Electron Bloch Oscillations and Electromagnetic Transparency of Semiconductor Superlattices in Multi-Frequency Electric Fields

We examine phenomenon of electromagnetic transparency in semiconductor superlattices (having various miniband dispersion laws) in the presence of multi-frequency periodic and non-periodic electric fields. Effects of induced transparency and spontaneous generation of static fields are discussed. We paid a special attention on a self-induced electromagnetic transparency and its correlation to dynamic electron localization. Processes and mechanisms of the transparency formation, collapse, and stabilization in the presence of external fields are studied. In particular, we present the numerical results of the time evolution of the superlattice current in an external biharmonic field showing main channels of transparency collapse and its partial stabilization in the case of low electron density superlattices

Pseudoscalar mesons and their radial excitations from the Effective Chiral Lagrangian

Effective Chiral Lagrangian is derived from QCD in the framework of Field Correlator Method. It contains the effects of both confinement and chiral symmetry breaking due to a special structure of the resulting quark mass operator. It is shown that this Lagrangian describes light pseudoscalar mesons, and Gell-Mann-Oakes-Renner relations for pions, eta and K mesons are reproduced. Spectrum of radial excitations of pions and K mesons is found and compared to experimentally known masses.Comment: 6 pages; v3: minor corrections, references adde

Scalar products of symmetric functions and matrix integrals

We present relations between Hirota-type bilinear operators, scalar products on spaces of symmetric functions and integrals defining matrix model partition functions. Using the fermionic Fock space representation, a proof of the expansion of an associated class of KP and 2-Toda tau functions $\tau_{r,n}$ in a series of Schur functions generalizing the hypergeometric series is given and related to the scalar product formulae. It is shown how special cases of such $\tau$-functions may be identified as formal series expansions of partition functions. A closed form exapnsion of $\log \tau_{r,n}$ in terms of Schur functions is derived.Comment: LaTex file. 15 pgs. Based on talks by J. Harnad and A. Yu. Orlov at the workshop: Nonlinear evolution equations and dynamical systems 2002, Cadiz (Spain) June 9-16, 2002. To appear in proceedings. (Minor typographical corrections added, abstract expanded

Matrix integrals as Borel sums of Schur function expansions

The partition function for unitary two matrix models is known to be a double KP tau-function, as well as providing solutions to the two dimensional Toda hierarchy. It is shown how it may also be viewed as a Borel sum regularization of divergent sums over products of Schur functions in the two sequences of associated KP flow variables.Comment: PlainTex file. 8 pgs. Based on talk by J. Harnad at the workshop: Symmetry and Perturbation Theory 2002, Cala Gonoone (Sardinia), May 1-26, 2002. To appear in proceedings. (World Scientific, Singapore, eds. S. Abenda, G. Gaeta). Typographical correction made to formula (2.7) to include previously omitted powers of r and

Localizable invariants of combinatorial manifolds and Euler characteristic

It is shown that if a real value PL-invariant of closed combinatorial manifolds admits a local formula that depends only on the f-vector of the link of each vertex, then the invariant must be a constant times the Euler characteristic.Comment: 14 pages, 5 figures. Some arguments are improved and one picture is adde

The matrix Hamiltonian for hadrons and the role of negative-energy components

The world-line (Fock-Feynman-Schwinger) representation is used for quarks in arbitrary (vacuum and valence gluon) field to construct the relativistic Hamiltonian. After averaging the Green's function of the white $q\bar q$ system over gluon fields one obtains the relativistic Hamiltonian, which is matrix in spin indices and contains both positive and negative quark energies. The role of the latter is studied in the example of the heavy-light meson and the standard einbein technic is extended to the case of the matrix Hamiltonian. Comparison with the Dirac equation shows a good agreement of the results. For arbitrary $q\bar q$ system the nondiagonal matrix Hamiltonian components are calculated through hyperfine interaction terms. A general discussion of the role of negative energy components is given in conclusion.Comment: 29 pages, no figure