Non-equilibrium transition from dissipative quantum walk to classical random walk

We have investigated the time-evolution of a free particle in interaction with a phonon thermal bath, using the tight-binding approach. A dissipative quantum walk can be defined and many important non-equilibrium decoherence properties can be investigated analytically. The non-equilibrium statistics of a pure initial state have been studied. Our theoretical results indicate that the evolving wave-packet shows the suppression of Anderson's boundaries (ballistic peaks) by the presence of dissipation. Many important relaxation properties can be studied quantitatively, such as von Neumann's entropy and quantum purity. In addition, we have studied Wigner's function. The time-dependent behavior of the quantum entanglement between a free particle -in the lattice- and the phonon bath has been characterized analytically. This result strongly suggests the non-trivial time-dependence of the off-diagonal elements of the reduced density matrix of the system. We have established a connection between the quantum decoherence and the dissipative parameter arising from interaction with the phonon bath. The time-dependent behavior of quantum correlations has also been pointed out, showing continuous transition from quantum random walk to classical random walk, when dissipation increases.Comment: Submitted for publication. 17 pages, 6 figure

Age-Related Adaptation of Bone-PDL-Tooth Complex: Rattus-Norvegicus as a Model System

Functional loads on an organ induce tissue adaptations by converting mechanical energy into chemical energy at a cell-level. The transducing capacity of cells alters physico-chemical properties of tissues, developing a positive feedback commonly recognized as the form-function relationship. In this study, organ and tissue adaptations were mapped in the bone-tooth complex by identifying and correlating biomolecular expressions to physico-chemical properties in rats from 1.5 to 15 months. However, future research using hard and soft chow over relevant age groups would decouple the function related effects from aging affects. Progressive curvature in the distal root with increased root resorption was observed using micro X-ray computed tomography. Resorption was correlated to the increased activity of multinucleated osteoclasts on the distal side of the molars until 6 months using tartrate resistant acid phosphatase (TRAP). Interestingly, mononucleated TRAP positive cells within PDL vasculature were observed in older rats. Higher levels of glycosaminoglycans were identified at PDL-bone and PDL-cementum entheses using alcian blue stain. Decreasing biochemical gradients from coronal to apical zones, specifically biomolecules that can induce osteogenic (biglycan) and fibrogenic (fibromodulin, decorin) phenotypes, and PDL-specific negative regulator of mineralization (asporin) were observed using immunohistochemistry. Heterogeneous distribution of Ca and P in alveolar bone, and relatively lower contents at the entheses, were observed using energy dispersive X-ray analysis. No correlation between age and microhardness of alveolar bone (0.7±0.1 to 0.9±0.2 GPa) and cementum (0.6±0.1 to 0.8±0.3 GPa) was observed using a microindenter. However, hardness of cementum and alveolar bone at any given age were significantly different (P<0.05). These observations should be taken into account as baseline parameters, during development (1.5 to 4 months), growth (4 to 10 months), followed by a senescent phase (10 to 15 months), from which deviations due to experimentally induced perturbations can be effectively investigated