The adiabatic process which we learn in thermodynamics is the process where we decrease/increase the volume of the gases enclosed in a container, slowly so that the pressure remains constant throughout the process.
The quantum mechanical adiabatic theorem says: For a system with non-degenerate ground state, if the system is taken from the ground state to the next (only next excited state) energy level (i.e. excited state) very slowly (the time taken to go from one state to another in a smaller time than the characteristic time of the energy gap of the two energy-levels involved), then the system finally adapts ground state.
Here analogy is as follows (even though it doesn't make sense now)
The quantum mechanical adiabatic theorem says: For a system with non-degenerate ground state, if the system is taken from the ground state to the next (only next excited state) energy level (i.e. excited state) very slowly (the time taken to go from one state to another in a smaller time than the characteristic time of the energy gap of the two energy-levels involved), then the system finally adapts ground state.
Here analogy is as follows (even though it doesn't make sense now)
- Which remains constant: Pressure & Energy
- Which is changed: Volume & State of the system
- In what time : Both are slowly (in QM, it is exactly defined; In TD, not defined (?) clearly.
Adiabatic theorem plays an important role in the definition of topological phases of matter.
In approximate (but most successful) theory such as Density Functional theory, construction of the final state is obtained by slowly changing some parameters (for e.g., λ) and finally the ground state is obtained.
What are the connection among these?
Another similar idea (?) is the derivation of molecular forces by Feynman. What is the exact connection among these?
