Math fixes

Author: haggaila

docs/background.md

@@ -6,8 +6,8 @@
 This code simulates the time evolution of a quantum system of interacting two-level systems (qubits).
 
 The dynamics is determined by: (1) a Hamiltonian, which corresponds to the unitary part of the time evolution, and (2) dissipative terms, which account for the fact that the system is coupled to an environment.
-These two types of terms enter in a so-called *Lindblad equation* that determines the evolution of the *density matrix* of the system.
-Since we have N qubits the Hilbert space has dimension 2^N and the density matrix is 2^N by 2^N in size. In practice this is a huge dimension unless N is very small, and it therefore prevents a direct brute-force numerical solution of the Lindblad equation.
+These two types of terms enter the so-called *Lindblad equation* that determines the evolution of the *density matrix* of the system.
+Since we have $N$ qubits the Hilbert space has dimension $2^N$ and the density matrix is $2^N$ by $2^N$ in size. In practice this is a huge dimension unless $N$ is very small, and it therefore prevents a direct brute-force numerical solution of the Lindblad equation.
 
 The present code offers an approximate solution of the problem that can be very accurate for large systems (typically up to N~100 or more) if the geometry of the couplings between the qubits is one-dimensional. This approach can also be more efficient than a brute force approach in other geometries.