Ab initio quantum dynamics using coupled-cluster

The curse of dimensionality (COD) limits the current state-of-the-art {\it ab initio} propagation methods for non-relativistic quantum mechanics to relatively few particles. For stationary structure calculations, the coupled-cluster (CC) method overcomes the COD in the sense that the method scales polynomially with the number of particles while still being size-consistent and extensive. We generalize the CC method to the time domain while allowing the single-particle functions to vary in an adaptive fashion as well, thereby creating a highly flexible, polynomially scaling approximation to the time-dependent Schr\"odinger equation. The method inherits size-consistency and extensivity from the CC method. The method is dubbed orbital-adaptive time-dependent coupled-cluster (OATDCC), and is a hierarchy of approximations to the now standard multi-configurational time-dependent Hartree method for fermions. A numerical experiment is also given.Comment: 5 figure

Repulsive Casimir and Casimir-Polder Forces

Casimir and Casimir-Polder repulsion have been known for more than 50 years. The general "Lifshitz" configuration of parallel semi-infinite dielectric slabs permits repulsion if they are separated by a dielectric fluid that has a value of permittivity that is intermediate between those of the dielectric slabs. This was indirectly confirmed in the 1970s, and more directly by Capasso's group recently. It has also been known for many years that electrically and magnetically polarizable bodies can experience a repulsive quantum vacuum force. More amenable to practical application are situations where repulsion could be achieved between ordinary conducting and dielectric bodies in vacuum. The status of the field of Casimir repulsion with emphasis on recent developments will be surveyed. Here, stress will be placed on analytic developments, especially of Casimir-Polder (CP) interactions between anisotropically polarizable atoms, and CP interactions between anisotropic atoms and bodies that also exhibit anisotropy, either because of anisotropic constituents, or because of geometry. Repulsion occurs for wedge-shaped and cylindrical conductors, provided the geometry is sufficiently asymmetric, that is, either the wedge is sufficiently sharp or the atom is sufficiently far from the cylinder.Comment: 24 pages, 14 figures, contribution to the special issue of J. Phys. A honoring Stuart Dowker. This revision corrects typos and adds additional references and discussio

Casimir-Polder interaction of fullerene molecules with surfaces

We calculate the thermal Casimir--Polder potential of C60 and C70 fullerene molecules near gold and silicon nitride surfaces, motivated by their relevance for molecular matter wave interference experiments. We obtain the coefficients governing the asymptotic power laws of the interaction in the thermal, retarded and nonretarded distance regimes and evaluate the full potential numerically. The interaction is found to be dominated by electronic transitions, and hence independent of the internal temperature of the molecules. The contributions from phonon transitions, which are affected by the molecular temperature, give rise to only a small correction. Moreover, we find that the sizeable molecular line widths of thermal fullerenes may modify the nonretarded interaction, depending on the model used. Detailed measurements of the nonretarded potential of fullerene thus allow one to distinguish between different theories of incorporating damping.Comment: 9 pages, 8 figures, 9 table

Analytical and Numerical Verification of the Nernst Theorem for Metals

In view of the current discussion on the subject, an effort is made to show very accurately both analytically and numerically how the Drude dispersion model gives consistent results for the Casimir free energy at low temperatures. Specifically, for the free energy near T=0 we find the leading term to be proportional to T^2 and the next-to-leading term proportional to T^{5/2}. These terms give rise to zero Casimir entropy as T approaches zero, and is thus in accordance with Nernst's theorem.Comment: 19 pages latex, 3 figures. v4: Figures updated. This is the final version, accepted for publication in Physical Review

Sign of the Casimir-Polder interaction between atoms and oil-water interfaces: Subtle dependence on dielectric properties

We demonstrate that Casimir-Polder energies between noble gas atoms (dissolved in water) and oil-water interfaces are highly surface specific. Both repulsion (e.g. hexane) and attraction (e.g. glycerine and cyclodecane) is found with different oils. For several intermediate oils (e.g. hexadecane, decane, and cyclohexane) both attraction and repulsion can be found in the same system. Near these oil-water interfaces the interaction is repulsive in the non-retarded limit and turns attractive at larger distances as retardation becomes important. These highly surface specific interactions may have a role to play in biological systems where the surface may be more or less accessible to dissolved atoms.Comment: 5 pages, 6 figure

Casimir-Foucault interaction: Free energy and entropy at low temperature

It was recently found that thermodynamic anomalies which arise in the Casimir effect between metals described by the Drude model can be attributed to the interaction of fluctuating Foucault (or eddy) currents [Phys. Rev. Lett. 103, 130405 (2009)]. We show explicitly that the two leading terms of the low-temperature correction to the Casimir free energy of interaction between two plates, are identical to those pertaining to the Foucault current interaction alone, up to a correction which is very small for good metals. Moreover, a mode density along real frequencies is introduced, showing that the Casimir free energy, as given by the Lifshitz theory, separates in a natural manner in contributions from eddy currents and propagating cavity modes, respectively. The latter have long been known to be of little importance to the low-temperature Casimir anomalies. This convincingly demonstrates that eddy current modes are responsible for the large temperature correction to the Casimir effect between Drude metals, predicted by the Lifshitz theory, but not observed in experiments.Comment: 10 pages, 1 figur

Reply to "Comment on 'Analytic and Numerical Verification of the Nernst Theorem for Metals'"

In this Reply to the preceding Comment of Klimchitskaya and Mostepanenko (cf. also quant-ph/0703214), we summarize and maintain our position that the Drude dispersion relation when inserted in the Lifshitz formula gives a thermodynamically satisfactory description of the Casimir force, also in the limiting case when the relaxation frequency goes to zero (perfect crystals).Comment: 4 pages, no figures; to appear in Phys. Rev.

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