Reduced density matrix and entanglement entropy of permutationally invariant quantum many-body systems

In this paper we discuss the properties of the reduced density matrix of quantum many body systems with permutational symmetry and present basic quantification of the entanglement in terms of the von Neumann (VNE), Renyi and Tsallis entropies. In particular, we show, on the specific example of the spin $1/2$ Heisenberg model, how the RDM acquires a block diagonal form with respect to the quantum number $k$ fixing the polarization in the subsystem conservation of $S_{z}$ and with respect to the irreducible representations of the $\mathbf{S_{n}}$ group. Analytical expression for the RDM elements and for the RDM spectrum are derived for states of arbitrary permutational symmetry and for arbitrary polarizations. The temperature dependence and scaling of the VNE across a finite temperature phase transition is discussed and the RDM moments and the R\'{e}nyi and Tsallis entropies calculated both for symmetric ground states of the Heisenberg chain and for maximally mixed states.Comment: Festschrift in honor of the 60th birthday of Professor Vladimir Korepin (11 pages, 5 figures

Quantum limits of super-resolution in reconstruction of optical objects

We investigate analytically and numerically the role of quantum fluctuations in reconstruction of optical objects from diffraction-limited images. Taking as example of an input object two closely spaced Gaussian peaks we demonstrate that one can improve the resolution in the reconstructed object over the classical Rayleigh limit. We show that the ultimate quantum limit of resolution in such reconstruction procedure is determined not by diffraction but by the signal-to-noise ratio in the input object. We formulate a quantitative measure of super-resolution in terms of the optical point-spread function of the system.Comment: 23 pages, 7 figures. Submitted to Physical Review A e-mail: [email protected]

Theoretical and experimental investigations of the process of vibration treatment of liquid metals containing nanoparticles

It is known that the use of external effects, such as acoustic fields (from ultrasonic to low-frequency range), help in breaking down agglomerates, improving particle wettability, providing uniform particle distribution in the melt volume, and reducing the grain size. The fragmentation of growing crystals, de-agglomeration of particles and their mixing in liquid metal under the influence of vibration (with frequencies of 10–100 Hz) are considered in this paper. The major advantage of such a technique in comparison with high-frequency methods (sonic, ultrasonic) is the capability of processing large melt volumes proportional to the wavelength. The mechanisms of the breaking down of particle agglomerates and the mixing of particles under conditions of cavitation and turbulence during the vibration treatment of the melt are considered. Expressions linking the threshold intensity and frequency with the amplitude necessary to activate mechanisms of turbulence and cavitation were obtained. The results of vibration treatment experiments for an aluminum alloy containing diamond nanoparticles are given. This treatment makes it possible to significantly reduce the grain size and to improve the casting homogeneity and thus improve the mechanical properties of the alloy

Xenobiotic-induced activation of human aryl hydrocarbon receptor target genes in Drosophila is mediated by the epigenetic chromatin modifiers

Aryl hydrocarbon receptor (AHR) is the key transcription factor that controls animal development and various adaptive processes. The AHR\u27s target genes are involved in biodegradation of endogenous and exogenous toxins, regulation of immune response, organogenesis, and neurogenesis. Ligand binding is important for the activation of the AHR signaling pathway. Invertebrate AHR homologs are activated by endogenous ligands whereas vertebrate AHR can be activated by both endogenous and exogenous ligands (xenobiotics). Several studies using mammalian cultured cells have demonstrated that transcription of the AHR target genes can be activated by exogenous AHR ligands, but little is known about the effects of AHR in a living organism. Here, we examined the effects of human AHR and its ligands using transgenic Drosophila lines with an inducible human AhR gene. We found that exogenous AHR ligands can increase as well as decrease the transcription levels of the AHR target genes, including genes that control proliferation, motility, polarization, and programmed cell death. This suggests that AHR activation may affect the expression of gene networks that could be critical for cancer progression and metastasis. Importantly, we found that AHR target genes are also controlled by the enzymes that modify chromatin structure, in particular components of the epigenetic Polycomb Repressive complexes 1 and 2. Since exogenous AHR ligands (alternatively - xenobiotics) and small molecule inhibitors of epigenetic modifiers are often used as pharmaceutical anticancer drugs, our findings may have significant implications in designing new combinations of therapeutic treatments for oncological diseases. © Akishina et al

Why spontaneous symmetry breaking disappears in a bridge system with PDE-friendly boundaries

We consider a driven diffusive system with two types of particles, A and B, coupled at the ends to reservoirs with fixed particle densities. To define stochastic dynamics that correspond to boundary reservoirs we introduce projection measures. The stationary state is shown to be approached dynamically through an infinite reflection of shocks from the boundaries. We argue that spontaneous symmetry breaking observed in similar systems is due to placing effective impurities at the boundaries and therefore does not occur in our system. Monte-Carlo simulations confirm our results.Comment: 24 pages, 7 figure

Exactly solvable statistical model for two-way traffic

We generalize a recently introduced traffic model, where the statistical weights are associated with whole trajectories, to the case of two-way flow. An interaction between the two lanes is included which describes a slowing down when two cars meet. This leads to two coupled five-vertex models. It is shown that this problem can be solved by reducing it to two one-lane problems with modified parameters. In contrast to stochastic models, jamming appears only for very strong interaction between the lanes.Comment: 6 pages Latex, submitted to J Phys.

Study of influence of aluminum nitride nanoparticles on the structure, phase composition and mechanical properties of AZ91 alloy

In this work, magnesium-based composites were obtained by shock-wave compaction of a powder mixture of Mg-5 wt.% AlN at a shock-wave pressure of 2 GPa. Their microstructure was investigated and the phase composition was determined, from which it follows that the nanoparticles retain their phase composition and are uniformly distributed in the magnesium matrix. The materials obtained by shock-wave compaction were used as master alloys for the production of magnesium alloys by die casting. The amount of aluminum nitride nanoparticles in the AZ91 magnesium alloy was 0.5 wt.%. Studies of the microstructure of the magnesium alloys showed a decrease in the average grain size of the magnesium matrix from 610 to 420 m. Studies of mechanical properties have shown that the introduction of aluminum nitride nanoparticles increases the yield strength from 55 to 119 MPa, the tensile strength from 122 to 171 MPa and the plasticity from 4 to 6.5%, respectively. The effect of nanoparticles on the fracture behavior of the magnesium alloy under tension was determine

Wave packet evolution approach to ionization of hydrogen molecular ion by fast electrons

The multiply differential cross section of the ionization of hydrogen molecular ion by fast electron impact is calculated by a direct approach, which involves the reduction of the initial 6D Schr\"{o}dinger equation to a 3D evolution problem followed by the modeling of the wave packet dynamics. This approach avoids the use of stationary Coulomb two-centre functions of the continuous spectrum of the ejected electron which demands cumbersome calculations. The results obtained, after verification of the procedure in the case atomic hydrogen, reveal interesting mechanisms in the case of small scattering angles.Comment: 7 pages, 8 Postscript figure