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An exact renormalization group equation is derived for the free energy of matrix models. The renormalization group equation turns out to be nonlinear for matrix models, as opposed to linear for vector models. An algorithm for determining…
By following the conventional similarity renormalization group (SRG) expansion of the Dirac equation developed in [J.-Y. Guo, Phys. Rev. C \textbf{85}, 021302 (2012)], we work out the analytic expression of the ${1}/{M^4}$ order and verify…
The renormalization group method is applied to the study of discrete dynamical systems. As a particular example, the Henon map is considered as applied to describe the transverse betatron oscillations in a cyclic accelerator or storage ring…
A renormalization group method with the Lie symmetry is presented for the singular perturbation problems. Asymptotic solutions are obtained as group-invariant solutions under approximate Lie group admitted by perturbed differential…
We analyze the renormalization of wave functionals and energy eigenvalues in field theory. A discussion of the structure of the renormalization group equation for a general Hamiltonian system is also given.
Numerical approaches are an important tool to study strongly correlated quantum systems. However, their fragility with respect to rounding errors is not well studied and numerically verified enclosures of the results are not available. In…
Inverse Vandermonde matrix calculation is a long-standing problem to solve nonsingular linear system $Vc=b$ where the rows of a square matrix $V$ are constructed by progression of the power polynomials. It has many applications in…
A new method, called the method of self-similar approximants, and its recent developments are described. The method is based on the ideas of renormalization group theory and optimal control theory. It allows for the effective extrapolation…
Using topological methods, we study the structure of the set of forced oscillations of a class of parametric, implicit ordinary differential equations with a generalized $\Phi$-Laplacian type term. We work in the Carath\'eodory setting.…
Application of asymptotic freedom to the ultraviolet stability in Euclidean quantum field theories is revisited and illustrated through the hierarchical model making also use of a few technical developments that followed the original works…
Synchronization is an important dynamical phenomenon in coupled nonlinear systems, which has been studied extensively in recent years. However, analysis focused on individual orbits seems hard to extend to complex systems while a global…
Callan-Symanzik and renormalization group equation are discussed for the $U(1)$-axial model and it is shown that the symmetric model is not the asymptotic version of the spontaneously broken one due to mass logarithms in the…
The equation of state is investigated for an Ising-like model in the framework of collective variables method. The peculiar feature of the theory is that a non-classical van der Waals loop is extracted. The results are compared with the…
Two different models exhibiting self-organized criticality are analyzed by means of the dynamic renormalization group. Although the two models differ by their behavior under a parity transformation of the order parameter, it is shown that…
I give an outline of recent applications of the renormalisation group to effective theories of nuclear forces, focussing on the use of a Wilsonian approach to analyse systems of two or three nonrelativistic particles.
The Renormalization Group flow equations obtained by means of a proper time regulator are used to analyze the restoration of the discrete chiral symmetry at non-zero density and temperature in the Gross-Neveu model in d=2+1 dimensions. The…
We derive quantum kinetic equations from a quantum field theory implementing a diagrammatic perturbative expansion improved by a resummation via the dynamical renormalization group. The method begins by obtaining the equation of motion of…
We report on the current status of recent efforts to develop the Density Matrix Renormalization Group method for use in large-scale nuclear shell-model calculations.
We develop a renormalization-group formalism for non-renormalizable theories and apply it to Einstein gravity theory coupled to a scalar field with the Lagrangian $L=\sqrt{g} [R U(\phi)-{1/2} G(\phi) g^{\mu\nu} \partial_{\mu}\phi…
We investigate the renormalization group theory of generalized multi-vertex sine-Gordon model by employing the dimensional regularization method and also the Wilson renormalization group method. The vertex interaction is given by…