1,481 research outputs found
Long-time asymptotic series for the Painleve II equation: Riemann-Hilbert approach
We elaborate a systematic way to obtain higher order contributions in the
nonlinear steepest descent method for Riemann-Hilbert problem associated with
homogeneous Painleve II equation. The problem is reformulated as a matrix
factorization problem on two circles and can be solved perturbatively reducing
it to finite systems of algebraic linear equations. The method is applied to
find explicitly long-time asymptotic behaviour for tau function of Painleve II
equation.Comment: 26 pages, 5 figure
The new approaches to problem of polymorbidity
High prevalence of polymorbidity in outpatient therapeutic practice calls for improvement of diagnostic approaches, in particular, the development of methods for its measurement and using the results for optimization the number of medical, rehabilitation, expert and prevention processes. The methodology of integrated evaluation of polymorbidity based on the principles of polyparametric analysis allows to stratify degree polymorbidity and significantly optimize the program of clinical supervision, treatment (including - assessing pharmacological load), prevention, rehabilitation, sanatorium selection, predicting the course and outcome of diseases, perform express-analysis of the degree of disability, cardiovascular risk in complex diagnostic and treatment intervention
Quality estimation of structurally ordered assembly for threaded connection welding
Structurally ordered assembly for threaded connection welding allowing supporting high accuracy of relative position of a product connectable components has been considere
On Landauer--B\"uttiker formalism from a quantum quench
We study transport in the free fermionic one-dimensional systems subjected to
arbitrary local potentials. The bias needed for the transport is modeled by the
initial highly non-equilibrium distribution where only half of the system is
populated. Additionally to that, the local potential is also suddenly changed
when the transport starts. For such a quench protocol we compute the Full
Counting Statistics (FCS) of the number of particles in the initially empty
part. In the thermo\-dynamic limit, the FCS can be expressed via the Fredholm
determinant with the kernel depending on the scattering data and Jost solutions
of the pre-quench and the post-quench potentials. We discuss the large-time
asymptotic behavior of the obtained determinant and observe that if two or more
bound states are present in the spectrum of the post-quench potential the
information about the initial state manifests itself in the persistent
oscillations of the FCS. On the contrary, when there are no bound states the
asymptotic behavior of the FCS is determined solely by the scattering data of
the post-quench potential, which for the current (the first moment) is given by
the Landauer--B\"uttiker formalism. The information about the initial state can
be observed only in the transient dynamics
Effective free-fermionic form factors and the XY spin chain
We introduce effective form factors for one-dimensional lattice fermions with
arbitrary phase shifts. We study tau functions defined as series of these form
factors. On the one hand we perform the exact summation and present tau
functions as Fredholm determinants in the thermodynamic limit. On the other
hand simple expressions of form factors allow us to present the corresponding
series as integrals of elementary functions. Using this approach we re-derive
the asymptotics of static correlation functions of the XY quantum chain at
finite temperature
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