The Friedrichs-Model with fermion-boson couplings II

In this work we present a formal solution of the extended version of the Friedrichs Model. The Hamiltonian consists of discrete and continuum bosonic states, which are coupled to fermions. The simultaneous treatment of the couplings of the fermions with the discrete and continuous sectors of the bosonic degrees of freedom leads to a system of coupled equations, whose solutions are found by applying standard methods of representation of bound and resonant states.Comment: 13 page

Ion characteristics of laser-produced plasma using a pair of collinear femtosecond laser pulses

Femtosecond laser-pulse absorption is studied in silicon ablation plasmas by means of a pair of identical 1016 W/cm21016W/cm2 collinear pulses separated on a picosecond time scale. The second laser-pulse modifies ionic characteristics of the preformed plasma, such as ion yield, ion energy, and average charge state. Resonance absorption is demonstrated to be the dominant mechanism by comparing results of ss and pp polarization. It is shown that maximum effects occur when a well defined critical density surface of the initial plasma forms together with an optimum density gradient scale length of kL = 1.5.kL=1.5. The optimal enhancement of ion yield, which occurs at 5 ps delay, is a factor of 2 greater than that produced by a single pulse with twice the energy of each individual double pulse. Applications are identified in regard to cluster beam formation and plasma isotope enrichment in ultrafast ablation plumes. © 2003 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70825/2/APPLAB-83-3-431-1.pd

The arctic curve of the domain-wall six-vertex model in its anti-ferroelectric regime

An explicit expression for the spatial curve separating the region of ferroelectric order (`frozen' zone) from the disordered one (`temperate' zone) in the six-vertex model with domain wall boundary conditions in its anti-ferroelectric regime is obtained.Comment: 12 pages, 1 figur

Multi-diagnostic comparison of femtosecond and nanosecond pulsed laser plasmas

Understanding and fully characterizing highly dynamic and rapidly streaming laser ablation plasmas requires multiple techniques for monitoring effects at different stages. By combining multiple diagnostic methods, it is possible to analyze the broad time window over which these ablation plasmas develop and to learn more about the related physical processes that occur. Two laser sources, an 80 fs Ti:Sapphire laser (780 nm) and a 6 ns Nd:YAG laser (1.06 μm), are used in this work in order to compare pulse duration effects at similar wavelengths. Characteristics of the plasma produced by these two lasers are compared under conditions of comparable ablation flux. Results are presented involving correlation of time-resolved Langmuir probe data and electrostatic energy analysis for aluminum plasmas as a representative investigation for metallic systems. In addition, continuous-wave refractive index laser beam deflection is used to characterize the plasma and hot gas generated from boron nitride targets in terms of their ion and neutral atom densities. A self-similarity plasma expansion model is used to analyze the plumes under various conditions. Fundamental data obtained in this way can be relevant to laser micro-machining, laser induced breakdown spectroscopy, and pulsed laser deposition. © 2002 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70715/2/JAPIAU-92-5-2867-1.pd

Exotic solutions in string theory

Solutions of classical string theory, correspondent to the world sheets, mapped in Minkowsky space with a fold, are considered. Typical processes for them are creation of strings from vacuum, their recombination and annihilation. These solutions violate positiveness of square of mass and Regge condition. In quantum string theory these solutions correspond to physical states |DDF>+|sp> with non-zero spurious component.Comment: accepted in Il Nuovo Cimento A for publication in 199

Classical and quantum three-dimensional integrable systems with axial symmetry

We study the most general form of a three dimensional classical integrable system with axial symmetry and invariant under the axis reflection. We assume that the three constants of motion are the Hamiltonian, $H$, with the standard form of a kinetic part plus a potential dependent on the position only, the $z$-component of the angular momentum, $L$, and a Hamiltonian-like constant, $\widetilde H$, for which the kinetic part is quadratic in the momenta. We find the explicit form of these potentials compatible with complete integrability. The classical equations of motion, written in terms of two arbitrary potential functions, is separated in oblate spheroidal coordinates. The quantization of such systems leads to a set of two differential equations that can be presented in the form of spheroidal wave equations.Comment: 17 pages, 3 figure