Exploring Quantum Systems: Steady States and Eigenstate Behavior

In the world of quantum physics, understanding how systems behave is crucial. One key idea is the Eigenstate Thermalization Hypothesis (ETH).

Eigenstate Thermalization Hypothesis (ETH)

• Suggests that individual quantum states can represent the thermal properties of a system.
• But what about systems that are always changing, not in balance?

Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) Master Equation

• Helps describe these open quantum systems.
• Researchers have found that the eigenstates of non-equilibrium steady state (NESS) density matrices also follow a version of ETH.

Non-Equilibrium Steady State Eigenstate Thermalization Hypothesis (NESS-ETH)

• Similar to how eigenstates of Gibbs density matrices behave in systems at equilibrium.
• Can help find pure states that show the same properties as the NESS.
• These pure states can be seen as solutions to the GKLS Master Equation.

Limitations of NESS-ETH

• Does NESS-ETH always work? Not necessarily.
• Can break down when there are:
• Symmetries
• Integrability
• Many-body localization in the system.
• This means the behavior of quantum systems can be quite complex and depends on various factors.

Conclusion

Understanding these concepts can help in:

• Developing new technologies
• Improving our knowledge of quantum mechanics.

It's a fascinating area of study that continues to evolve.