For a range of values of the numbers of complex order parameter components and of replicas, the renormalization group trajectories exhibit a stable focus, surrounded by an unstable limit cycle. By evaluating the free energy and the equation of state, we find that flows within the limit cycle ...
We formulate a renormalization group (RG) for the interaction parameters of the general two-body problem and show how a limit cycle emerges in the RG flow if the interaction approaches an inverse square law. This limit cycle generates a scaling structure in the energy spectrum. Our demonstration...
Estimating the boundaries of a limit cycle in a 2D dynamical system using renormalization groupWhile the plausibility of formation of limit cycle has been a well studied topic in context of the Poincare-Bendixson theorem, studies on estimates in regard to the possible size and shape of the limit...
In this work, we study the Kondo singlet by the newly developed natural orbitals renormalization group (NORG) method. We first examine the occupancy of natural orbitals in the ground state of the single-impurity Kondo model. In whichever case of either finite size or thermodynamic limit, we ...
Based on our studies done on two-dimensional autonomous systems, forced non-autonomous systems and time-delayed systems, we propose a unified methodology – that uses renormalization group theory – for finding out existence of periodic solutions in a plethora of nonlinear dynamical systems appearing ...
We investigate renormalization group limit cycles within the similarity renormalization group (SRG) and discuss their signatures in the evolved interaction. A quantitative method to detect limit cycles in the interaction and to extract their period is proposed. Several SRG generators are compared ...
renormalization groupparameter spaceFormation and study of periodic orbits in phase space in the case of nonlinear oscillators have been a topic of much interest in the recent past. In the current work, a method to go deep inside the limit cycle zone on one side of the bifurcation curve of ...
We show that the renormalization group allows a unified analysis of the limit cycle and centre in a Lienard system of differential equations. While the approach is perturbative, it is possible to make a stronger statement in this regard. Two different classes of Lienard systems have been ...
RENORMALIZATION groupNONLINEAR oscillatorsPHASE spaceFORECASTINGHOPF bifurcationsCURVESFormation and study of periodic orbits in phase space in the case of nonlinear oscillators have been a topic of much interest in the recent past. In the current work, a method to go deep inside ...
renormalization group flowsthermodynamicsspace patternsdamped periodic dependenceThe thermodynamics of a system with a limit cycle in RG flows is studied. The unusual properties of such a system (damped periodic dependence of thermodynamic quantities on external parameters, "freezing" of metastable states,...