arXiv subjects

Christian Beck

Publications and source records attributed to Christian Beck.

At least 145 records · Page 8Linked to original sources

arXiv2005

Dark energy, chaotic fields, and fundamental constants

To explain the currently observed accelerated expansion of the universe, a large number of different theoretical models are presently being discussed. In one way or another, all of these contain `new physics', though at different levels. The big question is how to select out of infinitely many possible models the right one. Here we discuss a possibility that has so far been somewhat neglected, namely that the new physics underlying dark energy arises out of a gravitationally active amendment of the electroweak and strong sector of the standard model. This amendment basically consists of a rapidly fluctuating gravitationally active dynamics of vacuum fluctuations with a cutoff of the order of the neutrino mass scale. We consider a concrete model for this based on second-quantized self-interacting scalar fields, which evolve in a chaotic way. It is shown that expectations with respect to the chaotic dynamics yield statements on the observed numerical values of the electroweak coupling constants with amazing precision, thus providing evidence for the physical relevance of this model.

astro-ph↗

arXiv2005

Asymptotics of superstatistics

Superstatistics are superpositions of different statistics relevant for driven nonequilibrium systems with spatiotemporal inhomogeneities of an intensive variable (e.g., the inverse temperature). They contain Tsallis statistics as a special case. We develop here a technique that allows us to analyze the large energy asymptotics of the stationary distributions of general superstatistics. A saddle-point approximation is developed which relates this problem to a variational principle. Several examples are worked out in detail.

cond-mat.stat-mech↗

arXiv2004

Could dark energy be measured in the lab?

The experimentally measured spectral density of current noise in Josephson junctions provides direct evidence for the existence of zero-point fluctuations. Assuming that the total vacuum energy associated with these fluctuations cannot exceed the presently measured dark energy of the universe, we predict an upper cutoff frequency of nu_c=(1.69 +- 0.05) x 10^12 Hz for the measured frequency spectrum of zero-point fluctuations in the Josephson junction. The largest frequencies that have been reached in the experiments are of the same order of magnitude as nu_c and provide a lower bound on the dark energy density of the universe. It is shown that suppressed zero-point fluctuations above a given cutoff frequency can lead to 1/f noise. We propose an experiment which may help to measure some of the properties of dark energy in the lab.

astro-ph↗

arXiv2004

Chaotic scalar fields as models for dark energy

We consider stochastically quantized self-interacting scalar fields as suitable models to generate dark energy in the universe. Second quantization effects lead to new and unexpected phenomena is the self interaction strength is strong. The stochastically quantized dynamics can degenerate to a chaotic dynamics conjugated to a Bernoulli shift in fictitious time, and the right amount of vacuum energy density can be generated without fine tuning. It is numerically observed that the scalar field dynamics distinguishes fundamental parameters such as the electroweak and strong coupling constants as corresponding to local minima in the dark energy landscape. Chaotic fields can offer possible solutions to the cosmological coincidence problem, as well as to the problem of uniqueness of vacua.

astro-ph↗

arXiv2003

Nonextensive scalar field theories and dark energy models

Current astronomical measurements indicate that approximately 73% of the universe is made up of dark energy. Stochastically quantized self-interacting scalar fields can serve as suitable models to generate dark energy. We study a particular model where the scalar field theory underlying dark energy exhibits strongest possible chaotic behaviour. It is shown that the fluctuating chaotic field momenta obey a generalized (nonextensive) statistical mechanics, with an entropic index q given by q=3, respectively q=-1 if the escort formalism is used.

cond-mat↗

arXiv2003

Superstatistics, escort distributions, and applications

Superpositions of different statistics on different time or spatial scales (in short, superstatistics) can naturally lead to an effective description by nonextensive statistical mechanics. We first discuss the role of escort distributions within the superstatistical framework, and then briefly describe recent physical applications of this concept to turbulent and pattern forming systems.

cond-mat.stat-mech↗

arXiv2003

Chaotic quantization and the parameters of the standard model

In the chaotic quantization approach one replaces the Gaussian white noise of the Parisi-Wu approach of stochastic quantization by a deterministic chaotic process on a very small scale. We consider suitable coupled chaotic noise processes as generated by Tchebyscheff maps, and show that the vacuum energy of these models is minimized for coupling constants that coincide with running standard model couplings at energy scales given by the known fermion and boson masses. Chaotic quantization thus allows to predict fundamental constants of nature from first principles. At the same time, it provides a natural framework to understand the dynamical origin of vacuum energy in our universe.

hep-th↗

arXiv2003

Superstatistics: Theory and Applications

Superstatistics is a superposition of two different statistics relevant for driven nonequilibrium systems with a stationary state and intensive parameter fluctuations. It contains Tsallis statistics as a special case. After briefly summarizing some of the theoretical aspects, we describe recent applications of this concept to three different physical problems, namely a) fully developed hydrodynamic turbulence b) pattern formation in thermal convection states and c) the statistics of cosmic rays.

cond-mat.stat-mech↗

arXiv2003

Superstatistics in hydrodynamic turbulence

Superstatistics is a `statistics of a statistics' relevant for driven nonequilibrium systems with fluctuating intensive parameters. It contains Tsallis statistics as a special case. We show that the probability density functions of velocity differences and accelerations measured in Eulerian and Lagrangian turbulence experiments are well reproduced by simple superstatistics models. We compare fits obtained for log-normal superstatistics and chi-squared superstatistics (= Tsallis statistics).

physics.flu-dyn↗

arXiv2003

Defect turbulence and generalized statistical mechanics

We present experimental evidence that the motion of point defects in thermal convection patterns in an inclined fluid layer is well-described by Tsallis statistics with an entropic index $q \approx 1.5$. The dynamical properties of the defects (anomalous diffusion, shape of velocity distributions, power law decay of correlations) are in good agreement with typical predictions of nonextensive models, over a range of driving parameters.

cond-mat.stat-mech↗

arXiv2003

Generalized statistical mechanics of cosmic rays

We consider a generalized statistical mechanics model for the creation process of cosmic rays which takes into account local temperature fluctuations. This model yields Tsallis statistics for the cosmic ray spectrum. It predicts an entropic index q given by q=11/9 at largest energies (equivalent to a spectral index of alpha=5/2), and an effective temperature given by (5/9)T_H, where kT_H approximately equal to 180 MeV is the Hagedorn temperature measured in collider experiments. Our theoretically obtained formula is in very good agreement with the experimentally measured energy spectrum of primary cosmic rays.

cond-mat.stat-mech↗

arXiv2002

Lagrangian acceleration statistics in turbulent flows

We show that the probability densities af accelerations of Lagrangian test particles in turbulent flows as measured by Bodenschatz et al. [Nature 409, 1017 (2001)] are in excellent agreement with the predictions of a stochastic model introduced in [C. Beck, PRL 87, 180601 (2001)] if the fluctuating friction parameter is assumed to be log-normally distributed. In a generalized statistical mechanics setting, this corresponds to a superstatistics of log-normal type. We analytically evaluate all hyperflatnes factors for this model and obtain a flatness prediction in good agreement with the experimental data. There is also good agreement with DNS data of Gotoh et al. We relate the model to a generalized Sawford model with fluctuating parameters, and discuss a possible universality of the small-scale statistics.

cond-mat.stat-mech↗

arXiv2002

Spatio-temporal Chaos and Vacuum Fluctuations of Quantized Fields

We consider deterministic chaotic models of vacuum fluctuations on a small (quantum gravity) scale. As a suitable small-scale dynamics, nonlinear versions of strings, so-called `chaotic strings' are introduced. These can be used to provide the `noise' for second quantization of ordinary strings via the Parisi- Wu approach of stochastic quantization. Extensive numerical evidence is presented that the vacuum energy of chaotic strings is minimized for the numerical values of the observed standard model parameters, i.e. in this extended approach to second quantization concrete predictions for vacuum expectations of dilaton-like fields and hence on masses and coupling constants can be given. Low-energy fermion and boson masses are correctly obtained with a precision of 3-4 digits, the electroweak and strong coupling strengths with a precision of 4-5 digits. In particular, the minima of the vacuum energy yield high-precision predictions of the Higgs mass (154 GeV), of the neutrino masses (1.45E-5 eV, 2.57E-3 eV, 4.92E-2 eV) and of the GUT scale (1.73E16 GeV).

hep-th↗

arXiv2001

Nonextensive methods in turbulence and particle physics

We describe some recent applications of Tsallis statistics in fully developed hydrodynamic turbulence and high energy physics. For many of these applications nonextensive properties arise from spatial fluctuations of the temperature or the energy dissipation rate. The entropic index q is related to the relative magnitude of these fluctuations. We concentrate on a recently derived formula for the energy dependence of q that is experimentally verified by fits of cross sections in e+e- annihilation experiments. Evaluating this formula for much smaller energies E of the order of the recombination temperature, one obtains the correct order of magnitude of the fluctuations of the cosmic microwave background. Evaluating it for E going to infinity, one obtains (under certain assumptions) possible evidence for the existence of 6 compactified dimensions, as predicted by superstring theory.

cond-mat.stat-mech↗

arXiv2001

Generalized statistical mechanics and fully developed turbulence

The statistical properties of fully developed hydrodynamic turbulence can be successfully described using methods from nonextensive statistical mechanics. The predicted probability densities and scaling exponents precisely coincide with what is measured in various turbulence experiments. As a dynamical basis for nonextensive behaviour we consider nonlinear Langevin equations with fluctuating friction forces, where Tsallis statistics can be rigorously proved.

cond-mat.stat-mech↗

arXiv2001

On the small-scale statistics of Lagrangian turbulence

We provide evidence that the small-scale statistics of the acceleration of a test particle in high-Reynolds number Lagrangian turbulence is correctly described by Tsallis statistics with entropic index q=3/2. We present theoretical arguments why Tsallis statistics can naturally arise in Lagrangian turbulence and why at the smallest scales q=3/2 is relevant. A generalized Heisenberg-Yaglom formula is derived from the nonextensive model.

physics.flu-dyn↗

arXiv2001

Dynamical foundations of nonextensive statistical mechanics

We construct classes of stochastic differential equations with fluctuating friction forces that generate a dynamics correctly described by Tsallis statistics and nonextensive statistical mechanics. These systems generalize the way in which ordinary Langevin equations underly ordinary statistical mechanics to the more general nonextensive case. As a main example, we construct a dynamical model of velocity fluctuations in a turbulent flow, which generates probability densities that very well fit experimentally measured probability densities in Eulerian and Lagrangian turbulence. Our approach provides a dynamical reason why many physical systems with fluctuations in temperature or energy dissipation rate are correctly described by Tsallis statistics.

cond-mat.stat-mech↗

arXiv2001

Non-additivity of Tsallis entropies and fluctuations of temperature

We show that the non-additivity relation of the Tsallis entropies in nonextensive statistical mechanics has a simple physical interpretation for systems with fluctuating temperature or fluctuating energy dissipation rate. We also show that there is a distinguished dependence of the entropic index q on the spatial scale that makes the Tsallis entropies quasi-additive. Quasi-additivity implies that q is a strictly monotonously decreasing function of the spatial scale r, as indeed observed in various experiments.

cond-mat.stat-mech↗