The double Caldeira-Leggett model: Derivation and solutions of the master equations, reservoir-induced interactions and decoherence

In this paper we analyze the double Caldeira-Leggett model: the path integral approach to two interacting dissipative harmonic oscillators. Assuming a general form of the interaction between the oscillators, we consider two different situations: (i) when each oscillator is coupled to its own reservoir, and (ii) when both oscillators are coupled to a common reservoir. After deriving and solving the master equation for each case, we analyze the decoherence process of particular entanglements in the positional space of both oscillators. To analyze the decoherence mechanism we have derived a general decay function, for the off-diagonal peaks of the density matrix, which applies both to common and separate reservoirs. We have also identified the expected interaction between the two dissipative oscillators induced by their common reservoir. Such a reservoir-induced interaction, which gives rise to interesting collective damping effects, such as the emergence of relaxation- and decoherence-free subspaces, is shown to be blurred by the high-temperature regime considered in this study. However, we find that different interactions between the dissipative oscillators, described by rotating or counter-rotating terms, result in different decay rates for the interference terms of the density matrix. (C) 2010 Elsevier B.V. All rights reserved.

Effect of a Single Application of TiF(4) and NaF Varnishes and Solutions Combined with Nd:YAG Laser Irradiation on Enamel Erosion in Vitro

Objective: This in vitro study aimed to analyze the influence of neodymium-doped yttrium aluminum garnet (Nd:YAG) laser irradiation on the efficacy of titanium tetrafluoride (TiF(4)) and sodium fluoride (NaF) varnishes and solutions to protect enamel against erosion. Background data: The effect of Nd:YAG laser irradiation on NaF and AmF was analyzed; however, there is no available data on the interaction between Nd:YAG laser irradiation and TiF(4). Methods: Bovine enamel specimens were pre-treated with NaF varnish, TiF(4) varnish, NaF solution, TiF(4) solution, placebo varnish, Nd:YAG (84.9 J/cm(2)), Nd:YAG prior to or through NaF varnish, Nd:YAG prior to or through TiF(4) varnish, Nd:YAG prior to or through NaF solution, Nd:YAG prior to or through TiF(4) solution, and Nd:YAG prior to or through placebo varnish. Controls remained untreated. Ten specimens in each group were then subjected to an erosive demineralization (Sprite Zero, 4x90 s/day) and remineralization (artificial saliva, between the erosive cycles) cycling for 5 days. Enamel loss was measured profilometrically (mu m). Additionally, treated but non-eroded specimens were additionally analyzed by scanning electron microscope (SEM) (each group n-2). The data were statistically analyzed by ANOVA and Tukey's post-hoc test (p < 0.05). Results: Only TiF(4) varnish (1.8 +/- 0.6 mu m), laser prior to TiF(4) varnish (1.7 +/- 0.3 mu m) and laser prior to TiF(4) solution (1.4 +/- 0.3 mu m) significantly reduced enamel erosion compared to the control (4.1 +/- 0.6 mu m). SEM pictures showed that specimens treated with TiF(4) varnish presented a surface coating. Conclusions: Nd:YAG laser irradiation was not effective against enamel erosion and it did not have any influence on the efficacy of F, except for TiF(4) solution. On the other hand, TiF(4) varnish protected against enamel erosion, without the influence of laser irradiation.

Effect of a single application of TiF(4) and NaF varnishes and solutions on dentin erosion in vitro

Objectives: This in vitro study aimed to analyse the effect of a single application of TiF(4) and NaF varnishes and solutions to protect against dentin erosion. Methods: Bovine root dentin samples were pre-treated with NaF-Duraphat varnish (2.26%F, pH 4.5), NaF/CaF(2)-Duofluorid varnish (5.63%F, pH 8.0), NaF-experimental varnish (2.45%F, pH 4.5), TiF(4)-experimental varnish (2.45%F, pH 1.2), NaF solution (2.26%F, pH 4.5), TiF(4) solution (2.45%F, pH 1.2) and placebo varnish (pH 5.0, no-F varnish control). Controls remained untreated. Ten samples in each group were then subjected to an erosive demineralisation (Sprite Zero, 4x 90 s/day) and remineralisation (artificial saliva, between the erosive cycles) cycling for S days. Dentin loss was measured profilometrically after pretreatment and after 1, 3 and 5 days of de-remineralisation cycling. The data were statistically analysed by two-way ANOVA and Bonferroni`s post hoc test (p < 0.05). Results: After pre-treatment, TiF(4) solution significantly induced surface loss (1.08 +/- 0.53 mu m). Only Duraphat reduced the dentin loss overtime, but it did not significantly differ from placebo varnish (at 3rd and 5th days) and TiF(4) varnish (at 3rd day). Conclusions: Duraphat varnish seems to be the best option to partially reduce dentin erosion. However, the maintenance of the effects of this treatment after successive erosive challenges is limited. (C) 2009 Elsevier Ltd. All rights reserved.