Functional renormalization group for quantized anharmonic oscillator

Functional renormalization group methods formulated in the real-time formalism are applied to the $O(N)$ symmetric quantum anharmonic oscillator, considered as a $0+1$ dimensional quantum field-theoric model, in the next-to-leading order of the gradient expansion of the one- and two-particle irreducible effective action. The infrared scaling laws and the sensitivity-matrix analysis show the existence of only a single, symmetric phase. The field-independent term of the wavefunction renormalization turned out to be negligible, but its field-dependent piece is noticeable. It is shown that the infrared limits of the running couplings depend on the renormalization group scheme used, when the perturbation expansion in the bare quartic coupling is truncated keeping the terms up to the second order.Comment: 30 pages, 11 figure

Oscillator Models of the Solar Cycle and the Waldmeier Effect

We study the behaviour of the van der Pol oscillator when either its damping parameter $\mu$ or its nonlinearity parameter $\xi$ is subject to additive or multiplicative random noise. Assuming various power law exponents for the relation between the oscillating variable and the sunspot number, for each case we map the parameter plane defined by the amplitude and the correlation time of the perturbation and mark the parameter regime where the sunspot number displays solar-like behaviour. Solar-like behaviour is defined here as a good correlation between the rise rate and cycle amplitude {\it and} the lack of a good correlation between the decay rate and amplitude, together with significant (\ga 10\,%) r.m.s. variation in cycle lengths and cycle amplitudes. It is found that perturbing $\mu$ alone the perturbed van der Pol oscillator does not show solar-like behaviour. When the perturbed variable is $\xi$, solar-like behaviour is displayed for perturbations with a correlation time of about 3--4 years and significant amplitude. Such studies may provide useful constraints on solar dynamo models and their parameters.Comment: 4 pages, 2 figure

Asymptotic safety in the sine-Gordon model

In the framework of the functional renormalization group method it is shown that the phase structure of the 2-dimensional sine-Gordon model possesses a nontrivial UV fixed point which makes the model asymptotically safe. The fixed point exhibits strong singularity similarly to the scaling found in the vicinity of the infrared fixed point. The singularity signals the upper energy-scale limit to the validity of the model. We argue that the sine-Gordon model with a momentum-dependent wavefunction renormalization is in a dual connection with the massive sine-Gordon model.Comment: 8 pages, 3 figure

Phase structure of the O(2)O(2) ghost model with higher-order gradient term

The phase structure and the infrared behaviour of the Euclidean 3-dimensional $O(2)$ symmetric ghost scalar field model with higher-order derivative term has been investigated in Wegner and Houghton's renormalization group framework. The symmetric phase in which no ghost condensation occurs and the phase with restored symmetry but with a transient presence of a ghost condensate have been identified. Finiteness of the correlation length at the phase boundary hints to a phase transition of first order. The results are compared with those for the ordinary $O(2)$ symmetric scalar field model.Comment: 15 pages, 13 figure

Optimized regulator for the quantized anharmonic oscillator

The energy gap between the first excited state and the ground state is calculated for the quantized anharmonic oscillator in the framework of the functional renormalization group method. The compactly supported smooth regulator is used which includes various types of regulators as limiting cases. It was found that the value of the energy gap depends on the regulator parameters. We argue that the optimization based on the disappearance of the false, broken symmetric phase of the model leads to the Litim's regulator. The least sensitivity on the regulator parameters leads however to an IR regulator being somewhat different of the Litim's one, but it can be described as a perturbatively improved, or generalized Litim's regulator and provides analytic evolution equations, too.Comment: 8 pages, 4 figure

Quantitative foraminiferal and palynomorph biostratigraphy of the Paleogene in the southwestern Barents Sea

The stratigraphic distribution of both foraminifera and dinoflagellate cysts is recorded from the Paleocene to Eocene Torsk Formation in 12 petroleum exploration wells drilled in the southwestern Barents Sea. The foraminiferal assemblages are wholly agglutinated, and are referred to outer shelf to middle bathyal environments. A quantitative analysis of biostratigraphic events, mainly last occurrences (first downhole occurrences), is performed by means of the Ranking and Scaling (RASC) program. This procedure combined with conventional stratigraphic treatment has enabled us to establish the most likely order of microfossil events, and to propose a new quantitative zonal scheme for the southwestern Barents Sea. In the studied wells the following six zones and subzones are distinguished (in ascending order): BSP 1, Psmmosphaera fusca – Hyperammina rugosa, late early to early late Paleocene; BSP 2, Spiroplectammina spectabilis early late Paleocene; BSP 3A, Reticulophragmium pauperum, middle late Paleocene; BSP 3B, Haplophragmoides aff. eggeri, latest Paleocene; BSP 4, Spiroplectammina navarroana, earliest Eocene; BSP 5, Reticulophragmium amplectens, early to middle Eocene. Owing to the occurrence of cosmopolitan deep-water agglutinated foraminifera, the new zonal scheme compares well with previous zonations developed for the Paleogene of the mid-Norwegian shelf, the North Sea and Labrador Shelf