1 function [varargout] = quKineticSpec(Psir,
m,
dx,
q,
avg,
iii)
2 % QUKINETICSPEC Evalutes the quantum kinetic energy spectrum [PRA 89, 053631 (2014)]
3 % Built
on work
by Dr
A. White, and extended
by (Dr?) Lee James O
'Riordan. 4 % Ek = quKineticSpec(Psir,m,dx,q,avg,iii), 5 % Psir N-dim wavefunction in r space with grid spacing dx and mass m 6 % q = include phase for quantum spectrum, 1=yes,0=no; 7 % avg = perform angled average. Likely always want this to be yes, 1 8 % iii output index for naming the figure files. Useful when looped with 12 %##############################################################################% 14 rDim = size(Psir); xDim = rDim(1); yDim = rDim(2); 15 %##############################################################################% 16 % Build camp in K-space 17 dkx = 2*pi/(dx*xDim); dky = 2*pi/(dx*yDim); 19 kx = [linspace(0,(xDim/2-1)*dkx,xDim/2) linspace(-xDim/2*dkx,-dkx,xDim/2)]';
20 ky = [linspace(0,(yDim/2-1)*dky,yDim/2) linspace(-yDim/2*dky,-dky,yDim/2)]
'; 22 [kxm,kym] = meshgrid(kx,ky); 23 %##############################################################################% 25 km_mag = sqrt(kxm.^2 + kym.^2); 26 k_mag = sqrt(kx.^2 + ky.^2); 27 kMax = max(max(k_mag)); 29 %##############################################################################% 32 %##############################################################################% 33 %##############################################################################% 34 % Velocity field calculation 35 %##############################################################################% 39 np1=unwrap(phase,[],1); 40 np2=unwrap(phase,[],2); 42 [velnp1x,velnp1y] = gradient(np1,dx,dx); 43 [velnp2x,velnp2y] = gradient(np2,dx,dx); 45 v_y = (hbar/m)*(velnp1y); 46 v_x = (hbar/m)*(velnp2x); 49 v_x(find(v_x==0)) = 1e-100; 50 v_y(find(v_y==0)) = 1e-100; 52 u_x=exp(q*1i*angle(Psir)).*abs(Psir).*(v_x); 53 u_y=exp(q*1i*angle(Psir)).*abs(Psir).*(v_y); 55 %figure(4);pcolor(abs(u_x.^2 + u_y.^2));shading interp;title('|
U|
');colorbar;axis square 61 uc_kx=(kxm.^2.*u_kx + kxm.*kym.*u_ky)./(km_mag.^2+1e-100); 62 uc_ky=(kxm.*kym.*u_kx + kym.^2.*u_ky)./(km_mag.^2+1e-100); 67 uc_x = ifft2(uc_kx); uc_y = ifft2(uc_ky); 68 ui_x = ifft2(ui_kx); ui_y = ifft2(ui_ky); 70 Ec = 0.5*abs(uc_x.^2 + uc_y.^2); 71 Ei = 0.5*abs(ui_x.^2 + ui_y.^2); 74 xx = linspace(-(dimSize(1)/2)*dx,(dimSize(1)/2)*dx,dimSize(1)); 75 figure;pcolor(xx,xx,log10(Ec));shading interp;colorbar;axis square; title(['Comp
',int2str(iii)]) 77 set(gca,'DefaultTextInterpreter
','Latex
') 82 print('-dpng','-r300',['./Comp_CBAR_',int2str(
iii),'.png']);
84 print(
'-dpng',
'-r300',[
'./Comp_',int2str(
iii),
'.png']);
87 set(gca,
'TickLabelInterpreter',
'latex');
88 set(gca,
'DefaultTextInterpreter',
'Latex')
89 set(gca,
'FontName',
'Latin Modern Roman',
'FontSize',24);
90 xlabel(
' $x$ [m] ',
'Interpreter',
'latex')
93 print('-dpng','-r300',['./Incomp_CBAR_',int2str(
iii),'.png']);
95 print('-dpng','-r300',['./Incomp_',int2str(
iii),'.png']);
114 %
title('EK');%
axis([1e4 1.2e7 1e-18 1e-6]);
115 legend({
'$E^c(k)$',
'$E^i(k)$'},
'FontSize',20,
'FontWeight',
'bold',
'Interpreter',
'latex');
116 set(gca,
'TickLabelInterpreter',
'latex');
117 set(gca,
'DefaultTextInterpreter',
'Latex')
118 set(gca,
'FontName',
'Latin Modern Roman',
'FontSize',24);
119 xlabel(
' $k$ [m$^{-1}$] ',
'Interpreter',
'latex')
121 print('-dpng','-r300',['./EK_',int2str(
iii),'.png']);
end if(length(DT.vertexAttachments{ii})==5) if plotit plot(x(ii)
loglog(k_mag(1:(xDim/2-1)), ekc, k_mag(1:(xDim/2-1)), eki, 'LineWidth', 2)
Latin Modern xlabel(' $x$ [m] ', 'Interpreter', 'latex') ylabel(' $y$ [m] '
pcolor(abs(u_x.^ 2+u_y.^ 2))
ylabel(' $y$(m)', 'Interpreter', 'latex') % Defect marker size MarkerSize
% % iii output index for naming the figure files Useful when looped with % kinSpec script % Setup % hbar
and extended by(Dr?) Lee James O 'Riordan. % Ek
% Used for determining interaction strength of system % % Constants required for simulation m
end if sqrt(sum([x(ii), y(ii)].^ 2))< radius %% ignore edges if(length(DT.vertexAttachments
% vline(2 *pi/hl, 'r', 'Healing')
% axis([1e4 1e7 5e-18 1e-10])
Latin Modern latex print('-dpng','-r300', ['./Comp_CBAR_', int2str(iii),'.png'])
% % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % % phase singularity for vortex creation annihilation for iii
legend({' $E^ c(k)$',' $E^ i(k)$'}, 'FontSize', 20, 'FontWeight', 'bold', 'Interpreter', 'latex')