topquantmat/tutorial.py at main · quantummasterbarcelonacode/topquantmat · GitHub

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import sys
sys.path.append("/content/conda_dir")
import kwant
import qsymm
import sympy as sp
import numpy as np
import matplotlib.pyplot as plt
from numpy.random import random
from sympy import Q

welcome="Packages are loaded. ¡Welcome!"

def Print(message):
  display(Markdown(message))
def print_eq(suffix, eq):
  display(Markdown(suffix + r" $%s$ "%latex(eq)))


euler = (sp.Symbol("e",positive=True),sp.exp(1));
def Rz(phi):
  return sp.Matrix([  [ sp.cos(phi),-sp.sin(phi), 0 ],
                      [ sp.sin(phi), sp.cos(phi), 0 ],
                      [ 0            , 0        , 1 ]
                    ]);

def Rz_2D(phi):
  return sp.Matrix([  [ sp.cos(phi),-sp.sin(phi) ],
                      [ sp.sin(phi), sp.cos(phi) ]
                    ]);


def FirstOrderTaylor( h, x,x0 ):
    dx   = x; evalx=  list(zip(x,x0));
    h=h.expand(complex=True)
    happ = h.subs( evalx );
    for xi,dxi in zip(x,dx):
        happ += sp.diff(h,xi).subs(evalx)*dxi;
    return sp.simplify(happ);

class Hexagonal:
  lat_vec= sp.Array( [
            [sp.Rational( 1,2), sp.sqrt(3)/2,sp.Integer(0)],
            [sp.Rational(-1,2), sp.sqrt(3)/2,sp.Integer(0)],
            [sp.Integer(0),sp.Integer(0),sp.Integer(1)]
         ]);

  rec_vec = sp.Array( sp.Matrix(lat_vec).inv().T*2*sp.pi );
  K0 =np.array(sp.Matrix( (rec_vec[0]-rec_vec[1])/3)).flatten();
  K1 =np.array(sp.Matrix(-(rec_vec[0]-rec_vec[1])/3)).flatten();

graphene = Hexagonal();


def dot(x,y):
  return sp.simplify( ( sp.conjugate(x.T) * y )[0] );

def norm(x):
  return sp.sqrt(dot(x,x));

def normalize(x):
  return sp.simplify(x)/norm(x);

def delta(x,y):
    if(x==y):
      return 1
    return 0;

def EigenSystem( H, coord_syst=[] ):
  Es  = []; Psis= [];
  eigsyst = H.eigenvects();
  for eigv,mul,deg_eigs in eigsyst:
    for eig in deg_eigs:
      Es.append(eigv.subs(coord_syst));
      Psis.append(eig.subs(coord_syst));
  Es  = [ E for E  in Es ];
  Psis= [ sp.simplify(normalize(sp.simplify(Psi) )) for Psi in Psis]
  return Es,Psis;

def exps2trig(x):
    return sp.trigsimp(sp.simplify(x).rewrite(sp.sin))

def half_angles(expr,theta):
  half_ang  = [ ( 1-sp.cos(theta) , 2 * sp.sin(theta/2)**2 ),
                ( 1+sp.cos(theta) , 2 * sp.cos(theta/2)**2 ),
                ( 2+2*sp.cos(theta) , 4 * sp.cos(theta/2)**2 ),
              ];
  trig_assum= Q.positive(sp.sin(theta/2)) & Q.positive(sp.cos(theta/2));

  return exps2trig(sp.refine(sp.simplify(sp.simplify(expr).subs(half_ang)),trig_assum));


import requests
import IPython.display as Disp
grafeno_real = 'https://i.pinimg.com/564x/27/73/60/277360f8a8265b0a8008d1d03023a7be.jpg'
grafeno_disp = 'https://icn2.cat/images/20190802_spin-communication.jpg'
def ejemplo_grafeno_real():
  return Disp.Image(requests.get(grafeno_real).content);
def ejemplo_dispositivo_grafeno():
  return Disp.Image(requests.get(grafeno_disp).content);