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 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.

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.

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.

scholarly journals Spectral Functions for the Vector-Valued Fourier Transform

2018 ◽  
Vol 2018 ◽  
pp. 1-17
Author(s):  
Vadim Mogilevskii
Keyword(s):  
Distribution Function ◽  
Fourier Transform ◽  
Spectral Function ◽  
Vector Function ◽  
Finite Interval ◽  
Spectral Functions ◽  
The Matrix ◽  
The Fourier Transform ◽  
Vector Valued

A scalar distribution function σ(s) is called a spectral function for the Fourier transform φ^(s)=∫Reitsφ(t)dt (with respect to an interval I⊂R) if for each function φ∈L2(R) with support in I the Parseval identity ∫Rφ^s2dσ(s)=∫Rφt2dt holds. We show that in the case I=R there exists a unique spectral function σ(s)=(1/2π)s, in which case the above Parseval identity turns into the classical one. On the contrary, in the case of a finite interval I=(0,b), there exist infinitely many spectral functions (with respect to I). We introduce also the concept of the matrix-valued spectral function σ(s) (with respect to a system of intervals {I1,I2,…,In}) for the vector-valued Fourier transform of a vector-function φ(t)={φ1(t),φ2(t),…,φn(t)}∈L2(I,Cn), such that support of φj lies in Ij. The main result is a parametrization of all matrix (in particular scalar) spectral functions σ(s) for various systems of intervals {I1,I2,…,In}.

Spectral functions of a symmetric linear relation with a directing mapping, I

1984 ◽  
Vol 97 ◽  
pp. 165-176 ◽  
Author(s):  
H. Langer ◽  
B. Textorius
Keyword(s):  
Spectral Function ◽  
Differential System ◽  
Linear Relation ◽  
Spectral Functions ◽  
First Order ◽  
Symmetric Linear Relation

SynopsisFor a symmetric linear relation S with a directing mapping, the notion of a spectral function is defined by means of a Bessel–Parseval inequality, and a description of all such spectral functions is given. As an application, we describe the set of all spectral functions of a canonical regular first order differential system.

Differentiability of spectral functions for nearly stable processes and large deviations

2014 ◽  
Vol 17 (03) ◽  
pp. 1450017
Author(s):  
Yoshihiro Tawara ◽  
Kaneharu Tsuchida
Keyword(s):  
Large Deviations ◽  
Spectral Function ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Characteristic Exponent ◽  
Stable Processes ◽  
Slowly Varying Function ◽  
Spectral Functions ◽  
Additive Functionals ◽  
Deviation Principle

We consider the differentiability of a spectral function generated by a Lévy process M with characteristic exponent |ξ|αl(|ξ|2), where l(x) is a slowly varying function at ∞. As an application, we obtain the large deviation principle for positive continuous additive functionals of M. Finally, we show that the exponent l(x) = ( log (1 + x))β/2 (0 < β < 2 - α) is an example for which our theorem is applicable.

SPECTRAL FUNCTION SUM RULES IN SU(3) × SU(3)

1967 ◽  
Vol 45 (12) ◽  
pp. 3901-3902 ◽  
Author(s):  
J. W. Moffat ◽  
P. J. O'Donnell
Keyword(s):  
Spectral Function ◽  
Sum Rules ◽  
The Other ◽  
Mass Ratio ◽  
Spectral Functions ◽  
Other Hand ◽  
Mass Ratios

Recently derived spectral function sum rules have been used to obtain mass ratios, assuming that the spectral functions are dominated by certain low-lying states. The strangeness-carrying resonance mass ratio is investigated and the predicted value is found to depend critically upon the ratio FK/Fπ. Using the experimental value FK/Fπ = 1.28 ± 0.02, it is found that [Formula: see text]. On the other hand, from the input value [Formula: see text] we get [Formula: see text].

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