Diagnosis of weaknesses in modern error correction codes: a physics approach

One of the main obstacles to the wider use of the modern error-correction codes is that, due to the complex behavior of their decoding algorithms, no systematic method which would allow characterization of the Bit-Error-Rate (BER) is known. This is especially true at the weak noise where many systems operate and where coding performance is difficult to estimate because of the diminishingly small number of errors. We show how the instanton method of physics allows one to solve the problem of BER analysis in the weak noise range by recasting it as a computationally tractable minimization problem.Comment: 9 pages, 8 figure

Integrability and action operators in quantum Hamiltonian systems

For a (classically) integrable quantum mechanical system with two degrees of freedom, the functional dependence $\hat{H}=H_Q(\hat{J}_1,\hat{J}_2)$ of the Hamiltonian operator on the action operators is analyzed and compared with the corresponding functional relationship $H(p_1,q_1;p_2,q_2) = H_C(J_1,J_2)$ in the classical limit of that system. The former is shown to converge toward the latter in some asymptotic regime associated with the classical limit, but the convergence is, in general, non-uniform. The existence of the function $\hat{H}=H_Q(\hat{J}_1,\hat{J}_2)$ in the integrable regime of a parametric quantum system explains empirical results for the dimensionality of manifolds in parameter space on which at least two levels are degenerate. The comparative analysis is carried out for an integrable one-parameter two-spin model. Additional results presented for the (integrable) circular billiard model illuminate the same conclusions from a different angle.Comment: 9 page

Beyond the Point Ps Approximation

In application to positron annihilation spectroscopy, Ps atom is considered not as a point particle, but as a finite size e+ e- pair localized in a bubble-state in a medium. Variation of the internal Coulombic e+ -e- attraction vs. the bubble radius is estimated

Positronium in a liquid phase: formation, bubble state and chemical reactions

This chapter reviews the following items: 1. Energy deposition and track structure of fast positrons: ionization slowing down, number of ion-electron pairs, typical sizes, thermalization, electrostatic interaction between e+ and its blob, effect of local heating; 2. Positronium formation in condensed media: the Ore model, quasifree Ps state, intratrack mechanism of Ps formation; 3. Fast intratrack diffusion-controlled reactions: Ps oxidation and ortho-para conversion by radiolytic products, reaction rate constants, interpretation of the PAL spectra in water at different temperatures; 4. Ps bubble models. "Non-point" positronium: wave function, energy contributions, relationship between the pick-off annihilation rate and the bubble radius