8,645 research outputs found
On the explicit solutions of the elliptic Calogero system
Let be the coordinates of particles on the circle,
interacting with the integrable potential , where
is the Weierstrass elliptic function. We show that every symmetric
elliptic function in is a meromorphic function in time. We
give explicit formulae for these functions in terms of genus theta
functions.Comment: 18 pages, Late
Dirac equation in the magnetic-solenoid field
We consider the Dirac equation in the magnetic-solenoid field (the field of a
solenoid and a collinear uniform magnetic field). For the case of Aharonov-Bohm
solenoid, we construct self-adjoint extensions of the Dirac Hamiltonian using
von Neumann's theory of deficiency indices. We find self-adjoint extensions of
the Dirac Hamiltonian in both above dimensions and boundary conditions at the
AB solenoid. Besides, for the first time, solutions of the Dirac equation in
the magnetic-solenoid field with a finite radius solenoid were found. We study
the structure of these solutions and their dependence on the behavior of the
magnetic field inside the solenoid. Then we exploit the latter solutions to
specify boundary conditions for the magnetic-solenoid field with Aharonov-Bohm
solenoid.Comment: 23 pages, 2 figures, LaTex fil
One-loop energy-momentum tensor in QED with electric-like background
We have obtained nonperturbative one-loop expressions for the mean
energy-momentum tensor and current density of Dirac's field on a constant
electric-like background. One of the goals of this calculation is to give a
consistent description of back-reaction in such a theory. Two cases of initial
states are considered: the vacuum state and the thermal equilibrium state.
First, we perform calculations for the vacuum initial state. In the obtained
expressions, we separate the contributions due to particle creation and vacuum
polarization. The latter contributions are related to the Heisenberg-Euler
Lagrangian. Then, we study the case of the thermal initial state. Here, we
separate the contributions due to particle creation, vacuum polarization, and
the contributions due to the work of the external field on the particles at the
initial state. All these contributions are studied in detail, in different
regimes of weak and strong fields and low and high temperatures. The obtained
results allow us to establish restrictions on the electric field and its
duration under which QED with a strong constant electric field is consistent.
Under such restrictions, one can neglect the back-reaction of particles created
by the electric field. Some of the obtained results generalize the calculations
of Heisenberg-Euler for energy density to the case of arbitrary strong electric
fields.Comment: 35 pages; misprints in the sign in definitions (40)-(43), and (68)
corrected, results unchange
Lambda-prophage induction modeled as a cooperative failure mode of lytic repression
We analyze a system-level model for lytic repression of lambda-phage in E.
coli using reliability theory, showing that the repressor circuit comprises 4
redundant components whose failure mode is prophage induction. Our model
reflects the specific biochemical mechanisms involved in regulation, including
long-range cooperative binding, and its detailed predictions for prophage
induction in E. coli under ultra-violet radiation are in good agreement with
experimental data.Comment: added referenc
Integration of D-dimensional 2-factor spaces cosmological models by reducing to the generalized Emden-Fowler equation
The D-dimensional cosmological model on the manifold describing the evolution of 2 Einsteinian factor spaces,
and , in the presence of multicomponent perfect fluid source is
considered. The barotropic equation of state for mass-energy densities and the
pressures of the components is assumed in each space. When the number of the
non Ricci-flat factor spaces and the number of the perfect fluid components are
both equal to 2, the Einstein equations for the model are reduced to the
generalized Emden-Fowler (second-order ordinary differential) equation, which
has been recently investigated by Zaitsev and Polyanin within discrete-group
analysis. Using the integrable classes of this equation one generates the
integrable cosmological models. The corresponding metrics are presented. The
method is demonstrated for the special model with Ricci-flat spaces
and the 2-component perfect fluid source.Comment: LaTeX file, no figure
Coherent states of non-relativistic electron in magnetic-solenoid field
We construct coherent states of a nonrelativistic electron in the
magnetic-solenoid field, which is a superposition of the Aharonov-Bohm field
and a collinear uniform magnetic field. In the problem under consideration
there are two kind of coherent states, the first kind corresponds to classical
trajectories which embrace the solenoid and the second one to trajectories
which do not. Mean coordinates in the constructed coherent states are moving
along classical trajectories, the coherent states maintain their form under the
time evolution, and represent a complete set of functions, which can be useful
in semi classical calculations. In the absence of the Aharonov-Bohm filed these
states are reduced to the well-known in the case of uniform magnetic field
Malkin-Man'ko coherent states.Comment: 11 pages, version accepted for publication in J. Phys. A, 3 figures
adde
On the multiplicity of the hyperelliptic integrals
Let be an Abelian integral, where
is a hyperelliptic polynomial of Morse type, a
horizontal family of cycles in the curves , and a polynomial
1-form in the variables and . We provide an upper bound on the
multiplicity of , away from the critical values of . Namely: $ord\
I(t) \leq n-1+\frac{n(n-1)}{2}\deg \omega <\deg H=n+1\delta(t)nHHI(t)\gamma(t)\textbf C^ n\gamma(t)\omegaHI(t)\{H=t\}
\subseteq \textbf C^2\omega\gamma(t)\textbf C^{n+1}ord I(t)\deg \omega$.Comment: 18 page
Variations in geoacoustic emissions in a deep borehole and its correlation with seismicity
Continuous geoacoustic emission (GAE) measurements were acquired using a three-component geophone
placed in a borehole at a depth of near 1000 m at Petropavlovsk-Kamchatsky starting in August 2000. Using
geophones consisting of magneto-elastic crystal ferromagnetic sensors, and installed at such a depth allows
measurement of natural geoacoustic background with signal amplitude less than 1×10-4 m/s3 in frequency band
from 3 to 1500 Hz. According to the data from a 4-year survey period the characteristics of diurnal geoacoustic
variations change before every earthquake with MLH≥ 5.0 that occurs at a distance of less than 300 km from the
observation point or before each earthquake with MLH≥5.5 occurring at distance R≤550 km from the observation
point. The changes in GAE regime correlate with the strongest earthquakes that occurred during survey period.
Measurements of the natural electromagnetic field of the Earth were carried out simultaneously with the help of
an underground electric antenna. The behavior of GAE in aseismic periods appears to be related to the effect of
diurnal variations of the natural electromagnetic field
Toda chains with type A_m Lie algebra for multidimensional m-component perfect fluid cosmology
We consider a D-dimensional cosmological model describing an evolution of
Ricci-flat factor spaces, M_1,...M_n (n > 2), in the presence of an m-component
perfect fluid source (n > m > 1). We find characteristic vectors, related to
the matter constants in the barotropic equations of state for fluid components
of all factor spaces.
We show that, in the case where we can interpret these vectors as the root
vectors of a Lie algebra of Cartan type A_m=sl(m+1,C), the model reduces to the
classical open m-body Toda chain.
Using an elegant technique by Anderson (J. Math. Phys. 37 (1996) 1349) for
solving this system, we integrate the Einstein equations for the model and
present the metric in a Kasner-like form.Comment: LaTeX, 2 ps figure
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