%Fig1_4.m %Essential Electron Transport for Device Physics %monatomic linear chain dispersion; clear; clf; FS = 12; %label fontsize 18 FSN = 12; %number fontsize 16 LW = 1; %linewidth % Change default axes fonts. set(0,'DefaultAxesFontName', 'Times'); set(0,'DefaultAxesFontSize', FSN); % Change default text fonts. set(0,'DefaultTextFontname', 'Times'); set(0,'DefaultTextFontSize', FSN); kappa=1; %spring constant m1=1; %mass of particle ymax=(4*kappa/m1)^0.5; %maximum frequency x=[-pi:.01:pi]; %wave vector [start:increment:stop] y21=sqrt(4*kappa/m1)*abs(sin(x(:)/2)); %the acoustic branch figure(1); plot(x,y21,'b'); %the acoustic branch axis([-pi,pi,0,1.1*ymax]); temp2=['\rmFig1.4a, \kappa = ',num2str(kappa),', m = ',num2str(m1)]; title(temp2); xlabel(['Wave vector, q/L']); ylabel(['Frequency, \omega(q)']); x=[0.01:.01:2*pi]; %wave vector [start:increment:stop] vg=sqrt(4*kappa/m1)*(cos(x(:)/2))/2; %group velocity vp=sqrt(4*kappa/m1)*(sin(x(:)/2))./x(:); %phase velocity figure(2); plot(x,vg,'b'); %group velocity hold on plot(x,vp,'r'); %phase velocity %axis([0,2*pi,1.1*min(vg),1.1*max(vg)]); axis([0,pi,0,1.1*max(vg)]); temp2=['\rmFig1.4b, \kappa = ',num2str(kappa),', m = ',num2str(m1)]; title(temp2); xlabel(['Wave vector, q/L']); ylabel(['\upsilon_g (blue), \upsilon_p (red), ( \kappa/m )^{1/2}L']);