite information undergo a transition beyond which they identically change their values. We find that the behavior of the transition curves depends on the sign of the Gauss–Bonnet coupling \(\lambda \). The transition for \(\lambda >0\) takes place in larger separation of subsystems than that of \(\lambda <0\). Finally, we examine the behavior of modified part of the force between external point-like objects as a function of Gauss–Bonnet coupling and its sign.     

Inclusive photoproduction of <Emphasis Type="Italic">D</Emphasis><Superscript>*±</Superscript>-mesons at next-to-leading order in the general-mass variable-flavor-number scheme

We discuss the inclusive production of D ^*±-mesons in γ p collisions at DESY HERA, based on a calculation at next-to-leading order in the general-mass variable-flavor-number scheme. In this approach, subtraction is applied in such a way that large logarithmic corrections are resummed in universal parton distribution and fragmentation functions and finite-mass terms are taken into account. We present detailed numerical results for a comparison with data obtained at HERA and discuss various sources of theoretical uncertainties.     

Coulomb corrections to bremsstrahlung in the electric field of a heavy atom at high energies

We consider the differential and partially integrated cross sections for bremsstrahlung from high-energy electrons in an atomic field, with this field taken into account exactly. We use the semiclassical electron Green function and wavefunctions in an external electric field. It is shown that the Coulomb corrections to the differential cross section are very susceptible to screening. Nevertheless, the Coulomb corrections to the cross section summed over the final-electron states are independent of screening in the leading approximation in the small parameter 1/mr _scr (r _scr is the screening radius and m is the electron mass, ? = c = 1). We also consider bremsstrahlung from a finite-size electron beam on a heavy nucleus. The Coulomb corrections to the differential probability are also very susceptible to the beam shape, while the corrections to the probability integrated over momentum transfer are independent of it, apart from the trivial factor, which is the electron-beam density at zero impact parameter. For the Coulomb corrections to the bremsstrahlung spectrum, the next-to-leading terms with respect to the parameters mε (ε is the electron energy) and 1/mr _scr are obtained.