Related papers: Higher order normal modes
In this paper we describe physical properties arising in the vicinity of two coupled quantum phase transitions. We consider a phenomenological model based on two scalar order parameter fields locally coupled biquadratically and having a…
Using supervector fields and graded forms along a morphism, we study the geometry of ordinary differential superequations, extend the formalism of higher order Lagrangian mechanics to the graded context and prove a generalization of…
It has been shown recently that predictions from Mode-Coupling Theory for the glass transition of hard-spheres become increasingly bad when dimensionality increases, whereas replica theory predicts a correct scaling. Nevertheless if one…
Semiclassical methods are essential in analyzing quantum mechanical systems. Although they generally produce approximate results, relatively rare potentials exist for which these methods are exact. Such intriguing potentials serve as…
Methods of large amplitude collective motion in the adiabatic limit are examined with a special emphasis on conservation laws. We show that the restriction to point transformations, which is a usual assumption of the adiabatic…
A model is constructed in which pair potentials are combined with the cluster expansion method in order to better describe the energetics of structurally relaxed substitutional alloys. The effect of structural relaxations away from the…
Motivated by various applications and examples, the standard notion of potential for dynamical systems has been generalized to almost additive and asymptotically additive potential sequences, and the corresponding thermodynamic formalism,…
In this lecture notes I concentrate on the classic and widely applicable characterization of higher order statistics by joint moments, a.k.a. higher order correlation functions, and directly related statistics. I put special emphasis on…
We present a family of high order trapezoidal rule-based quadratures for a class of singular integrals, where the integrand has a point singularity. The singular part of the integrand is expanded in a Taylor series involving terms of…
I present an analysis of the relaxation rate for long-wavelength fluctuations of the order parameter in an O(N) scalar theory near the critical point. Our motivation is to model the non-equilibrium dynamics of critical fluctuations near the…
We introduce a general framework for the construction of well-balanced finite volume methods for hyperbolic balance laws. We use the phrase well-balancing in a broader sense, since our proposed method can be applied to exactly follow any…
We study sharpened forms of the concentration of measure phenomenon typically centered at stochastic expansions of order $d-1$ for any $d \in \mathbb{N}$. The bounds are based on $d$-th order derivatives or difference operators. In…
In this letter we study how deterministic features presented by a system can be used to perform direct transport in a {\it quasi}-symmetric potential and weak dissipative system. We show that the presence of nonhyperbolic regions around…
Resonance expansions are an intuitive approach to capture the interaction of an optical resonator with light. Here, we present a quasinormal mode expansion approach for quadratic observables exploiting the rigorous Riesz projection method.…
We study the families of nonlinear modes described by the nonlinear Schr\"odinger equation with the PT-symmetric harmonic potential $x^2-2i\alpha x$. The found nonlinear modes display a number of interesting features. In particular, we have…
We discuss classical and quantum symmetries of extended Hubbard models. The quantum symmetries are shown to be related to the known superconducting SU(2) symmetry of the original Hubbard model at half filling via generalized Lang-Firsov…
We extend recent work by Tremblay, Turbiner, and Winternitz which analyzes an infinite family of solvable and integrable quantum systems in the plane, indexed by the positive parameter k. Key components of their analysis were to demonstrate…
We establish a theorem concerning the normal forms by examining the newly presented concept of $\mu$-dichotomy. This work establishes the nonresonance condition based on the associated spectrum of this general nonautonomous hyperbolicity.
We prove a criterion of convergence in the augmented Teichmueller space that can be phrased in terms of convergence of the hyperbolic metrics or of quasiconformal convergence away from the nodes.
We provide a rigorous definition of quasinormal modes for the Kerr black hole. They are obtained as the discrete set of poles of the meromorphically continued cutoff resolvent. The construction combines the method of complex scaling near…