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 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.

scholarly journals RESONANT RAMAN SCATTERING OF QUANTUM WIRE IN STRONG MAGNETIC FIELD

1999 ◽  
Vol 13 (17) ◽  
pp. 2275-2283 ◽  
Author(s):  
HYUN C. LEE
Keyword(s):  
Magnetic Field ◽  
Raman Scattering ◽  
Strong Magnetic Field ◽  
Coulomb Interaction ◽  
Quantum Wire ◽  
Spin Excitation ◽  
Momentum Dependence ◽  
Near Resonance ◽  
Resonant Raman ◽  
Resonant Raman Scattering

The resonant Raman scattering of a quantum wire in a strong magnetic field is studied, focused on the effect of long range Coulomb interaction and the spin–charge separation. The energy–momentum dispersions of charge and spin excitation obtained from Raman cross-section show the characteristc cross-over behaviour induced by inter-edge Coulomb interaction. The "SPE" peak near resonance in polarized spectra becomes broad due to the momentum dependence of charge velocity. The broad peak in the depolarized spectra is shown to originate from the disparity between charge and spin excitation velocity.

scholarly journals Investigating the roots of the nonlinear Luttinger liquid phenomenology

2019 ◽  
Vol 7 (4) ◽  
Author(s):  
Lisa Markhof ◽  
Mikhail Pletyukov ◽  
Volker Meden
Keyword(s):  
Spectral Function ◽  
Power Law ◽  
Single Particle ◽  
Structure Factor ◽  
Particle Interaction ◽  
Luttinger Liquid ◽  
Power Laws ◽  
Second Order ◽  
Dynamical Structure ◽  
Momentum Dependence

The nonlinear Luttinger liquid phenomenology of one-dimensional correlated Fermi systems is an attempt to describe the effect of the band curvature beyond the Tomonaga-Luttinger liquid paradigm. It relies on the observation that the dynamical structure factor of the interacting electron gas shows a logarithmic threshold singularity when evaluated to first order perturbation theory in the two-particle interaction. This term was interpreted as the linear one in an expansion which was conjectured to resum to a power law. A field theory, the mobile impurity model, which is constructed such that it provides the power law in the structure factor, was suggested to be the proper effective model and used to compute the single-particle spectral function. This forms the basis of the nonlinear Luttinger liquid phenomenology. Surprisingly, the second order perturbative contribution to the structure factor was so far not studied. We first close this gap and show that it is consistent with the conjectured power law. Secondly, we critically assess the steps leading to the mobile impurity Hamiltonian. We show that the model does not allow to include the effect of the momentum dependence of the (bulk) two-particle potential. This dependence was recently shown to spoil power laws in the single-particle spectral function which previously were believed to be part of the Tomonaga-Luttinger liquid universality. Although our second order results for the structure factor are consistent with power-law scaling, this raises doubts that the conjectured nonlinear Luttinger liquid phenomenology can be considered as universal. We conclude that more work is required to clarify this.

Excitations in a quantum Hall ferromagnet with strong Coulomb interaction

JETP Letters ◽  
2002 ◽  
Vol 75 (7) ◽  
pp. 348-353 ◽  
Author(s):  
S. V. Iordanski ◽  
A. Kasbuba
Keyword(s):  
Coulomb Interaction ◽  
Quantum Hall ◽  
Strong Coulomb

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 Ultra-small MOSFETs: The Importance of the Full Coulomb Interaction on Device Characteristics

VLSI Design ◽  
2001 ◽  
Vol 13 (1-4) ◽  
pp. 75-78 ◽  
Author(s):  
W. J. Gross ◽  
D. Vasileska ◽  
D. K. Ferry
Keyword(s):  
Coulomb Interaction ◽  
Short Range ◽  
Three Dimensional ◽  
Real Space ◽  
Relaxation Processes ◽  
Dimensional Model ◽  
Impurity Effects ◽  
Three Dimensional Model ◽  
Momentum Relaxation ◽  
Energy And Momentum

We discuss a full three-dimensional model of an ultra-small MOSFET, in which the transport is treated by a coupled EMC and molecular dynamics (MD) procedure to treat the Coulomb interaction in real space. The inclusion of the proper Coulomb interaction affects both the energy and momentum relaxation processes, but also has a dramatic effect on the characteristic curves of the device. We find that the short-range e–e and e–i terms, combined with discrete impurity effects, is also needed for accurate measurement of the device threshold voltage.

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