Spectral statistics in damped systems. Part II. Spectral density fluctuations

1996 ◽  
Vol 100 (1) ◽  
pp. 327-334
Author(s):  
John Burkhardt ◽  
Richard L. Weaver
Keyword(s):  
Spectral Density ◽  
Density Fluctuations ◽  
Spectral Statistics ◽  
Damped Systems

scholarly journals Chaos on the hypercube

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Yiyang Jia ◽  
Jacobus J. M. Verbaarschot
Keyword(s):  
Magnetic Flux ◽  
Spectral Density ◽  
Hermite Polynomials ◽  
Weighted Sums ◽  
Majorana Fermions ◽  
Chord Diagrams ◽  
Magnetic Inversion ◽  
Constant Magnitude ◽  
Kitaev Model ◽  
Spectral Statistics

Abstract We analyze the spectral properties of a d-dimensional HyperCubic (HC) lattice model originally introduced by Parisi. The U(1) gauge links of this model give rise to a magnetic flux of constant magnitude ϕ but random orientation through the faces of the hypercube. The HC model, which also can be written as a model of 2d interacting Majorana fermions, has a spectral flow that is reminiscent of Maldacena-Qi (MQ) model, and its spectrum at ϕ = 0, actually coincides with the coupling term of the MQ model. As was already shown by Parisi, at leading order in 1/d, the spectral density of this model is given by the density function of the Q-Hermite polynomials, which is also the spectral density of the double-scaled Sachdev-Ye-Kitaev model. Parisi demonstrated this by mapping the moments of the HC model to Q-weighted sums on chord diagrams. We point out that the subleading moments of the HC model can also be mapped to weighted sums on chord diagrams, in a manner that descends from the leading moments. The HC model has a magnetic inversion symmetry that depends on both the magnitude and the orientation of the magnetic flux through the faces of the hypercube. The spectrum for fixed quantum number of this symmetry exhibits a transition from regular spectra at ϕ = 0 to chaotic spectra with spectral statistics given by the Gaussian Unitary Ensembles (GUE) for larger values of ϕ. For small magnetic flux, the ground state is gapped and is close to a Thermofield Double (TFD) state.

Spectral statistics in damped systems. Part I. Modal decay rate statistics

1996 ◽  
Vol 100 (1) ◽  
pp. 320-326 ◽  
Author(s):  
John Burkhardt ◽  
Richard L. Weaver
Keyword(s):  
Decay Rate ◽  
Spectral Statistics ◽  
Damped Systems

scholarly journals Minimal-supersymmetric extended inflation field in Horava–Lifshitz gravity

2017 ◽  
Vol 26 (14) ◽  
pp. 1750166 ◽  
Author(s):  
Abdel Nasser Tawfik ◽  
Abdel Magied Diab ◽  
Eiman Abou El Dahab
Keyword(s):  
Dark Energy ◽  
Scalar Field ◽  
Spectral Density ◽  
Equations Of State ◽  
Field Potential ◽  
Density Fluctuations ◽  
Friedmann Equations ◽  
Cosmic Background ◽  
Theories Of Gravity ◽  
Scalar Perturbations

We study the Friedmann inflation in general covariant Horava–Lifshitz gravity (HLG) without the projectability conditions and with detailed and nondetailed balance conditions. Accordingly, we derive modifications in the Friedmann equations due to a single-scalar field potential describing minimal-supersymmetrically extended inflation. By implementing two time-independent equations of state (EoS) characterizing the cosmic background geometry filled up with dark energy, the dependence of the tensorial and scalar density fluctuations and their ratios on the inflation field are determined. The latter refers to the time evolution of the inflationary field relative to the Hubble parameter. Furthermore, the ratios of tensorial-to-spectral density fluctuations are calculated in dependence on the spectral index. For cold dark energy EoS [Formula: see text], we find that the tensorial-to-spectral density fluctuations are not depending on the different theories of gravity and the results are very small relative to the recent BICEP2/Keck Array-Planck observations, [Formula: see text]. We have also calculated the tensorial and scalar perturbations of the primordial spectra.

scholarly journals Friedmann inflation in Horava–Lifshitz gravity with a scalar field

2016 ◽  
Vol 31 (09) ◽  
pp. 1650042 ◽  
Author(s):  
Abdel Nasser Tawfik ◽  
Abdel Magied Diab ◽  
Eiman Abou El Dahab
Keyword(s):  
Scalar Field ◽  
Spectral Density ◽  
Equations Of State ◽  
Density Fluctuations ◽  
Regular Pattern ◽  
Field Potentials ◽  
Potential Models ◽  
Friedmann Equations ◽  
Slow Roll ◽  
Cosmic Background

We study Friedmann inflation in general Horava–Lifshitz (HL) gravity with detailed and nondetailed and also without the projectability conditions. Accordingly, we derive the modifications in the Friedmann equations due to single scalar field potentials describing power-law and minimal-supersymmetrically extended inflation. By implementing four types of the equations-of-state characterizing the cosmic background geometry, the dependence of the tensorial and spectral density fluctuations and their ratio on the inflation field is determined. The latter characterizes the time evolution of the inflation field relative to the Hubble parameter. Furthermore, the ratio of tensorial-to-spectral density fluctuations is calculated in dependence on the spectral index. The resulting slow-roll parameters apparently differ from the ones deduced from the standard General Relativity (Friedmann gravity). We also observe that the tensorial-to-spectral density fluctuations continuously decrease when moving from nondetailed HL gravity, to Friedmann gravity, to HL gravity without the projectability, and to detailed HL gravity. This regular pattern is valid for three types of cosmic equations-of-state and different inflation potential models. The results fit well with the recent Planck observations.

Randomness and Earth’s Climate Variability

2016 ◽  
Vol 15 (01) ◽  
pp. 1650006 ◽  
Author(s):  
Michael Levinshtein ◽  
Valentin Dergachev ◽  
Alexander Dmitriev ◽  
Pavel Shmakov
Keyword(s):  
Spectral Density ◽  
Characteristic Time ◽  
Decisive Role ◽  
Random Processes ◽  
Noise Spectrum ◽  
Climatic Changes ◽  
Density Fluctuations ◽  
Natural Phenomena ◽  
Periodic Processes ◽  
Earth’S Climate

Paleo-Sciences including palaeoclimatology and palaeoecology have accumulated numerous records related to climatic changes. The researchers have usually tried to identify periodic and quasi-periodic processes in these paleoscientific records. In this paper, we show that this analysis is incomplete. As follows from our results, random processes, namely processes with a single-time-constant [Formula: see text] (noise with a Lorentzian noise spectrum), play a very important and, perhaps, a decisive role in numerous natural phenomena. For several of very important natural phenomena the characteristic time constants [Formula: see text] are very similar and equal to [Formula: see text] years. However, this value of [Formula: see text] is not universal. For example, the spectral density fluctuations of the atmospheric radiocarbon [Formula: see text]C are characterized by a Lorentzian with [Formula: see text] years. The frequency dependence of spectral density fluctuations for benthic [Formula: see text]O records contains two Lorentzians with [Formula: see text] years and [Formula: see text] years.

scholarly journals Inkohärente Lichtstreuung an Ladungsdichteschwankungen schwach ionisierter Plasmen in Magnetfeldern / Incoherent Scattering of Light from Charge-Density Fluctuations in Weakly Ionized Magnetoplasmas

1972 ◽  
Vol 27 (8-9) ◽  
pp. 1375-1376
Author(s):  
G. Klingenberg ◽  
E. W. Richter
Keyword(s):  
Magnetic Field ◽  
Spectral Density ◽  
Debye Length ◽  
Scattered Wave ◽  
Homogeneous Magnetic Field ◽  
Incoherent Scattering ◽  
Density Fluctuations ◽  
Electron Plasmas ◽  
Weakly Ionized ◽  
The Difference

Abstract The spectral density of light scattering from weakly ionized plasmas embedded in a homogeneous magnetic field Bis given by the work of WILLIAMS and CHAPPELL 1, 2 and KLINGENBERG 3 . The spectral density has been computed for electron plasmas and is analyzed for the case k ⊥B ( is the difference between the wave vectors of the incident wave and the scattered wave) in the regimes k D ≫ 1 and k D ≪ 1 (D is the Debye length).

A POWER SERIES EXPANSION OF THE MASTER EQUATION

1961 ◽  
Vol 39 (4) ◽  
pp. 551-567 ◽  
Author(s):  
N. G. van Kampen
Keyword(s):  
Power Series ◽  
Spectral Density ◽  
Master Equation ◽  
Approximation Method ◽  
Power Series Expansion ◽  
Planck Equation ◽  
Density Fluctuations ◽  
Mean Square ◽  
Approach To Equilibrium ◽  
The Mean

In order to solve the master equation by a systematic approximation method, an expansion in powers of some parameter is needed. The appropriate parameter is the reciprocal size of the system, defined as the ratio of intensive and extensive variables. The lowest approximation yields the phenomenological law for the approach to equilibrium. The next approximation determines the mean square of the fluctuations about the phenomenological behavior. In equilibrium this approximation has the form of a linear Fokker–Planck equation. The higher approximations describe the effect of the non-linearity on the fluctuations, in particular on their spectral density. The method is applied to three examples: density fluctuations, Alkemade's diode, and Rayleigh's piston. The relation to the expansion recently given by Siegel is also discussed.

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