I Unitary time evolution

1. Mar 31, 2016

jamie.j1989

Hi, im a bit confused about unitary time evolution, I understand that a closed quantum system can be explained by unitary time evolution which ensures that the probability of all possible outcomes is always 1. But for an open quantum system we can't in general explain it with a unitary time evolution. This is where I get confused, we explain the evolution of an open quantum systems with the density matrix $\rho(t)$, which must always satisfy $Tr[\rho(t)]=1$, so my question is, how is this not unitary time evolution? Thanks.

2. Mar 31, 2016

ShayanJ

The density matrix may refer to the state of the system+environment which we expect to have a unitary evolution. But when we trace out the environmental degrees of freedom, we are left with a density matrix which describes what we should expect if we have don't have access to the environmental degrees the freedom. So $\rho_{total}$ has a unitary evolution but $\rho_{system}=Tr_{environment}(\rho_{total})$ doesn't!

3. Mar 31, 2016

Zafa Pi

More often than not open system measurements are described by the Copenhagen/Collapse Interpretation. Collapse is not invertible let alone unitary.

4. Apr 1, 2016

A. Neumaier

Collapse preserves the condition $\mbox{Tr}~ \rho=1$. This is a much weaker condition than nitarity, which says that $\rho(t)=U(t)\rho(0)U(t)^*$ with a unitary $U(t)$.

5. Apr 1, 2016

Zafa Pi

Indeed, ρ becomes the projection onto the collapsed eigenvector.