Harmonic system in a random field

We study a model which may describe a dislocation-free commensurate phase in the presence of quenched impurities, or a vortex-freeXY model in a quenched random anisotropy. For a dimensionD between 2 and 4, we obtain an algebraic decay of the spin pair correlation function. This result was already obtained (without excluding vortices) by Aharony and Pytte, but our exponent is different and vanishes whenD approaches 4. ForD=2, a phase transition is obtained in agreement with previous theories, but without using the replica trick, and the low temperature phase is found to be more disordered than predicted by Cardy and Ostlund. Our conclusions disagree with the results of Dotsenko and Feigelman.     

Nonlinear Schrödinger equations from prequantum classical statistical field theory

We derive some important features of the standard quantum mechanics from a certain classical-like model—prequantum classical statistical field theory, PCSFT. In this approach correspondence between classical and quantum quantities is established through asymptotic expansions. PCSFT induces not only linear Schrödinger's equation, but also its nonlinear generalizations. This coupling with “nonlinear wave mechanics” is used to evaluate the small parameter of PCSFT.     

The possibility of describing a two-particle quantum system and interparticle correlations in the self-consistent field approximation

The possibility of determining the energy spectrum and the wave function structure of the stationary states of a model two-particle system is examined in the self-consistent field approximation. The results of exact calculations are compared with the data obtained in the self-consistent field approximation with the use of orthogonal and nonorthogonal orbitals. The possibility of using these approximations for describing the interparticle quantum correlations is discussed.     

Spatial correlations in the near field of random media

The conventional coherence theory suggests that the fields radiated by statistically homogeneous sources correlate over spatial regions of the order of the wavelength irrespective of the distance from the surface of the source. Contrary to these predictions, we show that the spatial correlations of optical fields in close proximity of highly scattering, randomly inhomogeneous media depend on this distance and, moreover, their extent can be significantly smaller than the wavelength. The contribution of evanescent fields is experimentally demonstrated and the coherence length in the near field is shown to relate to the coherence properties at the surface which are, in turn, determined by the structural characteristics of the random media.     

Pairwise correlations and wetting transitions at a solid-gas interface

We summarize the main results of our study of the density-density correlation function for Sullivan's model of a gas adsorbed on a solid substrate. In the approach to complete wetting, when a thick film of liquid density is adsorbed at the substrate, long-ranged transverse (parallel to the surface) correlations develop at the edge of the film where the density profile is similar to that of a liquid-gas interface. For a class I wetting situation the range of the transverse correlations increases and ultimately diverges as the bulk gas pressure approaches the saturated vapour pressure. We comment on other situations where long-ranged correlations arise and mention the possibility of observing these in diffraction experiments and in computer simulations. Sullivan's model always predicts a second-order phase transition between class II and class I wetting. By extending his model and allowing the attractive part of the solid-fluid potential to be longer-ranged than the attractive fluid-fluid potential we find that this wetting transition can become a first-order (Cahn) transition.     

Analysis of a long-range random field quantum antiferromagnetic Ising model

We introduce a solvable quantum antiferromagnetic model. The model, with Ising spins in a transverse field, has infinite range antiferromagnetic interactions and random fields on each site following an arbitrary distribution. As is well-known, frustration in the random field Ising model gives rise to a many valley structure in the spin-configuration space. In addition, the antiferromagnetism also induces a regular frustration even for the ground state. In this paper, we investigate analytically the critical phenomena in the model, having both randomness and frustration and we report some analytical results for it.     

Magnetic field correlations in random flow with strong steady shear

We analyze the magnetic kinematic dynamo in a conducting fluid where a stationary shear flow is accompanied by relatively weak random velocity fluctuations. The diffusionless and diffusion regimes are described. The growth rates of the magnetic field moments are related to the statistical characteristics of the flow describing divergence of the Lagrangian trajectories. The magnetic field correlation functions are examined, and their growth rates and scaling behavior are established. General assertions are illustrated by the explicit solution of a model where the velocity field is short-correlated in time.     

Fourier magnitude of the field incident on a random scattering medium from spatial speckle intensity correlations

Spatial speckle intensity correlations are used to determine the spatial Fourier magnitude of a field incident on a random scattering medium. The patterned beam is scanned across the scattering medium, and the speckle pattern on the opposite side is imaged at each beam position. A theory based on a Green's function representation is used to reconstruct the spatial Fourier magnitude of the patterned incident field.     

Influence of a quasiclassical random potential on electron correlations in a one-dimensional system

The influence of a quasiclassical random potential on the behaviour of the correlation functions in a one-dimensional electron system is investigated in the generalized Luttinger model. We prove rigorously that in the case of a not-half-filled band the quasiclassical electron scattering suppresses dielectric and antiferromagnetic correlations, but has no effect on superconductive correlations. The case of a half-filled band, in which the existence of a gap Δ_ρ in the density excitation spectrum results in the exponential decrease of superconductive correlations in the pure system, is also considered. It is shown that in the “dirty” limit, Δ_ρτ ⪡ 1 (τ is the electron relaxation time), the quasiclassical random potential recovers a long-range, power law behaviour of superconductive correlations, typical for a gapless regime.     

Simulation of euclidean quantum field theories by a random walk process

A new Monte Carlo method for euclidean lattice field theory is introduced by writing the Boltzmann distribution e^?s as a solution of a diffusion type equation and constructing the associated random walk process. It is practically tested for a quantum mechanical model and a non-compact version of lattice QCD. It is explained where the main interest in this algorithm lies: the diffusion process coming from an action that can be generalized to include non-conservative forces. This possibility is exploited in our QCD version to implement gauge fixing without Faddeev-Popov ghosts.     

Fully nonlocal, monogamous, and random genuinely multipartite quantum correlations

Local measurements on bipartite maximally entangled states can yield correlations that are maximally nonlocal, monogamous, and with fully random outcomes. This makes these states ideal for bipartite cryptographic tasks. Genuine-multipartite nonlocality constitutes a stronger notion of nonlocality in the multipartite case. Maximal genuine-multipartite nonlocality, monogamy, and random outcomes are thus highly desired properties for genuine-multipartite cryptographic scenarios. We prove that local measurements on any Greenberger-Horne-Zeilinger state can produce correlations that are fully genuine-multipartite nonlocal, monogamous, and with fully random outcomes. A key ingredient in our proof is a multipartite chained Bell inequality detecting genuine-multipartite nonlocality, which we introduce. Finally, we discuss applications to device-independent secret sharing.     

Dispersion of a three-level quantum system in a bichromatic field

We consider aspects of the interaction between a V-type three-level quantum system and the bichromatic field of two waves, one of which is assumed to be weak. We trace the dynamics of splitting into individual components for the spectral contours of the absorption coefficient (gain) for the signal wave. We discuss the effect of amplification of the signal wave for its frequency-degenerate two-wave interaction with pumping, when the field frequency is tuned to the “zero dispersion” point. We determine the conditions with respect to the concentration of resonant atoms and the spectral regions of the frequencies of the interacting waves for which, in order to correctly describe the effects under consideration, we need to take into account the effect of pumping and the signal in both dipole-allowed transitions of an ensemble of V type three-level quantum systems. We present the results of numerical calculations of the imaginary and real parts of the susceptibility of the resonant medium at the frequency of the signal wave, as a function of the parameters for the high-power radiation and resonant transitions of the quantum V system. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 5, pp. 631–636, September–October, 2007.     

Micromagnetism in a planar system with a random magnetic anisotropy and two-dimensional magnetic correlations

The hysteresis loops and the micromagnetic structure of a ferromagnetic nanolayer with a randomly oriented local easy magnetization axis and two-dimensional magnetization correlations are studied using a micromagnetic simulation. The properties and the micromagnetic structure of the nanolayer are determined by the competition between the anisotropy and exchange energies and by the dipole–dipole interaction energy. The magnetic microstructure can be described as an ensemble of stochastic magnetic domains and topological magnetization defects. Dipole–dipole interaction suppresses the formation of topological magnetization defects. The topological defects in the magnetic microstructure can cause a sharper change in the coercive force with the crystallite size than that predicted by the random magnetic anisotropy model.     

Noise correlations in a Coulomb-blockaded quantum dot

We report measurements of current noise auto- and cross correlation in a tunable quantum dot with two or three leads. As the Coulomb blockade is lifted at finite source-drain bias, the autocorrelation evolves from super- to sub-Poissonian in the two-lead case, and the cross correlation evolves from positive to negative in the three-lead case, consistent with transport through multiple levels. Cross correlations in the three-lead dot are found to be proportional to the noise in excess of the Poissonian value in the limit of weak output tunneling.     

Susceptibility of a three-level V-type quantum system in a bichromatic field

A theory of interaction of a three-level V-type quantum system with a bichromatic field of two waves, one of which is weak, has been developed. It is suggested that the upper two levels of this system are closely spaced and, therefore, both waves interact simultaneously with both allowed transitions. An expression for nonlinear macroscopic polarization of the V-system has been obtained by the density-matrix method.__________Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 1, pp. 67–71, January–February, 2005.