Related papers: Nonlinear Regge Trajectories in Theory and Practic…
In this talk I will present some of the main difficulties we encounter in studying the large scale behavior of disordered systems. This presentation will be done using a field theory language. The difficulties in applying the standard…
Several problems in number theory when reformulated in terms of homogenous dynamics involve study of limiting distributions of translates of algebraically defined measures on orbits of reductive groups. The general non-divergence and…
Behavior of hysteretic trajectories for cyclical input is investigated as a function of the internal structure of a system modeled by the classical random network of binary spins. Different regimes of hysteretic behavior are discovered for…
The high energy (Regge) limit provides a playground for understanding all loop structures of scattering amplitudes, and plays an important role in the description of many phenomenologically relevant cross-sections. While well understood in…
The renormalization group flow in two-dimensional field theories that are coupled to gravity has unusual features: First, the flow equations are second order in derivatives. Second, in the presence of handles the flow has quantum mechanical…
We discuss the problem of the existence of a regular invariant Lagrangian for a given system of invariant second-order differential equations on a Lie group $G$, using approaches based on the Helmholtz conditions. Although we deal with the…
Immersion and Invariance is a technique for the design of stabilizing and adaptive controllers and state observers for nonlinear systems. In all these applications the problem considered is the stabilization of equilibrium points. Motivated…
Perturbation theory is a crucial tool for many physical systems, when exact solutions are not available, or nonperturbative numerical solutions are intractable. Naive perturbation theory often fails on long timescales, leading to secularly…
In this paper, we consider a nonlinear second order equation modelling rocket motion in the gravitational field obstructed by the drag force. The proofs of the main results are based on topological fixed point approach.
The magnetic-Rayleigh--Taylor (MRT) instability is a ubiquitous phenomenon that occurs in magnetically-driven Z-pinch implosions. It is important to understand this instability since it can decrease the performance of such implosions. In…
We propose a new concept upon the renormalization group (RG) procedure for an interacting many-electron correlated system in the framework of natural orbitals, and formulate an algorithm for this RG approach. To demonstrate its…
Renormalisation group (RG) equations in two-dimensional N=1 supersymmetric field theories with boundary are studied. It is explained how a manifestly N=1 supersymmetric scheme can be chosen, and within this scheme the RG equations are…
Renormalization-group equations (RGE) is one of the key tools in studying high-energy behavior of the Standard Model (SM). We begin by reviewing one-loop RGE for the dimensionless couplings of the SM and proceed to the state-of-the-art…
Quantum dots are versatile systems for exploring quantum transport, electron correlations, and many-body phenomena such as the Kondo effect. While equilibrium properties are well understood through methods like the numerical renormalization…
The local free field theory for Regge trajectory is described in the framework of the BRST - quantization method. The corresponding BRST - charge is constructed with the help of the method of dimensional reduction.
This paper focuses on extending our previous discussion of an Abelian U(1) gauge theory involving infinite derivatives to a non-Abelian SU(N) case. The renormalization group equation (RGEs) of the SU(N) gauge coupling is calculated and…
The formulas for subregular characters of the unitriangular Lie group are obtained. The supports of regular and subregular characters are described in terms of the orbit method.
We study non-linear phenomena in quantum dots. Non linearities are reflected in the I-V characteristic curve as bistabilities, instabilities and time dependent oscillations of the currents. The nature of the non-linear behavior depends upon…
We obtain smoothing estimates for certain nonlinear convolution operators on prime fields, leading to quantitative nonlinear Roth type theorems. Compared with the usual linear setting (i.e. arithmetic progressions), the nonlinear nature of…
We consider a class of non-linear PDE systems, whose equations possess Noether identities (the equations are redundant), including non-variational systems (not coming from Lagrangian field theories), where Noether identities and…