Unpacking the Physics Behind the Annihilator-Creator Operator Formula

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SUMMARY

The discussion centers on the Annihilator-Creator Operator Formula, specifically focusing on the components involved: the density operator ρ(0) representing the initial state, the annihilator operator 'a', and the creator operator 'a+'. The steady state density operator ρss is also referenced, indicating its role in the system's evolution post-measurement. The formula reflects the outcome of a Positive Operator-Valued Measure (POVM) measurement, highlighting the transition from initial to steady state and the implications of non-eigenvalues of the Hamiltonian on time evolution.

PREREQUISITES
  • Understanding of quantum mechanics concepts, particularly density operators.
  • Familiarity with annihilator and creator operators in quantum field theory.
  • Knowledge of Positive Operator-Valued Measures (POVM) and their applications.
  • Basic grasp of Hamiltonian mechanics and eigenvalue problems.
NEXT STEPS
  • Study the mathematical formulation of density operators in quantum mechanics.
  • Explore the role of annihilator and creator operators in quantum field theory.
  • Research the implications of POVM measurements on quantum state evolution.
  • Examine Hamiltonian dynamics and the significance of eigenvalues in quantum systems.
USEFUL FOR

Quantum physicists, researchers in quantum mechanics, and students studying advanced quantum theory concepts will benefit from this discussion.

Lizzie Mann
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a
In the formula above, on the left hand side, ρ(0) is a system's density operator in its initial state. a is the annihilator operator of the system, and a+ is the create operator of the system. ρss is the system's density operator in its steady state.

But I don't understand why this formula writes in this way. Could anyone tell me what is the physics behind this formula?

Many thanks!
 
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A link would help!
 
Maybe an idea:
http://en.wikipedia.org/wiki/POVM#Post-measurement_state

It looks like the result of the density matrix after a POVM measurement on your steady state. You get it as a post measurement result at t = 0. If it is not an eigen value of the hamiltonian, it evolves in time.
 

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