Related papers: A BV subtlety
A general theory of electronic excitations in aggregates of molecules coupled to intramolecular vibrations and the harmonic environment is developed for simulation of the third-order nonlinear spectroscopy signals. The model is applied in…
Let $G$ be a finite group and $\Z G$ its integral group ring. We show that if $\alpha$ is a non-trivial bicyclic unit of $\Z G$, then there are bicyclic units $\beta$ and $\gamma$ of different types, such that $\GEN{\alpha,\beta}$ and…
We solve explicitly the two-dimensional harmonic oscillator and the harmonic oscillator in a background magnetic field in noncommutative phase-space without making use of any type of representation. A key observation that we make is that…
We consider some aspects of the global evolution problem of Hamiltonian homogeneous, anisotropic cosmologies derived from a purely quadratic action functional of the scalar curvature. We show that models can isotropize in the positive…
In a model of an Abelian vector boson with a Maxwell kinetic term and non-negative mass-squared it is demonstrated that, under fairly general conditions during inflation, a scale-invariant spectrum of perturbations for the components of a…
Using a group theoretical approach we derive an equation of motion for a mixed quantum-classical system. The quantum-classical bracket entering the equation preserves the Lie algebra structure of quantum and classical mechanics: The bracket…
A set of Hamiltonians that are not self-adjoint but have the spectrum of the harmonic oscillator is studied. The eigenvectors of these operators and those of their Hermitian conjugates form a bi-orthogonal system that provides a…
Given small initial solutions of the nonlinear quantum harmonic oscillator on $\mathbb{R}$, we are interested in their long time behavior in the energy space which is an adapted Sobolev space. We perturbate the linear part by $V$ taken as…
We prove that vanishing viscosity solutions to smooth non-degenerate systems of balance laws having small bounded variation, in one space dimension, must be functions of special bounded variation. For more than one equation, this is new…
We examine the dynamics of a particle in a general rotating quadratic potential, not necessarily stable or isotropic, using a general complex mode formalism. The problem is equivalent to that of a charged particle in a quadratic potential…
We investigate the cosmology of a class of model with noncanonical scalar field and matter in an anisotropy background. We find fixed points and their stability which constraints equation of state parameter for the matter. This is done…
The eigenfunctions and eigenenergies for a Dirac Hamiltonian with equal scalar and vector harmonic oscillator potentials are derived. Equal scalar and vector potentials may be applicable to the spectrum of an antinucleion imbedded in a…
The canonical theory of $N=1$ supergravity is applied to Bianchi class A spatially homogeneous cosmologies. The full set of quantum constraints are then solved with the possible ordering ambiguity taken into account by introducing a free…
Let $b_d$ be the Weyl symbol of the inverse to the harmonic oscillator on $\R^d$. We prove that $b_d$ and its derivatives satisfy convenient bounds of Gevrey and Gelfand-Shilov type, and obtain explicit expressions for $b_d$. In the…
We show that a large class of null electromagnetic fields are immune to any modifications of Maxwell's equations in the form of arbitrary powers and derivatives of the field strength. These are thus exact solutions to virtually any…
It is shown that a string carrying a field of harmonic type can have circular vorton states of a new "throbbing" kind, for which the worldsheet geometry is stationary but the internal structure undergoes periodic oscillation.
We study BV solutions for a $2\times2$ system of hyperbolic balance laws. We show that when initial data have small total variation on $(-\infty,\infty)$ and small amplitude, and decay sufficiently fast to a constant equilibrium state as…
A hypercycle equation with infinitely many types of macromolecules is formulated and studied both analytically and numerically. The resulting model is given by an integro-differential equation of the mixed type. Sufficient conditions for…
We obtain the most general solution of the Einstein electro - vacuum equation for the stationary axially symmetric spacetime in which the Hamilton-Jacobi and Klein - Gordon equations are separable. The most remarkable feature of the…
We prove that Thompson's group $V$ is acyclic, answering a 1992 question of Brown in the positive. More generally, we identify the homology of the Higman-Thompson groups $V_{n,r}$ with the homology of the zeroth component of the infinite…