%Fig1_6.m
%Essential Electron Transport for Device Physics
%diatomic 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=0.5;								%mass of particle 1
m2=1.0;								%mass of particle 2
ymax=(2*kappa*(m1+m2)/(m1*m2))^0.5;	%maximum frequency

x=[-pi:.01:pi];						%wave vector [start:increment:stop]   
a=1;
b=2*kappa*(m1+m2)/(m1*m2);
c=2*kappa*kappa*(1-cos(x(:)))/(m1*m2);

y21=(abs((-b+((b.*b-4.*a.*c).^.5))/(2*a))).^0.5; 	%the acoustic branch
y22=(abs((-b-((b.*b-4.*a.*c).^.5))/(2*a))).^0.5;	%the optical branch

figure(1);
hold on;
plot(x,y21,'b');								%the acoustic branch
plot(x,y22,'r');								%the optical branch
axis([-pi,pi,0,1.1*ymax]);
temp2=['\rmFig1.6, \kappa_0 = ',num2str(kappa),...
', m_1 = ',num2str(m1),', m_2 = ',num2str(m2)];
title(temp2);
grid on
xlabel(['Wave vector, q/L']);
ylabel(['Frequency,  \omega (q)']);
hold off;