Spectra of Some Charmed Hadrons in a Non Relativistic Model

We implement a recent model proposed by Serrano–Liska (SL) (Alonso-Serrano and Liška, JHEP, 12:196, 2020) to study the ultra-compact star properties. The matter in the interior star is modeled by the quark model, deducted from QCD theory equipped with anisotropic pressure. Anisotropy is used to increase the compactness of the stars. We intend to see the signature of the “quantum gravity” effect through the SL model in ultra-compact stars. The SL model was motivated by quantum correction appearing in the black hole by adding a logarithmic term in gravity entropy used to derive the effective Einstein field equation. We expect this correction term in the SL model also affects ultra-compact star properties. The SL model with coupling constant {tilde{c}} in logarithmic term equipped with spherically symmetric metric yields correction terms mathscr {O}({tilde{c}}) that can be expressed by a function varXi (r). The varXi (r) function vanishes at the star’s exterior. We found that the mass-radius relation prediction by the SL model with anisotropic matter deviates from the one predicted by the standard Tolman–Oppenheimer–Volkoff (TOV) equation for {tilde{c}}ge 10^7 m^2. We also have a sufficiently deep enough effective potential to produce a quasi-normal mode. We obtain the echo frequency of 15.2 kHz using maximum anisotropic pressure contribution and {tilde{c}}= 10^7 m^2. Because the corresponding effective potential is almost indistinguishable from that of GR, this echo frequency value can be indistinguishable to one of GR, but not comparable to the result from GW170817 data analysis, i.e., 72 Hz. To circumvent this problem, we can decrease the value of echo frequency by increasing the magnitude of {tilde{c}} to orders of magnitude than {tilde{c}}= 10^7 m^2. On the other hand, too large a strength from the logarithmic correction term is not physically favored because we learn from the black hole case that the logarithmic term is expected to be smaller than that of the Bekenstein term. Therefore, more precise gravitation echo measurements are crucial to understand this issue.

The logarithmic correction terms in the repulsive Hubbard chain is investigated by using the Bethe Ansatz . The magnetic susceptibility χ of this model has a field dependent logarithmic correction term in small magnetic field at zero-temperature. This term causes ∂χ/∂ h ∣ h =0 =∞ . In arbitrary n and U the existence of the logarithmic correction term is shown for the susceptibility. We consider how this term depends on n and U . We also discuss the logarithmic correction term of the super-symmetric t-J model.

It is known that almost all approaches to quantum gravity produce a logarithmic correction term to the entropy of a black hole, but the exact coefficient of such a term varies between the different approach to quantum gravity. Such logarithmic terms can also occur due to thermal fluctuations in both analogous and real black holes so that we will analyze the effects of logarithmic corrections term with variable coefficient on properties of analogous black hole. As these properties can be experimentally tested, they can be used to obtain the correct coefficient for such terms for an analogous black hole. We will argue that as even the real black holes can be considered as thermodynamical objects in Jacobson formalism, so such analogous black holes can be used to obtain the correct coefficient for the real black holes, and this in turn can be used to select the correct approach to quantum gravity. In that case, we use an adaptive model of graphene, which is still far from real graphene, to investigate some thermodynamics quantities of BTZ black hole.

The classical monomer-dimer model in two-dimensional lattices has been shown to belong to the "#P-complete" class, which indicates the problem is computationally "intractable." We use exact computational method to investigate the number of ways to arrange dimers on mxn two-dimensional rectangular lattice strips with fixed dimer density rho . For any dimer density 0<rho<1 , we find a logarithmic correction term in the finite-size correction of the free energy per lattice site. The coefficient of the logarithmic correction term is exactly -12 . This logarithmic correction term is explained by the newly developed asymptotic theory of Pemantle and Wilson. The sequence of the free energy of lattice strips with cylinder boundary condition converges so fast that very accurate free energy f{2}(rho) for large lattices can be obtained. For example, for a half-filled lattice, f{2}(12)=0.633195588930 , while f{2}(14)=0.4413453753046 and f{2}(34)=0.64039026 . For rho<0.65 , f{2}(rho) is accurate at least to ten decimal digits. The function f{2}(rho) reaches the maximum value f{2}(rho{*})=0.662798972834 at rho{*}=0.6381231 , with 11 correct digits. This is also the monomer-dimer constant for two-dimensional rectangular lattices. The asymptotic expressions of free energy near close packing are investigated for finite and infinite lattice widths. For lattices with finite width, dependence on the parity of the lattice width is found. For infinite lattices, the data support the functional form obtained previously through series expansions.

We confront the predictions of S. Hod [Phys. Rev. D 60, 104053 (1999)] for the late-time decay rate of black hole perturbations with numerical data. Specifically, we ask two questions: First, are corrections to the Price tail dominated by logarithmic terms, as predicted by Hod? Second, if there were logarithmic correction terms, do they take the specific form predicted in Hod's paper? The answer to both questions is ``no.''

Using exact computations we study the classical hard-core monomer-dimer models on m x n plane lattice strips with free boundaries. For an arbitrary number v of monomers (or vacancies), we found a logarithmic correction term in the finite-size correction of the free energy per lattice site. The coefficient of the logarithmic correction term depends on the number of monomers present (v) and the parity of the width n of the lattice strip: the coefficient equals to v when n is odd, and v/2 when n is even. The results are generalizations of the previous results for a single monomer in an otherwise fully packed lattice of dimers. We also study the finite-size correction in the low dimer density limit, where the number of dimers d is fixed. In this case the coefficient of the logarithmic correction term equals to d, for both odd and even n.

Complete results were obtained by us in [Can. J. Phys. 71, 389 (1993)] for convergent series representations of both the real and the imaginary part of the QED effective action; these derivations were based on correct intermediate steps. In this comment, we argue that the physical significance of the "logarithmic correction term" found by Cho and Pak in [Phys. Rev. Lett. 86, 1947 (2001)] in comparison to the usual expression for the QED effective action remains to be demonstrated. Further information on related subjects can be found in Appendix A of hep-ph/0308223 and in hep-th/0210240.

Logarithmic corrections in Fisher–KPP type porous medium equations

The classical nucleation theory (CNT) is tested systematically by computer simulations of the two-dimensional (2D) and three-dimensional (3D) Ising models with a Glauber-type spin flip dynamics. While previous studies suggested potential problems with CNT, our numerical results show that the fundamental assumption of CNT is correct. In particular, the Becker-Döring theory accurately predicts the nucleation rate if the correct droplet free energy function is provided as input. This validates the coarse graining of the system into a one dimensional Markov chain with the largest droplet size as the reaction coordinate. Furthermore, in the 2D Ising model, the droplet free energy predicted by CNT matches numerical results very well, after a logarithmic correction term from Langer's field theory and a constant correction term are added. But significant discrepancies are found between the numerical results and existing theories on the magnitude of the logarithmic correction term in the 3D Ising model. Our analysis underscores the importance of correctly accounting for the temperature dependence of surface energy when comparing numerical results and nucleation theories.

We compute the entanglement entropy of minimally coupled scalar fields on subtracted geometry black hole backgrounds, focusing on the logarithmic corrections. We notice that matching between the entanglement entropy of original black holes and their subtracted counterparts is only at the order of the area term. The logarithmic correction term is not only different but also, in general, changes sign in the subtracted case. We apply Harrison transformations to the original black holes and find out the choice of the Harrison parameters for which the logarithmic corrections vanish.

After considering the generalized uncertainty principle, we discuss the quantum tunneling radiation of a five-dimensional Schwarzschild anti de Sitter black hole. The radiation spectrum and the correction value of the Bekenstein–Hawking entropy are derived. In a five-dimensional black hole the one order correction term in the Bekenstein–Hawking entropy correction term is proportional to the third power of the area, and the logarithmic correction term is a two-order small quantity. The correction term is related to the dimension constant introduced in the generalized uncertainty principle. Because the black hole entropy is not divergent, the lowest value of the five-dimensional Schwarzschild anti de Sitter black hole horizon radius is obtained. After considering the generalized uncertainty principle, the radiation spectrum is still consistent with normalization theory.

We analyze the ripening process where, in a dispersion of vesicles, amphiphile monomers diffuse between vesicles of different sizes, leading to a change in the size distribution. Since, typically, vesicles are not under tension, the driving force for the process comes from the curvature energy. With the conventional expansion of the curvature energy density, gc, to harmonic order we find that the free energy change on adding a monomer is independent of vesicle radius. The monomer exchange is then a purely random process. By introducing corrections to the harmonic curvature energy, either by expanding gc to fourth order in the curvatures, or by a term logarithmic in the vesicle size, one obtains a driving force for ripening. Depending on the correction, different scenarios are predicted. The fourth-order correction and a negative logarithmic correction term result in a ripening toward unimodal vesicle distribution around the mean vesicle size of the initial distribution. For a positive logarithmic correction term, on the other hand, the ripening by itself should result in the formation of many small vesicles and a few very big ones. The rate of the monomer redistribution is primarily determined by the magnitude of the thermodynamic driving force and by the monomer solubility. For vesicles formed by single chain surfactants we estimate that the size redistribution should occur at a measurable rate, providing an opportunity to experimentally study which correction to the leading curvature energy is most significant.

The behavior of coherent anomalies in Weiss-type and Bethe-type cluster approximations is studied. In the Weiss-type case, logarithmic corrections to the naive coherent-anomaly-method (CAM) scaling relation, which have been ignored in previous works, play an important role in the CAM analysis. A phenomenological theory of the Bethe-type approximation is proposed to show that a logarithmic correction term also exists in this approximation. The correction has, however, smaller influence on the CAM analysis in this case.

In this paper, we will analyze the thermodynamics of a small singly spinning Kerr-AdS black hole. As the black hole will be sufficient small, its temperature will be large and so we can not neglect the effects of thermal fluctuations. We will demonstrate that these thermal fluctuations correct the entropy of singly spinning Kerr-AdS black hole by a logarithmic correction term. We will analyze the implications of the logarithmic correction on other thermodynamic properties of this black hole, and analyze the stability of such a black hole. We will observe that this form of correction becomes important when the size of the black hole is sufficient small. We will also analyze the effect of these thermal fluctuations on the critical phenomena for such a black hole.

We consider a massive black hole in four dimensional AdS space and study the effect of thermal fluctuations on the thermodynamics of the black hole. We consider thermal fluctuations as logarithmic correction terms in the entropy. We analyse the effect of logarithmic correction on thermodynamics potentials like Helmholtz and Gibbs which are found decreasing functions. We study critical points and stability and find that presence of logarithmic correction is necessary to have stable phase and critical point.