Logarithmic Corrections Research Articles

High energy resummed predictions for the production of a Higgs boson with at least one jet

We present all-order predictions for Higgs boson production plus at least one jet which are accurate to leading logarithm in hat{s}/{left|{p}_{perp}right|}^2 . Our calculation includes full top and bottom quark mass dependence at all orders in the logarithmic part, and to highest available order in the tree-level matching. The calculation is implemented in the framework of High Energy Jets (HEJ). This is the first cross section calculated with log( hat{s} ) resummation and matched to fixed order for a process requiring just one jet, and our results also extend the region of resummation for processes with two jets or more. This is possible because the resummation is performed explicitly in phase space. We compare the results of our new calculation to LHC data and to next-to-leading order predictions and find a numerically significant impact of the logarithmic corrections in the shape of key distributions, which remains after normalisation of the cross section.

Scale-dependent theory of the disordered electron liquid

We review the scaling theory of disordered itinerant electrons with e−e interactions. We first show how to adjust the microscopic Fermi-liquid theory to the presence of disorder. Then we describe the non-linear sigma model (NLSM) with interactions (Finkel’stein’s model). This model is closely connected to the Fermi liquid, but is more generally applicable, since it can also be viewed as a minimal effective functional describing disordered interacting electrons. Our discussion emphasizes the general structure of the theory, and the connection of the scaling parameters to conservation laws. We then move on to discuss the metal–insulator transition (MIT) in the disordered electron liquid in two and three dimensions. Generally speaking, this MIT is a non-trivial example of a quantum phase transition. The NLSM approach allows to identify the dynamical exponent connecting the spatial and energy scales, which is central for the description of the kinetic and thermodynamic behavior of the system in the critical region of the MIT in three dimensions. In two dimensions, the system can be discussed in terms of a flow in the disorder-interaction phase plane, which is controlled by a fixed point. We demonstrate that the two-parameter RG-equations accurately describe electrons in Si-MOSFETs including the observed non-monotonic behavior of the resistance and its strong drop at low temperatures. The theory can also be applied to systems with an attractive interaction in the Cooper channel, where it describes the suppression of superconductivity in disordered amorphous films. We extend our discussion to heat transport in the two-dimensional electron liquid. Similar to the electric conductivity, the thermal conductivity also acquires logarithmic corrections induced by the interplay of the electron interaction and disorder. The resulting thermal conductivity can be calculated in the NLSM formalism after introducing so-called gravitational potentials. It may be concluded that the combined effect of disorder and e−e interactions determines all aspects of the physics of itinerant electrons in the presence of disorder.

Thermodynamics and logarithmic corrections of symmergent black holes

In this paper, we study quantum gravity effect on the symmergent black hole which is derived from quadratic-curvature gravity. To do so, we use the Klein–Gordon equation which is modified by generalized uncertainty principle (GUP). After solving the field equations, we examine the symmergent black hole’s tunneling and Hawking temperature. We explore the graphs of the temperature through the outer horizon to check the GUP influenced conditions of symmergent black hole stability. We also explain how symmergent black holes behave physically when influenced by quantum gravity. The impacts of thermal fluctuations on the thermodynamics of a symmergent black holes spacetime are examined. We first evaluate the model under consideration’s thermodynamic properties, such as its Hawking temperature, angular velocity, entropy, and electric potential. We evaluate the logarithmic correction terms for entropy around the equilibrium state in order to examine the impacts of thermal fluctuations. In the presence of these correction terms, we also examine the viability of the first law of thermodynamics. Finally, we evaluate the system’s stability using the Hessian matrix and heat capacity. It is determined that a stable model is generated by logarithmic corrections arising from thermal fluctuations.

Logarithmic corrections to O(a) and O(a^2) effects in lattice QCD with Wilson or Ginsparg–Wilson quarks

We derive the asymptotic lattice spacing dependence a^n[2b_0bar{g}^2(1/a)]^{hat{Gamma }_i} relevant for spectral quantities of lattice QCD, when using Wilson, textrm{O}(a) improved Wilson or Ginsparg–Wilson quarks. We give some examples for the spectra encountered for hat{Gamma }_i including the partially quenched case, mixed actions and using two different discretisations for dynamical quarks. This also includes maximally twisted mass QCD relying on automatic textrm{O}(a) improvement. At textrm{O}(a^2), all cases considered have min _ihat{Gamma }_igtrsim -0.3 if N_{textrm{f}}le 4, which ensures that the leading order lattice artifacts are not severely logarithmically enhanced in contrast to the O(3) non-linear sigma model (Balog et al. in Nucl Phys B 824:563–615, 2010; Balog et al. in Phys Lett B 676:188–192, 2009). However, we find a very dense spectrum of these leading powers, which may result in major pile-ups and cancellations. We present in detail the computational strategy employed to obtain the 1-loop anomalous dimensions already used in Husung et al. (Phys Lett B 829:137069, 2022).

Droplet finite-size scaling of the contact process on scale-free networks revisited

We present an alternative finite-size scaling (FSS) of the contact process on scale-free networks compatible with mean-field scaling and test it with extensive Monte Carlo simulations. In our FSS theory, the dependence on the system size enters the external field, which represents spontaneous contamination in the context of an epidemic model. In addition, dependence on the finite size in the scale-free networks also enters the network cutoff. We show that our theory reproduces the results of other mean-field theories on finite lattices already reported in the literature. To simulate the dynamics, we impose quasi-stationary states by reactivation. We insert spontaneously infected individuals, equivalent to a droplet perturbation to the system scaling as [Formula: see text]. The system presents an absorbing phase transition where the critical behavior obeys the mean-field exponents, as we show theoretically and by simulations. However, the quasi-stationary state gives finite-size logarithmic corrections, predicted by our FSS theory, and reproduces equivalent results in the literature in the thermodynamic limit. We also report the critical threshold estimates of basic reproduction number [Formula: see text] of the model as a linear function of the network connectivity inverse [Formula: see text], and the extrapolation of the critical threshold function for [Formula: see text] yields the basic reproduction number [Formula: see text] of the complete graph, as expected. Decreasing the network connectivity increases the critical [Formula: see text] for this model.

Scaling in Rayleigh–Bénard convection

We consider the Nusselt–Rayleigh number problem of Rayleigh–Bénard convection and make the hypothesis that the velocity and thermal boundary layer widths, $\delta _u$ and $\delta _T$ , in the absence of a strong mean flow are controlled by the dissipation scales of the turbulence outside the boundary layers and, therefore, are of the order of the Kolmogorov and Batchelor scales, respectively. Under this assumption, we derive $Nu \sim Ra^{1/3}$ in the high $Ra$ limit, independent of the Prandtl number, $\delta _T/L \sim Ra^{-1/3}$ and $\delta _u/L \sim Ra^{-1/3} Pr^{1/2}$ , where $L$ is the height of the convection cell. The scaling relations are valid as long as the Prandtl number is not too far from unity. For $Pr \sim 1$ , we make a more general ansatz, $\delta _u \sim \nu ^{\alpha }$ , where $\nu$ is the kinematic viscosity and assume that the dissipation scales as $\sim u^3/L$ , where $u$ is a characteristic turbulent velocity. Under these assumptions we show that $Nu \sim Ra^{\alpha /(3-\alpha )}$ , implying that $Nu \sim Ra^{1/5}$ if $\delta _u$ were scaling as in a Blasius boundary layer and $Nu \sim Ra^{1/2}$ (with some logarithmic correction) if it were scaling as in a standard turbulent shear boundary layer. It is argued that the boundary layers will retain the intermediate scaling $\alpha = 3/4$ in the limit of high $Ra$ .

Noncommutativity and logarithmic correction to the black hole entropy

We study the noncommutative corrections to the entropy of the Reissner-Nordström black hole using a κ-deformed scalar probe within the brick-wall framework. The noncommutativity is encoded in an Abelian Drinfeld twist constructed from the Killing vector fields of the Reissner-Nordström black hole. We show that the noncommutative effects naturally lead to a logarithmic correction to the Bekenstein-Hawking entropy even at the lowest order of the WKB approximation. In contrast, such logarithmic corrections in the commutative setup appear only after the quantum effects are included through higher order WKB corrections or through higher loop effects. Our analysis thus provides further evidence towards the hypothesis that the noncommutative framework is capable of encoding at least some quantum effects in curved spacetime, although additional contributions will appear when the NC effects are fully incorporated in a gravity theory.

Noncommutative Correction to the Entropy of Charged BTZ Black Hole

Noncommutative geometry is an established potential candidate for including quantum phenomena in gravitation. We outlined the formalism of Hopf algebras and its connection to the algebra of infinitesimal diffeomorphisms. Using a Drinfeld twist, we deformed spacetime symmetries, algebra of vector fields and differential forms, leading to a formulation of noncommutative Einstein equations. We studied a concrete example of charged BTZ spacetime and deformations steaming from the so-called angular twist. The entropy of the noncommutative charged BTZ black hole was obtained using the brick-wall method. We used a charged scalar field as a probe and obtained its spectrum and density of states via WKB approximation. We provide the method used to calculate corrections to the Bekenstein–Hawking entropy in higher orders in WKB, but we present the final result in the lowest WKB order. The result is that, even in the lowest order in WKB, the entropy, in general, contains higher powers in ℏ, and it has logarithmic corrections and polynomials of logarithms of the black hole area.

Real quantum amplitude estimation

We introduce the Real Quantum Amplitude Estimation (RQAE) algorithm, an extension of Quantum Amplitude Estimation (QAE) which is sensitive to the sign of the amplitude. RQAE is an iterative algorithm which offers explicit control over the amplification policy through an adjustable parameter. We provide a rigorous analysis of the RQAE performance and prove that it achieves a quadratic speedup, modulo logarithmic corrections, with respect to unamplified sampling. Besides, we corroborate the theoretical analysis with a set of numerical experiments.

Entanglement negativity in a fermionic chain with dissipative defects: exact results

We investigate the dynamics of the fermionic logarithmic negativity in a free-fermion chain with a localized loss, which acts as a dissipative impurity. The chain is initially prepared in a generic Fermi sea. In the standard hydrodynamic limit of large subsystems and long times, with their ratio fixed, the negativity between two subsystems is described by a simple formula, which depends only on the effective absorption coefficient of the impurity. The negativity grows linearly at short times, then saturating to a volume-law scaling. Physically, this reflects the continuous production with time of entangling pairs of excitations at the impurity site. Interestingly, the negativity is not the same as the Rényi mutual information with Rényi index , in contrast with the case of unitary dynamics. This reflects the interplay between dissipative and unitary processes. The negativity content of the entangling pairs is obtained in terms of an effective two-state mixed density matrix for the subsystems. Criticality in the initial Fermi sea is reflected in the presence of logarithmic corrections. The prefactor of the logarithmic scaling depends on the loss rate, suggesting a nontrivial interplay between dissipation and criticality.

Tunneling and thermodynamics evolution of the magnetised Ernst-like black hole

We investigate the tunneling phenomenon of particles through the horizon of a magnetized Ernst-like black hole. We employ the modified Lagrangian equation with the extended uncertainty principle for this black hole. We determine a tunneling rate and the related Hawking temperature for this black hole by using the WKB approach in the field equation. In addition, we examine the graph behavior of the Hawking temperature in relation to the black hole event horizon. We explore the stability analysis of this black hole by taking into account the impact of quantum gravity on Hawking temperatures. The temperature for a magnetised Ernst-like black hole rises as the correction parameter is decreased. Moreover, we analyze the thermodynamics quantities such as Hawking temperature, heat capacity and Bekenstein entropy by using the different approach. We obtain the corrected entropy to study the impact of logarithmic corrections on the different thermodynamic quantities. It is shown that these correction terms makes the system stable under thermal fluctuations.

Domain wall melting across a defect

We study the melting of a domain wall in a free-fermionic chain with a localised impurity. We find that the defect enhances quantum correlations in such a way that even the smallest scatterer leads to a linear growth of the entanglement entropy contrasting the logarithmic behaviour in the clean system. Exploiting the hydrodynamic approach and the quasiparticle picture, we provide exact predictions for the evolution of the entanglement entropy for arbitrary bipartitions. In particular, the steady production of pairs at the defect gives rise to non-local correlations among distant points. We also characterise the subleading logarithmic corrections, highlighting some universal features.

Non-analyticity in holographic complexity near critical points

The region near a critical point is studied using holographic models of second-order phase transitions. In a previous paper, we argued that the quantum circuit complexity of the vacuum (C 0) is the largest at the critical point. When deforming away from the critical point by a term the complexity has a piece non-analytic in τ, namely . Here, as usual, and ξ is the correlation length and there are possible logarithmic corrections to this expression. That was derived using numerical results for the Bose–Hubbard model and general scaling considerations. In this paper, we show that the same is valid in the case of holographic complexity providing evidence that the results are universal, and at the same time providing evidence for holographic computations of complexity.

Modified Metrics of Acoustic Black Holes: A Review

In this brief review, we will address acoustic black holes arising from quantum field theory in the Lorentz-violating and non-commutative background. Thus, we consider canonical acoustic black holes with effective metrics for the purpose of investigating Hawking radiation and entropy. We show that due to the generalized uncertainty principle and the modified dispersion relation, the Hawking temperature is regularized, that is, free from the singularity when the horizon radius goes to zero. In addition, we also find logarithmic corrections in the leading order for entropy.

Watermelons on the half-plane

We study the watermelon probabilities in the uniform spanning forests on the two-dimensional semi-infinite square lattice near either the open or closed boundary to which the forests can or cannot be rooted, respectively. We derive universal power laws describing the asymptotic decay of these probabilities with the distance between the reference points growing to infinity, as well as their non-universal constant prefactors. The obtained exponents match with the previous predictions made for the related dense polymer models using the Coulomb gas technique and conformal field theory, as well as with the lattice calculations made by other authors in different settings. We also discuss the logarithmic corrections some authors argued to appear in the watermelon correlation functions on the infinite lattice. We show that the full account for diverging terms of the lattice Green function, which ensures the correct probability normalization, provides the pure power law decay in the case of semi-infinite lattice with the closed boundary studied here, as well as in the case of infinite lattice discussed elsewhere. The solution is based on the all-minors generalization of the Kirchhoff matrix tree theorem, the image method and the developed asymptotic expansion of the Kirchhoff determinants.

Finite-size scaling of the majority-voter model above the upper critical dimension

The majority-voter model is studied by Monte Carlo simulations on hypercubic lattices of dimension d = 2 to 7 with periodic boundary conditions. The critical exponents associated to the finite-size scaling of the magnetic susceptibility are shown to be compatible with those of the Ising model. At dimension d = 4, the numerical data are compatible with the presence of multiplicative logarithmic corrections. For d ≥ 5, the estimates of the exponents are close to the prediction d/2 when taking into account the dangerous irrelevant variable at the Gaussian fixed point. Moreover, the universal values of the Binder cumulant are also compatible with those of the Ising model. This indicates that the upper critical dimension of the majority-voter model is not dc = 6 as claimed in the literature, but dc = 4 like the equilibrium Ising model.

The grazing collisions limit from the linearized Boltzmann equation to the Landau equation for short-range potentials

The Landau equation and the Boltzmann equation are connected through the limit of grazing collisions. This has been proved rigorously for certain families of Boltzmann operators concentrating on grazing collisions. In this contribution, we study the collision kernels associated to the two-particle scattering via a finite range potential $ \Phi(x) $ in three dimensions. We then consider the limit of weak interaction given by $ \Phi_ \epsilon(x) = \epsilon \Phi(x) $. Here $ \epsilon\rightarrow 0 $ is the grazing parameter, and the rate of collisions is rescaled to obtain a non-trivial limit. The grazing collisions limit is of particular interest for potentials with a singularity of order $ s\geq 0 $ at the origin, i.e. $ \phi(x) \sim |x|^{-s} $ as $ |x|\rightarrow 0 $. For $ s\in [0,1] $, we prove the convergence to the Landau equation with diffusion coefficient given by the Born approximation, as predicted in the works of Landau and Balescu. On the other hand, for potentials with $ s>1 $ we obtain the non-cutoff Boltzmann equation in the limit. The Coulomb singularity $ s = 1 $ appears as a threshold value with a logarithmic correction to the diffusive timescale, the so-called Coulomb logarithm.

4D Einstein–Gauss–Bonnet Gravity Coupled to Modified Logarithmic Nonlinear Electrodynamics

Spherically symmetric solution in 4D Einstein–Gauss–Bonnet gravity coupled to modified logarithmic nonlinear electrodynamics (ModLogNED) is found. This solution at infinity possesses the charged black hole Reissner–Nordström behavior. We study the black hole thermodynamics, entropy, shadow, energy emission rate and quasinormal modes. It was shown that black holes can possess the phase transitions and at some range of event horizon radii black holes are stable. The entropy has the logarithmic correction to the area law. The shadow radii were calculated for variety of parameters. We found that there is a peak of the black hole energy emission rate. The real and imaginary parts of the quasinormal modes frequencies were calculated. The energy conditions of ModLogNED are investigated.

Number theory, borderline dimension and extensive entropy in distributions of ranked data.

The consideration of an existing stochastic approach for the reproduction of ranked data pointed at a formal equivalence between its key mathematical expression and that for trajectories at the tangent bifurcation. This fact led to a nonlinear dynamical approach for rank distributions that shows similarities with universality classes in critical phenomena. The renormalization group (RG) fixed-point map f*(x) for a tangent bifurcation of arbitrary nonlinearity z > 1 has proved to be a powerful tool into which the formalism can be couched. The source distribution P(N) of the stochastic approach can be linked to f*(x) while the size-rank N(k) and frequency-rank F(k') distributions are obtained, respectively, from the map trajectories xt and the sums of its positions. We provide now an extension to Number Theory as we obtain from the trajectories xt of f*(x) the numbers, or asymptotic approximations of them, for the Factorial, Natural, Prime and Fibonacci sets. A measure of the advance of these numbers towards infinity is given by sums of positions that represent their reciprocals. We specify rank distribution universality classes, already associated with real data, to these number sets. We find that the convergence of the series of number reciprocals occurs first at nonlinearity z = 2, that which corresponds to the classical Zipf law, and link this transition edge to the action of the attractor when it first reduces the fractal dimension of trajectory positions to zero. Furthermore, the search of logarithmic corrections common to borderline dimensions provides a link to the Prime numbers set. Finally, we find corroborating evidence of these logarithmic corrections from the analysis of large data sets for ranked earthquake magnitudes. The formalism links all types of ranked distributions to a generalized extensive entropy.

Scaling of the disorder operator at deconfined quantum criticality

We study scaling behavior of the disorder parameter, defined as the expectation value of a symmetry transformation applied to a finite region, at the deconfined quantum critical point in (2+1)d in the J-Q_3J−Q3 model via large-scale quantum Monte Carlo simulations. We show that the disorder parameter for U(1) spin rotation symmetry exhibits perimeter scaling with a logarithmic correction associated with sharp corners of the region, as generally expected for a conformally-invariant critical point. However, for large rotation angle the universal coefficient of the logarithmic corner correction becomes negative, which is not allowed in any unitary conformal field theory. We also extract the current central charge from the small rotation angle scaling, whose value is much smaller than that of the free theory.