Related papers: Quantum Stability for the Heisenberg Ferromagnet
Here I give a direct proof that smooth curves with distinct marked points are asymptotically Hilbert stable with respect to a wide range of parameter spaces and linearizations. This result can be used to construct the coarse moduli space of…
The search for departures from standard hydrodynamics in many-body systems has yielded a number of promising leads, especially in low dimension. Here we study one of the simplest classical interacting lattice models, the nearest-neighbour…
A class of linear hyperbolic partial differential equations, sometimes called networks of waves, is considered. For this class of systems, necessary and sufficient conditions are formulated on the system matrices for the operator dynamics…
We consider several different bidirectional Whitham equations that have recently appeared in the literature. Each of these models combine the full two-way dispersion relation from the incompressible Euler equations with a canonical shallow…
Almost one century ago, string states - complex bound states (Wellenkomplexe) of magnetic excitations - have been predicted to exist in one-dimensional quantum magnets and since then become a subject of intensive theoretical study. However,…
We propose a notion of stability for constant k-mean curvature hypersurfaces in a general Riemannian manifold and we give some applications. When the ambient manifold is a Space Form, our notion coincides with the known one, given by means…
We consider the stochastic Swift-Hohenberg equation on a large domain near its change of stability. We show that, under the appropriate scaling, its solutions can be approximated by a periodic wave, which is modulated by the solutions to a…
Two-dimensional Heisenberg antiferromagnets play a central role in quantum magnetism, yet the nature of dynamic correlations in these systems at finite temperature has remained poorly understood for decades. We solve this long-standing…
Stability of a half-quantum vortex (HQV) in superfluid $^3$He has been discussed recently by Kawakami, Tsutsumi and Machida in Phys. Rev. B {\bf 79}, 092506 (2009). We further extend this work here and consider the A$_2$ phase of superfluid…
We present the first concrete evidence for the classical stability of vortons, circular cosmic string loops stabilized by the angular momentum of the charge and current trapped on the string. We begin by summarizing what is known about…
e study the solitons, stabilized by spin precession in a classical two--dimensional lattice model of Heisenberg ferromagnets with non-small easy--axis anisotropy. The properties of such solitons are treated both analytically using the…
The well-posedness of the three dimensional Prandtl equation is an outstanding open problem due to the appearance of the secondary flow even though there are studies on analytic and Gevrey function spaces. This problem is raised as the…
The goal of this paper is to investigate the stability of the Helmholtz equation in the high- frequency regime with non-smooth and rapidly oscillating coefficients on bounded domains. Existence and uniqueness of the problem can be proved…
It is well known that the linear stability of solutions of partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the…
Stability and instability bands in classical mechanics are well-studied in connection with systems such as described by the Mathieu equation. We examine whether such band structure can arise in classical field theory in the context of an…
We study the planar antiferromagnetic Heisenberg model on a decorated hexagonal lattice, involving both classical spins (occupying the vertices) and quantum spins (occupying the middle of the links). This study is motivated by the…
We examine the spectral stability and instability of periodic traveling waves for regularized long-wave models. Examples include the regularized Boussinesq, Benney--Luke, and Benjamin--Bona--Mahony equations. Of particular interest is a…
The dynamical stability of cosmic rings, or vortons, is investigated for the particular equation of state given by the Witten bosonic model. It is found that there exists a finite range of the state parameter for which the vorton states are…
We discuss stability of spherically symmetric static solutions in Newtonian limit of Jordan, Brans-Dicke field equations. The behavior of the stable equilibrium solutions for the spherically symmetric configurations considered here, it…
We study the dynamics of fuzzy two-spheres in a matrix model which represents string theory in the presence of RR flux. We analyze the stability of known static solutions of such a theory which contain commuting matrices and SU(2)…