Boris Kastening

Bose-Einstein condensation temperature of a homogenous weakly interacting Bose gas in variational perturbation theory through seven loops

The shift of the Bose-Einstein condensation temperature for a homogenous weakly interacting Bose gas in leading order in the scattering length a is computed for given particle density n. Variational perturbation theory is used to resum the corresponding perturbative series for {delta} /Nu in a classical three-dimensional scalar field theory with coupling u and where the physical case of N=2 field components is generalized to arbitrary N. Our results for N=1,2,4 are in agreement with recent Monte Carlo simulations; for N=2, we obtain {delta}T{sub c}/T{sub 0}=(1.27{+-}0.11)an{sup 1/3}. We use seven-loop perturbative coefficients, extending earlier work by one loop order.

Interplay of ferromagnetism and triplet superconductivity in a Josephson junction

In this work we extend our earlier analysis of the novel Josephson effect in triplet superconductor-ferromagnet-triplet superconductor (TFT) junctions [Kastening et al., Phys. Rev. Lett. 96, 047009 (2006)]. In our more general formulation of the TFT junction, we allow for potential scattering at the barrier and an arbitrary orientation of the ferromagnetic moment. Several new effects are found upon the inclusion of these extra terms: for example, we find that a Josephson current can flow even when there is vanishing phase difference between the superconducting condensates on either side of the barrier. The critical current for a barrier with magnetization parallel to the interface is calculated as a function of the junction parameters, and is found to display strong nonanalyticities. Furthermore, the Josephson current switches identified in our previous work are found to be robust features of the junction, while the unconventional temperature dependence of the current is very sensitive to the extra terms in the barrier Hamiltonian.

Novel Josephson effect in triplet-superconductor-ferromagnet-triplet-superconductor junctions.

We predict a novel type of Josephson effect to occur in triplet-superconductor-ferromagnet-triplet-superconductor Josephson junctions. We show that the Josephson current, IJ, exhibits a rich dependence on the relative orientation between the ferromagnetic moment and the d vectors of the superconductors. This dependence can be used to build several types of Josephson current switches. Moreover, we predict an unconventional sign change of IJ with increasing temperature.

Nonuniversal critical quantities from variational perturbation theory and their application to the Bose-Einstein condensation temperature shift

For an O(N)-symmetric scalar field theory with Euclidean action {integral}d{sup 3} x[(1/2){nabla}{phi}{sup 2}+(1/2)r{phi}{sup 2}+(1/4{exclamation_point})u{phi}{sup 4}], where {phi}=({phi}{sub 1},...,{phi}{sub N}) is a vector of N real-field components, variational perturbation theory through seven loops is employed for N=0,1,2,3,4 to compute the renormalized value of r/(N+2)u{sup 2} at the phase transition. Its exact large-N limit is determined as well. We also extend an earlier computation of the interaction-induced shift {delta} /Nu from N=1,2,4 to N=0,3. For N=2, the results for the two quantities are used to compute the second-order shift of the condensation temperature of a dilute Bose gas, both in the homogenous case and for the wide limit of a harmonic trap. Our results are in agreement with earlier Monte Carlo simulations for N=1,2,4. The Appendix contains previously unpublished numerical seven-loop data.

Fluctuation pressure of a membrane between walls through five loops.

An earlier four-loop calculation of the fluctuation pressure of a fluid membrane between two infinite walls is extended to five loops. Variational perturbation theory is used to extract the hard-wall limit from perturbative results obtained with a smooth potential. Comparison with a structurally similar quantum mechanics problem of a particle in a box is used for an alternative way of extracting the membrane pressure and also to estimate the quality of the results. Our values lie above the best available Monte Carlo data.

Simplified transfer matrix approach in the two-dimensional Ising model with various boundary conditions.

A recent simplified transfer matrix solution of the two-dimensional Ising model on a square lattice with periodic boundary conditions is generalized to periodic-antiperiodic, antiperiodic-periodic, and antiperiodic-antiperiodic boundary conditions. It is suggested to employ linear combinations of the resulting partition functions to investigate finite-size scaling. An exact relation of such a combination to the partition function corresponding to Brascamp-Kunz boundary conditions is found.

Three-loop ground-state energy of O ( N ) -symmetric Ginzburg-Landau theory above T c in 4 − ɛ dimensions with minimal subtraction

As a step towards deriving universal amplitude ratios of the superconductive phase transition we calculate the vacuum energy density in the symmetric phase of

Simplifying Kaufman's solution of the two-dimensional Ising model.

\mathrm{O}(N)

Anisotropy and universality in finite-size scaling: critical Binder cumulant of a two-dimensional Ising model.

-symmetric scalar QED in

Universal anisotropic finite-size critical behavior of the two-dimensional Ising model on a strip and of d-dimensional models on films.

D=4\ensuremath{-}\ensuremath{\varepsilon}