Численное восстановление функции распределения по энергии электронов в плазме по спектру излучения

The results of the numerical solution of the integral equation of the first kind occurred under the operation of distribution function recovery on electrons energy through the spectrum of radiation are presented. The Tikhonov functional with the stabilizers of the first and the second order is used.Приведены результаты численного решения интегрального уравнения первого рода, возникающего при операции восстановления функции распределения по энергии электронов (ФРЭЭ) по спектру тормозного излучения. Использован функционал Тихонова со стабилизаторами первого и второго порядка

Nearest-neighbor distribution for singular billiards

The exact computation of the nearest-neighbor spacing distribution P(s) is performed for a rectangular billiard with point-like scatterer inside for periodic and Dirichlet boundary conditions and it is demonstrated that for large s this function decreases exponentially. Together with the results of [Bogomolny et al., Phys. Rev. E 63, 036206 (2001)] it proves that spectral statistics of such systems is of intermediate type characterized by level repulsion at small distances and exponential fall-off of the nearest-neighbor distribution at large distances. The calculation of the n-th nearest-neighbor spacing distribution and its asymptotics is performed as well for any boundary conditions.Comment: 38 pages, 10 figure

Magnetic fluctuations in 2D metals close to the Stoner instability

We consider the effect of potential disorder on magnetic properties of a two-dimensional metallic system (with conductance $g\gg 1$) when interaction in the triplet channel is so strong that the system is close to the threshold of the Stoner instability. We show, that under these conditions there is an exponentially small probability for the system to form local spin droplets which are local regions with non zero spin density. Using a non-local version of the optimal fluctuation method we find analytically the probability distribution and the typical spin of a local spin droplet (LSD). In particular, we show that both the probability to form a LSD and its typical spin are independent of the size of the droplet (within the exponential accuracy). The LSDs manifest themselves in temperature dependence of observable quantities. We show, that below certain cross-over temperature the paramagnetic susceptibility acquires the Curie-like temperature dependence, while the dephasing time (extracted from magneto-resistance measurements) saturates.Comment: 15 pages, 4 figure

Ballistic electron motion in a random magnetic field

Using a new scheme of the derivation of the non-linear $\sigma$-model we consider the electron motion in a random magnetic field (RMF) in two dimensions. The derivation is based on writing quasiclassical equations and representing their solutions in terms of a functional integral over supermatrices $Q$ with the constraint $Q^2=1$. Contrary to the standard scheme, neither singling out slow modes nor saddle-point approximation are used. The $\sigma$-model obtained is applicable at the length scale down to the electron wavelength. We show that this model differs from the model with a random potential (RP).However, after averaging over fluctuations in the Lyapunov region the standard $\sigma$-model is obtained leading to the conventional localization behavior.Comment: 10 pages, no figures, to be submitted in PRB v2: Section IV is remove

Peculiarities of the stochastic motion in antiferromagnetic nanoparticles

Antiferromagnetic (AFM) materials are widely used in spintronic devices as passive elements (for stabilization of ferromangetic layers) and as active elements (for information coding). In both cases switching between the different AFM states depends in a great extent from the environmental noise. In the present paper we derive the stochastic Langevin equations for an AFM vector and corresponding Fokker-Planck equation for distribution function in the phase space of generalised coordinate and momentum. Thermal noise is modeled by a random delta-correlated magnetic field that interacts with the dynamic magnetisation of AFM particle. We analyse in details a particular case of the collinear compensated AFM in the presence of spin-polarised current. The energy distribution function for normal modes in the vicinity of two equilibrium states (static and stationary) in sub- and super-critical regimes is found. It is shown that the noise-induced dynamics of AFM vector has pecuilarities compared to that of magnetisation vector in ferromagnets.Comment: Submitted to EPJ ST, presented at the 4-th Conference on Statistical Physics, Lviv, Ukraine, 201

Energy level dynamics in systems with weakly multifractal eigenstates: equivalence to 1D correlated fermions

It is shown that the parametric spectral statistics in the critical random matrix ensemble with multifractal eigenvector statistics are identical to the statistics of correlated 1D fermions at finite temperatures. For weak multifractality the effective temperature of fictitious 1D fermions is proportional to (1-d_{n})/n, where d_{n} is the fractal dimension found from the n-th moment of inverse participation ratio. For large energy and parameter separations the fictitious fermions are described by the Luttinger liquid model which follows from the Calogero-Sutherland model. The low-temperature asymptotic form of the two-point equal-parameter spectral correlation function is found for all energy separations and its relevance for the low temperature equal-time density correlations in the Calogero-Sutherland model is conjectured.Comment: 4 pages, Revtex, final journal versio

Spectral Correlations from the Metal to the Mobility Edge

We have studied numerically the spectral correlations in a metallic phase and at the metal-insulator transition. We have calculated directly the two-point correlation function of the density of states $R(s,s')$. In the metallic phase, it is well described by the Random Matrix Theory (RMT). For the first time, we also find numerically the diffusive corrections for the number variance $$ predicted by Al'tshuler and Shklovski\u{\i}. At the transition, at small energy scales, $R(s-s')$ starts linearly, with a slope larger than in a metal. At large separations $|s - s'| \gg 1$, it is found to decrease as a power law $R(s,s') \sim - c / |s -s'|^{2-\gamma}$ with $c \sim 0.041$ and $\gamma \sim 0.83$, in good agreement with recent microscopic predictions. At the transition, we have also calculated the form factor $\tilde K(t)$, Fourier transform of $R(s-s')$. At large $s$, the number variance contains two terms $= B ^\gamma + 2 \pi \tilde K(0) where$\tilde{K}(0)$is the limit of the form factor for$t \to 0$.Comment: 7 RevTex-pages, 10 figures. Submitted to PR

Andreev reflections in the pseudogap state of cuprate supercondcutors

We propose that, if the pseudogap state in the cuprate superconductors can be described in terms of the phase-incoherent preformed pairs, there should exist Andreev reflection from these pairs even above the superconducting transition temperature, $T_c$. After giving qualitative arguments for this effect, we present more quantitative calculations based on the Bogoliubov--de Gennes equation. Experimental observations of the effects of Andreev reflections above $T_c$---such as an enhanced tunneling conductance below the gap along the copper oxide plane---could provide unambiguous evidence for the preformed pairs in the pseudogap state.Comment: 5 pages, 1 figur

Theory of Two-Dimensional Quantum Heisenberg Antiferromagnets with a Nearly Critical Ground State

We present the general theory of clean, two-dimensional, quantum Heisenberg antiferromagnets which are close to the zero-temperature quantum transition between ground states with and without long-range N\'{e}el order. For N\'{e}el-ordered states, `nearly-critical' means that the ground state spin-stiffness, $\rho_s$, satisfies $\rho_s \ll J$, where $J$ is the nearest-neighbor exchange constant, while `nearly-critical' quantum-disordered ground states have a energy-gap, $\Delta$, towards excitations with spin-1, which satisfies $\Delta \ll J$. Under these circumstances, we show that the wavevector/frequency-dependent uniform and staggered spin susceptibilities, and the specific heat, are completely universal functions of just three thermodynamic parameters. Explicit results for the universal scaling functions are obtained by a $1/N$ expansion on the $O(N)$ quantum non-linear sigma model, and by Monte Carlo simulations. These calculations lead to a variety of testable predictions for neutron scattering, NMR, and magnetization measurements. Our results are in good agreement with a number of numerical simulations and experiments on undoped and lightly-doped $La_{2-\delta} Sr_{\delta}Cu O_4$.Comment: 81 pages, REVTEX 3.0, smaller updated version, YCTP-xxx

Multifractality and critical fluctuations at the Anderson transition

Critical fluctuations of wave functions and energy levels at the Anderson transition are studied for the family of the critical power-law random banded matrix ensembles. It is shown that the distribution functions of the inverse participation ratios (IPR) $P_q$ are scale-invariant at the critical point, with a power-law asymptotic tail. The IPR distribution, the multifractal spectrum and the level statistics are calculated analytically in the limits of weak and strong couplings, as well as numerically in the full range of couplings.Comment: 14 pages, 13 eps figure