10,988 research outputs found
On the reduction of the multidimensional Schroedinger equation to a first order equation and its relation to the pseudoanalytic function theory
Given a particular solution of a one-dimensional stationary Schroedinger
equation (SE) this equation of second order can be reduced to a first order
linear differential equation. This is done with the aid of an auxiliary Riccati
equation. We show that a similar fact is true in a multidimensional situation
also. We consider the case of two or three independent variables. One
particular solution of (SE) allows us to reduce this second order equation to a
linear first order quaternionic differential equation. As in one-dimensional
case this is done with the aid of an auxiliary Riccati equation. The resulting
first order quaternionic equation is equivalent to the static Maxwell system.
In the case of two independent variables it is the Vekua equation from theory
of generalized analytic functions. We show that even in this case it is
necessary to consider not complex valued functions only, solutions of the Vekua
equation but complete quaternionic functions. Then the first order quaternionic
equation represents two separate Vekua equations, one of which gives us
solutions of (SE) and the other can be considered as an auxiliary equation of a
simpler structure. For the auxiliary equation we always have the corresponding
Bers generating pair, the base of the Bers theory of pseudoanalytic functions,
and what is very important, the Bers derivatives of solutions of the auxiliary
equation give us solutions of the main Vekua equation and as a consequence of
(SE). We obtain an analogue of the Cauchy integral theorem for solutions of
(SE). For an ample class of potentials (which includes for instance all radial
potentials), this new approach gives us a simple procedure allowing to obtain
an infinite sequence of solutions of (SE) from one known particular solution
On a factorization of second order elliptic operators and applications
We show that given a nonvanishing particular solution of the equation
(divpgrad+q)u=0 (1) the corresponding differential operator can be factorized
into a product of two first order operators. The factorization allows us to
reduce the equation (1) to a first order equation which in a two-dimensional
case is the Vekua equation of a special form. Under quite general conditions on
the coefficients p and q we obtain an algorithm which allows us to construct in
explicit form the positive formal powers (solutions of the Vekua equation
generalizing the usual powers of the variable z). This result means that under
quite general conditions one can construct an infinite system of exact
solutions of (1) explicitly, and moreover, at least when p and q are real
valued this system will be complete in ker(divpgrad+q) in the sense that any
solution of (1) in a simply connected domain can be represented as an infinite
series of obtained exact solutions which converges uniformly on any compact
subset of . Finally we give a similar factorization of the operator
(divpgrad+q) in a multidimensional case and obtain a natural generalization of
the Vekua equation which is related to second order operators in a similar way
as its two-dimensional prototype does
Quaternionic factorization of the Schroedinger operator and its applications to some first order systems of mathematical physics
We consider the following first order systems of mathematical physics.
1.The Dirac equation with scalar potential. 2.The Dirac equation with
electric potential. 3.The Dirac equation with pseudoscalar potential. 4.The
system describing non-linear force free magnetic fields or Beltrami fields with
nonconstant proportionality factor. 5.The Maxwell equations for slowly changing
media. 6.The static Maxwell system.
We show that all this variety of first order systems reduces to a single
quaternionic equation the analysis of which in its turn reduces to the solution
of a Schroedinger equation with biquaternionic potential. In some important
situations the biquaternionic potential can be diagonalized and converted into
scalar potentials
Instability of the Two-Dimensional Metallic Phase to Parallel Magnetic Field
We report on magnetotransport studies of the unusual two-dimensional metallic
phase in high mobility Si-MOS structures. We have observed that the magnetic
field applied in the 2D plane suppresses the metallic state, causing the
resistivity to increase dramatically by more than 30 times. Over the total
existence range of the metallic state, we have found three distinct types of
the magnetoresistance, related to the corresponding quantum corrections to the
conductivity. Our data suggest that the unusual metallic state is a consequence
of both spin- and Coulomb-interaction effects.Comment: 6 pages, Latex, 4 ps fig
On a complex differential Riccati equation
We consider a nonlinear partial differential equation for complex-valued
functions which is related to the two-dimensional stationary Schrodinger
equation and enjoys many properties similar to those of the ordinary
differential Riccati equation as, e.g., the famous Euler theorems, the Picard
theorem and others. Besides these generalizations of the classical
"one-dimensional" results we discuss new features of the considered equation
like, e.g., an analogue of the Cauchy integral theorem
Comparative study of radio pulses from simulated hadron-, electron-, and neutrino-initiated showers in ice in the GeV-PeV range
High energy particle showers produce coherent Cherenkov radio emission in
dense, radio-transparent media such as cold ice. Using PYTHIA and GEANT
simulation tools, we make a comparative study among electromagnetic (EM) and
hadronic showers initiated by single particles and neutrino showers initiated
by multiple particles produced at the neutrino-nucleon event vertex. We include
all the physics processes and do a complete 3-D simulation up to 100 TeV for
all showers and to 1 PeV for electron and neutrino induced showers. We
calculate the radio pulses for energies between 100 GeV and 1 PeV and find
hadron showers, and consequently neutrino showers, are not as efficient below 1
PeV at producing radio pulses as the electromagnetic showers. The agreement
improves as energy increases, however, and by a PeV and above the difference
disappears. By looking at the 3-D structure of the showers in time, we show
that the hadronic showers are not as compact as the EM showers and hence the
radiation is not as coherent as EM shower emission at the same frequency. We
show that the ratio of emitted pulse strength to shower tracklength is a
function only of a single, coherence parameter, independent of species and
energy of initiating particle.Comment: a few comments added, to bo published in PRD Nov. issue, 10 pages, 3
figures in tex file, 3 jpg figures in separate files, and 1 tabl
On the Klein-Gordon equation and hyperbolic pseudoanalytic function theory
Elliptic pseudoanalytic function theory was considered independently by Bers
and Vekua decades ago. In this paper we develop a hyperbolic analogue of
pseudoanalytic function theory using the algebra of hyperbolic numbers. We
consider the Klein-Gordon equation with a potential. With the aid of one
particular solution we factorize the Klein-Gordon operator in terms of two
Vekua-type operators. We show that real parts of the solutions of one of these
Vekua-type operators are solutions of the considered Klein-Gordon equation.
Using hyperbolic pseudoanalytic function theory, we then obtain explicit
construction of infinite systems of solutions of the Klein-Gordon equation with
potential. Finally, we give some examples of application of the proposed
procedure
Flow diagram of the metal-insulator transition in two dimensions
The discovery of the metal-insulator transition (MIT) in two-dimensional (2D)
electron systems challenged the veracity of one of the most influential
conjectures in the physics of disordered electrons, which states that `in two
dimensions, there is no true metallic behaviour'; no matter how weak the
disorder, electrons would be trapped and unable to conduct a current. However,
that theory did not account for interactions between the electrons. Here we
investigate the interplay between the electron-electron interactions and
disorder near the MIT using simultaneous measurements of electrical resistivity
and magnetoconductance. We show that both the resistance and interaction
amplitude exhibit a fan-like spread as the MIT is crossed. From these data we
construct a resistance-interaction flow diagram of the MIT that clearly reveals
a quantum critical point, as predicted by the two-parameter scaling theory
(Punnoose and Finkel'stein, Science 310, 289 (2005)). The metallic side of this
diagram is accurately described by the renormalization group theory without any
fitting parameters. In particular, the metallic temperature dependence of the
resistance sets in when the interaction amplitude reaches gamma_2 = 0.45 - a
value in remarkable agreement with the one predicted by the theory.Comment: as publishe
Synthesis and study of the antimicrobial activity of nifuroxazide derivatives
The number of infections caused by microorganisms that are resistant to antibiotics and synthetic antibacterial drugs is growing fast worldwide. This is one of the most important and urgent problems in health care. The main efforts of researchers around the world are focused on solving this issue. Nitrofurans represent one of the most effective classes of antibacterial drugs. We have synthesized 4 analogues of nifuroxazide – a well known nitrofuran antibiotic – and confirmed their structures by NMR, IR spectroscopy, and mass-spectrometry. All of the obtained compounds were studied for antimicrobial and antifungal activity. Activity against Escherichia coli, Staphylococcus aureus, Staphylococcus haemolyticus, and Pseudomonas aeruginosa was evaluated by the agar diffusion method. The synthesized compounds suppressed the growth of all the studied bacterial strains except Escherichia coli; the diameter of the inhibition zones ranged from 13.5 to 28 mm depending on the concentration of the tested compound and bacterial strain. One of the compounds studied in this project – the pyridine analogue of nifuroxazide – exceeded the activity of the standard (nifuroxazide) against the Staphylococcus aureus. The inhibitory activity of the synthesized compounds against the Candida albicans and Cryptococcus neoformans yeasts was determined using the microdilution method. The results were assessed according to the indicator color change. None of the studied compounds showed activity against these cultures. The obtained results confirm that substituted nifuroxazides have significant antimicrobial activity and, therefore, can be considered as promising candidates for developing new antibacterial drugs.The number of infections caused by microorganisms that are resistant to antibiotics and synthetic antibacterial drugs is growing fast worldwide. This is one of the most important and urgent problems in health care. The main efforts of researchers around the world are focused on solving this issue. Nitrofurans represent one of the most effective classes of antibacterial drugs. We have synthesized 4 analogues of nifuroxazide – a well known nitrofuran antibiotic – and confirmed their structures by NMR, IR spectroscopy, and mass-spectrometry. All of the obtained compounds were studied for antimicrobial and antifungal activity. Activity against Escherichia coli, Staphylococcus aureus, Staphylococcus haemolyticus, and Pseudomonas aeruginosa was evaluated by the agar diffusion method. The synthesized compounds suppressed the growth of all the studied bacterial strains except Escherichia coli; the diameter of the inhibition zones ranged from 13.5 to 28 mm depending on the concentration of the tested compound and bacterial strain. One of the compounds studied in this project – the pyridine analogue of nifuroxazide – exceeded the activity of the standard (nifuroxazide) against the Staphylococcus aureus. The inhibitory activity of the synthesized compounds against the Candida albicans and Cryptococcus neoformans yeasts was determined using the microdilution method. The results were assessed according to the indicator color change. None of the studied compounds showed activity against these cultures. The obtained results confirm that substituted nifuroxazides have significant antimicrobial activity and, therefore, can be considered as promising candidates for developing new antibacterial drugs
A Droplet State in an Interacting Two-Dimensional Electron System
It is well known that the dielectric constant of two-dimensional (2D)
electron system goes negative at low electron densities. A consequence of the
negative dielectric constant could be the formation of the droplet state. The
droplet state is a two-phase coexistence region of high density liquid and low
density "gas". In this paper, we carry out energetic calculations to study the
stability of the droplet ground state. The possible relevance of the droplet
state to recently observed 2D metal-insulator transition is also discussed.Comment: 4 pages, 4 figures. To appear in Phys. Rev. B (Rapid Communications
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