Entanglement of a Single Spin-1 Object: An Example of Ubiquitous Entanglement

Using a single spin-1 object as an example, we discuss a recent approach to quantum entanglement. The key idea of the approach consists in presetting of basic observables in the very definition of quantum system. Specification of basic observables defines the dynamic symmetry of the system. Entangled states of the system are then interpreted as states with maximal amount of uncertainty of all basic observables. The approach gives purely physical picture of entanglement. In particular, it separates principle physical properties of entanglement from inessential. Within the model example under consideration, we show relativity of entanglement with respect to dynamic symmetry and argue existence of single-particle entanglement. A number of physical examples are considered.Comment: 12 pages, 2 figure : title has been changed, paper is re-organized, new section "Violation of Bell-type condition by single spin-1" is adde

Cytoskeletal interactions at the nuclear envelope mediated by Nesprins

Nesprin-1 is a giant tail-anchored nuclear envelope protein composed of an N-terminal F-actin binding domain, a long linker region formed by multiple spectrin repeats and a C-terminal transmembrane domain. Based on this structure, it connects the nucleus to the actin cytoskeleton. Earlier reports had shown that Nesprin-1 binds to nuclear envelope proteins emerin and lamin through C-terminal spectrin repeats. These repeats can also self-associate. We focus on the N-terminal Nesprin-1 sequences and show that they interact with Nesprin-3, a further member of the Nesprin family, which connects the nucleus to the intermediate filament network. We show that upon ectopic expression of Nesprin-3 in COS7 cells, which are nearly devoid of Nesprin-3 in vitro, vimentin filaments are recruited to the nucleus and provide evidence for an F-actin interaction of Nesprin-3 in vitro. We propose that Nesprins through interactions amongst themselves and amongst the various Nesprins form a network around the nucleus and connect the nucleus to several cytoskeletal networks of the cell

Geometric Dequantization

Dequantization is a set of rules which turn quantum mechanics (QM) into classical mechanics (CM). It is not the WKB limit of QM. In this paper we show that, by extending time to a 3-dimensional "supertime", we can dequantize the system in the sense of turning the Feynman path integral version of QM into the functional counterpart of the Koopman-von Neumann operatorial approach to CM. Somehow this procedure is the inverse of geometric quantization and we present it in three different polarizations: the Schroedinger, the momentum and the coherent states ones.Comment: 50+1 pages, Late

Optical-thermal mathematical model for endovenous laser ablation of varicose veins

Endovenous laser ablation (EVLA) is successfully used to treat varicose veins. However, the exact working mechanism is still not fully identified and the clinical procedure is not yet standardized. Mathematical modeling of EVLA could strongly improve our understanding of the influence of the various EVLA processes. The aim of this study is to combine Mordon's optical-thermal model with the presence of a strongly absorbing carbonized blood layer on the fiber tip. The model anatomy includes a cylindrically symmetric blood vessel surrounded by an infinite homogenous perivenous tissue. The optical fiber is located in the center of the vessel and is withdrawn with a pullback velocity. The fiber tip includes a small layer of strongly absorbing material, representing the layer of carbonized blood, which absorbs 45 % of the emitted laser power. Heat transfer due to boiling bubbles is taken into account by increasing the heat conduction coefficient by a factor of 200 for temperatures above 95°C. The temperature distribution in the blood, vessel wall, and surrounding medium is calculated from a numerical solution of the bioheat equation. The simulations were performed in MATLAB™ and validated with the aid of an analytical solution. The simulations showed, first, that laser wavelength did virtually not influence the simulated temperature profiles in blood and vessel wall, and, second, that temperatures of the carbonized blood layer varied slightly, from 952 to 1,104°C. Our improved mathematical optical-thermal EVLA model confirmed previous predictions and experimental outcomes that laser wavelength is not an important EVLA parameter and that the fiber tip reaches exceedingly high temperatures

Maxwell equations in matrix form, squaring procedure, separating the variables, and structure of electromagnetic solutions

The Riemann -- Silberstein -- Majorana -- Oppenheimer approach to the Maxwell electrodynamics in vacuum is investigated within the matrix formalism. The matrix form of electrodynamics includes three real 4 \times 4 matrices. Within the squaring procedure we construct four formal solutions of the Maxwell equations on the base of scalar Klein -- Fock -- Gordon solutions. The problem of separating physical electromagnetic waves in the linear space \lambda_{0}\Psi^{0}+\lambda_{1}\Psi^{1}+\lambda_{2}\Psi^{2}+ lambda_{3}\Psi^{3} is investigated, several particular cases, plane waves and cylindrical waves, are considered in detail.Comment: 26 pages 16 International Seminar NCPC, May 19-22, 2009, Minsk, Belaru

Agricultura familiar, multifuncionalidade da agricultura e ruralidade: interfaces de uma realidade complexa.

Nas últimas décadas, assistimos à revitalização do debate em torno da agricultura familiar pela incorporação das discussões sobre as múltiplas funções da agricultura num rural que não pode mais ser visto como domínio exclusivo da atividade agrícola e dos agricultores. No contexto brasileiro, acreditamos que essa discussão deva ser permeada pela análise de como processos diferenciados de distribuição fundiária e desenvolvimento econômico e o tipo de agricultura resultante geram ruralidades específicas com características como, no caso da agricultura familiar, a manutenção de práticas sociais e de trabalho marcadas pelas relações de parentesco e vizinhança presentes numa sociedade de interconhecimento. Partindo desse princípio, este trabalho analisa a agricultura familiar de um bairro rural do município de Ouro Fino - MG, sua herança histórica e sua participação na criação de uma paisagem natural e humana que muito contribui para a atratividade da região

Chiral symmetry breaking, color superconductivity and color neutral quark matter: a variational approach

We investigate the vacuum realignment for chiral symmetry breaking and color superconductivity at finite density in Nambu-Jona-Lasinio model in a variational method. The treatment allows us to investigate simultaneous formation of condensates in quark antiquark as well as in diquark channels. The methodology involves an explicit construction of a variational ground state and minimisation of the thermodynamic potential. Color and electric charge neutrality conditions are imposed through introduction of appropriate chemical potentials. Color and flavor dependent condensate functions are determined through minimisation of the thermodynamic potential. The equation of state is calculated. Simultaneous existence of a mass gap and superconducting gap is seen in a small window of quark chemical potential within the model when charge neutrality conditions are not imposed. Enforcing color and electric charge neutrality conditions gives rise to existence of gapless superconducting modes depending upon the magnitude of the gap and the difference of the chemical potentials of the condensing quarks.Comment: 13 pages, 6 figures,to appear in Phys. Rev.

Higgs Bundles, Gauge Theories and Quantum Groups

The appearance of the Bethe Ansatz equation for the Nonlinear Schr\"{o}dinger equation in the equivariant integration over the moduli space of Higgs bundles is revisited. We argue that the wave functions of the corresponding two-dimensional topological U(N) gauge theory reproduce quantum wave functions of the Nonlinear Schr\"{o}dinger equation in the $N$-particle sector. This implies the full equivalence between the above gauge theory and the $N$-particle sub-sector of the quantum theory of Nonlinear Schr\"{o}dinger equation. This also implies the explicit correspondence between the gauge theory and the representation theory of degenerate double affine Hecke algebra. We propose similar construction based on the $G/G$ gauged WZW model leading to the representation theory of the double affine Hecke algebra. The relation with the Nahm transform and the geometric Langlands correspondence is briefly discussed.Comment: 48 pages, typos corrected, one reference adde