Existence of the Abrikosov vortex state in two-dimensional type-II superconductors without pinning

Theory alternative to the vortex lattice melting theories is advertised. The vortex lattice melting theories are science fiction cond-mat/9811051 because the Abrikosov state is not the vortex lattice with crystalline long-range order. Since the fluctuation correction to the Abrikosov solution is infinite in the thermodynamic limit (K.Maki and H.Takayama, 1972) any fluctuation theory of the mixed state should consider a superconductor with finite sizes. Such nonperturbative theory for the easiest case of two-dimensional superconductor in the lowest Landau level approximation is presented in this work. The thermodynamic averages of the spatial average order parameter and of the Abrikosov parameter $\beta_{a}$ are calculated. It is shown that the position H_{c4} of the transition into the Abrikosov state (i.e. in the mixed state with long-range phase coherence) depends strongly on sizes of two-dimensional superconductor. Fluctuations eliminate the Abrikosov vortex state in a wide region of the mixed state of thin films with real sizes and without pinning disorders, i.e. H_{c4} << H_{c2}. The latter has experimental corroboration in Phys.Rev.Lett. 75, 2586 (1995).Comment: 4 pages, 0 figure

Preparation of facilities for fundamental research with ultracold neutrons at PNPI

The WWR-M reactor of PNPI offers a unique opportunity to prepare a source for ultracold neutrons (UCN) in an environment of high neutron flux (about 3*10^12 n/cm^2/s) at still acceptable radiation heat release (about 4*10^-3 W/g). It can be realized within the reactor thermal column situated close to the reactor core. With its large diameter of 1 m, this channel allows to install a 15 cm thick bismuth shielding, a graphite premoderator (300 dm^3 at 20 K), and a superfluid helium converter (35 dm^3). At a temperature of 1.2 K it is possible to remove the heat release power of about 20 W. Using the 4pi flux of cold neutrons within the reactor column can bring more than a factor 100 of cold neutron flux incident on the superfluid helium with respect to the present cold neutron beam conditions at the ILL reactor. The storage lifetime for UCN in superfluid He at 1.2 K is about 30 s, which is sufficient when feeding experiments requiring a similar filling time. The calculated density of UCN with energy between 50 neV and 250 neV in an experimental volume of 40 liters is about 10^4 n/cm^3. Technical solutions for realization of the project are discussed.Comment: 10 pages, more detail

Hastings' additivity counterexample via Dvoretzky's theorem

The goal of this note is to show that Hastings' counterexample to the additivity of minimal output von Neumann entropy can be readily deduced from a sharp version of Dvoretzky's theorem on almost spherical sections of convex bodies.Comment: 12 pages; v.2: added references, Appendix A expanded to make the paper essentially self-containe

Inverse spectral problems for Dirac operators with summable matrix-valued potentials

We consider the direct and inverse spectral problems for Dirac operators on $(0,1)$ with matrix-valued potentials whose entries belong to $L_p(0,1)$, $p\in[1,\infty)$. We give a complete description of the spectral data (eigenvalues and suitably introduced norming matrices) for the operators under consideration and suggest a method for reconstructing the potential from the corresponding spectral data.Comment: 32 page

Local Eigenvalue Density for General MANOVA Matrices

We consider random n\times n matrices of the form (XX*+YY*)^{-1/2}YY*(XX*+YY*)^{-1/2}, where X and Y have independent entries with zero mean and variance one. These matrices are the natural generalization of the Gaussian case, which are known as MANOVA matrices and which have joint eigenvalue density given by the third classical ensemble, the Jacobi ensemble. We show that, away from the spectral edge, the eigenvalue density converges to the limiting density of the Jacobi ensemble even on the shortest possible scales of order 1/n (up to \log n factors). This result is the analogue of the local Wigner semicircle law and the local Marchenko-Pastur law for general MANOVA matrices.Comment: Several small changes made to the tex

On the Two Spectra Inverse Problem for Semi-Infinite Jacobi Matrices

We present results on the unique reconstruction of a semi-infinite Jacobi operator from the spectra of the operator with two different boundary conditions. This is the discrete analogue of the Borg-Marchenko theorem for Schr{\"o}dinger operators in the half-line. Furthermore, we give necessary and sufficient conditions for two real sequences to be the spectra of a Jacobi operator with different boundary conditions.Comment: In this slightly revised version we have reworded some of the theorems, and we updated two reference

Reconstruction of field theory from excitation spectra of defects

We show how to reconstruct a field theory from the spectrum of bound states on a topological defect. We apply our recipe to the case of kinks in 1+1 dimensions with one or two bound states. Our recipe successfully yields the sine-Gordon and $\lambda \phi^4$ field theories when suitable bound state spectra are assumed. The recipe can also be used to globally reconstruct the inflaton potential of inflationary cosmology if the inflaton produces a topological defect. We discuss how defects can provide ``smoking gun'' evidence for a class of inflationary models.Comment: 10 pages, 4 figures. Included proof (Appendix B) that wall fluctuation potentials have supersymmetric form. Added reference

Influence of longitudinal magnetic field in the MPC channel on the density of generated plasma stream

The paper is devoted to experimental measurements and analysis of parameters of the plasma streams generated by magnetoplasma compressor (MPC) upgraded with an external axial magnetic field. Influence of the external axial magnetic field of 0.24 T on helium plasma streams (P=2 Torr) has been studied. The measurements of average electron density distributions were performedboth with and without an external axial B-field. Distributions of plasma electron density Ne (L) were measured with spectroscopy in the plasma stream and in the compression zone using Stark broadening of He I and He II spectral lines. Plasma-surface interaction processes were also analyzed.Представлено експериментальні вимірювання та аналіз параметрів плазмових потоків, що генеруються магнітоплазмовим компресором (МПК), який було оснащено зовнішнім магнітним полем. Вивчено вплив зовнішнього магнітного поля 0,24 Тл на потоки гелієвої плазми (Р=2 Торр). Представлено просторові розподіли електронної густини плазми як із зовнішнім магнітним полем, так і без нього. Розподіли електронної густини плазми Ne (L) отримано зі штарківського розширення спектральних ліній He I та He II. Також представлені вимірювання розподілів Ne (L) при налітанні пламового потоку МПК на сталеву мішень.Представлены экспериментальные измерения и анализ параметров плазменных потоков, генерируемых магнитоплазменным компрессором (МПК), который был оснащен внешним магнитным полем. Изучено влияние внешнего магнитного поля 0,24 Тл на потоки гелиевой плазмы (P=2 Торр). Представлены пространственные распределения электронной плотности плазмы как с внешним магнитным полем, так и без него. Распределения электронной плотности плазмы Ne (L) получены из штарковского уширения спектральных линий He I и He II. Также привeдены измерения распределений Ne (L) при налетании плазменного потока МПК на мишень из нержавеющей стали