Related papers: Orbit structure of interval exchange transformatio…
We consider a model of strongly correlated $e_g$ electrons interacting by superexchange orbital interactions in the ferromagnetic phase of LaMnO$_3$. It is found that the classical orbital order with alternating occupied $e_g$ orbitals has…
Consider the action of a connected complex reductive group on a finite-dimensional vector space. A fundamental result in invariant theory states that the orbit closure of a vector v is separated from the origin if and only if some…
We demonstrate how electric fields with arbitrary time profile can be used to control the time-dependent parameters of spin and orbital exchange Hamiltonians. Analytic expressions for the exchange constants are derived from a time-dependent…
An interval translation map (ITM) is a map $T \colon I \to I$ defined as a piecewise translation on a finite partition of an interval $I$ into $r \ge 2$ subintervals. Unlike classical interval exchange transformations (IETs), the images of…
Orbitally degenerate systems provide a promising platform for realizing novel quantum phases driven by spin-orbital exchange interactions, as described by the Kugel-Khomskii model. Spinel vanadates, in which orbital degrees of freedom…
We develop a theoretical framework for computer-assisted proofs of the existence of invariant objects in semilinear PDEs. The invariant objects considered in this paper are equilibrium points, traveling waves, periodic orbits and invariant…
We present a controlled method for computing the exchange coupling in strongly correlated one-dimensional electron systems. It is based on the asymptotically exact relation between the exchange constant and the pair-correlation function of…
The understanding of the universe is confused by the unknown nature of about 95% of its matter, required to confine the motions of space objects in cosmic structures. The idea of this paper is that the self-similar transformations of one…
We ask what happens when the index set carries modal structure, with possibilities organized into a Kripke frame. We define modal exchangeability as invariance under accessibility-preserving automorphisms that fix a designated base world,…
For composite systems made of $N$ different particles living in a space characterized by the same deformed Heisenberg algebra, but with different deformation parameters, we define the total momentum and the center-of-mass position to first…
We consider the model of a point-vortex under a periodic perturbation and give sufficient conditions for the existence of generalized quasi-periodic solutions with rotation number. The proof uses Aubry-Mather theory to obtain the existence…
We apply the self-interaction corrected local spin density %(SIC-LSD) approximation to study the electronic structure and magnetic properties of the spinel ferrites MnFe$_{2}$O$_{4}$, Fe$_{3}$O$_{4}$, CoFe$_{2}$O$_{4}$, and…
A characterization of finitely generated shift-invariant subspaces is given when generators are g-minimal. An algorithm is given for the determination of the coefficients in the well known representation of the Fourier transform of an…
The spin flip of the conduction electrons at the interface of a ferromagnetic and a nonmagnetic part of a metallic wire, suspended between two electrodes, is shown to tort the wire when a current is driven through it. In order to enhance…
The current paper is devoted to the investigation of the influence of nested invariant cone structure on the dynamics, in the context of non-autonomous (time almost periodic)cases. We first prove that the nested invariant cone structure can…
An empirical fit is described to measurements of inclusive inelastic electron-deuteron cross sections in the kinematic r ange of four-momentum transfer $0 \le Q^2<10$ GeV$^2$ and final state invariant mass $1.1<W<3.2$ GeV. The deuteron fit…
We present a simple algorithm to switch between $N$-body time integrators in a reversible way. We apply it to planetary systems undergoing arbitrarily close encounters and highly eccentric orbits, but the potential applications are broader.…
We study the dynamics of two bodies moving on elliptic Keplerian orbits around a fixed center of attraction and interacting only by means of elastic or inelastic collisions. We show that there exists a bounded invariant region: for suitable…
We define variational properties for dynamical systems with subexponential complexity, and study these properties in certain specific examples. By computing the value of slow entropy directly, we show that some subshifts are not…
We consider interacting electrons in a quantum wire in the case of a shallow confining potential and low electron density. In a certain range of densities, the electrons form a two-row (zigzag) Wigner crystal whose spin properties are…