Renormalization Method Research Articles

Configuration entropy and confinement-deconfinement transition in higher-dimensional hard wall model

We consider a higher-dimensional hard wall model with an infrared (IR) cut-off in asymptotically AdS space and investigate its thermodynamics via the holographic renormalization method. We find a relation between the confinement temperature and the IR cut-off for any dimension. It is also shown that the entropy of p-branes with the number of coincident branes (the number of the gauge group) N jumps from leading order in O(N0) at the confining low temperature phase to O(Np+12) at the deconfining high temperature phase like D3-branes (p=3) case. On the other hand, we calculate the configuration entropy (CE) of various magnitudes of an inverse temperature at an given IR cut-off scale. It is shown that as the inverse temperature grows up, the CE above the critical temperature decreases and AdS black hole (BH) is stable while it below the critical temperature is constant and thermal AdS (ThAdS) is stable. In particular, we also find that the CE below the critical temperature becomes constant and its magnitude increases as a dimension of AdS space increases.

Systematic coarse-graining of epoxy resins with machine learning-informed energy renormalization

A persistent challenge in molecular modeling of thermoset polymers is capturing the effects of chemical composition and degree of crosslinking (DC) on dynamical and mechanical properties with high computational efficiency. We established a coarse-graining (CG) approach combining the energy renormalization method with Gaussian process surrogate models of molecular dynamics simulations. This allows a machine-learning informed functional calibration of DC-dependent CG force field parameters. Taking versatile epoxy resins consisting of Bisphenol A diglycidyl ether combined with curing agent of either 4,4-Diaminodicyclohexylmethane or polyoxypropylene diamines, we demonstrated excellent agreement between all-atom and CG predictions for density, Debye-Waller factor, Young’s modulus, and yield stress at any DC. We further introduced a surrogate model-enabled simplification of the functional forms of 14 non-bonded calibration parameters by quantifying the uncertainty of a candidate set of calibration functions. The framework established provides an efficient methodology for chemistry-specific, large-scale investigations of the dynamics and mechanics of epoxy resins.

Singular paths spaces and applications

Motivated by recent applications in rough volatility and regularity structures, notably the notion of singular modeled distribution, we study paths, rough paths and related objects with a quantified singularity at zero. In a pure path setting, this allows us to leverage on existing SLE Besov estimates to see that SLE traces takes values in a singular Hölder space, which quantifies a well-known boundary effect in the regime We then consider the integration theory against singular rough paths and some extensions thereof. This gives a method to reconcile, from a regularity structure point of view, different singular kernels used to construct (fractional) rough volatility models and an effective reduction to the stationary case which is crucial to apply general renormalization methods.

Renormalized holographic entanglement entropy for quadratic curvature gravity

We derive a covariant expression for the renormalized holographic entanglement entropy for conformal field theories (CFTs) dual to quadratic curvature gravity in arbitrary dimensions. This expression is written as the sum of the bare entanglement entropy functional obtained using standard conical defect techniques, and a counterterm defined at the boundary of the extremal surface of the functional. The latter corresponds to the cod-2 self-replicating part of the extrinsic counterterms when evaluated on the replica orbifold. This renormalization method isolates the universal terms of the holographic entanglement entropy functional. We use it to compute the standard $C$-function candidate for CFTs of arbitrary dimension, and the type-B anomaly coefficient $c$ for four-dimensional CFTs.

Применение методов спектральной и пространственной обработки к изображениям, полученным с помощью гидролокатора.

The paper proposes the use of the method of renormalization with limitation (MRL) for suppressing the speckle noise of images obtained using sonar. The method is tested on real images obtained by the interferometric side-view sonar. The principal possibility of a significant reduction in the speckle noise level is found due to the fact that the MRL renormalizes the spectrum of the sonar image to the universal reference spectrum (URS) model, which is a model of the spectrum of a "good" quality grayscale image. To increase the overall sharpness of the image, after applying the MRL, it is proposed to use spatial brightness transformations. The study allows us to conclude that the application of MRL to sonar images can significantly reduce speckle noise.

Renormalization and non-renormalization of scalar EFTs at higher orders

We renormalize massless scalar effective field theories (EFTs) to higher loop orders and higher orders in the EFT expansion. To facilitate EFT calculations with the R* renormalization method, we construct suitable operator bases using Hilbert series and related ideas in commutative algebra and conformal representation theory, including their novel application to off-shell correlation functions. We obtain new results ranging from full one loop at mass dimension twelve to five loops at mass dimension six. We explore the structure of the anomalous dimension matrix with an emphasis on its zeros, and investigate the effects of conformal and orthonormal operators. For the real scalar, the zeros can be explained by a ‘non-renormalization’ rule recently derived by Bern et al. For the complex scalar we find two new selection rules for mixing n- and (n− 2)-field operators, with n the maximal number of fields at a fixed mass dimension. The first appears only when the (n− 2)-field operator is conformal primary, and is valid at one loop. The second appears in more generic bases, and is valid at three loops. Finally, we comment on how the Hilbert series we construct may be used to provide a systematic enumeration of a class of evanescent operators that appear at a particular mass dimension in the scalar EFT.

Asymptotic analysis to domain walls between traveling waves modeled by real coupled Ginzburg-Landau equations

We apply an asymptotic analysis to one-dimensional domain wall between traveling waves. The governing partial differential equations are firstly transformed into a real coupled nonlinear ordinary equations system, and then the homotopy renormalization (HTR) method is used to solve it. These solutions are analytical and under some special conditions of the parameters, are exact. In particular, the phenomena revealed by the solutions, namely the sinks and sources, are discussed and it can be seen easily that the source is narrower than the sink, which agrees well with the experimental results. Moreover, compared with the numerical results graphically, we can guarantee that the obtained simple analytical solutions are accurate in the whole domain.

Quantum Parity Conservation in Planar Quantum Electrodynamics

Quantum parity conservation is verified at all orders in perturbation theory for a massless parity-even $U(1)\times U(1)$ planar quantum electrodynamics (QED$_3$) model. The presence of two massless fermions requires the Lowenstein-Zimmermann (LZ) subtraction scheme, in the framework of the Bogoliubov-Parasiuk-Hepp-Zimmermann-Lowenstein (BPHZL) renormalization method, in order to subtract the infrared divergences induced by the ultraviolet subtractions at 1- and 2-loops, however thanks to the superrenormalizability of the model the ultraviolet divergences are bounded up to 2-loops. Finally, it is proved that the BPHZL renormalization method preserves parity for the model taken into consideration, contrary to what happens to the ordinary massless parity-even $U(1)$ QED$_3$.

Multifractal Power Network Based on the Two Scales Cantor Set Topology

This paper proposes a transition from monofractal to multifractal topology to study the dynamic behavior of modern power networks. For this purpose, a multifractal power network is proposed based on the two scales Cantor set topology. The dynamic properties of the proposed network are investigated using the renormalization method, Continuous Wavelet Transform (CWT) and Multifractal Detrended Fluctuation Analysis (MFDFA). Our findings prove that the scale-invariant behavior of the proposed network is governed by two scales factors. The results of CWT indicate that the frequency responses corresponding to the two scales Cantor network exhibit a self-similar behavior. As for the MFDFA results, they revealed that a set of fractal dimensions is required to reproduce the dynamics of the proposed multifractal network.

Local rigidity for periodic generalised interval exchange transformations

In this article we study local rigidity properties of generalised interval exchange maps using renormalisation methods. We study the dynamics of the renormalisation operator $$\mathcal {R}$$ acting on the space of $$\mathcal {C}^{3}$$ -generalised interval exchange transformations at fixed points (which are standard periodic type IETs). We show that $$\mathcal {R}$$ is hyperbolic and that the number of unstable direction is exactly that predicted by the ergodic theory of IETs and the work of Forni and Marmi–Moussa–Yoccoz. As a consequence we prove that the local $$\mathcal {C}^1$$ -conjugacy class of a periodic interval exchange transformation, with d intervals, whose associated surface has genus g and whose Lyapounoff exponents are all non zero is a codimension $$g-1 +d-1$$ $$\mathcal {C}^1$$ -submanifold of the space of $$\mathcal {C}^{3}$$ -generalised interval exchange transformations. This solves a conjecture analogous to that of Marmi–Moussa–Yoccoz, stated for almost all IETs, in the special case of self-similar IETs.

On the ultraviolet finiteness of parity-preserving [formula omitted] massive QED[formula omitted

The parity-preserving UA(1)×Ua(1) massive QED3 is ultraviolet finiteness – exhibits vanishing β-functions, associated to the gauge coupling constants (electric and pseudochiral charges) and the Chern–Simons mass parameter, and all the anomalous dimensions of the fields – as well as is parity and gauge anomaly free at all orders in perturbation theory. The proof is independent of any regularization scheme and it is based on the quantum action principle in combination with general theorems of perturbative quantum field theory by adopting the Becchi–Rouet–Stora (BRS) algebraic renormalization method in the framework of Bogoliubov–Parasiuk–Hepp–Zimmermann (BPHZ) subtraction scheme.

Note on the pragmatic mode-sum regularization method: Translational-splitting in a cosmological background

The point-splitting renormalization method offers a prescription to calculate finite expectation values of quadratic operators constructed from quantum fields in a general curved spacetime. It has been recently shown by Levi and Ori that when the background metric possesses an isometry, like stationary or spherically symmetric black holes, the method can be upgraded into a pragmatic procedure of renormalization that produces efficient numerical calculations. In this note we show that when the background enjoys three-dimensional spatial symmetries, like homogeneous expanding universes, the above pragmatic regularization technique reduces to the well established adiabatic regularization method.

Application of standardised growth curves in quartz OSL dating of lacustrine sediments on the Mongolian Plateau

The standardised growth curves (SGCs) can compensate for the drawbacks of the single-aliquot regenerative-dose (SAR) procedure, such as low utilization of time and instrument in the optically stimulated luminescence (OSL) dating. In this study, 12 sedimentary samples of 6 lakes from the Mongolian Plateau were selected and 90–125 μm coarse-grains quartz was extracted to establish SGCs. The results show that the OSL signals are mainly composed of a fast component, which is applicable for SAR procedure. The difference in the shape of the dose response curves (DRCs) limits the application of the standardised growth curve (SGC) for which the growth curves among the aliquots corrected by the test dose are scattered. The equivalent dose (De) estimated by the global standardised growth curve (gSGC) by the regenerative normalization (re-normalization) method is more consistent with the full SAR procedure, so the gSGC method is suitable for determining the De values on the regional scale of Mongolian Plateau. For different lacustrine sedimentary samples, the De values estimated by full SAR procedure and gSGC method are consistent for the doses of up to ~280 Gy. The discrepancy of growth curves may result from the sensibility changes of inter-cycle in SAR measurement and the recuperation, also we do not exclude the influence of feldspar inclusions.

Signatures of optical conductivity in double-layer graphene excitonic condensate

Signatures of the excitonic condensation state and its optical properties in biased double-layer graphene (DLG) are discussed. In the framework of the generic bilayer graphene model involving a Coulomb interaction between electrons in one layer and holes in the opposite layer, we have derived a set of self-consistent equations determining the excitonic condensate order parameter by use of the projector-based renormalization method. Based on the Kubo theory of the linear optical response, a formula of the optical conductivity is also obtained with full contributions of the quantum fluctuations. Our results elucidate a possibility of the excitonic condensation formation in the biased system once the dielectric thickness is sufficiently small. As a function of the external electric field, the excitonic condensation dome suppresses rapidly as enlarging the dielectric thickness. The impression of the dielectric thickness and external electric field affecting the excitonic condensate is also addressed in the signature of the optical conductivity. Our findings are worthwhile to understand the formation and stability of the excitonic condensation states not only in DLG but also in other double-layer systems or in semimetal-semiconductor transition materials.

Capturing the Electron-Phonon Renormalization in Molecules from First-Principles.

Since the interaction between electrons and atomic nuclei can affect the electronic structure, in recent years, first-principles-based electron-phonon renormalization methods have been applied in the condensed matter physics community to account for the influence of the electron-phonon coupling in solid systems. However, little is yet known about the behavior and trends of the electron-phonon renormalization in the molecules. In this work, the method for the electron-phonon renormalization in molecules has been derived, using which, we exhaustively investigate the zero-point renormalization in 32 molecules with three different density functions. We find that the renormalization of the highest occupied molecular orbital-lowest unoccupied molecular orbital gap due to electron-vibration coupling does not relate to the atomic masses but quite relates to the electronic structure properties of the molecules.

Применение метода перенормировки с ограничением к изображениям дистанционного зондирования, полученным с помощью радиолокаторов с синтезированной апертурой.

This article proposes an application of the method of renormalization with limitation (MRL) to suppress speckle noise in SAR images. This is because the method of renormalization with limitation, by its definition, renormalizes the SAR image spectrum to a universal reference spectrum (URS) model, which is a "good" quality grayscale spectrum model. To increase the overall sharpness of the image, consistently with the MRL, it is proposed to apply the classical Laplacian. This study allows us to conclude that the application of MRL to SAR images can significantly reduce speckle noise.

Boundary CFT and Tensor Network Approach to Surface Critical Phenomena of the Tricritical 3-State Potts model

One-dimensional edges of classical systems in two dimension sometimes show surprisingly rich phase transitions and critical phenomena, particularly when the bulk is at criticality. As such a model, we study the surface critical behavior of the 3-state dilute Potts model whose bulk is tuned at the tricritical point. To investigate it more precisely than in the previous works [Y. Deng and H. W. J. Bl\"ote, Phys. Rev. E 70, 035107(R) (2004); Phys. Rev. E 71, 026109 (2005)], we analyze it from the viewpoint of the boundary conformal field theory (BCFT). The complete classification of the conformal boundary conditions for the minimal BCFTs discussed in [R. E. Behrend et al., Nucl. Phys. B 579, 707 (2000)] allows us to collect the twelve boundary fixed points in the tricritical 3-state Potts BCFT. Employing the tensor network renormalization method, we numerically study the surface phase diagram of the tricritical 3-state Potts model in detail, and reveal that the eleven boundary fixed points among the twelve can be realized on the lattice by controlling the external field and coupling strength at the boundary. The last unfound fixed point would be out of the physically sound region in the parameter space, similarly to the `new' boundary condition in the 3-state Potts BCFT.

A thermophysically balanced multiscale coarse-grained potential for glass-forming polymers with the energy renormalization method

Coarse-grained molecular dynamics simulations are a widely accepted methodology in the field of studying the viscoelasticity of elastomers. In this paper, a thermophysically balanced multiscale coarse-grained potential for glass-forming polymers is presented with the energy renormalization (ER) method by redefining temperature transferable correlation effects between rescaling factors for energy parameter and length-scale parameter. The correlation effects have not been investigated in the literature, to the best knowledge of authors. The coarse-grained potential was demonstrated for the polyisoprene model generated from the anionic polymerization. The ER enables temperature transferability by adopting renormalization parameters as function of the temperature. Considering the correlation effects, a multi objective-optimization algorithm was adopted to find proper solution sets of and matching mean square displacement (MSD) and density to the all-atom model simultaneously. Meanwhile, shear stress was matched to find first, then, density was fitted in the low-temperature regime. To verify the coarse-grained potential in the middle-temperature regime, MSD was compared to those from the all-atom model, and it was successfully matched.

Coarse-Grained Quantum Theory of Organic Photovoltaic Devices.

Understanding the exciton dissociation process in organic solar cells is a fundamental issue for the design of high-performance photovoltaic devices. In this article, a parameterized quantum theory based on a coarse-grained tight-binding model plus non-local electron-hole interactions is presented, while the diffusion and recombination of excitons are studied in a square lattice of excitonic states, where a real-space renormalization method on effective chains has been used. The Hamiltonian parameters are determined by fitting the measured quantum efficiency spectra and the theoretical short-circuit currents without adjustable parameters show a good agreement with the experimental ones obtained from several polymer:fullerene and polymer:polymer heterojunctions. Moreover, the present study reveals the degree of polymerization and the true driving force at donor-acceptor interface in each analyzed organic photovoltaic device.

Effect of streaming velocity, magnetic field, and higher-order correction on the nature of ion acoustic solitons in the Venusian ionosphere

Propagation properties of weakly nonlinear ion acoustic waves are investigated in a plasma at the Venusian ionosphere. The plasma model consists of two positive cold ions (oxygen O + and hydrogen H +), as well as isothermal electrons. The basic set of fluid equations is reduced to Zakharov-Kuznetsov (ZK) equation and linear inhomogeneous ZK-type equation (LIZKT) equation. The renormalization method is adopted to obtain solitary solutions of both equations. The effects of plasma parameters and higher-order correction on the nature of the solitary waves are investigated. It is found that the wave phase velocity is supersonic, which is in agreement with the observations. Furthermore, the higher-order correction enlarges the soliton amplitude, which is suitable for describing the solitary waves when the wave amplitude grows.