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@ -50,6 +50,12 @@ function visualizeSpace(Transf)
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'FontWeight', 'normal', ...
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'FontAngle', 'normal')
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x = Transf.kx;
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y = Transf.ky;
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z = Transf.kz;
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[X,Y] = meshgrid(x,y);
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subplot(1,2,2)
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zlin = ones(size(X, 1)) * z(1); % Generate z data
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mesh(x, y, zlin, 'EdgeColor','b') % Plot the surface
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@ -1,5 +1,4 @@
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function visualizeTrapPotential(V,Params,Transf)
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set(0,'defaulttextInterpreter','latex')
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set(groot, 'defaultAxesTickLabelInterpreter','latex'); set(groot, 'defaultLegendInterpreter','latex');
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@ -12,11 +11,11 @@ function visualizeTrapPotential(V,Params,Transf)
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%Plotting
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height = 10;
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width = 35;
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width = 45;
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figure(1)
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clf
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set(gcf, 'Units', 'centimeters')
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set(gcf, 'Position', [2 4 width height])
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set(gcf, 'Position', [2 8 width height])
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set(gcf, 'PaperPositionMode', 'auto')
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subplot(1,3,1)
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@ -25,6 +24,10 @@ function visualizeTrapPotential(V,Params,Transf)
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nyz = squeeze(trapz(n*dx,1));
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nxy = squeeze(trapz(n*dz,3));
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nxz = nxz./max(nxz(:));
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nyz = nyz./max(nyz(:));
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nxy = nxy./max(nxy(:));
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plotxz = pcolor(x,z,nxz');
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set(plotxz, 'EdgeColor', 'none');
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xlabel(gca, {'$x$ ($\mu$m)'}, ...
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@ -12,11 +12,11 @@ function visualizeWavefunction(psi,Params,Transf)
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%Plotting
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height = 10;
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width = 35;
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width = 45;
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figure(1)
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clf
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set(gcf, 'Units', 'centimeters')
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set(gcf, 'Position', [2 4 width height])
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set(gcf, 'Position', [2 8 width height])
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set(gcf, 'PaperPositionMode', 'auto')
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subplot(1,3,1)
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@ -7,13 +7,14 @@
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OptionsStruct = struct;
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OptionsStruct.NumberOfAtoms = 1E6;
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OptionsStruct.DipolarAngle = pi/2;
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OptionsStruct.DipolarPolarAngle = pi/2;
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OptionsStruct.DipolarAzimuthAngle = 0;
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OptionsStruct.ScatteringLength = 86;
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OptionsStruct.TrapFrequencies = [125, 125, 250];
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OptionsStruct.NumberOfPoints = [64, 64, 48];
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OptionsStruct.NumberOfGridPoints = [64, 64, 48];
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OptionsStruct.Dimensions = [40, 40, 20];
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OptionsStruct.CutoffType = 'Cylindrical';
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OptionsStruct.PotentialType = 'Harmonic';
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OptionsStruct.TrapPotentialType = 'Harmonic';
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OptionsStruct.SimulationMode = 'ImaginaryTimeEvolution'; % 'ImaginaryTimeEvolution' | 'RealTimeEvolution'
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OptionsStruct.TimeStep = 50e-06; % in s
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@ -32,9 +33,9 @@ pot = Simulator.Potentials(options{:});
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%-% Run Simulation %-%
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[Params, Transf, psi, V, VDk] = sim.runSimulation(calc);
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%% - Plot results
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% Plotter.visualizeSpace(Transf)
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%% - Plot numerical grid
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Plotter.visualizeSpace(Transf)
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%% - Plot trap potential
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Plotter.visualizeTrapPotential(V,Params,Transf)
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% Plotter.visualizeWavefunction(psi,Params,Transf)
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%% - Plot initial wavefunction
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Plotter.visualizeWavefunction(psi,Params,Transf)
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@ -2,15 +2,23 @@ classdef Calculator < handle & matlab.mixin.Copyable
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properties (Access = private)
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CalculatorDefaults = struct('OrderParameter', 1, ...
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CalculatorDefaults = struct('ChemicalPotential', 1, ...
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'EnergyComponents', 1, ...
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'NormalizedResiduals', 1, ...
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'OrderParameter', 1, ...
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'PhaseCoherence', 1, ...
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'TotalEnergy', 1, ...
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'CutoffType', 'Cylindrical');
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end
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properties (Access = public)
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ChemicalPotential;
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EnergyComponents;
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NormalizedResiduals;
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OrderParameter;
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PhaseCoherence;
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TotalEnergy;
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CutoffType;
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end
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@ -19,14 +27,22 @@ classdef Calculator < handle & matlab.mixin.Copyable
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methods
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function this = Calculator(varargin)
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this.ChemicalPotential = this.CalculatorDefaults.ChemicalPotential;
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this.EnergyComponents = this.CalculatorDefaults.EnergyComponents;
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this.NormalizedResiduals = this.CalculatorDefaults.NormalizedResiduals;
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this.OrderParameter = this.CalculatorDefaults.OrderParameter;
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this.PhaseCoherence = this.CalculatorDefaults.PhaseCoherence;
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this.TotalEnergy = this.CalculatorDefaults.TotalEnergy;
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this.CutoffType = this.CalculatorDefaults.CutoffType;
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end
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function restoreDefaults(this)
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this.OrderParameter = this.PotentialDefaults.OrderParameter;
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this.ChemicalPotential = this.CalculatorDefaults.ChemicalPotential;
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this.EnergyComponents = this.CalculatorDefaults.EnergyComponents;
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this.NormalizedResiduals = this.CalculatorDefaults.NormalizedResiduals;
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this.OrderParameter = this.CalculatorDefaults.OrderParameter;
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this.PhaseCoherence = this.CalculatorDefaults.PhaseCoherence;
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this.TotalEnergy = this.CalculatorDefaults.TotalEnergy;
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this.CutoffType = this.CalculatorDefaults.CutoffType;
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end
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@ -4,6 +4,13 @@ function VDk = calculateVDCutoff(this,Params,Transf,TransfRad)
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% VDk needs to be multiplied by Cdd
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% approach is that of Lu, PRA 82, 023622 (2010)
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% == Calulating the DDI potential in Fourier space with appropriate cutoff == %
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% Cylindrical (semianalytic)
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% Cylindrical infinite Z, polarized along x (analytic)
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% Spherical
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switch this.CutoffType
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case 'Cylindrical' %Cylindrical (semianalytic)
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Zcutoff = Params.Lz/2;
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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));
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alph(1) = pi/2;
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@ -28,3 +35,30 @@ VDkNon = interpn(KR,KZ,fullVDK,KR3D,KZ3D,'spline',0); %Last argument is -1/3 for
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VDkNon = fftshift(VDkNon);
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VDk = VDk + VDkNon;
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case 'CylindricalInfiniteZ' %Cylindrical infinite Z, polarized along x -- PRA 107, 033301 (2023)
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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));
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alph(1) = pi/2;
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rhoc = max([abs(Transf.x),abs(Transf.y)]);
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KR = sqrt(Transf.KX.^2+Transf.KY.^2);
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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));
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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);
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VDk = (1/3)*(3*(cos(alph).^2)-1) - VDk;
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VDk(KR==0) = -1/3 + 1/2*abs(Transf.KZ(KR==0))*rhoc.*besselk(1,abs(Transf.KZ(KR==0))*rhoc);
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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));
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VDk(1,1,1) = 1/6;
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case 'Spherical' %Spherical
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Rcut = min(Params.Lx/2,Params.Ly/2,Params.Lz/2);
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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));
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alph(1) = pi/2;
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K = sqrt(Transf.KX.^2+Transf.KY.^2+Transf.KZ.^2);
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VDk = (cos(alph).^2-1/3).*(1 + 3*cos(Rcut*K)./(Rcut^2.*K.^2) - 3*sin(Rcut*K)./(Rcut^3.*K.^3));
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otherwise
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disp('Choose a valid DDI cutoff type!')
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return
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end
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end
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@ -2,13 +2,12 @@ classdef DipolarGas < handle & matlab.mixin.Copyable
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properties (Access = public)
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NumberOfAtoms;
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DipolarAngle;
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DipolarPolarAngle;
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DipolarAzimuthAngle
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ScatteringLength;
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TrapFrequencies;
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NumberOfPoints;
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NumberOfGridPoints;
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Dimensions;
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CutoffType;
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PotentialType;
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SimulationMode;
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TimeStep;
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@ -31,13 +30,15 @@ classdef DipolarGas < handle & matlab.mixin.Copyable
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p.KeepUnmatched = true;
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addParameter(p, 'NumberOfAtoms', 1E6,...
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@(x) assert(isnumeric(x) && isscalar(x) && (x > 0)));
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addParameter(p, 'DipolarAngle', pi/2,...
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addParameter(p, 'DipolarPolarAngle', pi/2,...
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@(x) assert(isnumeric(x) && isscalar(x) && (x > -2*pi) && (x < 2*pi)));
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addParameter(p, 'DipolarAzimuthAngle', pi/2,...
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@(x) assert(isnumeric(x) && isscalar(x) && (x > -2*pi) && (x < 2*pi)));
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addParameter(p, 'ScatteringLength', 120,...
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@(x) assert(isnumeric(x) && isscalar(x) && (x > -150) && (x < 150)));
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addParameter(p, 'TrapFrequencies', 100 * ones(1,3),...
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@(x) assert(isnumeric(x) && isvector(x) && all(x > 0)));
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addParameter(p, 'NumberOfPoints', 128 * ones(1,3),...
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addParameter(p, 'NumberOfGridPoints', 128 * ones(1,3),...
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@(x) assert(isnumeric(x) && isvector(x) && all(x > 0)));
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addParameter(p, 'Dimensions', 10 * ones(1,3),...
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@(x) assert(isnumeric(x) && isvector(x) && all(x > 0)));
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@ -57,10 +58,11 @@ classdef DipolarGas < handle & matlab.mixin.Copyable
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p.parse(varargin{:});
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this.NumberOfAtoms = p.Results.NumberOfAtoms;
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this.DipolarAngle = p.Results.DipolarAngle;
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this.DipolarPolarAngle = p.Results.DipolarPolarAngle;
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this.DipolarAzimuthAngle = p.Results.DipolarAzimuthAngle;
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this.ScatteringLength = p.Results.ScatteringLength;
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this.TrapFrequencies = p.Results.TrapFrequencies;
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this.NumberOfPoints = p.Results.NumberOfPoints;
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this.NumberOfGridPoints = p.Results.NumberOfGridPoints;
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this.Dimensions = p.Results.Dimensions;
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this.SimulationMode = p.Results.SimulationMode;
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@ -14,7 +14,7 @@ else
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VDk = calcObj.calculateVDCutoff(Params,Transf,TransfRad);
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save(sprintf(strcat(this.SaveDirectory, '/VDk_M.mat')),'VDk');
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end
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disp('Finished DDI')
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fprintf('Computed and saved DDI potential in Fourier space with %s cutoff.', calcObj.CutoffType)
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% == Setting up the initial wavefunction == %
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psi = this.setupWavefunction(Params,Transf);
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@ -11,9 +11,9 @@ w0 = 2*pi*100; % Angular frequency unit [s^-1]
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mu0factor = 0.3049584233607396; % =(m0/me)*pi*alpha^2 -- me=mass of electron, alpha=fine struct. const.
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% mu0=mu0factor *hbar^2*a0/(m0*muB^2)
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% Number of points in each direction
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Params.Nx = this.NumberOfPoints(1);
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Params.Ny = this.NumberOfPoints(2);
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Params.Nz = this.NumberOfPoints(3);
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Params.Nx = this.NumberOfGridPoints(1);
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Params.Ny = this.NumberOfGridPoints(2);
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Params.Nz = this.NumberOfGridPoints(3);
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% Dimensions (in units of l0)
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Params.Lx = this.Dimensions(1);
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@ -28,8 +28,8 @@ l0 = sqrt(hbar/(Params.m*w0)); % Defining a harmonic oscillator length
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Params.N = this.NumberOfAtoms;
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% Dipole angle
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Params.theta = this.DipolarAngle; % pi/2 dipoles along x, theta=0 dipoles along z
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Params.phi = 0;
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Params.theta = this.DipolarPolarAngle; % pi/2 dipoles along x, theta=0 dipoles along z
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Params.phi = this.DipolarAzimuthAngle;
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% Dipole lengths (units of muB)
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Params.mu = CONSTANTS.DyMagneticMoment;
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@ -2,11 +2,12 @@ classdef Potentials < handle & matlab.mixin.Copyable
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properties (Access = private)
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PotentialDefaults = struct('TrapFrequency', 100e3);
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PotentialDefaults = struct('TrapPotentialType', 'Harmonic', ...
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'TrapFrequency', 100e3);
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end
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properties (Access = public)
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TrapPotentialType;
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TrapFrequency;
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end
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