Dunajski generalization of the second heavenly equation: dressing method and the hierarchy

Dunajski generalization of the second heavenly equation is studied. A dressing scheme applicable to Dunajski equation is developed, an example of constructing solutions in terms of implicit functions is considered. Dunajski equation hierarchy is described, its Lax-Sato form is presented. Dunajsky equation hierarchy is characterized by conservation of three-dimensional volume form, in which a spectral variable is taken into account.Comment: 13 page

Solutions for real dispersionless Veselov-Novikov hierarchy

We investigate the dispersionless Veselov-Novikov (dVN) equation based on the framework of dispersionless two-component BKP hierarchy. Symmetry constraints for real dVN system are considered. It is shown that under symmetry reductions, the conserved densities are therefore related to the associated Faber polynomials and can be solved recursively. Moreover, the method of hodograph transformation as well as the expressions of Faber polynomials are used to find exact real solutions of the dVN hierarchy.Comment: 14 page

Lattice and q-difference Darboux-Zakharov-Manakov systems via ∂ˉ\bar{\partial}-dressing method

A general scheme is proposed for introduction of lattice and q-difference variables to integrable hierarchies in frame of $\bar{\partial}$-dressing method . Using this scheme, lattice and q-difference Darboux-Zakharov-Manakov systems of equations are derived. Darboux, B\"acklund and Combescure transformations and exact solutions for these systems are studied.Comment: 8 pages, LaTeX, to be published in J Phys A, Letters

New Perturbation Theory for Nonstationary Anharmonic Oscillator

The new perturbation theory for the problem of nonstationary anharmonic oscillator with polynomial nonstationary perturbation is proposed. As a zero order approximation the exact wave function of harmonic oscillator with variable frequency in external field is used. Based on some intrinsic properties of unperturbed wave function the variational-iterational method is proposed, that make it possible to correct both the amplitude and the phase of wave function. As an application the first order correction are proposed both for wave function and S-matrix elements for asymmetric perturbation potential of type $V(x,\tau)=\alpha (\tau)x^3+\beta (\tau)x^4.$ The transition amplitude ''ground state - ground state'' $W_{00}(\lambda ;\rho)$ is analyzed in detail depending on perturbation parameter $\lambda$ (including strong coupling region $$ $\sim 1$) and one-dimensional refraction coefficient $\rho$.Comment: LaTeX, 13 page

Non-Linear Evolution Equations with Non-Analytic Dispersion Relations in 2+1 Dimensions. Bilocal Approach

A method is proposed of obtaining (2+1)-dimensional non- linear equations with non-analytic dispersion relations. Bilocal formalism is shown to make it possible to represent these equations in a form close to that for their counterparts in 1+1 dimensions.Comment: 13 pages, to be published in J. Phys.

Thermal X-rays from Millisecond Pulsars: Constraining the Fundamental Properties of Neutron Stars

Abridged) We model the X-ray properties of millisecond pulsars (MSPs) by considering hot spot emission from a weakly magnetized rotating neutron star (NS) covered by an optically-thick hydrogen atmosphere. We investigate the limitations of using the thermal X-ray pulse profiles of MSPs to constrain the mass-to-radius ($M/R$) ratio of the underlying NS. The accuracy is strongly dependent on the viewing angle and magnetic inclination. For certain systems, the accuracy is ultimately limited only by photon statistics implying that future X-ray observatories could, in principle, achieve constraints on $M/R$ and hence the NS equation of state to better than $\sim$5%. We demonstrate that valuable information regarding the basic properties of the NS can be extracted even from X-ray data of fairly limited photon statistics through modeling of archival spectroscopic and timing observations of the nearby isolated PSRs J0030+0451 and J2124--3358. The X-ray emission from these pulsars is consistent with the presence of a hydrogen atmosphere and a dipolar magnetic field configuration, in agreement with previous findings for PSR J0437--4715. For both MSPs, the favorable geometry allows us to place interesting limits on the allowed $M/R$ of NSs. Assuming 1.4 M$_{\odot}$, the stellar radius is constrained to be $R > 9.4$ km and $R > 7.8$ km (68% confidence) for PSRs J0030+0451 and J2124--3358, respectively. We explore the prospects of using future observatories such as \textit{Constellation-X} and \textit{XEUS} to conduct blind X-ray timing searches for MSPs not detectable at radio wavelengths due to unfavorable viewing geometry. Using the observational constraints on the pulsar obliquities we are also able to place strong constraints on the magnetic field evolution model proposed by Ruderman.Comment: 9 pages, 7 figures, published in the Astrophysical Journal (Volume 689, Issue 1, pp. 407-415

Statistical Estimation of Quantum Tomography Protocols Quality

A novel operational method for estimating the efficiency of quantum state tomography protocols is suggested. It is based on a-priori estimation of the quality of an arbitrary protocol by means of universal asymptotic fidelity distribution and condition number, which takes minimal value for better protocol. We prove the adequacy of the method both with numerical modeling and through the experimental realization of several practically important protocols of quantum state tomography

Ground states of Heisenberg evolution operator in discrete three-dimensional space-time and quantum discrete BKP equations

In this paper we consider three-dimensional quantum q-oscillator field theory without spectral parameters. We construct an essentially big set of eigenstates of evolution with unity eigenvalue of discrete time evolution operator. All these eigenstates belong to a subspace of total Hilbert space where an action of evolution operator can be identified with quantized discrete BKP equations (synonym Miwa equations). The key ingredients of our construction are specific eigenstates of a single three-dimensional R-matrix. These eigenstates are boundary states for hidden three-dimensional structures of U_q(B_n^1) and U_q(D_n^1)$.Comment: 13 page

IR spectral analysis for the diagnostics of crust earthquake precursors

Some possible physical processes are analysed that cause, under the condition of additional ionisation in a pre-breakdown electric field, emissions in the infrared (IR) interval. The atmospheric transparency region of the IR spectrum at wavelengths of 7–15 μm is taken into account. This transparency region corresponds to spectral lines of small atmospheric constituents like CH<sub>4</sub>, CO<sub>2</sub>, N<sub>2</sub>O, NO<sub>2</sub>, NO, and O<sub>3</sub>. The possible intensities of the IR emissions observable in laboratories and in nature are estimated. The acceleration process of the electrons in the pre-breakdown electrical field before its adhesion to the molecules is analyzed. For daytime conditions, modifications of the adsorption spectra of the scattered solar emissions are studied; for nighttime, variations of emission spectra may be used for the analysis

Polarization ququarts

We discuss the concept of polarization states of four-dimensional quantum systems based on frequency non-degenerate biphoton field. Several quantum tomography protocols were developed and implemented for measurement of an arbitrary state of ququart. A simple method that does not rely on interferometric technique is used to generate and measure the sequence of states that can be used for quantum communication purposes.Comment: 13 pages, 10 figure