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Crystalline silicon (Si) nanoparticles present an extremely promising object for bioimaging based on photoluminescence (PL) in the visible and near-infrared spectral regions, but their efficient PL emission in aqueous suspension is typically observed after wet chemistry procedures leading to residual toxicity issues. Here, we introduce ultrapure laser-synthesized Si-based quantum dots (QDs), which are water-dispersible and exhibit bright exciton PL in the window of relative tissue transparency near 800 nm. Based on the laser ablation of crystalline Si targets in gaseous helium, followed by ultrasound-assisted dispersion of the deposited films in physiological saline, the proposed method avoids any toxic by-products during the synthesis. We demonstrate efficient contrast of the Si QDs in living cells by following the exciton PL. We also show that the prepared QDs do not provoke any cytoxicity effects while penetrating into the cells and efficiently accumulating near the cell membrane and in the cytoplasm. Combined with the possibility of enabling parallel therapeutic channels, ultrapure laser-synthesized Si nanostructures present unique object for cancer theranostic applications.

A field-theoretic description of the critical behaviour of systems with quenched defects obeying a power law correlations ∼ |x| −a for large separations x is given. Directly for three-dimensional systems and different values of correlation parameter 2 ≤ a ≤ 3 a renormalization analysis of scaling function in the two-loop approximation is carried out, and the fixed points corresponding to stability of the various types of critical behaviour are identified. The obtained results essentially differ from results evaluated by double ε, δ -expansion. The critical exponents in the two-loop approximation are calculated with the use of the Pade-Borel summation technique.

We study the distribution of threshold forces at the depinning transition for an elastic system of finite size, driven by an external force in a disordered medium at zero temperature. Using the functional renormalization group (FRG) technique, we compute the distribution of pinning forces in the quasi-static limit. This distribution is universal up to two parameters, the average critical force, and its width. We discuss possible definitions for threshold forces in finite-size samples. We show how our results compare to the distribution of the latter computed recently within a numerical simulation of the so-called critical configuration.

We adapt the non-linear σ model to study the nonequilibrium critical dynamics of O(n) symmetric ferromagnetic system. Using the renormalization group analysis in d = 2 + ε dimensions we investigate the pure relaxation of the system starting from a completely ordered state. We find that the average magnetization obeys the long-time scaling behavior almost immediately after the system starts to evolve while the correlation and response functions demonstrate scaling behavior which is typical for aging phenomena. The corresponding fluctuation-dissipation ratio is computed to first order in ε and the relation between transverse and longitudinal fluctuations is discussed. [4] as in a ferromagnetic system below the critical temperature T c or by critical slowing down as in a ferromagnetic system exactly at criticality [5]. One expects that the critical aging phenomena can be cast into different universality classes of nonequilibrium critical dynamics. Most of studies consider the relaxation of a ferromagnetic system starting from a completely disordered state after quenching it to the fixed temperature T ≤ T c . It was found that the response function R(t, s) and the correlation function C(t, s) depend nontrivially on the ratio x = t/s similar to that found in glassy systems. Here s and t are waiting and observation times respectively. The distance from equilibrium can be measured by the fluctuation-dissipation ratio (FDR) X(t, s) = T R(t, s)/∂ s C(t, s). It has been argued that for critical aging the limit X ∞ = lim t,s→∞ X(t, s) is a novel universal quantity of critical phenomena [5]. The FDR was computed for the d dimensional spherical model [5], O(n) symmetric ferromagnetic model [6] and diluted spin models [7,8,9]. In all these systems X ∞ has values ranging between 0 and 1/2. The mean field calculations show that the aging behavior is modified in the presence of long-range correlations in the initial disordered state [10,11]. Much less known about the relaxation starting from an ordered state. The numerical simulations show that the correlation function demonstrates behavior which is typical for aging phenomena [8,12], while the magnetization obeys the long-time scaling behavior almost immediately after the system starts to evolve [13,14]. This observation was used to develop new effective numerical methods to determine the critical exponents, which are based on the short-time critical dynamics and do not require the time-consuming equilibration of the system [15]. However, up to now there is no any theoretical explanation why the long-time scaling behavior emerges already in the macroscopically early initial stage of relaxation and there is no theoretical framework which allows one to take properly into account the critical fluctuations in this regime of aging.In this paper we study the nonequilibrium critical dynamics of a ferromagnetic system starting from a completely ordered state. The long-distance properties of the O(n) symmetric system below the transition point can be related to the non-linear σ model d...

The Weyl semimetals are topologically protected from a gap opening against weak disorder in three dimensions. However, a strong disorder drives this relativistic semimetal through a quantum transition towards a diffusive metallic phase characterized by a finite density of states at the band crossing. This transition is usually described by a perturbative renormalization group in d = 2 + ε of a U (N ) Gross-Neveu model in the limit N → 0. Unfortunately, this model is not multiplicatively renormalizable in 2+ε dimensions: An infinite number of relevant operators are required to describe the critical behavior. Hence its use in a quantitative description of the transition beyond one-loop is at least questionable. We propose an alternative route, building on the correspondence between the Gross-Neveu and Gross-Neveu-Yukawa models developed in the context of high energy physics. It results in a model of Weyl fermions with a random non-Gaussian imaginary potential which allows one to study the critical properties of the transition within a d = 4 − ε expansion. We also discuss the characterization of the transition by the multifractal spectrum of wave functions.

We study the single particle density of states of a one-dimensional speckle potential, which is correlated and non-Gaussian. We consider both the repulsive and the attractive cases. The system is controlled by a single dimensionless parameter determined by the mass of the particle, the correlation length and the average intensity of the field. Depending on the value of this parameter, the system exhibits different regimes, characterized by the localization properties of the eigenfunctions. We calculate the corresponding density of states using the statistical properties of the speckle potential. We find good agreement with the results of numerical simulations.Comment: 11 pages, 11 figures, revtex

We study the long-distance behavior of the O(N ) model in the presence of random fields and random anisotropies correlated as ∼ 1/x d−σ for large separation x using the functional renormalization group. We compute the fixed points and analyze their regions of stability within a double ε = d − 4 and σ expansion. We find that the long-range disorder correlator remains analytic but generates short-range disorder whose correlator develops the usual cusp. This allows us to obtain the phase diagrams in (d, σ, N ) parameter space and compute the critical exponents to first order in ε and σ. We show that the standard renormalization group methods with a finite number of couplings used in previous studies of systems with long-range correlated random fields fail to capture all critical properties. We argue that our results may be relevant to the behavior of 3 He-A in aerogel.