17,356 research outputs found
Functional renormalization group for quantized anharmonic oscillator
Functional renormalization group methods formulated in the real-time
formalism are applied to the symmetric quantum anharmonic oscillator,
considered as a 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 or its nonlinearity parameter 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 alone the perturbed van der Pol
oscillator does not show solar-like behaviour. When the perturbed variable is
, 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
Some consequences of GUP induced ultraviolet wavevector cutoff in one-dimensional Quantum Mechanics
A projection method is proposed to treat the one-dimensional Schrodinger
equation for a single particle when the Generalized Uncertainty Principle (GUP)
generates an ultraviolet (UV) wavevector cutoff. The existence of a unique
coordinate representation called the naive one is derived from the
one-parameter family of discrete coordinate representations. In this
bandlimited Quantum Mechanics a continuous potential is reconstructed from
discrete sampled values observed by means of a particle in maximally localized
states. It is shown that bandlimitation modifies the speed of the center and
the spreading time of a Gaussian wavepacket moving in free space. Indication is
found that GUP accompanied by bandlimitation may cause departures of the
low-lying energy levels of a particle in a box from those in ordinary Quantum
Mechanics much less suppressed than commonly thought when GUP without
bandlimitation is in work.Comment: 20 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 ghost model with higher-order gradient term
The phase structure and the infrared behaviour of the Euclidean 3-dimensional
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 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
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