We derive inequalities for the ground-state energy of $N$ bosons or fermions in the two-body confining potential $V(x,y)=\gamma \mathrm{}|x-y|\mathrm{}$. We comment on why the results on this problem, derived previously, are incorrect.

A method is proposed to determine partial cross sections for transfer into high-$n$ projectile shells in collisions between highly charged ions and atoms at energies around the energy of maximum transfer. Starting from the semiclassical close-coupling method with atomic-orbital basis sets, each group of orbitals belonging to a particular high-$n$ shell is coupled separately to those orbitals which dominate the capture process. Partial transfer cross sections ${\sigma }_{\mathrm{nl}}$ are calculated for ${\mathrm{C}}^{6+}$+H, ${\mathrm{N}}^{7+}$+H, and ${\mathrm{O}}^{8+}$+H collisions at 4-25 keV/amu with quantum numbers $n$ labeling shells up to those from which visible transitions take place.

Doubly differential cross sections (DDCS) for electron ejection in electron-argon collisions have been studied for ejected electron energies 25 to 300 eV, ejection angle ${\theta }_{\delta }=90\mathrm{}°$, and incident electron energies of 300 eV to 8 keV. Performing a charge-state analysis of the recoil ion in coincidence with the ejected electron, we were able to distinguish between singly and multiply ionizing collisions. It was observed that the relative importance of multiple ionization events increases with increasing energy of the ejected electron. At an ejected electron energy corresponding to $\mathrm{LMM}$ Auger transitions, ${\mathrm{Ar}}^{2+}$ and ${\mathrm{Ar}}^{3+}$ are predominantly produced by $L$-shell ionization. From an analysis of the corresponding DDCS, information about simultaneous $L$- and $M$-shell ionization is obtained.

Ab initio calculations are presented for the vibrational branching ratios in three-photon resonant four-photon ionization of ${\mathrm{H}}_2$ via the $C {}_{}{}^1{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ state. Energy and internuclear distance dependences of the boundfree electronic transition matrix element are explicitly included to estimate deviations from the Franck-Condon approximation. While our calculated branching ratios confirm certain important trends seen experimentally, some differences remain.

A transit-time broadened swept-gain laser amplifier is investigated theoretically. General values of the slippage parameter, which measures the relative values of the time of transit of the radiating sources across the device and the pulse width of the sources, are considered. The sources in this calculation are two-level atoms, but the result should be directly applicable to the free-electron laser (FEL). Both the linear and nonlinear operation are considered, and the results are in much better agreement with FEL experiment than are the corresponding FEL calculations. A formula is found which predicts maximum output power for all values of slippage parameter.

The problem of the dynamics of the small polaron—an electron strongly and locally coupled to a lattice deformation—is mapped into a model of a spin ½ strongly interacting with a highly polarizable magnetic environment of uniaxial symmetry. The nonlinear coupling between the spin and the self-induced polarization of its environment leads to self-trapping of the spin. The mechanism for this is described in terms of nonlinear stochastic equations exhibiting multiplicative noise.

The localization of a light particle (electron, positron, or positronium atom) in a classical fluid is investigated via mean-field theory. Under circumstances where the light-particle (LP) wave function varies slowly over the pair-correlation length and mean interatom separation of the host fluid, a self-consistent quantum hydrodynamics and an equilibrium free-energy functional of the LP-fluid system are developed. In equilibrium, the localized state is defined by a pair of coupled equations in the LP wave function and the local fluid density. An application to the case where the local fluid density is only slightly reduced by the LP shows that these "shallow" bound states are metastable.

To account for the periodic-chaotic sequence observed in a driven nonlinear oscillator, a new one-dimensional map is proposed. Next, a modification of the proposed map is suggested to explain self-replicating attractors.

Considered here is one parameter family of one-dimensional point mappings. A method is presented in the paper for constructing generating partitions for these maps at a countable set of parameter values. These generating partitions allow us to evaluate the measure theoretic entropy of the mappings.

A simple method is presented for ensuring the reality of solutions of the periodic sine-Gordon equation. The method consists of forcing a simple polynomial constraint on the initial conditions of a set of auxiliary variables. Numerical results are presented to demonstrate the method's practicality.

In order for a Fokker-Planck equation $\frac{\partial P}{\partial t}=-\Sigma \stackrel{n}{i=1\mathrm{}}\frac{\partial \left[Q_i\mathrm{}\right(q\left)P\right]}{\partial q_i}+\frac{1}{2}\Sigma \stackrel{n}{i,j=1\mathrm{}}{\sigma }_{\mathrm{ij}}\frac{{\partial }^{2}P}{\partial q_i\partial q_j}$ with $n>~3$ to admit an asymptotic steady-state solution $P\to P_{\mathrm{eq}}\mathrm{}\left(q\right)\mathrm{}$ which is independent of $t$, the quantity $S=S\left(q\right)\mathrm{}\equiv \Sigma \stackrel{n}{i=1\mathrm{}}\frac{\partial Q_i\mathrm{}\left(q\right)\mathrm{}}{\partial q_i}$ must satisfy the inequality ${\left[\int {\Omega }^{}{\mathrm{}\left|S\right|\mathrm{}}^{\frac{n}{2}}{d}^{n}q\right]}^{\frac{2}{n}}>2^{-2+\frac{2}{n}}{\pi }^{1+\frac{1}{n}}(n^2-2n){\left[\Gamma \left[\frac{n+1\mathrm{}}{2}\right]\right]}^{-\frac{2}{n}}{\left[\det \right({\sigma }_{\mathrm{ij}}\left)\right]}^{\frac{1}{n}}$ where the integral is over the $q$-space region $\Omega \equiv \{q \epsilon R_n$ such that $S\left(q\right)<0\}$. The application of this general necessary condition for Fokker-Planck statistical equilibrium is illustrated here for $n$ trophic-level ecosystems of the Nisbet-McKinstry-Gurney type with Montroll stochasticity in the population growth-rate functions.

We use generating functions to analyze the kinetics of the reaction $A+B\to (1+\epsilon )A+B$ where $-1\mathrm{}<~\epsilon <0\mathrm{}$ and $\epsilon >0\mathrm{}$ correspond, respectively, to $B$ particles that are traps or "sources." For an arbitrary configuration and strengths of static $B$'s and mobile $A$'s, an exact formal expression for the kinetics of the reaction is derived. This solution yields either exponential growth, power-law growth or decay, or no growth asymptotically, depending on the configuration and strength of the $B$'s.

We derive an amplitude equation for the convective instability of a binary fluid mixture in a porous medium near the nonequilibrium analog of a tricritical point. We find that the prefactor of the quintic term in this equation is always stabilizing in the vicinity of the "tricritical" point. Therefore, it seems posible to observe experimentally (e.g., via measurement of the Nusselt number) the crossover from classical-mean-field to tricritical behavior.

The influence of an electric field on the phase-transition temperatures of cholesterogenic mixtures CB 15/M 18 exhibiting blue phases (BP) has been investigated. From temperature-voltage phase diagrams it can be seen that the transition temperature BP I/cholesteric depends on the field strength $E$, whereas that of BP II/cholesteric does not. The effect $\Delta T\left(E\right)\mathrm{}$ can be understood by means of the Kirkwood-Helfrich equation considering the nonlinear field dependence of the BP I permittivity.