The gravitational asymptotic safety program envisions the high-energy completion of gravity through an interacting renormalization group fixed point, the Reuter fixed point. The predictive power of the construction is encoded in the spectrum of the stability matrix which is obtained from linearizing the renormalization group flow around this fixed point. A key result of the asymptotic safety program is that parts of this spectrum exhibit an almost-Gaussian scaling behavior, entailing that operators which are classically highly UV irrelevant do not induce new free parameters. In this article, we track down the origin of this property by contrasting the structure of the stability matrix computed from the Wetterich equation and the composite-operator equation within the realm of f(R) truncations. We show that the almost-Gaussian scaling is not linked to the classical part of the beta functions. It is a quantum-induced almost-Gaussian scaling originating from the quantum corrections in the flow equation. It relies on a subtle interplay among the analytic structure of the theory’s two-point function and the way the Wetterich equation integrates out fluctuation modes. As a byproduct we determine the parts of the eigenmode spectrum that is robust with respect to changing the regularization procedure. Published by the American Physical Society 2024

We discuss peculiarities of the Schwinger-DeWitt technique for quantum effective action, associated with the origin of dimensionally regularized double-pole divergences of the one-loop functional determinant for massive Proca model in a curved spacetime. These divergences have the form of the total-derivative term generated by integration by parts in the functional trace of the heat kernel for the Proca vector field operator. Because of the nonminimal structure of second-order derivatives in this operator, its vector field heat kernel has a nontrivial form, involving the convolution of the scalar d’Alembertian Green’s function with its heat kernel. Moreover, its asymptotic expansion is very different from the universal predictions of Gilkey-Seeley heat kernel theory because the Proca operator violates one of the basic assumptions of this theory—the nondegeneracy of the principal symbol of an elliptic operator. This modification of the asymptotic expansion explains the origin of double-pole total-derivative terms. Another hypostasis of such terms is in the problem of multiplicative determinant anomalies—lack of factorization of the functional determinant of a product of differential operators into the product of their individual determinants. We demonstrate that this anomaly should have the form of total-derivative terms and check this statement by calculating divergent parts of functional determinants for products of minimal and nonminimal second-order differential operators in curved spacetime. Published by the American Physical Society 2024

Direct numerical simulation of three-dimensional acoustic turbulence has been performed for both weak and strong regimes. Within the weak turbulence, we demonstrate the existence of the Zakharov-Sagdeev spectrum ∝k^{-3/2} not only for weak dispersion but in the nondispersion (ND) case as well. Such spectra in the k space are accompanied by jets in the form of narrow cones. These distributions are realized due to small nonlinearity compared with both dispersion or diffraction. Increasing pumping in the ND case due to dominant nonlinear effects leads to the formation of shocks. As a result, the acoustic turbulence turns into an ensemble of random shocks with the Kadomtsev-Petviashvili spectrum.

We suggest a new technique of the asymptotic heat kernel expansion for minimal higher derivative operators of a generic 2Mth order, F(∇)=(−□)M+⋯, in the background field formalism of gauge theories and quantum gravity. This technique represents the conversion of the recently suggested Fourier integral method of generalized exponential functions [A. O. Barvinsky and W. Wachowski, Heat kernel expansion for higher order minimal and nonminimal operators, ] into the commutator algebra of special differential operators, which allows one to express expansion coefficients for F(∇) in terms of the Schwinger-DeWitt coefficients of a minimal second-order operator H(∇). This procedure is based on special functorial properties of the formalism including the Mellin-Barnes representation of the complex operator power HM(∇) and naturally leads to the origin of generalized exponential functions without directly appealing to the Fourier integral method. The algorithm is essentially more straightforward than the Fourier method and consists of three steps ready for a computer codification by symbolic manipulation programs. They begin with the decomposition of the operator into a power of some minimal second-order operator H(∇) and its lower derivative perturbation part W(∇), F(∇)=HM(∇)+W(∇), followed by considering their multiple nested commutators. The second step is the construction of special local differential operators—the perturbation theory in powers of the lower derivative part W(∇). The final step is the so-called procedure of their “Syngification,” consisting of a special modification of the covariant derivative monomials in these operators by the Synge world function σ(x,x′) with their subsequent action on the Hadamard-Minakshisundaram-DeWitt coefficients of H(∇). Published by the American Physical Society 2024

We analyzed spin polarization dynamics in a two-dimensional system of spin 1/2 charged particles with spin-orbit interaction in perpendicular magnetic field in the presence of external noise. It was shown that spin polarization reveals quantum oscillations, collapses, and revivals. The hierarchy of time scales corresponding to quantum oscillations, collapses, and revivals was identified and analyzed. It was demonstrated that variation of external magnetic field and noise intensity results in the significant changing of spin fluctuations spectra, which modifies from the triplet structure to the well resolved fine structure.

We calculate the cross sections of associated J/ψ+ψ′ and J/ψ+J/ψ production in pp collisions at s=13 TeV in the forward kinematic region. The high-energy factorization (kT-factorization) framework supplemented with the Catani-Ciafaloni-Fiorani-Marchesini evolution of gluon densities in a proton is applied. We demonstrate that the latest data on J/ψ+J/ψ production and first experimental data on J/ψ+ψ′ events taken very recently by the LHCb Collaboration can be described well by the color singlet terms and contributions from double parton scattering (DPS) with the standard choice for σeff parameter. The relative production rate σ(J/ψ+ψ′)/σ(J/ψ+J/ψ) is found to be sensitive to the DPS terms as well as to feeddown contributions. Published by the American Physical Society 2024

We consider an arbitrary deformation of the Gaussian matrix model parametrized by Miwa variables za. One can look at it as a mixture of the Gaussian and logarithmic (Selberg) potentials, which are both superintegrable. The mixture is not, still one can find an explicit expression for an arbitrary Schur average as a linear transform of a polynomial made from the values of skew Schur functions at the Gaussian locus pk=δk,2. This linear operation includes multiplication with an exponential eza2/2 and a kind of Borel transform of the resulting product, which we call multiple and enhanced. The existence of such remarkable formulas appears intimately related to the theory of auxiliary K-polynomials, which appeared in superintegrable correlators at the Gaussian point (strict superintegrability). We also consider in great detail the generating function of correlators ⟨(TrX)k⟩ in this model, and discuss its integrable determinant representation. At last, we describe deformation of all results to the Gaussian β-ensemble. Published by the American Physical Society 2024