1,082 research outputs found
Fermionic construction of partition functions for two-matrix models and perturbative Schur function expansions
A new representation of the 2N fold integrals appearing in various two-matrix
models that admit reductions to integrals over their eigenvalues is given in
terms of vacuum state expectation values of operator products formed from
two-component free fermions. This is used to derive the perturbation series for
these integrals under deformations induced by exponential weight factors in the
measure, expressed as double and quadruple Schur function expansions,
generalizing results obtained earlier for certain two-matrix models. Links with
the coupled two-component KP hierarchy and the two-component Toda lattice
hierarchy are also derived.Comment: Submitted to: "Random Matrices, Random Processes and Integrable
Systems", Special Issue of J. Phys. A, based on the Centre de recherches
mathematiques short program, Montreal, June 20-July 8, 200
Fermionic construction of partition function for multi-matrix models and multi-component TL hierarchy
We use -component fermions to present -fold
integrals as a fermionic expectation value. This yields fermionic
representation for various -matrix models. Links with the -component
KP hierarchy and also with the -component TL hierarchy are discussed. We
show that the set of all (but two) flows of -component TL changes standard
matrix models to new ones.Comment: 16 pages, submitted to a special issue of Theoretical and
Mathematical Physic
Bound, virtual and resonance -matrix poles from the Schr\"odinger equation
A general method, which we call the potential -matrix pole method, is
developed for obtaining the -matrix pole parameters for bound, virtual and
resonant states based on numerical solutions of the Schr\"odinger equation.
This method is well-known for bound states. In this work we generalize it for
resonant and virtual states, although the corresponding solutions increase
exponentially when . Concrete calculations are performed for the
ground and the first excited states of , the resonance
states (, ), low-lying states of and
, and the subthreshold resonances in the proton-proton system. We
also demonstrate that in the case the broad resonances their energy and width
can be found from the fitting of the experimental phase shifts using the
analytical expression for the elastic scattering -matrix. We compare the
-matrix pole and the -matrix for broad resonance in
Comment: 14 pages, 5 figures (figures 3 and 4 consist of two figures each) and
4 table
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
Fermionic approach to the evaluation of integrals of rational symmetric functions
We use the fermionic construction of two-matrix model partition functions to
evaluate integrals over rational symmetric functions. This approach is
complementary to the one used in the paper ``Integrals of Rational Symmetric
Functions, Two-Matrix Models and Biorthogonal Polynomials'' \cite{paper2},
where these integrals were evaluated by a direct method.Comment: 34 page
Representations for Three-Body T-Matrix on Unphysical Sheets: Proofs
A proof is given for the explicit representations which have been formulated
in the author's previous work (nucl-th/9505028) for the Faddeev components of
three-body T-matrix continued analytically on unphysical sheets of the energy
Riemann surface. Also, the analogous representations for analytical
continuation of the three-body scattering matrices and resolvent are proved. An
algorithm to search for the three-body resonances on the base of the Faddeev
differential equations is discussed.Comment: 98 Kb; LaTeX; Journal-ref was added (the title changed in the
journal
Representations for Three-Body T-Matrix on Unphysical Sheets
Explicit representations are formulated for the Faddeev components of
three-body T-matrix continued analytically on unphysical sheets of the energy
Riemann surface. According to the representations, the T-matrix on unphysical
sheets is obviously expressed in terms of its components taken on the physical
sheet only. The representations for T-matrix are used then to construct similar
representations for analytical continuation of three-body scattering matrices
and resolvent. Domains on unphysical sheets are described where the
representations obtained can be applied.Comment: 123 Kb; LaTeX; Journal-ref was added (the title changed in the
journal
Quasi-classical limit of BKP hierarchy and W-infinity symmeties
Previous results on quasi-classical limit of the KP and Toda hierarchies are
now extended to the BKP hierarchy. Basic tools such as the Lax representation,
the Baker-Akhiezer function and the tau function are reformulated so as to fit
into the analysis of quasi-classical limit. Two subalgebras \WB_{1+\infty}
and \wB_{1+\infty} of the W-infinity algebras and
are introduced as fundamental Lie algebras of the BKP hierarchy
and its quasi-classical limit, the dispersionless BKP hierarchy. The quantum
W-infinity algebra \WB_{1+\infty} emerges in symmetries of the BKP hierarchy.
In quasi-classical limit, these \WB_{1+\infty} symmetries are shown to be
contracted into \wB_{1+\infty} symmetries of the dispersionless BKP
hierarchy.Comment: 12 pages, Kyoto University KUCP-0058/9
hbar-Dependent KP hierarchy
This is a summary of a recursive construction of solutions of the
hbar-dependent KP hierarchy. We give recursion relations for the coefficients
X_n of an hbar-expansion of the operator X = X_0 + \hbar X_1 + \hbar^2 X_2 +
... for which the dressing operator W is expressed in the exponential form W =
\exp(X/\hbar). The asymptotic behaviours of (the logarithm of) the wave
function and the tau function are also considered.Comment: 12 pages, contribution to the Proceedings of the "International
Workshop on Classical and Quantum Integrable Systems 2011" (January 24-27,
2011 Protvino, Russia
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