Unrecognized function or variable

Goodnight! Whenever I run the following code, the error ''Unrecognized function or variable 'acav'.'' appears. Since the functions were all defined. Follow the codes. Anyone who can help me I would be very grateful.

clc

clear all

Nsim = 25; % Number of simulations

L = 2; % Number of cavities

wc = 1; % Cavity frequency

g = 1e-2* wc ; % Atom - light coupling

J = 1e-4* wc ; % Coupling between cavities

Nph = 2; % Number of photons per cavity

dimFock = Nph +1; % Dimension Fock space for photons

dimT = 2* dimFock ; % Dimension atom + cavity system

Deltai = 10^( -2) *g; % Initial detuning

Deltaf = 10^(+2) *g; % Final detuning

xi = log10 ( Deltai / g); % Initial detuning in log scale

xf = log10 ( Deltaf / g); % Final detuning in log scale

dx = (xf - xi ) /( Nsim -1) ; % Step dx

x = xi : dx : xf ; % Vector x to plot transition phase

OP_JC = zeros ( size (x) ); % Order parameter Jaynes - Cummings model

OP_R = zeros ( size ( x)); % Order parameter Rabi model

A = cell (1 , L); % Cell array to storage \hat{a}_i operators

Sp = cell (1 , L ); % Cell array to storage \ hat {\ sigma }_i ^+ operators

N_ex = cell (1 , L); % Cell array to storage N_i operators

Iatom = eye (2) ; % Identity matrix atom system

Icav = eye ( dimFock ); % Identity matrix cavity system

Is = eye (2* dimFock ); % Identity matrix atom + cavity system

accc

comple

for i =1:L

A{i} = acav(i ,L , Nph ,Is , Iatom ); % Photon operator \ hat {a}_i

Sp{i} = sigmap(i ,L ,Is , Icav ); % Atom operator \ hat {\ sigma }_i

N_ex {i} = A{i }'* A{i }+ Sp { i }* Sp {i }'; % number of excitations per cavity

end

Ad = ones (L); % Adyacent matrix

Ad = triu ( Ad ) - eye ( L); % A(i,j)=1 for j>i

Hhopp = zeros ( dimT ^L , dimT ^L); % Interaction Hamiltonian

for i =1: L

for j =1: L

Hhopp = Hhopp - J*Ad (i ,j)*A {i }'*A{j} - J*Ad (i ,j )*A{ i }*A{ j }';

end

end

Nt = 10000; % Length time vector

ti = 0.01/ J; % Initial time

tf = 1/ J ; % Final time

dt = (tf - ti ) /( Nt -1) ; % Step time dt

t = ti : dt : tf ; % Time vector

Lambda_R = zeros ( Nsim , Nt ) ;

Lambda_JC = zeros ( Nsim , Nt ) ;

parfor n =1: Nsim

D = g *10^( x(n) ); % Detuning in each simulation

Model = 'Rabi ';

[ OP_R(n) , P1m_R ] = QuantumSimulationCavityArray (wc ,D ,g , Nph ,L ,A ,Sp , N_ex , Hhopp ,t ,Model );

Model = 'Jaynes - Cummings ';

[ OP_JC(n ) , P1m_JC ] = QuantumSimulationCavityArray (wc ,D ,g , Nph ,L ,A ,Sp , N_ex , Hhopp ,t ,Model );

Lambda_R (n ,:) = -1/ L * log2 ( P1m_R ); % Rate function for the Rabi model

Lambda_JC (n ,:) = -1/ L * log2 ( P1m_JC ); % Rate function for the Jaynes - Cummings model

end

figure ()

box on

hold on

plot (J*t , Lambda_R (end ,:) ,'b-','Linewidth ' ,3)

plot (J*t , Lambda_JC (end ,:) ,'r-','Linewidth ' ,3)

hold off

xlabel ('$Jt$',' Interpreter ','LaTex ','Fontsize ', 30)

ylabel ('$\ Lambda (t)$',' Interpreter ','LaTex ','Fontsize ', 30)

set ( gca ,'fontsize ' ,21)

legend ({ '$\ mbox {RH }$ ','$\ mbox { JCH }$ '},' Interpreter ','latex ','Fontsize ', 21 , 'Location ','best ')

figure ()

box on

hold on

plot (x , real ( OP_R ) ,'.b','Markersize ' ,30)

plot (x , real ( OP_JC ) ,'.r','Markersize ' ,30)

hold off

xlabel ('$\ mbox { Log }_ {10}(\ Delta /g)$',' Interpreter ','LaTex ','Fontsize ', 30)

ylabel ('$\ mbox {OP }$ ',' Interpreter ','LaTex ','Fontsize ', 30)

set ( gca ,'fontsize ' ,21)

legend ({ '$\ mbox {RH }$ ','$\ mbox { JCH }$ '},' Interpreter ','latex ','Fontsize ', 21 , 'Location ','best ')

And the two functions accc and comple are defined as

Nsim = 25; % Number of simulations

L = 2; % Number of cavities

wc = 1; % Cavity frequency

g = 1e-2* wc ; % Atom - light coupling

J = 1e-4* wc ; % Coupling between cavities

Nph = 2; % Number of photons per cavity

dimFock = Nph +1; % Dimension Fock space for photons

dimT = 2* dimFock ; % Dimension atom + cavity system

Deltai = 10^( -2) *g; % Initial detuning

Deltaf = 10^(+2) *g; % Final detuning

xi = log10 ( Deltai / g); % Initial detuning in log scale

xf = log10 ( Deltaf / g); % Final detuning in log scale

dx = (xf - xi ) /( Nsim -1) ; % Step dx

x = xi : dx : xf ; % Vector x to plot transition phase

OP_JC = zeros ( size (x) ); % Order parameter Jaynes - Cummings model

OP_R = zeros ( size ( x)); % Order parameter Rabi model

A = cell (1 , L); % Cell array to storage \hat{a}_i operators

Sp = cell (1 , L ); % Cell array to storage \ hat {\ sigma }_i ^+ operators

N_ex = cell (1 , L); % Cell array to storage N_i operators

Iatom = eye (2) ; % Identity matrix atom system

Icav = eye ( dimFock ); % Identity matrix cavity system

Is = eye (2* dimFock ); % Identity matrix atom + cavity system

function [OP , P1m ]= QuantumSimulationCavityArray ( wc ,D ,g , Nphoton ,L ,A , Sp , N_ex , Hhopp ,t ,Model )

HJC = zeros (( Nphoton +1) ^L *2^ L ,( Nphoton +1) ^L *2^ L);

for i =1: L

switch Model

case 'Jaynes - Cummings '

HJC = HJC + wc *A{i }'* A{i } + (D+ wc )* Sp {i }* Sp {i }' + g *( Sp {i }* A{i }+ Sp {i }'* A{i}') ;

case 'Rabi '

HJC = HJC + wc *A{i }'* A{i } + (D+ wc )* Sp {i }* Sp {i }' + g *( Sp {i }+ Sp {i }') *( A {i }+ A {i }') ;

end

end

H = HJC + Hhopp ; % Total Hamiltonian

dt = t (2) -t (1) ; % Step time dt

U = expm ( -1i*H*dt ) ; % Time propagator with step dt

up = [1 0]'; % Excited state for the two - level system

down = [0 1]'; % Ground state for the two - level system

Fock = eye ( Nphoton +1) ; % Fock states

theta1 = 0.5* atan (2* g* sqrt (1) /D);

phi_1m = cos ( theta1 )* kron ( down , Fock (: ,2) )...

- sin ( theta1 )* kron (up , Fock (: ,1) ); % Initial state |1 , - >

PSI_0 = phi_1m ;

for k =1: L -12 PSI_0 = kron ( PSI_0 , phi_1m ); % Many body wavefunction |1 , - >...|1 , - > (L terms )

end

dn_T = zeros ( size ( t)); % Standard deviation dn_i = <n_i ^2 > - <n_i >^2

P1m = zeros ( size ( t)); % Population |1 , - > at time t

for n =1: length (t)

if n ==1

PSI = PSI_0 ; % Initial wavefunction

else

PSI = U* PSI ; % Wavefunction at time t_n

end

dn = 0;

for i =1: L

dn = dn + PSI'* N_ex {i }^2* PSI -( PSI'* N_ex {i }* PSI )^2;

end

P1m (n ) = abs ( PSI_0'* PSI ) ^2; % Ground state probability

dn_T (n) = dn ; % Standard deviation of the number of excitations

end

OP = mean ( dn_T ); % Order parameter

end

and

Nsim = 25; % Number of simulations

L = 2; % Number of cavities

wc = 1; % Cavity frequency

g = 1e-2* wc ; % Atom - light coupling

J = 1e-4* wc ; % Coupling between cavities

Nph = 2; % Number of photons per cavity

dimFock = Nph +1; % Dimension Fock space for photons

dimT = 2* dimFock ; % Dimension atom + cavity system

Deltai = 10^( -2) *g; % Initial detuning

Deltaf = 10^(+2) *g; % Final detuning

xi = log10 ( Deltai / g); % Initial detuning in log scale

xf = log10 ( Deltaf / g); % Final detuning in log scale

dx = (xf - xi ) /( Nsim -1) ; % Step dx

x = xi : dx : xf ; % Vector x to plot transition phase

OP_JC = zeros ( size (x) ); % Order parameter Jaynes - Cummings model

OP_R = zeros ( size ( x)); % Order parameter Rabi model

A = cell (1 , L); % Cell array to storage \hat{a}_i operators

Sp = cell (1 , L ); % Cell array to storage \ hat {\ sigma }_i ^+ operators

N_ex = cell (1 , L); % Cell array to storage N_i operators

Iatom = eye (2) ; % Identity matrix atom system

Icav = eye ( dimFock ); % Identity matrix cavity system

Is = eye (2* dimFock ); % Identity matrix atom + cavity system

function x =acav(i ,L , Nph ,Is , Iatom )

a = diag(sqrt(1:Nph)',1) ;

a = kron ( Iatom ,a);

Op_total = cell (1 , L) ;

for site = 1: L

Op_total { site } = Is + double ( eq (i , site ))*(a - Is );

end

x = Op_total {1};

for site = 2: L

x = kron (x , Op_total { site }) ;

end

end

function x = sigmap(i ,L , Is , Icav )

up = [1 0]';

down = [0 1]';

sigma_p = up * down';

sigma_p = kron ( sigma_p , Icav );

Op_total = cell (1 , L) ;

for site = 1: L

Op_total { site } = Is + double ( eq (i , site )) *( sigma_p - Is );

end

x = Op_total {1};

for site = 2: L

x = kron (x , Op_total { site }) ;

end

end

Answer 1

[Voss]

If the intent is that the local functions defined in the scripts accc.m and comple.m (those local functions being acav, sigmap, and QuantumSimulationCavityArray) be accessible from the main script, then that can be achieved by having those two scripts (accc.m and comple.m) create function handles to the functions they contain.

However, it's probably easier to make those three local functions defined in those two scripts into functions in their own m-files, which can then be called from anywhere. I've done this, and the m-files are attached here (including main_script.m, which no longer calls accc.m and comple.m, since they are no longer needed).

main_script

Starting parallel pool (parpool) using the 'local' profile ...
Connected to the parallel pool (number of workers: 2).

Error using QuantumSimulationCavityArray
Incorrect dimensions for matrix multiplication. Check that the number of columns in the first matrix matches the number of rows in the second matrix. To operate on each element of the matrix individually, use TIMES (.*) for
elementwise multiplication.

Error in main_script (line 50)
parfor n =1: Nsim

[Celso Júnior]

Good Afternoon ! Great! But why when I run the script the graph is still not generated? When I run main_script the error message appears:'' Unrecognized function or variable 'acav'. '' and no graphics appear.

I thank you in advance for your help.

[Walter Roberson]

Create a new directory and put the scripts that _ posted in the directory, and run the code from that directory. You will get an error about matrix multiplication, not an error about acav not found.