Explore the vast range of titles available.

Symmetry transformation methods are widely used in fluid flow problems. One such method is renormalization group analysis. Renormalization group methods are used to develop a macroscopic turbulence model for non-Newtonian fluids (Oldroyd-B type). This model accounts for the large-distance and large-time behavior of velocity correlations generated by the momentum equation for a randomly stirred, incompressible flow and does not account for empirical constants. The aim of this mathematical study was to develop a k-ε RNG turbulence model for non-Newtonian fluids (Oldroyd-B type). For the first time, using the renormalization procedure, the transport equations for the large-scale modes and expressions for effective transport coefficients are obtained. Expressions for the renormalized turbulent viscosity are also derived. This model explains the phenomenon of the abrupt growth of the irregularity of velocity at low values of the Reynolds number.

The stochastic partial differential equation proposed nearly three decades ago by Kardar, Parisi and Zhang (KPZ) continues to inspire, intrigue and confound its many admirers. Here, we (i) pay debts to heroic predecessors, (ii) highlight additional, experimentally relevant aspects of the recently solved 1+1 KPZ problem, (iii) use an expanding substrates formalism to gain access to the 3d radial KPZ equation and, lastly, (iv) examining extremal paths on disordered hierarchical lattices, set our gaze upon the fate of d=∞ KPZ. Clearly, there remains ample unexplored territory within the realm of KPZ and, for the hearty, much work to be done, especially in higher dimensions, where numerical and renormalization group methods are providing a deeper understanding of this iconic equation.

The appearance of certain spectral features in one-dimensional (1D) cuprate materials has been attributed to a strong, extended attractive coupling between electrons. Here, using time-dependent density matrix renormalization group methods on a Hubbard-extended Holstein model, we show that extended electron-phonon ( e–ph ) coupling presents an obvious choice to produce such an attractive interaction that reproduces the observed spectral features and doping dependence seen in angle-resolved photoemission experiments: diminished 3 k F spectral weight, prominent spectral intensity of a holon-folding branch, and the correct holon band width. While extended e–ph coupling does not qualitatively alter the ground state of the 1D system compared to the Hubbard model, it quantitatively enhances the long-range superconducting correlations and suppresses spin correlations. Such an extended e–ph interaction may be an important missing ingredient in describing the physics of the structurally similar two-dimensional high-temperature superconducting layered cuprates, which may tip the balance between intertwined orders in favor of uniform d -wave superconductivity. Recent photo-emission experiments reported a strong nearest-neighbour attraction in a 1D cuprate, possibly originating from long-range electron-phonon coupling. By using state-of-the-art numerical methods, the authors show that a Hubbard model with extended electron-phonon terms reproduces experimental features.

A bstract The off-diagonal parton-scattering channels g + γ * and q + ϕ * in deep-inelastic scattering are power-suppressed near threshold x → 1. We address the next-to-leading power (NLP) resummation of large double logarithms of 1 − x to all orders in the strong coupling, which are present even in the off-diagonal DGLAP splitting kernels. The appearance of divergent convolutions prevents the application of factorization methods known from leading power resummation. Employing d -dimensional consistency relations from requiring 1 /ϵ pole cancellations in dimensional regularization between momentum regions, we show that the resummation of the off-diagonal parton-scattering channels at the leading logarithmic order can be bootstrapped from the recently conjectured exponentiation of NLP soft-quark Sudakov logarithms. In particular, we derive a result for the DGLAP kernel in terms of the series of Bernoulli numbers found previously by Vogt directly from algebraic all-order expressions. We identify the off-diagonal DGLAP splitting functions and soft-quark Sudakov logarithms as inherent two-scale quantities in the large- x limit. We use a refactorization of these scales and renormalization group methods inspired by soft-collinear effective theory to derive the conjectured soft-quark Sudakov exponentiation formula.

A bstract We calculate 1-loop corrections to the Schwinger-Keldysh propagators of Standard-Model-like fields of spin-0, 1/2, and 1, with all renormalizable interactions during inflation. We pay special attention to the late-time divergences of loop corrections, and show that the divergences can be resummed into finite results in the late-time limit using dynamical renormalization group method. This is our first step toward studying both the Standard Model and new physics in the primordial universe.

All-electron electronic structure methods based on the linear combination of atomic orbitals method with Gaussian basis set discretization offer a well established, compact representation that forms much of the foundation of modern correlated quantum chemistry calculations-on both classical and quantum computers. Despite their ability to describe essential physics with relatively few basis functions, these representations can suffer from a quartic growth of the number of integrals. Recent results have shown that, for some quantum and classical algorithms, moving to representations with diagonal two-body operators can result in dramatically lower asymptotic costs, even if the number of functions required increases significantly. We introduce a way to interpolate between the two regimes in a systematic and controllable manner, such that the number of functions is minimized while maintaining a block-diagonal structure of the two-body operator and desirable properties of an original, primitive basis. Techniques are analyzed for leveraging the structure of this new representation on quantum computers. Empirical results for hydrogen chains suggest a scaling improvement from O(N4.5) in molecular orbital representations to O(N2.6) in our representation for quantum evolution in a fault-tolerant setting, and exhibit a constant factor crossover at 15 to 20 atoms. Moreover, we test these methods using modern density matrix renormalization group methods classically, and achieve excellent accuracy with respect to the complete basis set limit with a speedup of 1-2 orders of magnitude with respect to using the primitive or Gaussian basis sets alone. These results suggest our representation provides significant cost reductions while maintaining accuracy relative to molecular orbital or strictly diagonal approaches for modest-sized systems in both classical and quantum computation for correlated systems.

We study a class of close-packed dimer models on the square lattice, in the presence of small but extensive perturbations that make them non-determinantal. Examples include the 6-vertex model close to the free-fermion point, and the dimer model with plaquette interaction previously analyzed in previous works. By tuning the edge weights, we can impose a non-zero average tilt for the height function, so that the considered models are in general not symmetric under discrete rotations and reflections. In the determinantal case, height fluctuations in the massless (or ‘liquid’) phase scale to a Gaussian log-correlated field and their amplitude is a universal constant, independent of the tilt. When the perturbation strength λ is sufficiently small we prove, by fermionic constructive Renormalization Group methods, that log-correlations survive, with amplitude A that, generically, depends non-trivially and non-universally on λ and on the tilt. On the other hand, A satisfies a universal scaling relation (‘Haldane’ or ‘Kadanoff’ relation), saying that it equals the anomalous exponent of the dimer–dimer correlation.

The renormalization group is a pillar of the theory of scaling, scale invariance and universality in physics. Recently, this tool has been adapted to complex networks with pairwise interactions through a scheme based on diffusion dynamics. However, as the importance of polyadic interactions in complex systems becomes more evident, there is a pressing need to extend the renormalization group methods to higher-order networks. Here we fill this gap and propose a Laplacian renormalization group scheme for arbitrary higher-order networks. At the heart of our approach is the introduction of cross-order Laplacians, which generalize existing higher-order Laplacians by allowing the description of diffusion processes that can happen on hyperedges of any order via hyperedges of any other order. This approach enables us to probe higher-order structures, define scale invariance at various orders and propose a coarse-graining scheme. We validate our approach on controlled synthetic higher-order systems and then use it to detect the presence of order-specific scale-invariant profiles of real-world complex systems from multiple domains. The renormalization group is a powerful tool to study the universal properties of physical systems. A diffusion-based renormalization scheme now enables the study of scale invariance and universality in higher-order complex networks.

A bstract We apply the joint threshold and transverse momentum dependent (TMD) factorization theorem to introduce new threshold-TMD distribution functions, including threshold-TMD parton distribution functions (PDFs) and fragmentation functions (FFs). We apply Soft-Collinear Effective Theory and renormalization group methods to carry out QCD evolution for both threshold-TMD PDFs and FFs. We show the universality of threshold-TMD functions among three standard processes, i.e. the Drell-Yan production in pp collisions, semi-inclusive deep-inelastic scattering and back-to-back two hadron production in e + e − collisions. In the end, we present the numerical predictions for different threshold-TMD functions and also transverse momentum distributions at pp , ep , and e + e − collisions.

A bstract We use renormalization group methods to study composite operators existing at a boundary of an interacting conformal field theory. In particular we relate the data on boundary operators to short-distance (near-boundary) divergences of bulk two-point functions. We further argue that in the presence of running couplings at the boundary the anomalous dimensions of certain composite operators can be computed from the relevant beta functions and remark on the implications for the boundary (pseudo) stress-energy tensor. We apply the formalism to a scalar field theory in d = 3 − 𝜖 dimensions with a quartic coupling at the boundary whose beta function we determine to the first non-trivial order. We study the operators in this theory and compute their conformal data using 𝜖 − expansion at the Wilson-Fisher fixed point of the boundary renormalization group flow. We find that the model possesses a non-zero boundary stress-energy tensor and displacement operator both with vanishing anomalous dimensions. The boundary stress tensor decouples at the fixed point in accordance with Cardy’s condition for conformal invariance. We end the main part of the paper by discussing the possible physical significance of this fixed point for various values of 𝜖.