2,320 research outputs found
Ground states of Heisenberg evolution operator in discrete three-dimensional space-time and quantum discrete BKP equations
In this paper we consider three-dimensional quantum q-oscillator field theory
without spectral parameters. We construct an essentially big set of eigenstates
of evolution with unity eigenvalue of discrete time evolution operator. All
these eigenstates belong to a subspace of total Hilbert space where an action
of evolution operator can be identified with quantized discrete BKP equations
(synonym Miwa equations). The key ingredients of our construction are specific
eigenstates of a single three-dimensional R-matrix. These eigenstates are
boundary states for hidden three-dimensional structures of U_q(B_n^1) and
U_q(D_n^1)$.Comment: 13 page
Explicit Free Parameterization of the Modified Tetrahedron Equation
The Modified Tetrahedron Equation (MTE) with affine Weyl quantum variables at
N-th root of unity is solved by a rational mapping operator which is obtained
from the solution of a linear problem. We show that the solutions can be
parameterized in terms of eight free parameters and sixteen discrete phase
choices, thus providing a broad starting point for the construction of
3-dimensional integrable lattice models. The Fermat curve points parameterizing
the representation of the mapping operator in terms of cyclic functions are
expressed in terms of the independent parameters. An explicit formula for the
density factor of the MTE is derived. For the example N=2 we write the MTE in
full detail. We also discuss a solution of the MTE in terms of bosonic
continuum functions.Comment: 28 pages, 3 figure
Quantum 2+1 evolution model
A quantum evolution model in 2+1 discrete space - time, connected with 3D
fundamental map R, is investigated. Map R is derived as a map providing a zero
curvature of a two dimensional lattice system called "the current system". In a
special case of the local Weyl algebra for dynamical variables the map appears
to be canonical one and it corresponds to known operator-valued R-matrix. The
current system is a kind of the linear problem for 2+1 evolution model. A
generating function for the integrals of motion for the evolution is derived
with a help of the current system. The subject of the paper is rather new, and
so the perspectives of further investigations are widely discussed.Comment: LaTeX, 37page
Quasiclassical and ultraquantum decay of superfluid turbulence
This letter addresses the question which, after a decade-long discussion,
still remains open: what is the nature of the ultraquantum regime of decay of
quantum turbulence? The model developed in this work reproduces both the
ultraquantum and the quasiclassical decay regimes and explains their
hydrodynamical natures. In the case where turbulence is generated by forcing at
some intermediate lengthscale, e.g. by the beam of vortex rings in the
experiment of Walmsley and Golov [Phys. Rev. Lett. {\bf 100}, 245301 (2008)],
we explained the mechanisms of generation of both ultraquantum and
quasiclassical regimes. We also found that the anisotropy of the beam is
important for generating the large scale motion associated with the
quasiclassical regime
Simple Estimation of X- Trion Binding Energy in Semiconductor Quantum Wells
A simple illustrative wave function with only three variational parameters is
suggested to calculate the binding energy of negatively charged excitons (X-)
as a function of quantum well width. The results of calculations are in
agreement with experimental data for GaAs, CdTe and ZnSe quantum wells, which
differ considerably in exciton and trion binding energy. The normalized X-
binding energy is found to be nearly independent of electron-to-hole mass ratio
for any quantum well heterostructure with conventional parameters. Its
dependence on quantum well width follows an universal curve. The curve is
described by a simple phenomenological equation.Comment: 8 pages, 3 Postscript figure
The Limit Theorems for Transportation Networks
2000 Mathematics Subject Classi cation: 60K25 (primary); 60F05, 37A50 (secondary)The questions of ergodicity and of existence of explicit formulas for the stationary distribution are examined for various types of transportation networks which can be viewed as polling models. Also several limit theorems are proved both for large symmetric and asymmetric networks.The paper has been prepared under nancial support of RFBR, grants 05-01-00256a and
07-01-00362-(01-110)-a
Conserved Charges in the Principal Chiral Model on a Supergroup
The classical principal chiral model in 1+1 dimensions with target space a
compact Lie supergroup is investigated. It is shown how to construct a local
conserved charge given an invariant tensor of the Lie superalgebra. We
calculate the super-Poisson brackets of these currents and argue that they are
finitely generated. We show how to derive an infinite number of local charges
in involution. We demonstrate that these charges Poisson commute with the
non-local charges of the model
Highest weight modules over quantum queer Lie superalgebra U_q(q(n))
In this paper, we investigate the structure of highest weight modules over
the quantum queer superalgebra . The key ingredients are the
triangular decomposition of and the classification of finite
dimensional irreducible modules over quantum Clifford superalgebras. The main
results we prove are the classical limit theorem and the complete reducibility
theorem for -modules in the category .Comment: Definition 1.5 and Definition 6.1 are changed, and a remark is added
in the new versio
Comparison of artificial neural network, random forest and random perceptron forest for forecasting the spatial impurity distribution
The paper is present a comparison of modern approaches for predicting the spatial distribution in the upper soil layer of a chemical element chromium (Cr), which had spots of anomalously high concentration in the investigated region. The distribution of a normally distributed element copper (Cu) was also predicted. The data were obtained as a result of soil screening in the city of Tarko-Sale, Russia. Models based on artificial neural networks (multilayer perceptron MLP), random forests (RF), and also a model based on a random forest in which MLP used as a tree - a random perceptron forest (RMLPF) - were considered. The models were implemented in MATLAB. Approaches using artificial neural networks (MLP and RMLPF) were significantly more accurate for anomalously distributed Cr. Models based on RF algorithms proved to be more accurate for normally distributed copper. In general, the proposed model RMLPF was the most universal and accurate. © 2018 Author(s)
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