Dynamic susceptibility of Fermi liquids at finite temperature

1976 ◽  
Vol 54 (6) ◽  
pp. 648-654 ◽  
Author(s):  
F. C. Khanna ◽  
H. R. Glyde
Keyword(s):  
Temperature Dependence ◽  
Imaginary Part ◽  
Finite Temperature ◽  
Fermi Liquid ◽  
Fermi Liquids ◽  
Dynamic Susceptibility ◽  
Closed Expression ◽  
Numerical Examples ◽  
The Real

A closed expression for the dynamic susceptibility of a noninteracting Fermi liquid at finite temperature is presented. The expression for the imaginary part is particularly simple while the real part appears as a sum. The calculation of the sum is discussed and numerical examples displaying the temperature dependence of the susceptibility are given.

scholarly journals GAP EQUATION IN SCALAR FIELD THEORY AT FINITE TEMPERATURE

1999 ◽  
Vol 14 (04) ◽  
pp. 257-266
Author(s):  
KRISHNENDU MUKHERJEE
Keyword(s):  
Field Theory ◽  
Perturbation Theory ◽  
Scalar Field ◽  
Imaginary Part ◽  
Finite Temperature ◽  
Thermal Mass ◽  
Scalar Field Theory ◽  
Gap Equation ◽  
The Real

We investigate the two-loop gap equation for the thermal mass of hot massless g2ϕ4 theory and find that the gap equation itself has a nonzero finite imaginary part. This implies that it is not possible to find the real thermal mass as a solution of the gap equation beyond g2 order in perturbation theory. We have solved the gap equation and obtained the real and imaginary parts of the thermal mass which are correct up to g4 order in perturbation theory.

scholarly journals Cutting Rules at Finite Temperature

1997 ◽  
Vol 12 (33) ◽  
pp. 2481-2496 ◽  
Author(s):  
Paulo F. Bedaque ◽  
Ashok Das ◽  
Satchidananda Naik
Keyword(s):  
Field Theory ◽  
Temperature Field ◽  
Real Time ◽  
Imaginary Part ◽  
Physical Interpretation ◽  
Finite Temperature ◽  
Zero Temperature ◽  
Finite Temperature Field Theory ◽  
The Real

We discuss the cutting rules in the real-time approach to finite temperature field theory and show the existence of cancellations among classes of cut graphs which allows a physical interpretation of the imaginary part of the relevant amplitude in terms of the underlying microscopic processes. Furthermore, with these cancellations, any calculation of the imaginary part of an amplitude becomes much easier and completely parallel to the zero temperature case.

DYNAMIC SUSCEPTIBILITY IN A PARAELECTRIC PHASE IN A SMALL PARTICLE, BOUNDARY EFFECTS

2013 ◽  
Vol 27 (09) ◽  
pp. 1350015 ◽  
Author(s):  
MATEJ HUDAK ◽  
ONDREJ HUDAK
Keyword(s):  
Physical Properties ◽  
Imaginary Part ◽  
Small Particle ◽  
Paraelectric Phase ◽  
Boundary Effects ◽  
Dynamic Susceptibility ◽  
The Real ◽  
Two Peaks ◽  
Particle Boundary

The dielectric dynamic susceptibility of a particle is studied numerically using the exact susceptibility expression in other to understand particle physical properties. There exist one peak in the imaginary part and two peaks in the real part of the susceptibility. Constant behavior of peaks width and height is found in the imaginary and real part of the susceptibility going from the center. A decrease of peaks to zero is an effect of boundary. Our results are in contrast with behavior of susceptibility behavior found variationally where there is no constant behavior of the susceptibility peaks changing r. These results are new in literature of dielectrics.

COLE–COLE DIAGRAM IN A PARAELECTRIC PHASE IN A SMALL PARTICLE: MULTIRESONANCE SINGLE RELAXATION TIME CASE

2012 ◽  
Vol 26 (07) ◽  
pp. 1150042 ◽  
Author(s):  
MATEJ HUDAK ◽  
ONDREJ HUDAK
Keyword(s):  
Relaxation Time ◽  
Imaginary Part ◽  
Paraelectric Phase ◽  
Exact Expression ◽  
Dynamic Susceptibility ◽  
Single Relaxation Time ◽  
The Real ◽  
Cole Diagram ◽  
Single Maximum ◽  
Frequency Changes

We study the Cole–Cole diagram for the case of a paraelectric particle for which the relaxation time is the same for every mode and the resonance frequency changes and there is an infinite number of such modes. We will calculate the Cole–Cole diagram for temperature a = 10 and damping g = 1 in a and g units (see below) from exact expression for the dynamic susceptibility. We have found that there is a smooth Cole–Cole diagram the curve of which starts from small frequencies 0.001 from the point near Y = 1.5 and X = 0 on the diagram down to the peak (in imaginary part) values of X near 1.6 and Y near 0.5 increasing frequency. Increasing further frequency to 20, the real and imaginary parts tend to zero value. Thus there exists a single maximum of the imaginary part of the susceptibility (for 1000 modes and for 5000 modes), and a single maximum and minimum for the real part of the susceptibility.

Temperature Dependence of Dynamic Properties of Elastomers. Relaxation Distributions

1952 ◽  
Vol 25 (4) ◽  
pp. 720-729 ◽  
Author(s):  
John D. Ferry ◽  
Edwin R. Fitzgerald ◽  
Lester D. Grandine ◽  
Malcolm L. Williams
Keyword(s):  
Distribution Function ◽  
Temperature Dependence ◽  
Dynamic Properties ◽  
Relaxation Times ◽  
Dynamic Mechanical Properties ◽  
Relaxation Processes ◽  
The Real ◽  
Reduced Frequency ◽  
Dynamic Rigidity ◽  
Composite Curve

Abstract By the use of reduced variables, the temperature dependence and frequency dependence of dynamic mechanical properties of rubberlike materials can be interrelated without any arbitrary assumptions about the functional form of either The definitions of the reduced variables are based on some simple assumptions regarding the nature of relaxation processes. The real part of the reduced dynamic rigidity, plotted against the reduced frequency, gives a single composite curve for data over wide ranges of frequency and temperature; this is true also for the imaginary part of the rigidity or the dynamic viscosity. The real and imaginary parts of the rigidity, although independent measurements, are interrelated through the distribution function of relaxation times, and this relation provides a check on experimental results. First and second approximation methods of calculating the distribution function from dynamic data are given. The use of the distribution function to predict various types of time-dependent mechanical behavior is illustrated.

A Finite-Temperature Continuum Theory Based on Interatomic Potentials

2005 ◽  
Vol 127 (4) ◽  
pp. 408-416 ◽  
Author(s):  
H. Jiang ◽  
Y. Huang ◽  
K. C. Hwang
Keyword(s):  
Temperature Dependence ◽  
Finite Temperature ◽  
Interatomic Potential ◽  
Coefficient Of Thermal Expansion ◽  
Harmonic Approximation ◽  
Continuum Theory ◽  
Single Wall Carbon Nanotubes ◽  
Interatomic Potentials ◽  
Atomistic Models ◽  
Continuum Theories

There are significant efforts to develop continuum theories based on atomistic models. These atomistic-based continuum theories are limited to zero temperature (T=0K). We have developed a finite-temperature continuum theory based on interatomic potentials. The effect of finite temperature is accounted for via the local harmonic approximation, which relates the entropy to the vibration frequencies of the system, and the latter are determined from the interatomic potential. The focus of this theory is to establish the continuum constitutive model in terms of the interatomic potential and temperature. We have studied the temperature dependence of specific heat and coefficient of thermal expansion of graphene and diamond, and have found good agreements with the experimental data without any parameter fitting. We have also studied the temperature dependence of Young’s modulus and bifurcation strain of single-wall carbon nanotubes.

A tied Fermi liquid to Luttinger liquid model for the explanation of nonlinear transport in conducting polymers

2020 ◽  
Author(s):  
Jiawei Wang ◽  
Jiebin Niu ◽  
Bin Shao ◽  
Guanhua YANG ◽  
Congyan Lu ◽  
...  
Keyword(s):  
Conducting Polymers ◽  
Charge Transport ◽  
Fermi Liquid ◽  
Fermi Liquids ◽  
Nonlinear Transport ◽  
Luttinger Liquids ◽  
Resistive Network ◽  
Light Emitting ◽  
Organic Conjugated Polymers ◽  
Liquid Model

Abstract Organic conjugated polymers demonstrate great potential in the transistor, solar cell and light-emitting diodes. The performances of those devices are fundamentally governed by charge transport within the active materials. However, the morphology-property relationships and the underpinning charge transport mechanism in polymers remain unclear. Particularly, whether the nonlinear charge transport in doped conducting polymers, i.e., anomalous non-Ohmic behaviors at low temperature, is appropriately formulated within non-Fermi liquid picture is not clear. In this work, via varying crystalline degrees of samples, we carried out systematic investigations on the charge transport nonlinearity in conducting polymers. Possible charge carriers’ dimensionality was discussed with experiments when varying the molecular chain’s crystalline orders. A heterogeneous-resistive-network (HRN) model was proposed based on the tied link between Fermi liquids (FL) and Luttinger liquids (LL), related to the high-ordered crystalline zones and weak-coupled amorphous regions, respectively. This mesoscopic HRN model is experimentally supported by precise electrical and microstructural characterizations, together with theoretic evaluations. Significantly, such model well describes the nonlinear transport behaviors in conducting polymers universally and provides new insights into the microstructure-correlated charge transport in organic conducting/semiconducting systems.

scholarly journals Complex q-Rung Orthopair Fuzzy Aggregation Operators and Their Applications in Multi-Attribute Group Decision Making

Information ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 5 ◽  
Author(s):  
Liu ◽  
Mahmood ◽  
Ali
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Imaginary Part ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Uncertain Information ◽  
Membership Degree ◽  
The Real ◽  
Complex Valued

In this manuscript, the notions of q-rung orthopair fuzzy sets (q-ROFSs) and complex fuzzy sets (CFSs) are combined is to propose the complex q-rung orthopair fuzzy sets (Cq-ROFSs) and their fundamental laws. The Cq-ROFSs are an important way to express uncertain information, and they are superior to the complex intuitionistic fuzzy sets and the complex Pythagorean fuzzy sets. Their eminent characteristic is that the sum of the qth power of the real part (similarly for imaginary part) of complex-valued membership degree and the qth power of the real part (similarly for imaginary part) of complex-valued non‐membership degree is equal to or less than 1, so the space of uncertain information they can describe is broader. Under these environments, we develop the score function, accuracy function and comparison method for two Cq-ROFNs. Based on Cq-ROFSs, some new aggregation operators are called complex q-rung orthopair fuzzy weighted averaging (Cq-ROFWA) and complex q-rung orthopair fuzzy weighted geometric (Cq-ROFWG) operators are investigated, and their properties are described. Further, based on proposed operators, we present a new method to deal with the multi‐attribute group decision making (MAGDM) problems under the environment of fuzzy set theory. Finally, we use some practical examples to illustrate the validity and superiority of the proposed method by comparing with other existing methods.

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