75 research outputs found
Multiple Adaptive System of Identification
It will be useful for students, postgraduates and doctoral research scholars who study the real objects.This scientific work aims to represent some elements of the theory of identification that are important for both practical use and further theoretical research in order to build logically complete basic and applied theory of identification as mathematically reasonable theory of knowledge of the cause-and-effect relationship in the objects of the real world.
For those specialists who carry out theoretical and experimental researches (technical, economic, biological, social etc) of the real-world objects with the aim of their optimal adaptive control, diagnostics of state, forecasting the consequences and so on
Guided plasmons in graphene p-n junctions
Spatial separation of electrons and holes in graphene gives rise to existence
of plasmon waves confined to the boundary region. Theory of such guided plasmon
modes within hydrodynamics of electron-hole liquid is developed. For plasmon
wavelengths smaller than the size of charged domains plasmon dispersion is
found to be \omega ~ q^(1/4). Frequency, velocity and direction of propagation
of guided plasmon modes can be easily controlled by external electric field. In
the presence of magnetic field spectrum of additional gapless magnetoplasmon
excitations is obtained. Our findings indicate that graphene is a promising
material for nanoplasmonics.Comment: 4+ pages, 1 figure; published version, numerical estimates adde
Mesoscopic Spin-Hall Effect in 2D electron systems with smooth boundaries
Spin-Hall effect in ballistic 2D electron gas with Rashba-type spin-orbit
coupling and smooth edge confinement is studied. We predict that the interplay
of semiclassical electron motion and quantum dynamics of spins leads to several
distinct features in spin density along the edge that originate from
accumulation of turning points from many classical trajectories. Strong peak is
found near a point of the vanishing of electron Fermi velocity in the lower
spin-split subband. It is followed by a strip of negative spin density that
extends until the crossing of the local Fermi energy with the degeneracy point
where the two spin subbands intersect. Beyond this crossing there is a wide
region of a smooth positive spin density. The total amount of spin accumulated
in each of these features exceeds greatly the net spin across the entire edge.
The features become more pronounced for shallower boundary potentials,
controlled by gating in typical experimental setups.Comment: 4 pages, 4 figures, published versio
Decay of Quasi-Particle in a Quantum Dot: the role of Energy Resolution
The disintegration of quasiparticle in a quantum dot due to the electron
interaction is considered. It was predicted recently that above the energy
\eps^{*} = \Delta(g/\ln g)^{1/2} each one particle peak in the spectrum is
split into many components ( and are the one particle level spacing
and conductance). We show that the observed value of \eps^{*} should depend
on the experimental resolution \delta \eps. In the broad region of variation
of \delta \eps the should be replaced by \ln(\Delta/ g\delta \eps).
We also give the arguments against the delocalization transition in the Fock
space. Most likely the number of satellite peaks grows continuously with
energy, being at \eps \sim \eps^{*}, but remains finite at \eps >
\eps^{*}. The predicted logarithmic distribution of inter-peak spacings may be
used for experimental confirmation of the below-Golden-Rule decay.Comment: 5 pages, REVTEX, 2 eps figures, version accepted for publication in
Phys. Rev. Let
Chaos Thresholds in finite Fermi systems
The development of Quantum Chaos in finite interacting Fermi systems is
considered. At sufficiently high excitation energy the direct two-particle
interaction may mix into an eigen-state the exponentially large number of
simple Slater-determinant states. Nevertheless, the transition from Poisson to
Wigner-Dyson statistics of energy levels is governed by the effective high
order interaction between states very distant in the Fock space. The concrete
form of the transition depends on the way one chooses to work out the problem
of factorial divergency of the number of Feynman diagrams. In the proposed
scheme the change of statistics has a form of narrow phase transition and may
happen even below the direct interaction threshold.Comment: 9 pages, REVTEX, 2 eps figures. Enlarged versio
Quantum Mechanics with Random Imaginary Scalar Potential
We study spectral properties of a non-Hermitian Hamiltonian describing a
quantum particle propagating in a random imaginary scalar potential. Cast in
the form of an effective field theory, we obtain an analytical expression for
the ensemble averaged one-particle Green function from which we obtain the
density of complex eigenvalues. Based on the connection between non-Hermitian
quantum mechanics and the statistical mechanics of polymer chains, we determine
the distribution function of a self-interacting polymer in dimensions .Comment: 10 pages, 1 eps figur
Entropy production and wave packet dynamics in the Fock space of closed chaotic many-body systems
Highly excited many-particle states in quantum systems such as nuclei, atoms,
quantum dots, spin systems, quantum computers etc., can be considered as
``chaotic'' superpositions of mean-field basis states (Slater determinants,
products of spin or qubit states). This is due to a very high level density of
many-body states that are easily mixed by a residual interaction between
particles (quasi-particles). For such systems, we have derived simple
analytical expressions for the time dependence of energy width of wave packets,
as well as for the entropy, number of principal basis components and inverse
participation ratio, and tested them in numerical experiments. It is shown that
the energy width increases linearly and very quickly saturates.
The entropy of a system increases quadratically, at small
times, and after, can grow linearly, , before the saturation.
Correspondingly, the number of principal components determined by the entropy,
, or by the inverse participation ratio, increases
exponentially fast before the saturation. These results are explained in terms
of a cascade model which describes the flow of excitation in the Fock space of
basis components. Finally, a striking phenomenon of damped oscillations in the
Fock space at the transition to an equilibrium is discussed.Comment: RevTex, 14 pages including 12 eps-figure
Interaction-Driven Equilibrium and Statistical Laws in Small Systems. The Cerium Atom
It is shown that statistical mechanics is applicable to isolated quantum
systems with finite numbers of particles, such as complex atoms, atomic
clusters, or quantum dots in solids, where the residual two-body interaction is
sufficiently strong. This interaction mixes the unperturbed shell-model
(Hartree-Fock) basis states and produces chaotic many-body eigenstates. As a
result, an interaction-induced statistical equilibrium emerges in the system.
This equilibrium is due to the off-diagonal matrix elements of the Hamiltonian.
We show that it can be described by means of temperature introduced through the
canonical-type distribution. However, the interaction between the particles can
lead to prominent deviations of the equilibrium distribution of the occupation
numbers from the Fermi-Dirac shape. Besides that, the off-diagonal part of the
Hamiltonian gives rise to the increase of the effective temperature of the
system (statistical effect of the interaction). For example, this takes place
in the cerium atom which has four valence electrons and which is used in our
work to compare the theory with realistic numerical calculations.Comment: 25 pages, RevTeX, 5 figures in ps-format. Submitted to Phys. Rev.
Coherent propagation of interacting particles in a random potential: the Mechanism of enhancement
Coherent propagation of two interacting particles in weak random
potential is considered. An accurate estimate of the matrix element of
interaction in the basis of localized states leads to mapping onto the relevant
matrix model. This mapping allows to clarify the mechanism of enhancement of
the localization length which turns out to be rather different from the one
considered in the literature. Although the existence of enhancement is
transparent, an analytical solution of the matrix model was found only for very
short samples. For a more realistic situation numerical simulations were
performed. The result of these simulations is consistent with l_{2}/l_1 \sim
l_1^{\gamma} , where and are the single and two particle
localization lengths and the exponent depends on the strength of the
interaction. In particular, in the limit of strong particle-particle
interaction there is no enhancement of the coherent propagation at all ().Comment: 23 pages, REVTEX, 3 eps figures, improved version accepted for
publication in Phys. Rev.
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