Vertical pairing of identical particles suspended in the plasma sheath

It is shown experimentally that vertical pairing of two identical microspheres suspended in the sheath of a radio-frequency (rf) discharge at low gas pressures (a few Pa), appears at a well defined instability threshold of the rf power. The transition is reversible, but with significant hysteresis on the second stage. A simple model, which uses measured microsphere resonance frequencies and takes into account besides Coulomb interaction between negatively charged microspheres also their interaction with positive ion wake charges, seems to explain the instability threshold quite well.Comment: 4 pages, 6 figures. to appear in Phys. Rev. Lett. 86, May 14th (2001

Interaction between dust grains near a conducting wall

The effect of the conducting electrode on the interaction of dust grains in a an ion flow is discussed. It is shown that two grains levitating above the electrode at the same height may attract one another. This results in the instability of a dust layer in a plasma sheath.Comment: 9 pages. 3 figures. Submitted to Plasma Physics Report

Self-consistent model of unipolar transport in organic semiconductor diodes: accounting for a realistic density-of-states distribution

A self-consistent, mean-field model of charge-carrier injection and unipolar transport in an organic semiconductor diode is developed utilizing the effective transport energy concept and taking into account a realistic density-of-states distribution as well as the presence of trap states in an organic material. The consequences resulting from the model are discussed exemplarily on the basis of an indium tin oxide/organic semiconductor/metallic conductor structure. A comparison of the theory to experimental data of a unipolar indium tin oxide/poly-3-hexyl-thiophene/Al device is presented.Comment: 6 pages, 2 figures; to be published in Journal of Applied Physic

The Many Faces of a Character

We prove an identity between three infinite families of polynomials which are defined in terms of `bosonic', `fermionic', and `one-dimensional configuration' sums. In the limit where the polynomials become infinite series, they give different-looking expressions for the characters of the two integrable representations of the affine $su(2)$ algebra at level one. We conjecture yet another fermionic sum representation for the polynomials which is constructed directly from the Bethe-Ansatz solution of the Heisenberg spin chain.Comment: 14/9 pages in harvmac, Tel-Aviv preprint TAUP 2125-9

Exceptional structure of the dilute A3_3 model: E8_8 and E7_7 Rogers--Ramanujan identities

The dilute A$_3$ lattice model in regime 2 is in the universality class of the Ising model in a magnetic field. Here we establish directly the existence of an E$_8$ structure in the dilute A$_3$ model in this regime by expressing the 1-dimensional configuration sums in terms of fermionic sums which explicitly involve the E$_8$ root system. In the thermodynamic limit, these polynomial identities yield a proof of the E$_8$ Rogers--Ramanujan identity recently conjectured by Kedem {\em et al}. The polynomial identities also apply to regime 3, which is obtained by transforming the modular parameter by $q\to 1/q$. In this case we find an A_1\times\mbox{E}_7 structure and prove a Rogers--Ramanujan identity of A_1\times\mbox{E}_7 type. Finally, in the critical $q\to 1$ limit, we give some intriguing expressions for the number of $L$-step paths on the A$_3$ Dynkin diagram with tadpoles in terms of the E$_8$ Cartan matrix. All our findings confirm the E$_8$ and E$_7$ structure of the dilute A$_3$ model found recently by means of the thermodynamic Bethe Ansatz.Comment: 9 pages, 1 postscript figur

Self-consistent analytical solution of a problem of charge-carrier injection at a conductor/insulator interface

We present a closed description of the charge carrier injection process from a conductor into an insulator. Common injection models are based on single electron descriptions, being problematic especially once the amount of charge-carriers injected is large. Accordingly, we developed a model, which incorporates space charge effects in the description of the injection process. The challenge of this task is the problem of self-consistency. The amount of charge-carriers injected per unit time strongly depends on the energy barrier emerging at the contact, while at the same time the electrostatic potential generated by the injected charge- carriers modifies the height of this injection barrier itself. In our model, self-consistency is obtained by assuming continuity of the electric displacement and the electrochemical potential all over the conductor/insulator system. The conductor and the insulator are properly taken into account by means of their respective density of state distributions. The electric field distributions are obtained in a closed analytical form and the resulting current-voltage characteristics show that the theory embraces injection-limited as well as bulk-limited charge-carrier transport. Analytical approximations of these limits are given, revealing physical mechanisms responsible for the particular current-voltage behavior. In addition, the model exhibits the crossover between the two limiting cases and determines the validity of respective approximations. The consequences resulting from our exactly solvable model are discussed on the basis of a simplified indium tin oxide/organic semiconductor system.Comment: 23 pages, 6 figures, accepted to Phys.Rev.

Nonlinear vertical oscillations of a particle in a sheath of a rf discharge

A new simple method to measure the spatial distribution of the electric field in the plasma sheath is proposed. The method is based on the experimental investigation of vertical oscillations of a single particle in the sheath of a low-pressure radio-frequency discharge. It is shown that the oscillations become strongly nonlinear and secondary harmonics are generated as the amplitude increases. The theory of anharmonic oscillations provides a good qualitative description of the data and gives estimates for the first two anharmonic terms in an expansion of the sheath potential around the particle equilibrium.Comment: 11 pages, 4 figure

Continued Fractions and Fermionic Representations for Characters of M(p,p') minimal models

We present fermionic sum representations of the characters $\chi^{(p,p')}_{r,s}$ of the minimal $M(p,p')$ models for all relatively prime integers $p'>p$ for some allowed values of $r$ and $s$. Our starting point is binomial (q-binomial) identities derived from a truncation of the state counting equations of the XXZ spin ${1\over 2}$ chain of anisotropy $-\Delta=-\cos(\pi{p\over p'})$. We use the Takahashi-Suzuki method to express the allowed values of $r$ (and $s$) in terms of the continued fraction decomposition of $\{{p'\over p}\}$ (and ${p\over p'}$) where $\{x\}$ stands for the fractional part of $x.$ These values are, in fact, the dimensions of the hermitian irreducible representations of $SU_{q_{-}}(2)$ (and $SU_{q_{+}}(2)$) with $q_{-}=\exp (i \pi \{{p'\over p}\})$ (and $q_{+}=\exp ( i \pi {p\over p'})).$ We also establish the duality relation $M(p,p')\leftrightarrow M(p'-p,p')$ and discuss the action of the Andrews-Bailey transformation in the space of minimal models. Many new identities of the Rogers-Ramanujan type are presented.Comment: Several references, one further explicit result and several discussion remarks adde

Stationary Velocity and Charge Distributions of Grains in Dusty Plasmas

Within the kinetic approach velocity and charge distributions of grains in stationary dusty plasmas are calculated and the relations between the effective temperatures of such distributions and plasma parameters are established. It is found that the effective temperature which determines the velocity grain distribution could be anomalously large due to the action of accelerating ionic bombarding force. The possibility to apply the results obtained to the explanation of the increasing grain temperature in the course of the Coulomb-crystal melting by reduction of the gas pressure is discussed. This paper was received by Phys.Rev.Lett. on 11 August 1999. As potential referees the authors offered to Editor the following persons: V.N.Tsytovich, Russia; R.Bingham, UK; D.Resendes, Portugal; G.Morfill, P.Shukla, Y.M.Yu., Germany.Comment: 8 pages, no figure

Charge carrier injection into insulating media: single-particle versus mean-field approach

Self-consistent, mean-field description of charge injection into a dielectric medium is modified to account for discreteness of charge carriers. The improved scheme includes both the Schottky barrier lowering due to the individual image charge and the barrier change due to the field penetration into the injecting electrode that ensures validity of the model at both high and low injection rates including the barrier dominated and the space-charge dominated regimes. Comparison of the theory with experiment on an unipolar ITO/PPV/Au-device is presented.Comment: 32 pages, 9 figures; revised version accepted to PR