Abstract:
In the thesis we present an analytic approach towards exact description for steady state density operators of nonequilibrium quantum dynamics in the framework of open systems. We employ the so-called quantum Markovian semi-group evolution, i.e. a general form of time-autonomous positivity and trace-preserving dynamical equation for reduced density operators, by only allowing unitarity-breaking dissipative terms acting at the boundaries of a system. Such setup enables to simulate macroscopic reservoirs for different values of effective thermodynamic potentials, causing incoherent transitions between quantum states which are modeled with aid of the Lindblad operators. This serves as a simple minimalistic model for studying quantum transport properties, either in the linear response domain or in more general regimes far from canonical equilibrium. We are mainly exploring possibilities of identifying nonequilibrium situations which are amenable to exact description within matrix product state representation, by exclusively focusing on steady states, i.e. fixed points of the Lindblad equation, of certain prototypic interacting integrable spin chains driven by incoherent polarizing processes. Finally, we define a concept of pseudo-local extensive almost-conserved quantities by allowing a violation of time-invariance up to boundary-localized terms. We elucidate the role of such quantities on non-ergodic behaviour of temporal correlation functions rendering anomalous transport properties. It turns out that such conservation laws can be generated by means of boundary universal quantum transfer operators of the fundamental integrable models.

Abstract:
Background An emerging body of evidence indicates that early-life arsenic (As) exposure may influence the trajectory of health outcomes later in life. However, the mechanisms underlying these observations are unknown. Objective The objective of this study was to investigate the influence of prenatal As exposure on global methylation of cord blood DNA in a study of mother/newborn pairs in Matlab, Bangladesh. Design Maternal and cord blood DNA were available from a convenience sample of 101 mother/newborn pairs. Measures of As exposure included maternal urinary As (uAs), maternal blood As (mbAs) and cord blood As (cbAs). Several measures of global DNA methylation were assessed, including the [3H]-methyl-incorporation assay and three Pyrosequencing assays: Alu, LINE-1 and LUMA. Results In the total sample, increasing quartiles of maternal uAs were associated with an increase in covariate-adjusted means of newborn global DNA methylation as measured by the [3H]-methyl-incorporation assay (quartile 1 (Q1) and Q2 vs. Q4; p = 0.06 and 0.04, respectively). Sex-specific linear regression analyses, while not reaching significance level of 0.05, indicated that the associations between As exposures and Alu, LINE-1 and LUMA were positive among male newborns (N = 58) but negative among female newborns (N = 43); tests for sex differences were borderline significant for the association of cbAs and mbAs with Alu (p = 0.05 and 0.09, respectively) and for the association between maternal uAs and LINE-1 (p = 0.07). Sex-specific correlations between maternal urinary creatinine and newborn methyl-incorporation, Alu and LINE-1 were also evident (p<0.05). Conclusions These results suggest that prenatal As exposure is associated with global DNA methylation in cord blood DNA, possibly in a sex-specific manner. Arsenic-induced epigenetic modifications in utero may potentially influence disease outcomes later in life. Additional studies are needed to confirm these findings and to examine the persistence of DNA methylation marks over time.

Abstract:
We consider one-dimensional translationally invariant quantum spin (or fermionic) lattices and prove a Mazur-type inequality bounding the time-averaged thermodynamic limit of a finite-temperature expectation of a spatio-temporal autocorrelation function of a local observable in terms of quasi-local conservation laws with open boundary conditions. Namely, the commutator between the Hamiltonian and the conservation law of a finite chain may result in boundary terms only. No reference to techniques used in Suzuki's proof of Mazur bound is made (which strictly applies only to finite-size systems with exact conservation laws), but Lieb-Robinson bounds and exponential clustering theorems of quasi-local C^* quantum spin algebras are invoked instead. Our result has an important application in the transport theory of quantum spin chains, in particular it provides rigorous non-trivial examples of positive finite-temperature spin Drude weight in the anisotropic Heisenberg XXZ spin 1/2 chain [Phys. Rev. Lett. 106, 217206 (2011)].

Abstract:
We present an explicit construction of a family of steady state density matrices for an open integrable spin-1 chain with bilinear and biquadratic interactions, also known as the Lai-Sutherland model, driven far from equilibrium by means of two oppositely polarizing Markovian dissipation channels localized at the boundary. The steady state solution exhibits n+1 fold degeneracy, for a chain of length n, due to existence of (strong) Liouvillian U(1) symmetry. The latter can be exploited to introduce a chemical potential and define a grand canonical nonequilibrium steady state ensemble. The matrix product form of the solution entails an infinitely-dimensional representation of a non-trivial Lie algebra (semidirect product of sl_2 and a non-nilpotent radical) and hints to a novel Yang-Baxter integrability structure.

Abstract:
We present a general formulation of Floquet states of periodically time-dependent open Markovian quasi-free fermionic many-body systems in terms of a discrete Lyapunov equation. Illustrating the technique, we analyze periodically kicekd XY spin 1/2 chain which is coupled to a pair of Lindblad reservoirs at its ends. A complex phase diagram is reported with re-entrant phases of long range and exponentially decaying spin-spin correlations as some of the system's parameters are varied. The structure of phase diagram is reproduced in terms of counting non-trivial stationary points of Floquet quasi-particle dispersion relation.

Abstract:
For fundamental integrable quantum chains with deformed symmetries we outline a general procedure for defining a continuous family of quasi-local operators whose time-derivative is supported near the two boundary sites only. The program is implemented for a spin 1/2 XXZ chain, resulting in improved rigorous estimates for the high temperature spin Drude weight.

Abstract:
We present a systematic approach for constructing steady state density operators of Markovian dissipative evolution for open quantum chain models with integrable bulk interaction and boundary incoherent driving. The construction is based on fundamental solutions of the quantum Yang-Baxter equation pertaining to quantum algebra symmetries and their quantizations (q-deformations). In particular, we facilitate a matrix-product state description, by resorting to generic spin-s infinite-dimensional solutions associated with non-compact spins, serving as ancillary degrees of freedom. After formally deriving already known solutions for the anisotropic spin-1/2 Heisenberg chain from first symmetry principles, we obtain a class of solutions belonging to interacting quantum gases with SU(N)-symmetric Hamiltonians, using a restricted set of incoherent boundary jump processes, and point out how new non-trivial generalizations emerge from twists of quantum group structures. Finally, we discuss possibilities of analytic calculation of observables by employing algebraic properties of associated auxiliary vertex operators.

Abstract:
Structure is the most striking, visual aspect of vertisol morphology. The type and degree of structure development in a vertisol provides a digest of its genesis, constituent properties and agriculture management potential. The present study includes the results of the investigations of aggregate composition and water stability of structural aggregates in all horizons (Ap, A, AC, C) of 7 vertisol profiles formed over tertiary clayish and pyroclastic sediments in the central part of Macedonia ( tip, Probi tip and Ov e Pole valleys). The main objectives were to determine and compare aggregate composition and water stability of structural aggregates of vertisols which have been used as long-term arable fields (6 of the analyzed profiles) or as pasture (1 profile). The most represented fraction of aggregates in the process of dry sieving of the soil samples is the fraction of cloddy macro-aggregates (>10 mm), which is the most unfavourable from the agricultural point of view. Micro- aggregates fraction (<0.25 mm) is barely present, which means that in the dry state nearly all micro-aggregates and mechanical elements are associated in larger structural aggregates. The researched soils are characterized by different water stability of the structural aggregates. In the process of wet sieving, except surface horizon of the vertisol under natural vegetation, the cloddy macro-aggregates showed the greatest instability. With decrease of the dimension their stability increases so micro-aggregates have the highest water stability.

Abstract:
The research has been done on 48 participants - top male karate competitors, juniors, from 20 karate clubs from Macedonia. Subject of this research are karate elements which are most frequently used in karate fight, and the basic aim is to establish the structure of the same karate elements that are used in karate fight. In the research, 36 variables were applied: 4 anthropometric variables, 4 variables for estimation on the explosive strength, 4 variables for estimation on the segmented velocity (frequency of movements), 12 variables of the karate elements used in the karate fighting and 12 variables for estimation of the specific karate abilities in 3 motor spaces: 4 variables for estimation of the specific karate coordination, 4 variables for estimation of the specific karate precision and 4 variables for estimation of the specific karate balance. This research examines the factors of used karate elements in sports fighting. The results obtained show existing of grouping by space of the variables being used in the research.