993 resultados para zero-point quantum fluctuations
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Dissertação para obtenção do Grau de Mestre em Engenharia Química e Bioquímica
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An alternative approach to the fundamental general physics concepts has been proposed. We demonstrate that the electrostatic potential energy of a discrete or a continuous system of charges should be stored by the charges and not the field. It is found that there is a possibility that any electric field has no energy density, as well as magnetic field. It is found that there is no direct relation between the electric or magnetic energy and photons. An alternative derivation of the blackbody radiation formula is proposed. It is also found that the zero-point of energy of electromagnetic radiation may not exist.
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Restricted Hartree-Fock 6-31G calculations of electrical and mechanical anharmonicity contributions to the longitudinal vibrational second hyperpolarizability have been carried out for eight homologous series of conjugated oligomers - polyacetylene, polyyne, polydiacetylene, polybutatriene, polycumulene, polysilane, polymethineimine, and polypyrrole. To draw conclusions about the limiting infinite polymer behavior, chains containing up to 12 heavy atoms along the conjugated backbone were considered. In general, the vibrational hyperpolarizabilities are substantial in comparison with their static electronic counterparts for the dc-Kerr and degenerate four-wave mixing processes (as well as for static fields) but not for electric field-induced second harmonic generation or third harmonic generation. Anharmonicity terms due to nuclear relaxation are important for the dc-Kerr effect (and for the static hyperpolarizability) in the σ-conjugated polymer, polysilane, as well as the nonplanar π systems polymethineimine and polypyrrole. Restricting polypyrrole to be planar, as it is in the crystal phase, causes these anharmonic terms to become negligible. When the same restriction is applied to polymethineimine the effect is reduced but remains quantitatively significant due to the first-order contribution. We conclude that anharmonicity associated with nuclear relaxation can be ignored, for semiquantitative purposes, in planar π-conjugated polymers. The role of zero-point vibrational averaging remains to be evaluated
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In the finite field (FF) treatment of vibrational polarizabilities and hyperpolarizabilities, the field-free Eckart conditions must be enforced in order to prevent molecular reorientation during geometry optimization. These conditions are implemented for the first time. Our procedure facilities identification of field-induced internal coordinates that make the major contribution to the vibrational properties. Using only two of these coordinates, quantitative accuracy for nuclear relaxation polarizabilities and hyperpolarizabilities is achieved in π-conjugated systems. From these two coordinates a single most efficient natural conjugation coordinate (NCC) can be extracted. The limitations of this one coordinate approach are discussed. It is shown that the Eckart conditions can lead to an isotope effect that is comparable to the isotope effect on zero-point vibrational averaging, but with a different mass-dependence
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Geometries, vibrational frequencies, and interaction energies of the CNH⋯O3 and HCCH⋯O3 complexes are calculated in a counterpoise-corrected (CP-corrected) potential-energy surface (PES) that corrects for the basis set superposition error (BSSE). Ab initio calculations are performed at the Hartree-Fock (HF) and second-order Møller-Plesset (MP2) levels, using the 6-31G(d,p) and D95++(d,p) basis sets. Interaction energies are presented including corrections for zero-point vibrational energy (ZPVE) and thermal correction to enthalpy at 298 K. The CP-corrected and conventional PES are compared; the unconnected PES obtained using the larger basis set including diffuse functions exhibits a double well shape, whereas use of the 6-31G(d,p) basis set leads to a flat single-well profile. The CP-corrected PES has always a multiple-well shape. In particular, it is shown that the CP-corrected PES using the smaller basis set is qualitatively analogous to that obtained with the larger basis sets, so the CP method becomes useful to correctly describe large systems, where the use of small basis sets may be necessary
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To obtain a state-of-the-art benchmark potential energy surface (PES) for the archetypal oxidative addition of the methane C-H bond to the palladium atom, we have explored this PES using a hierarchical series of ab initio methods (Hartree-Fock, second-order Møller-Plesset perturbation theory, fourth-order Møller-Plesset perturbation theory with single, double and quadruple excitations, coupled cluster theory with single and double excitations (CCSD), and with triple excitations treated perturbatively [CCSD(T)]) and hybrid density functional theory using the B3LYP functional, in combination with a hierarchical series of ten Gaussian-type basis sets, up to g polarization. Relativistic effects are taken into account either through a relativistic effective core potential for palladium or through a full four-component all-electron approach. Counterpoise corrected relative energies of stationary points are converged to within 0.1-0.2 kcal/mol as a function of the basis-set size. Our best estimate of kinetic and thermodynamic parameters is -8.1 (-8.3) kcal/mol for the formation of the reactant complex, 5.8 (3.1) kcal/mol for the activation energy relative to the separate reactants, and 0.8 (-1.2) kcal/mol for the reaction energy (zero-point vibrational energy-corrected values in parentheses). This agrees well with available experimental data. Our work highlights the importance of sufficient higher angular momentum polarization functions, f and g, for correctly describing metal-d-electron correlation and, thus, for obtaining reliable relative energies. We show that standard basis sets, such as LANL2DZ+ 1f for palladium, are not sufficiently polarized for this purpose and lead to erroneous CCSD(T) results. B3LYP is associated with smaller basis set superposition errors and shows faster convergence with basis-set size but yields relative energies (in particular, a reaction barrier) that are ca. 3.5 kcal/mol higher than the corresponding CCSD(T) values
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Initial convergence of the perturbation series expansion for vibrational nonlinear optical (NLO) properties was analyzed. The zero-point vibrational average (ZPVA) was obtained through first-order in mechanical plus electrical anharmonicity. Results indicated that higher-order terms in electrical and mechanical anharmonicity can make substantial contributions to the pure vibrational polarizibility of typical NLO molecules
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Semiclassical Einstein-Langevin equations for arbitrary small metric perturbations conformally coupled to a massless quantum scalar field in a spatially flat cosmological background are derived. Use is made of the fact that for this problem the in-in or closed time path effective action is simply related to the Feynman-Vernon influence functional which describes the effect of the ``environment,'' the quantum field which is coarse grained here, on the ``system,'' the gravitational field which is the field of interest. This leads to identify the dissipation and noise kernels in the in-in effective action, and to derive a fluctuation-dissipation relation. A tensorial Gaussian stochastic source which couples to the Weyl tensor of the spacetime metric is seen to modify the usual semiclassical equations which can be veiwed now as mean field equsations. As a simple application we derive the correlation functions of the stochastic metric fluctuations produced in a flat spacetime with small metric perturbations due to the quantum fluctuations of the matter field coupled to these perturbations.
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We consider the classical stochastic fluctuations of spacetime geometry induced by quantum fluctuations of massless nonconformal matter fields in the early Universe. To this end, we supplement the stress-energy tensor of these fields with a stochastic part, which is computed along the lines of the Feynman-Vernon and Schwinger-Keldysh techniques; the Einstein equation is therefore upgraded to a so-called Einstein-Langevin equation. We consider in some detail the conformal fluctuations of flat spacetime and the fluctuations of the scale factor in a simple cosmological model introduced by Hartle, which consists of a spatially flat isotropic cosmology driven by radiation and dust.
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In inflationary cosmological models driven by an inflaton field the origin of the primordial inhomogeneities which are responsible for large-scale structure formation are the quantum fluctuations of the inflaton field. These are usually calculated using the standard theory of cosmological perturbations, where both the gravitational and the inflaton fields are linearly perturbed and quantized. The correlation functions for the primordial metric fluctuations and their power spectrum are then computed. Here we introduce an alternative procedure for calculating the metric correlations based on the Einstein-Langevin equation which emerges in the framework of stochastic semiclassical gravity. We show that the correlation functions for the metric perturbations that follow from the Einstein-Langevin formalism coincide with those obtained with the usual quantization procedures when the scalar field perturbations are linearized. This method is explicitly applied to a simple model of chaotic inflation consisting of a Robertson-Walker background, which undergoes a quasi-de Sitter expansion, minimally coupled to a free massive quantum scalar field. The technique based on the Einstein-Langevin equation can, however, deal naturally with the perturbations of the scalar field even beyond the linear approximation, as is actually required in inflationary models which are not driven by an inflaton field, such as Starobinsky¿s trace-anomaly driven inflation or when calculating corrections due to nonlinear quantum effects in the usual inflaton driven models.
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The key parameters associated to the thermally induced spin crossover process have been calculated for a series of Fe(II) complexes with mono-, bi-, and tridentate ligands. Combination of density functional theory calculations for the geometries and for normal vibrational modes, and highly correlated wave function methods for the energies, allows us to accurately compute the entropy variation associated to the spin transition and the zero-point corrected energy difference between the low- and high-spin states. From these values, the transition temperature, T 1/2, is estimated for different compounds.
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Tämän diplomityön tavoitteena oli löytää prosessiparametrejä nestepakkauskartongin reuna-alueiden kuivatuskutistuman hallintaan ja saada tuotteen reuna-alueiden sileystaso paremmaksi. Tarkoituksena oli parantaa reuna-alueiden painettavuusominaisuuksia sekä saada koneen poikkisuunnassa laadultaan parempi tuote. Työn kirjallisuusosassa on tarkasteltu työn kannalta nestepakkauskartongin kriittisimpiä ominaisuuksia, sileyttä ja jäykkyyttä. Lisäksi kirjallisuusosassa on tarkasteltu kuitujen ominaisuuksia, sylinterikuivatusta ja kuivatuskutistumaa. Kokeellisessa osassa on etsitty esitutkimuksella prosessiparametrejä, jotka ovat aiheuttaneet poikkisuunnan sileyserojen kasvun kartonkikoneen investoinnin jälkeen. Suoria korrelaatioita prosessiparametrien ja kuivatuskutistuman välille ei löydetty. Kokeellisen osan tehdasmittakaavaisissa koeajoissa tutkittiin kahdeksan eri parametrin vaikutusta kuivatuskutistumaan, jotka perustuivat kirjallisuuteen. Tutkituista parametreistä huulisuihkun iskukulman muutoksella sekä konesuuntaisella kuivatusprofiililla ei ollut vaikutusta kuivatuskutistumaan. Runkokerroksen mäntysellun korvaaminen koivusellulla vähensi kuivatuskutistumaa ja lisäsi sileyttä, mutta tuotteen palstautumislujuus ei tällöin ollut riittävä. Retentiokemikaalien reseptimuutoksilla pinta- ja taustakerroksen välillä, kuivatusosan nollatason laskulla ja perälaatikkosakeuksien pienentämisellä oli vähän vaikutusta kuivatuskutistumaan. Vaikutus reuna-alueiden sileyteen oli kuitenkin vähemmän kuin 10 %. Diplomityön perusteella kuivatusosan nopeuseroilla ja kuivatusviirojen kireyksillä oli suurin vaikutusta kuivatuskutistumaan ja reuna-alueiden sileystasoon. Lisäämällä nopeuseroja ja kiristämällä kuivatusviiroja reuna-alueiden sileyttä pystyttiin parantamaan yli 20 %.
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The aim of this thesis was to examine the existence of expectation gap in small and medium size Finnish companies. The existence of expectation gap was examined both in the different sectors of audit and in the behavior of the auditor. This goal was reached using a questionnaire that was send to 350 respondents. The results were divided evenly around the zero-point, which mend that the expectation gap could not be found. The results didn’t show any sign of significant existence of expectation gap. Because the results were so close to the zero-point, a small shift either way could change the results considerably. Because of this the auditors should be very careful that the level of their audit shouldn’t at least get any worse. Small improvement for current level of audit could better the customer satisfaction considerably.
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The present experiment describes an easy procedure for obtaining SiO2/ZrO2 by reacting ZrOCl2 with SiO2 with the following characteristics: S BET = 500 m² g-1 and an average pore diameter of 6 nm. The material obtained presented 1.3 wt% ZrO2 content corresponding to 140 mumol g-1. The average density of ZrO2 onto SiO2/ZrO2 matrix is 2.8x10-11 mol cm-2. The adsorption isotherm for Cr(VI) showed a maximum of adsorption value (200 mumol g-1) at pH 2. The adsorption can be described by the reaction: =Zr(OH)2 + 2HCrO4- + 2H+ [(=Zr(OH2+)2) (HCrO4-)2]. Above the zero point of charge, i.e. pH > 5.5 due to the surface charge inversion, desorption of Cr(VI) occurs according to the reaction: [(=Zr(OH2+)2) (HCrO4-)2] + 6OH-
(=ZrO2)2- + 6H2O + 2CrO4(2-).
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Potential energy surface (PES) of cis-trans and trans-trans formic acid dimers were sampled using a stochastic method, and the geometries, energies, and vibrational frequencies were computed at B3LYP/6-311++G(3df,2p) level of theory. The results show that molar free energy of dimerization deviated up to 108.4% when basis set superposition error (BSSE) and zero-point energy (ZPE) were not considered. For cis-trans dimers, C=O and O - H bond weakened, whereas C - O bonds strengthened due to dimerization. Also, trans-trans FA dimers did not show a trend regarding strengthening or weakening of the C=O, O - H and C - O bonds.