All Questions
Tagged with mathematical-physics open-quantum-systems
7
questions
4
votes
1
answer
126
views
Jensen's inequality on (super)operator exponential
Let us define the expectation value $\langle A\rangle_{\rho}$ of a superoperator $A$ over a density matrix $\rho$ as $(\rho, A(\rho))$, where the scalar product between operators reads $(O_1,O_2):= Tr[...
- 325
6
votes
1
answer
178
views
Are $\mathcal{PT}$-symmetric Hamiltonians dual to Hermitian Hamiltonians?
I was reading this review paper by Bender, in particular section VI where they show that, despite $\mathcal{PT}$-symmetric Hamiltonians not being hermitian, they can have a real spectra. They go on ...
- 1,544
3
votes
4
answers
242
views
Why energy-positivity?
In any relativistic quantum field theory, we require that the spectrum is bounded from below. The typical explanation is that this condition enforces the stability of the theory. However, to me this ...
- 506
1
vote
1
answer
53
views
Proof of differentiate form of dynamical semigroups
I am studying some basics of the pure mathematical background for open quantum systems from Angel Rivas`s book which is "Open quantum systems, an introduction".
Here is a theorem (Page 6, ...
- 119
1
vote
0
answers
159
views
Transient solution system of differential equations obtained from master equation
I have to solve the following equation (or at least obtain an approximate estimate) for the diagonal terms of the density matrix. We consider that the initial state is a coherent state $\rho_{n,n}(0)=...
- 11
0
votes
1
answer
286
views
Time dependence of Hamiltonian in Schrodinger picture in open quantum system
Many questions in StackExchange and papers that I see consider the following von Neumann equation for describing evolution of density matrix $\rho$ in time $t$ given a Hamiltonian $H$:
$$ \frac{d\rho}{...
- 399
5
votes
1
answer
94
views
Bounds on the effect of strong coupling
I am interested in bounding the effects of system-environment interaction.
Suppose I have an initial state $\rho \in \mathcal{H}_S \otimes \mathcal{H}_E$ where the system and environment might be ...
- 323