Graduate What Does Constant Fidelity in Quantum States Imply?

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Constant fidelity of 1 between the initial and final quantum states at discrete time intervals indicates that the quantum state does not evolve, suggesting it remains an energy eigenstate. In this scenario, the only change is an overall phase shift, which lacks physical significance. This phenomenon aligns with the principles of quantum dynamics, where systems typically evolve over time. Therefore, the implication is that the system is static in terms of observable properties despite the passage of time. Understanding this concept is crucial for interpreting quantum state behavior in various physical contexts.
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What does constant fidelity mean?
I have a fidelity between the initial state and final state is 1 at t=0,1,2...etc. What does it mean physically? Does it mean that the quantum state is not evolved here. But In quantum dynamics every physical system evolves with time.
 
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deepalakshmi said:
Summary:: What does constant fidelity mean?

I have a fidelity between the initial state and final state is 1 at t=0,1,2...etc. What does it mean physically? Does it mean that the quantum state is not evolved here. But In quantum dynamics every physical system evolves with time.
For pure states represented by vectors in a Hilbert space, it means that only the overall phase changes with time, which has no physical relevance. Such states are energy eigenstates.
 
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Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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