Discussion Overview
The discussion revolves around the thermodynamics of quantum systems, specifically focusing on the behavior of quantum harmonic oscillators at zero and finite temperatures. Participants explore how temperature is represented in quantum mechanics and the implications for Hamiltonians and state descriptions.
Discussion Character
- Exploratory
- Technical explanation
- Conceptual clarification
- Debate/contested
Main Points Raised
- One participant questions whether standard Hamiltonians for quantum systems, such as the harmonic oscillator, are modeled at absolute zero temperature and how temperature can be incorporated into these Hamiltonians.
- Another suggests studying the quantum harmonic oscillator at zero temperature using wave functions and at finite temperature using density operators, particularly in the context of canonical ensembles.
- It is proposed that the Hamiltonian remains unchanged regardless of temperature, with the ground state at zero temperature being a Gaussian coherent state, while a finite temperature state is described as a thermal coherent state.
- Participants discuss the nature of the first excited state at zero temperature, identifying it as a Fock state and noting its energy relative to the ground state.
- Concerns are raised about the applicability of temperature to Fock states, with some arguing that a Fock state cannot be assigned a meaningful temperature due to its fixed energy.
- There is mention of the probability distribution for energy eigenstates at a given temperature, suggesting that a Fock state does not correspond to a precise temperature.
Areas of Agreement / Disagreement
Participants express differing views on the relationship between Fock states and temperature, with some asserting that Fock states cannot be associated with a meaningful temperature, while others explore the implications of temperature on quantum states without reaching a consensus.
Contextual Notes
There are unresolved questions regarding the definitions of temperature in quantum systems and the implications for various states, particularly Fock states and coherent states. The discussion also highlights the complexity of relating Hamiltonians to thermal states.