Time dependent perturbation theory for density matrix

In summary, time dependent perturbation theory for density matrix is a mathematical framework used to study the behavior of quantum systems under the influence of time-dependent perturbations. It expands on time independent perturbation theory by allowing for the calculation of the system's time evolution and higher-order corrections. It has applications in various areas of quantum mechanics but has limitations such as assuming small perturbations and neglecting non-perturbative effects. It differs from time independent perturbation theory by taking into account the time evolution of the perturbation.
  • #1
paweld
255
0
Does anyone kown how to apply time dependent perturbation theory to densities
matricies (I'm interested in first order)?
Thanks.
 
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  • #2
Yes I know I am late, but for future reference. The idea is to use the Louisville's equation in the interaction picture ( can be found in wiki in interaction picture). Then you transform the equation into a integral equation and substitute it again in the Louisville's equation. Repeat the process for higher orders. I hope this helps.
 

Related to Time dependent perturbation theory for density matrix

1. What is time dependent perturbation theory for density matrix?

Time dependent perturbation theory for density matrix is a mathematical framework used to study the behavior of quantum systems that are under the influence of an external time-dependent perturbation. It is an extension of the more general time independent perturbation theory, and it allows for the calculation of the time evolution of the quantum system's density matrix.

2. How does time dependent perturbation theory for density matrix work?

This theory works by treating the perturbation as a small additional term in the Hamiltonian of the quantum system. The density matrix, which describes the state of the system, is then expanded in terms of the perturbation strength, allowing for the calculation of higher-order corrections to the system's evolution.

3. What are the applications of time dependent perturbation theory for density matrix?

This theory has many applications in quantum mechanics, such as in the study of atomic and molecular systems, quantum optics, and quantum computing. It is also used in the calculation of transition rates and probabilities for different physical processes in quantum systems.

4. What are the limitations of time dependent perturbation theory for density matrix?

One limitation of this theory is that it assumes that the perturbation is small, which may not always be the case in real-world systems. It also does not take into account any non-perturbative effects that may occur in the system. Additionally, it may become mathematically complex when dealing with higher-order corrections.

5. How does time dependent perturbation theory for density matrix differ from time independent perturbation theory?

Time dependent perturbation theory for density matrix is an extension of time independent perturbation theory, which only deals with stationary systems. Time independent perturbation theory assumes that the perturbation is time-independent, while time dependent perturbation theory takes into account the time evolution of the perturbation. This allows for a more accurate description of the system's behavior under the influence of time-varying perturbations.

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