Is the vacuum a thermal state?

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SUMMARY

The discussion centers on the nature of the vacuum as a thermal state, particularly in the context of thermal coherent states. It is established that the vacuum represents a peculiar thermal state at null temperature, where no energy can be extracted. The energy that can be borrowed from a thermal coherent state is quantified as N k T/2 when dealing with quadratic Hamiltonians, while more complex Hamiltonians require different considerations. This highlights the importance of understanding the specific Hamiltonian form when analyzing energy extraction from thermal states.

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  • Understanding of thermal coherent states
  • Familiarity with Hamiltonian mechanics
  • Knowledge of statistical mechanics concepts, particularly temperature and energy
  • Basic grasp of quantum mechanics principles
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This discussion is beneficial for physicists, quantum mechanics students, and researchers focusing on thermal states and energy dynamics in quantum systems.

naima
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Please look at the wikipedia article about thermal coherent states.
We can only consider the states centered at the origin (##\alpha## = 0). If i understand what is written the vacuum is a pecular thermal state in the limit of a null temperature. I can understand that no energy can be borrowed from a system at this temperature. But this is because we used the word "temperature". How can we compute the energy that can be borrowed from a thermal coherent state? Is it N k T?
Thanks.
 
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naima said:
How can we compute the energy that can be borrowed from a thermal coherent state? Is it N k T?
It's NKT/2 when the Hamiltonian is quadratic in canonical coordinates and momenta. For more general Hamiltonians the relation is not so simple.
 

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