From 3a4419fe67cb3336f7a4f7a77f64212c5aeb1a73 Mon Sep 17 00:00:00 2001
From: Karthik Chandrashekara <karthik@physi.uni-heidelberg.de>
Date: Tue, 18 Jun 2024 12:49:02 +0200
Subject: [PATCH] Restored individual files for functions of Calculator class.

---
 .../@Calculator/calculateChemicalPotential.m  | 29 +++++++++
 .../@Calculator/calculateEnergyComponents.m   | 35 ++++++++++
 .../calculateNormalizedResiduals.m            | 25 ++++++++
 .../calculateNumericalHankelTransform.m       | 39 +++++++++++
 .../@Calculator/calculateOrderParameter.m     | 58 +++++++++++++++++
 .../@Calculator/calculatePhaseCoherence.m     | 19 ++++++
 .../@Calculator/calculateTotalEnergy.m        | 32 ++++++++++
 .../@Calculator/calculateVDCutoff.m           | 64 +++++++++++++++++++
 8 files changed, 301 insertions(+)
 create mode 100644 Dipolar Gas Simulator/+Simulator/@Calculator/calculateChemicalPotential.m
 create mode 100644 Dipolar Gas Simulator/+Simulator/@Calculator/calculateEnergyComponents.m
 create mode 100644 Dipolar Gas Simulator/+Simulator/@Calculator/calculateNormalizedResiduals.m
 create mode 100644 Dipolar Gas Simulator/+Simulator/@Calculator/calculateNumericalHankelTransform.m
 create mode 100644 Dipolar Gas Simulator/+Simulator/@Calculator/calculateOrderParameter.m
 create mode 100644 Dipolar Gas Simulator/+Simulator/@Calculator/calculatePhaseCoherence.m
 create mode 100644 Dipolar Gas Simulator/+Simulator/@Calculator/calculateTotalEnergy.m
 create mode 100644 Dipolar Gas Simulator/+Simulator/@Calculator/calculateVDCutoff.m

diff --git a/Dipolar Gas Simulator/+Simulator/@Calculator/calculateChemicalPotential.m b/Dipolar Gas Simulator/+Simulator/@Calculator/calculateChemicalPotential.m
new file mode 100644
index 0000000..96a6a84
--- /dev/null
+++ b/Dipolar Gas Simulator/+Simulator/@Calculator/calculateChemicalPotential.m	
@@ -0,0 +1,29 @@
+function muchem = calculateChemicalPotential(~,psi,Params,Transf,VDk,V)
+
+    %Parameters
+    normfac = Params.Lx*Params.Ly*Params.Lz/numel(psi);
+    KEop= 0.5*(Transf.KX.^2+Transf.KY.^2+Transf.KZ.^2);
+    
+    % DDIs
+    frho=fftn(abs(psi).^2);
+    Phi=real(ifftn(frho.*VDk));
+    
+    Eddi = (Params.gdd*Phi.*abs(psi).^2);
+    
+    %Kinetic energy
+    Ekin = KEop.*abs(fftn(psi)*normfac).^2;
+    Ekin = trapz(Ekin(:))*Transf.dkx*Transf.dky*Transf.dkz/(2*pi)^3;
+    
+    %Potential energy
+    Epot = V.*abs(psi).^2;
+    
+    %Contact interactions
+    Eint = Params.gs*abs(psi).^4;
+    
+    %Quantum fluctuations
+    Eqf = Params.gammaQF*abs(psi).^5;
+    
+    %Total energy
+    muchem = Ekin + trapz(Epot(:) + Eint(:) + Eddi(:) + Eqf(:))*Transf.dx*Transf.dy*Transf.dz; %
+    muchem = muchem / Params.N;
+end
\ No newline at end of file
diff --git a/Dipolar Gas Simulator/+Simulator/@Calculator/calculateEnergyComponents.m b/Dipolar Gas Simulator/+Simulator/@Calculator/calculateEnergyComponents.m
new file mode 100644
index 0000000..92dd32c
--- /dev/null
+++ b/Dipolar Gas Simulator/+Simulator/@Calculator/calculateEnergyComponents.m	
@@ -0,0 +1,35 @@
+function E = calculateEnergyComponents(~,psi,Params,Transf,VDk,V)
+
+    %Parameters
+    
+    KEop= 0.5*(Transf.KX.^2+Transf.KY.^2+Transf.KZ.^2);
+    normfac = Params.Lx*Params.Ly*Params.Lz/numel(psi);
+    
+    % DDIs
+    frho = fftn(abs(psi).^2);
+    Phi = real(ifftn(frho.*VDk));
+    
+    Eddi = 0.5*Params.gdd*Phi.*abs(psi).^2;
+    E.Eddi = trapz(Eddi(:))*Transf.dx*Transf.dy*Transf.dz;
+    
+    % EddiTot = trapz(Eddi(:))*Transf.dx*Transf.dy*Transf.dz;
+    
+    %Kinetic energy
+    % psik = ifftshift(fftn(fftshift(psi)))*normfac;
+    
+    Ekin = KEop.*abs(fftn(psi)*normfac).^2;
+    E.Ekin = trapz(Ekin(:))*Transf.dkx*Transf.dky*Transf.dkz/(2*pi)^3;
+    
+    % Potential energy
+    Epot = V.*abs(psi).^2;
+    E.Epot = trapz(Epot(:))*Transf.dx*Transf.dy*Transf.dz;
+    
+    %Contact interactions
+    Eint = 0.5*Params.gs*abs(psi).^4;
+    E.Eint = trapz(Eint(:))*Transf.dx*Transf.dy*Transf.dz;
+    
+    %Quantum fluctuations
+    Eqf = 0.4*Params.gammaQF*abs(psi).^5;
+    E.Eqf = trapz(Eqf(:))*Transf.dx*Transf.dy*Transf.dz;
+    
+end
diff --git a/Dipolar Gas Simulator/+Simulator/@Calculator/calculateNormalizedResiduals.m b/Dipolar Gas Simulator/+Simulator/@Calculator/calculateNormalizedResiduals.m
new file mode 100644
index 0000000..134e426
--- /dev/null
+++ b/Dipolar Gas Simulator/+Simulator/@Calculator/calculateNormalizedResiduals.m	
@@ -0,0 +1,25 @@
+function res = calculateNormalizedResiduals(~,psi,Params,Transf,VDk,V,muchem)
+
+    KEop= 0.5*(Transf.KX.^2+Transf.KY.^2+Transf.KZ.^2);
+    
+    % DDIs
+    frho=fftn(abs(psi).^2);
+    Phi=real(ifftn(frho.*VDk));
+    
+    Eddi = Params.gdd*Phi.*psi;
+    
+    %Kinetic energy
+    Ekin = ifftn(KEop.*fftn(psi));
+    
+    %Potential energy
+    Epot = V.*psi;
+    
+    %Contact interactions
+    Eint = Params.gs*abs(psi).^2.*psi;
+    
+    %Quantum fluctuations
+    Eqf = Params.gammaQF*abs(psi).^3.*psi;
+    
+    %Total energy
+    res =  trapz(abs(Ekin(:) + Epot(:) + Eint(:) + Eddi(:) + Eqf(:) - muchem*psi(:))*Transf.dx*Transf.dy*Transf.dz)/trapz(abs(muchem*psi(:))*Transf.dx*Transf.dy*Transf.dz);
+end
\ No newline at end of file
diff --git a/Dipolar Gas Simulator/+Simulator/@Calculator/calculateNumericalHankelTransform.m b/Dipolar Gas Simulator/+Simulator/@Calculator/calculateNumericalHankelTransform.m
new file mode 100644
index 0000000..b3d96c6
--- /dev/null
+++ b/Dipolar Gas Simulator/+Simulator/@Calculator/calculateNumericalHankelTransform.m	
@@ -0,0 +1,39 @@
+function VDkSemi = calculateNumericalHankelTransform(~,kr,kz,Rmax,Zmax,Nr)
+
+    % accuracy inputs for numerical integration
+    if(nargin==5)
+        Nr = 5e4;
+    end
+    
+    Nz = 64;
+    farRmultiple = 2000;
+    
+    % midpoint grids for the integration over 0<z<Zmax, Rmax<r<farRmultiple*Rmax (i.e. starts at Rmax)
+    dr=(farRmultiple-1)*Rmax/Nr;
+    r = ((1:Nr)'-0.5)*dr+Rmax;
+    dz=Zmax/Nz;
+    z = ((1:Nz)-0.5)*dz;
+    [R, Z] = ndgrid(r,z);
+    Rsq = R.^2 + Z.^2;
+    
+    % real space interaction to be transformed
+    igrandbase = (1 - 3*Z.^2./Rsq)./Rsq.^(3/2);
+    
+    % do the Hankel/Fourier-Bessel transform numerically
+    % prestore to ensure each besselj is only calculated once
+    % cell is faster than (:,:,krn) slicing
+    Nkr = numel(kr);
+    besselr = cell(Nkr,1);
+    for krn = 1:Nkr
+        besselr{krn} = repmat(r.*besselj(0,kr(krn)*r),1,Nz);
+    end
+    
+    VDkSemi = zeros([Nkr,numel(kz)]);
+    for kzn = 1:numel(kz)
+        igrandbasez = repmat(cos(kz(kzn)*z),Nr,1) .* igrandbase;
+        for krn = 1:Nkr
+            igrand = igrandbasez.*besselr{krn};
+            VDkSemi(krn,kzn) = VDkSemi(krn,kzn) - sum(igrand(:))*dz*dr;
+        end
+    end
+end
\ No newline at end of file
diff --git a/Dipolar Gas Simulator/+Simulator/@Calculator/calculateOrderParameter.m b/Dipolar Gas Simulator/+Simulator/@Calculator/calculateOrderParameter.m
new file mode 100644
index 0000000..15a28f4
--- /dev/null
+++ b/Dipolar Gas Simulator/+Simulator/@Calculator/calculateOrderParameter.m	
@@ -0,0 +1,58 @@
+function [m_Order] = calculateOrderParameter(~,psi,Transf,Params,VDk,V,T,muchem)
+
+    NumRealiz = 100;
+
+    Mx = numel(Transf.x);
+    My = numel(Transf.y);
+    Mz = numel(Transf.z);
+
+    r = normrnd(0,1,size(psi));
+    theta = rand(size(psi));
+    noise = r.*exp(2*pi*1i*theta);
+    
+    KEop= 0.5*(Transf.KX.^2+Transf.KY.^2+Transf.KZ.^2);
+    Gamma = 1-1i*Params.gamma_S;
+    dt = Params.dt;
+
+    avgpsi = 0;
+    avgpsi2 = 0;
+
+    for jj = 1:NumRealiz
+        %generate initial state
+        xi = sqrt(2*Params.gamma_S*Params.kbol*T*10^(-9)*dt/(Params.hbar*Params.w0*Transf.dx*Transf.dy*Transf.dz));
+        swapx = randi(length(Transf.x),1,length(Transf.x));
+        swapy = randi(length(Transf.y),1,length(Transf.y));
+        swapz = randi(length(Transf.z),1,length(Transf.z));
+        psi_j = psi + xi * noise(swapx,swapy,swapz);
+        
+        % --- % propagate forward in time 1 time step:
+        %kin
+        psi_j = fftn(psi_j);
+        psi_j = psi_j.*exp(-0.5*1i*Gamma*dt*KEop);
+        psi_j = ifftn(psi_j);
+    
+        %DDI
+        frho = fftn(abs(psi_j).^2);
+        Phi = real(ifftn(frho.*VDk));
+    
+        %Real-space
+        psi_j = psi_j.*exp(-1i*Gamma*dt*(V + Params.gs*abs(psi_j).^2 + Params.gammaQF*abs(psi_j).^3 + Params.gdd*Phi - muchem));
+
+        %kin
+        psi_j = fftn(psi_j);
+        psi_j = psi_j.*exp(-0.5*1i*Gamma*dt*KEop);
+        psi_j = ifftn(psi_j);
+    
+        %Projection
+        kcut = sqrt(2*Params.e_cut);
+        K = (Transf.KX.^2+Transf.KY.^2+Transf.KZ.^2)<kcut.^2;
+        psi_j = ifftn(K.*fftn(psi_j));
+    
+        % --- %
+        avgpsi = avgpsi + abs(sum(psi_j(:)))/NumRealiz;
+        avgpsi2 = avgpsi2 + sum(abs(psi_j(:)).^2)/NumRealiz;
+
+    end
+
+    m_Order = 1/sqrt(Mx*My*Mz)*avgpsi/sqrt(avgpsi2);
+end
\ No newline at end of file
diff --git a/Dipolar Gas Simulator/+Simulator/@Calculator/calculatePhaseCoherence.m b/Dipolar Gas Simulator/+Simulator/@Calculator/calculatePhaseCoherence.m
new file mode 100644
index 0000000..449cf36
--- /dev/null
+++ b/Dipolar Gas Simulator/+Simulator/@Calculator/calculatePhaseCoherence.m	
@@ -0,0 +1,19 @@
+function [PhaseC] = calculatePhaseCoherence(~,psi,Transf,Params)
+
+    norm = sum(sum(sum(abs(psi).^2,1),2),3)*Transf.dx*Transf.dy*Transf.dz;
+    psi = psi/sqrt(norm);
+    
+    NumGlobalShifts = 800;
+    betas = []; phishift = [];
+    for jj = 1:NumGlobalShifts
+        phishift(jj) = -pi + 2*pi*(jj-1)/NumGlobalShifts;
+        betas(jj) = sum(sum(sum(abs(angle(psi*exp(-1i*phishift(jj)))).*abs(psi).^2)));
+    end
+    [minbeta,minidx] = min(betas);
+    
+    psi = psi*exp(-1i*phishift(minidx));
+    phi = angle(psi);
+    
+    avgphi = sum(sum(sum(phi.*abs(psi).^2,1),2),3)*Transf.dx*Transf.dy*Transf.dz;
+    PhaseC = sum(sum(sum(abs(angle(psi)-avgphi).*abs(psi).^2)))*Transf.dx*Transf.dy*Transf.dz;
+end
\ No newline at end of file
diff --git a/Dipolar Gas Simulator/+Simulator/@Calculator/calculateTotalEnergy.m b/Dipolar Gas Simulator/+Simulator/@Calculator/calculateTotalEnergy.m
new file mode 100644
index 0000000..f53f7a2
--- /dev/null
+++ b/Dipolar Gas Simulator/+Simulator/@Calculator/calculateTotalEnergy.m	
@@ -0,0 +1,32 @@
+function E = calculateTotalEnergy(~,psi,Params,Transf,VDk,V)
+
+    %Parameters
+    
+    KEop= 0.5*(Transf.KX.^2+Transf.KY.^2+Transf.KZ.^2);
+    normfac = Params.Lx*Params.Ly*Params.Lz/numel(psi);
+    
+    % DDIs
+    frho = fftn(abs(psi).^2);
+    Phi = real(ifftn(frho.*VDk));
+    
+    Eddi = 0.5*Params.gdd*Phi.*abs(psi).^2;
+    
+    % EddiTot = trapz(Eddi(:))*Transf.dx*Transf.dy*Transf.dz;
+    
+    %Kinetic energy
+    % psik = ifftshift(fftn(fftshift(psi)))*normfac;
+    
+    Ekin = KEop.*abs(fftn(psi)*normfac).^2;
+    Ekin = trapz(Ekin(:))*Transf.dkx*Transf.dky*Transf.dkz/(2*pi)^3;
+    
+    % Potential energy
+    Epot = V.*abs(psi).^2;
+    
+    %Contact interactions
+    Eint = 0.5*Params.gs*abs(psi).^4;
+    
+    %Quantum fluctuations
+    Eqf = 0.4*Params.gammaQF*abs(psi).^5;
+    
+    E = Ekin + trapz(Epot(:) + Eint(:) + Eddi(:) + Eqf(:))*Transf.dx*Transf.dy*Transf.dz;
+end
\ No newline at end of file
diff --git a/Dipolar Gas Simulator/+Simulator/@Calculator/calculateVDCutoff.m b/Dipolar Gas Simulator/+Simulator/@Calculator/calculateVDCutoff.m
new file mode 100644
index 0000000..3c49b4e
--- /dev/null
+++ b/Dipolar Gas Simulator/+Simulator/@Calculator/calculateVDCutoff.m	
@@ -0,0 +1,64 @@
+function VDk = calculateVDCutoff(this,Params,Transf,TransfRad)
+% makes the dipolar interaction matrix, size numel(Params.kr) * numel(Params.kz)
+% Rmax and Zmax are the interaction cutoffs
+% VDk needs to be multiplied by Cdd
+% approach is that of Lu, PRA 82, 023622 (2010)
+
+% == Calulating the DDI potential in Fourier space with appropriate cutoff == %
+% Cylindrical (semianalytic)
+% Cylindrical infinite Z, polarized along x (analytic)
+% Spherical
+
+    switch this.CutoffType
+	    case 'Cylindrical' %Cylindrical (semianalytic)
+            Zcutoff = Params.Lz/2;            
+            alph    = acos((Transf.KX*sin(Params.theta)*cos(Params.phi)+Transf.KY*sin(Params.theta)*sin(Params.phi)+Transf.KZ*cos(Params.theta))./sqrt(Transf.KX.^2+Transf.KY.^2+Transf.KZ.^2));
+            alph(1) = pi/2;
+            
+            % Analytic part of cutoff for slice 0<z<Zmax, 0<r<Inf Ronen, PRL 98, 030406 (2007)
+            cossq = cos(alph).^2;
+            VDk   = cossq-1/3;
+            sinsq = 1 - cossq;
+            VDk   = VDk + exp(-Zcutoff*sqrt(Transf.KX.^2+Transf.KY.^2)).*( sinsq .* cos(Zcutoff * Transf.KZ) - sqrt(sinsq.*cossq).*sin(Zcutoff * Transf.KZ) );
+            
+            % Nonanalytic part
+            % For a cylindrical cutoff, we need to construct a kr grid based on the 3D parameters using Bessel quadrature
+            VDkNon      = this.calculateNumericalHankelTransform(TransfRad.kr, TransfRad.kz, TransfRad.Rmax, Zcutoff);
+            
+            % Interpolating the nonanalytic part onto 3D grid
+            fullkr = [-flip(TransfRad.kr)',TransfRad.kr'];
+            [KR,KZ] = ndgrid(fullkr,TransfRad.kz);
+            [KX3D,KY3D,KZ3D] = ndgrid(ifftshift(Transf.kx),ifftshift(Transf.ky),ifftshift(Transf.kz));
+            KR3D = sqrt(KX3D.^2 + KY3D.^2);
+            fullVDK = [flip(VDkNon',2),VDkNon']';
+            VDkNon = interpn(KR,KZ,fullVDK,KR3D,KZ3D,'spline',0); %Last argument is -1/3 for full VDk. 0 for nonanalytic piece?
+            VDkNon = fftshift(VDkNon);
+            
+            VDk = VDk + VDkNon;
+    
+        case 'CylindricalInfiniteZ' %Cylindrical infinite Z, polarized along x -- PRA 107, 033301 (2023)
+	        alph = acos((Transf.KX*sin(Params.theta)*cos(Params.phi)+Transf.KY*sin(Params.theta)*sin(Params.phi)+Transf.KZ*cos(Params.theta))./sqrt(Transf.KX.^2+Transf.KY.^2+Transf.KZ.^2));
+	        alph(1) = pi/2;
+	        rhoc = max([abs(Transf.x),abs(Transf.y)]);
+	        KR = sqrt(Transf.KX.^2+Transf.KY.^2);
+	        func = @(n,u,v) v.^2./(u.^2+v.^2).*(v.*besselj(n,u).*besselk(n+1,v) - u.*besselj(n+1,u).*besselk(n,v));    
+	        VDk = -0.5*func(0,KR*rhoc,abs(Transf.KZ)*rhoc) + (Transf.KX.^2./KR.^2 - 0.5).*func(2,KR*rhoc,abs(Transf.KZ)*rhoc);
+	        VDk = (1/3)*(3*(cos(alph).^2)-1) - VDk;
+    
+            VDk(KR==0) = -1/3 + 1/2*abs(Transf.KZ(KR==0))*rhoc.*besselk(1,abs(Transf.KZ(KR==0))*rhoc);
+	        VDk(Transf.KZ==0) = 1/6 + (Transf.KX(Transf.KZ==0).^2-Transf.KY(Transf.KZ==0).^2)./(KR(Transf.KZ==0).^2).*(1/2 - besselj(1,KR(Transf.KZ==0)*rhoc)./(KR(Transf.KZ==0)*rhoc));
+	        VDk(1,1,1) = 1/6;            
+        
+        case 'Spherical' %Spherical
+            Rcut = min(Params.Lx/2,Params.Ly/2,Params.Lz/2);
+            alph = acos((Transf.KX*sin(Params.theta)*cos(Params.phi)+Transf.KY*sin(Params.theta)*sin(Params.phi)+Transf.KZ*cos(Params.theta))./sqrt(Transf.KX.^2+Transf.KY.^2+Transf.KZ.^2));
+	        alph(1) = pi/2;
+    
+            K = sqrt(Transf.KX.^2+Transf.KY.^2+Transf.KZ.^2);
+            VDk = (cos(alph).^2-1/3).*(1 + 3*cos(Rcut*K)./(Rcut^2.*K.^2) - 3*sin(Rcut*K)./(Rcut^3.*K.^3));
+        
+        otherwise
+	        disp('Choose a valid DDI cutoff type!')
+            return
+    end
+end
\ No newline at end of file