scholarly journals Non-Debye Relaxations: Two Types of Memories and Their Stieltjes Character

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 477
Author(s):  
Katarzyna Górska ◽  
Andrzej Horzela
Keyword(s):  
Stochastic Processes ◽  
Spectral Function ◽  
Evolution Equations ◽  
Memory Function ◽  
Relaxation Phenomena ◽  
Stieltjes Function ◽  
Infinitely Divisible ◽  
Spectral Functions ◽  
Debye Relaxation ◽  
Relaxation Functions

In this paper, we show that spectral functions relevant for commonly used models of the non-Debye relaxation are related to the Stieltjes functions supported on the positive semi-axis. Using only this property, it can be shown that the response and relaxation functions are non-negative. They are connected to each other and obey the time evolution provided by integral equations involving the memory function M(t), which is the Stieltjes function as well. This fact is also due to the Stieltjes character of the spectral function. Stochastic processes-based approach to the relaxation phenomena gives the possibility to identify the memory function M(t) with the Laplace (Lévy) exponent of some infinitely divisible stochastic processes and to introduce its partner memory k(t). Both memories are related by the Sonine equation and lead to equivalent evolution equations which may be freely interchanged in dependence of our knowledge on memories governing the process.

A Space Correlation and Its Associated Turbulence Spectral Function

1974 ◽  
Vol 52 (3) ◽  
pp. 219-222
Author(s):  
S. N. Samaddar
Keyword(s):  
Spectral Function ◽  
Isotropic Turbulence ◽  
Spectral Functions ◽  
Space Correlation ◽  
Special Cases

A space correlation associated with an isotropic turbulence spectral function is derived. A few special cases of this spectral function are also discussed. One of these special spectral functions was proposed previously for some valid physical grounds.

Connection formulae for spectral functions associated with singular Dirac equations

2004 ◽  
Vol 134 (1) ◽  
pp. 215-223 ◽  
Author(s):  
S. M. Riehl
Keyword(s):  
Dirac Equation ◽  
Spectral Function ◽  
Limit Point ◽  
Initial Condition ◽  
Spectral Functions ◽  
Dirac Equations ◽  
Special Cases ◽  
Limit Point Case ◽  
Image Position ◽  
Connection Formulae

We consider the Dirac equation given by with initial condition y1 (0) cos α + y2(0) sin α = 0, α ε [0; π ) and suppose the equation is in the limit-point case at infinity. Using to denote the derivative of the corresponding spectral function, a formula for is given when is known and positive for three distinct values of α. In general, if is known and positive for only two distinct values of α, then is shown to be one of two possibilities. However, in special cases of the Dirac equation, can be uniquely determined given for only two values of α.

scholarly journals Spectral Function of a Boson Ladder in an Artificial Gauge Field

2020 ◽  
Vol 5 (1) ◽  
pp. 15 ◽  
Author(s):  
Roberta Citro ◽  
Stefania De Palo ◽  
Nicolas Victorin ◽  
Anna Minguzzi ◽  
Edmond Orignac
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Spectral Function ◽  
Weak Interactions ◽  
Spectral Weight ◽  
Ultracold Atom ◽  
Spectral Functions ◽  
Vortex Phase ◽  
Bogoliubov Theory ◽  
Radio Frequency Spectroscopy

We calculate the spectral function of a boson ladder in an artificial magnetic field by means of analytic approaches based on bosonization and Bogoliubov theory. We discuss the evolution of the spectral function at increasing effective magnetic flux, from the Meissner to the Vortex phase, focussing on the effects of incommensurations in momentum space. At low flux, in the Meissner phase, the spectral function displays both a gapless branch and a gapped one, while at higher flux, in the Vortex phase, the spectral function displays two gapless branches and the spectral weight is shifted at a wavevector associated to the underlying vortex spatial structure, which can indicate a supersolid-like behavior. While the Bogoliubov theory, valid at weak interactions, predicts sharp delta-like features in the spectral function, at stronger interactions we find power-law broadening of the spectral functions due to quantum fluctuations as well as additional spectral weight at higher momenta due to backscattering and incommensuration effects. These features could be accessed in ultracold atom experiments using radio-frequency spectroscopy techniques.

scholarly journals Evolution of Spectral Functions in Doped Transition Metal Oxides

1997 ◽  
Vol 11 (32) ◽  
pp. 3849-3857 ◽  
Author(s):  
H. Kajueter ◽  
G. Kotliar ◽  
D. D. Sarma ◽  
S. R. Barman
Keyword(s):  
Transition Metal ◽  
Metal Oxides ◽  
Spectral Function ◽  
Transition Metal Oxides ◽  
Mean Field Theory ◽  
Mean Field ◽  
Correlated Electrons ◽  
Infinite Dimensions ◽  
Spectral Functions ◽  
Early Transition Metal

We discuss the experimental photoemission and inverse photoemission of early transition metal oxides, in the light of the dynamical mean field theory of correlated electrons which becomes exact in the limit of infinite dimensions. We argue that a comprehensive description of the experimental data requires spatial inhomogeneities and present a calculation of the evolution of the spectral function in an inhomogeneities and present a calculation of the evolution of the spectral function in an inhomogenous system with various degrees of inhomogeneity. We also point out that comparison of experimental results and large d calculations require that the degree of correlation and disorder is larger in the surface than in the bulk.

Relaxation phenomena of nicotinamide and benzamide with 1-propanol and 1-butanol in C6H6 under static and 9.385 GHz electric field

2016 ◽  
Vol 94 (7) ◽  
pp. 628-639 ◽  
Author(s):  
Swagatadeb Sahoo ◽  
Swapan K. Sit
Keyword(s):  
Electric Fields ◽  
Liquid Mixture ◽  
Dipole Moments ◽  
Relaxation Times ◽  
Relaxation Mechanism ◽  
Debye Model ◽  
Relaxation Phenomena ◽  
Debye Relaxation ◽  
Polar Groups ◽  
Polar Mixtures

Dielectric relaxation behaviors of nicotinamide+1-propanol, benzamide+1-propanol, and nicotinamide+1-butanol dissolved in C6H6 at 0.990, 0.985, 0.980, 0.975, 0.970; 0.990, 0.985, 0.980, and 0.980 mol fraction xj of 1-propanol or 1-butanol at temperature 30 °C and 30, 40, 50, and 60 °C, respectively, are studied using the Debye model of binary polar–non-polar liquid mixture to predict double relaxation times τ2 and τ1 and dipole moments μ2 and μ1 from susceptibility measurement of concentration variation solution data under static and 9.385 GHz electric fields. Nineteen systems exhibit τ2, τ1 and μ2, μ1. τ2 are found to increase with temperature for all the binary polar mixtures, whereas τ1, most probable τ0, and measured τ from slope methods are almost the same. They agree well with the τ reported by Higasi. The plots of τjk–xj and μjk–xj curves reveal solute–solute and solute–solvent molecular association through H-bonding, and variation of μ with t (°C) is noted from the μjk–t curve. The associational aspects are taken into consideration from theoretical μtheo from the standpoint of inductive, mesomeric, and electromeric effects within the polar groups of the molecules. The estimated Debye factor τjkT/η and Kalman factor τjkT/ηγ reveal that the polar mixture obeys the Debye relaxation mechanism.

scholarly journals EFFECTS OF QUANTUM HALL EDGE RECONSTRUCTION ON MOMENUM-RESOLVED TUNNELING

2004 ◽  
Vol 18 (27n29) ◽  
pp. 3521-3526 ◽  
Author(s):  
AKAKII MELIKIDZE ◽  
KUN YANG
Keyword(s):  
Spectral Function ◽  
Interaction Energy ◽  
Coulomb Interaction ◽  
Quantum Hall ◽  
Momentum Dependence ◽  
Spectral Functions ◽  
Edge Reconstruction ◽  
Energy And Momentum ◽  
Distinct Features ◽  
Additional Excitation

During the reconstruction of the edge of a quantum Hall liquid, Coulomb interaction energy is lowered through the change in the structure of the edge. We use theory developed earlier by one of the authors [K. Yang, Phys. Rev. Lett. 91, 036802 (2003)] to calculate the electron spectral functions of a reconstructed edge, and study the consequences of the edge reconstruction for the momentum-resolved tunneling into the edge. It is found that additional excitation modes that appear after the reconstruction produce distinct features in the energy and momentum dependence of the spectral function, which can be used to detect the presence of edge reconstruction.

Asymptotic distribution of the maximum of n independent stochastic processes

1993 ◽  
Vol 30 (1) ◽  
pp. 66-81 ◽  
Author(s):  
A. A. Balkema ◽  
L. De Haan ◽  
R. L. Karandikar
Keyword(s):  
Stochastic Processes ◽  
Asymptotic Distribution ◽  
Point Process ◽  
Poisson Point Process ◽  
Spectral Functions ◽  
Distribution Of The Maximum

Limits in distribution of maxima of independent stochastic processes are characterized in terms of spectral functions acting on a Poisson point process.

scholarly journals On regular variation for infinitely divisible random vectors and additive processes

2006 ◽  
Vol 38 (01) ◽  
pp. 134-148 ◽  
Author(s):  
Henrik Hult ◽  
Filip Lindskog
Keyword(s):  
Stochastic Processes ◽  
Regular Variation ◽  
Tail Behavior ◽  
Random Vectors ◽  
Lévy Measure ◽  
Infinitely Divisible ◽  
Additive Process ◽  
Asymptotic Decay ◽  
Stationary Increments ◽  
Additive Processes

We study the tail behavior of regularly varying infinitely divisible random vectors and additive processes, i.e. stochastic processes with independent but not necessarily stationary increments. We show that the distribution of an infinitely divisible random vector is tail equivalent to its Lévy measure and we study the asymptotic decay of the probability for an additive process to hit sets far away from the origin. The results are extensions of known univariate results to the multivariate setting; we exemplify some of the difficulties that arise in the multivariate case.

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