77 research outputs found
Field-asymmetric transverse magnetoresistance in a nonmagnetic quantum-size structure
A new phenomenon is observed experimentally in a heavily doped asymmetric
quantum-size structure in a magnetic field parallel to the quantum-well layers
- a transverse magnetoresistance which is asymmetric in the field (there can
even be a change in sign) and is observed in the case that the structure has a
built-in lateral electric field. A model of the effect is proposed. The
observed asymmetry of the magnetoresistance is attributed to an additional
current contribution that arises under nonequilibrium conditions and that is
linear in the gradient of the electrochemical potential and proportional to the
parameter characterizing the asymmetry of the spectrum with respect to the
quasimomentum.Comment: 10 pages, 5 figures. For correspondence, mail to
[email protected]
Quasi-linear Stokes phenomenon for the second Painlev\'e transcendent
Using the Riemann-Hilbert approach, we study the quasi-linear Stokes
phenomenon for the second Painlev\'e equation . The
precise description of the exponentially small jump in the dominant solution
approaching as is given. For the asymptotic power
expansion of the dominant solution, the coefficient asymptotics is found.Comment: 19 pages, LaTe
On the location of poles for the Ablowitz-Segur family of solutions to the second Painlev\'e equation
Using a simple operator-norm estimate we show that the solution to the second
Painlev\'e equation within the Ablowitz-Segur family is pole-free in a well
defined region of the complex plane of the independent variable. The result is
illustrated with several numerical examples.Comment: 8 pages, to appear in Nonlinearit
Hard loss of stability in Painlev\'e-2 equation
A special asymptotic solution of the Painlev\'e-2 equation with small
parameter is studied. This solution has a critical point corresponding to
a bifurcation phenomenon. When the constructed solution varies slowly
and when the solution oscillates very fast. We investigate the
transitional layer in detail and obtain a smooth asymptotic solution, using a
sequence of scaling and matching procedures
Quasi-linear Stokes phenomenon for the Painlev\'e first equation
Using the Riemann-Hilbert approach, the -function corresponding to the
solution of the first Painleve equation, , with the asymptotic
behavior as is constructed. The
exponentially small jump in the dominant solution and the coefficient
asymptotics in the power-like expansion to the latter are found.Comment: version accepted for publicatio
An Isomonodromy Cluster of Two Regular Singularities
We consider a linear matrix ODE with two coalescing regular
singularities. This coalescence is restricted with an isomonodromy condition
with respect to the distance between the merging singularities in a way
consistent with the ODE. In particular, a zero-distance limit for the ODE
exists. The monodromy group of the limiting ODE is calculated in terms of the
original one. This coalescing process generates a limit for the corresponding
nonlinear systems of isomonodromy deformations. In our main example the latter
limit reads as , where is the -th Painlev\'e equation. We
also discuss some general problems which arise while studying the
above-mentioned limits for the Painlev\'e equations.Comment: 44 pages, 8 figure
- …