def Cintegrate(phi,
               HC, 
               dt):
    """ 
    Explicit Euler integration to simulate a classical random walker.
    
    Parameters: 
    phi (array): prob. distr. at current time
    HC (sparse matrix): classical Hamiltonian
    dt (float): time step
  
    Returns: 
    sparse matrix: prob. distr. at next time step
  
    """

    phip1 = phi-HC.dot(phi)*dt
    
    return phip1