Abstract:
We analyze the spectral distribution of localisation in a 1D diagonally disordered chain of fragments each of which consist of m coupled two-level systems. The calculations performed by means of developed perturbation theory for joint statistics of advanced and retarded Green’s functions. We show that this distribution is rather inhomogeneous and reveals spectral regions of weakly localized states with sharp peaks of the localization degree in the centers of these regions.

Abstract:
In this paper, we consider informative potentialities of the "active" optical noise spectroscopy, under which we understand, generally, spectroscopy of response of a multilevel quantum system to the resonant optical field with its intensity modulated by "white" noise. We show that calculations of such a response can be most conveniently performed, in the linear approximation, by introducing the notion of light-intensity susceptibility (LIS) whose spectrum is determined by Laplace transform of the response to a small step-wise change of the optical field intensity. The results of calculations for a simple four-level quantum system show that its LIS spectrum may provide information not only about the ground-state structure (like conventional Faraday-rotation-based spin noise spectroscopy), but also about properties of the optical transitions (including nutation frequencies in the applied optical field). From the experimental point of view, such a noise spectroscopy of the intensity-related susceptibility can be especially efficient in combination with the up-to-date spectrum analyzers providing extremely fast data processing.

Abstract:
Non analytic behaviour of Hanle effect in InGaAs quantum dots is described in terms of a simple 4-level model. Despite simplicity the model makes it possible to explain the observed fracture of Hanle curve at zero magnetic field and obtain quantitative agreement with the experiment.

Abstract:
The nuclear spin fluctuations (NSF) as well as the dynamic nuclear polarization (DNP) and their effects on the electron spins in negatively charged (In,Ga)As/GaAs quantum dots have been studied by polarized pump-probe and photoluminescence spectroscopy techniques. The effective magnetic field of the NSF is about 30 mT at low excitation power. The NSF distribution becomes highly anisotropic at strong optical excitation by circularly polarized light with periodically alternating helicity. This phenomenon is attributed to a decrease of the nuclear spin entropy due to the hyperfine interaction with polarized electron spins. The DNP is limited to small values for intense, but short photoexcitation.

Abstract:
The intrinsic fluctuations of electron spins in semiconductors and atomic vapors generate a small, randomly-varying "spin noise" that can be detected by sensitive optical methods such as Faraday rotation. Recent studies have demonstrated that the frequency, linewidth, and lineshape of this spin noise directly reveals dynamical spin properties such as dephasing times, relaxation mechanisms and g-factors without perturbing the spins away from equilibrium. Here we demonstrate that spin noise measurements using wavelength-tunable probe light forms the basis of a powerful and novel spectroscopic tool to provide unique information that is fundamentally inaccessible via conventional linear optics. In particular, the wavelength dependence of the detected spin noise power can reveal homogeneous linewidths buried within inhomogeneously-broadened optical spectra, and can resolve overlapping optical transitions belonging to different spin systems. These new possibilities are explored both theoretically and via experiments on spin systems in opposite limits of inhomogeneous broadening (alkali atom vapors and semiconductor quantum dots).

Abstract:
Assume that the coefficients of a polynomial in a complex variable are Laurent polynomials in some complex parameters. The parameter space (a complex torus) splits into strata corresponding to different combinations of coincidence of the roots of the polynomial. For generic Laurent polynomials with fixed Newton polyhedra the Euler characteristics of these strata are also fixed. We provide explicit formulae for the Euler characteristics of the strata in terms of the polyhedra of the Laurent polynomials in the cases of degrees 2 and 3. We also obtain some corollaries in combinatorial geometry, which follows from two different ways of computing the Euler characteristic of the bifurcation set for a reduced polynomial of degree 2.

Abstract:
For a one-parameter deformation of an analytic complex function germ of several variables, there is defined its monodromy zeta-function. We give a Varchenko type formula for this zeta-function if the deformation is non-degenerate with respect to its Newton diagram.

Abstract:
The atoms moving within the waveguide with a critical frequency higher than the resonant frequency of atoms are suggested for obtaining the "slow light". Due to the absence of the resonant mode in the guide the atoms conserves excitation and coherence. The speed of this mixed excitation (electromagnetic field + moving atom) can be very low or even zero. The atoms moving within the waveguide with a critical frequency higher than the resonant frequency of atoms are suggested for obtaining the "slow light". Due to the absence of the resonant mode in the guide the atoms conserves excitation and coherence. The speed of this mixed excitation (electromagnetic field + moving atom) can be very low or even zero.

Abstract:
We solve exactly the spectral problem for the non-Hermitian operator $H_U f(x)\equiv f(U-1/x)/x^2$. Despite the absence of orthogonality, the eigen functions of this operator allow one to construct in a simple way the expansion of an arbitrary function in series. Explicit formulas for the expansion coefficients are presented. This problem is shown to be connected with that of calculating the strange attractor's density for the map $x_{n+1}=1/(U-x_n)$. The explicit formula for the strange attractor's density for this map is derived. All results are confirmed by direct computer simulations.

Abstract:
For the model Hamiltonian describing the electron-nuclear dynamics of a quantum dot, we obtained an exact expression for the limiting nuclear polarization as a function of the number of groups of equivalent nuclei. It is shown that the refinement of the model Hamiltonian by increasing the number of the groups results in a slow growth of the limiting nuclear polarization. This allowed us to put forward arguments in favor of applicability of the box-model (with all the nuclei being equivalent) for description of the electron-nuclear spin dynamics within the time intervals of around hundreds of periods of the optical orientation.