Related papers: Distribution of Eigenvalues for the Modular Group
We suggest kinetic models of dissipation for an ensemble of interacting oriented particles, for example, moving magnetized particles. This is achieved by introducing a double bracket dissipation in kinetic equations using an oriented…
The Klein-Gordon equation, the Maxwell equation, and the Dirac equation are presented as partial difference equations in the eight-dimensional covariant discrete phase space. These equations are also furnished as difference-differential…
We investigate the two-points correlation function for several boundary-driven interacting particle systems. Our goal is to show that the time evolution of that correlation function is solution to a partial differential equation that can be…
The large-time asymptotics of the density matrix solving a drift-diffusion-Poisson model for the spin-polarized electron transport in semiconductors is proved. The equations are analyzed in a bounded domain with initial and Dirichlet…
The Dyson Brownian motion model for transistions to the CUE is considered. For initial eigenvalue probability density functions corresponding to the COE and CSE, the density-density correlation function between an eigenvalue at position…
We calculate the photoionization with excitation-to photoionization ratios for atomic helium and heliumlike ions at intermediate values of the photon energies. The final state interactions between the electrons are included in the lowest…
We study the structure of the spectrum of a two-level quantum system weakly coupled to a boson field (spin-boson model). Our analysis allows to avoid the cutoff in the number of bosons, if their spectrum is bounded below by a positive…
We investigate the excitation spectrum and momentum distribution of the ionic Bose-Hubbard model by the standard basis operator method. We derive Green's functions in the random phase approximation in Mott insulator, superfluid, charge…
We show that charge-sign-dependent asymmetric hydration can be modeled accurately using linear Poisson theory but replacing the standard electric-displacement boundary condition with a simple nonlinear boundary condition. Using a single…
Exact expressions of the boundary state and the form factors of the Ising model are used to derive differential equations for the one-point functions of the energy and magnetization operators of the model in the presence of a boundary…
On any denumerable product of probability spaces, we construct a Malliavin gradient and then a divergence and a number operator. This yields a Dirichlet structure which can be shown to approach the usual structures for Poisson and Brownian…
Universal properties of the Coulomb interaction energy apply to all many-electron systems. Bounds on the exchange-correlation energy, inparticular, are important for the construction of improved density functionals. Here we investigate one…
A class of fast-slow Hamiltonian systems with potential $U_\varepsilon$ describing the interaction of non-ergodic fast and slow degrees of freedom is studied. The parameter $\varepsilon$ indicates the typical timescale ratio of the fast and…
Absolute two-photon detachment cross sections and photoelectron angular distribution are calculated for halogen negative ions within lowest-order perturbation theory. The Dyson equation method is used to obtain the outer np ground-state…
We give a new proof of correlation estimates for arbitrary moments of the resolvent of random Schr\"odinger operators on the lattice that generalizes and extends the correlation estimate of Minami for the second moment. We apply this moment…
Diffusion in a multidimensional energy surface with minima and barriers is a problem of importance in statistical mechanics and also has wide applications, such as protein folding. To understand it in such a system, we carry out theory and…
We calculate the single-particle states of a two-dimensional electron gas (2DEG) in a perpendicular quantizing magnetic field, which is periodic in one direction of the electron layer. We discuss the modulation of the electron density in…
We study equivariant families of discrete Hamiltonians on amenable geometries and their integrated density of states (IDS). We prove that the eigenspace of a fixed energy is spanned by eigenfunctions with compact support. The size of a jump…
We use the two-electron wavefunctions (geminals) and the simple screened Coulomb potential proposed by Overhauser [Can. J. Phys. 73, 683 (1995)] to compute the pair-distribution function for a uniform electron gas. We find excellent…
This article examines the Dirichlet boundary control problem governed by the Poisson equation, where the control variables are square integrable functions defined on the boundary of a two dimensional bounded, convex, polygonal domain. It…