Does Bose Einstein Condensate Defy the Pauli Exclusion Principle?

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Bose-Einstein condensates (BECs) do not violate the Pauli Exclusion Principle because they consist of bosons, which are not subject to this principle. In contrast, fermions, which are governed by the Pauli Exclusion Principle, cannot form BECs but can create superfluids and superconductors. Superconductors are formed by Cooper pairs, which are bosonic in nature, suggesting a connection to BECs, although the underlying mechanisms differ significantly. The discussion clarifies the distinctions between bosons and fermions in the context of quantum states. Understanding these differences is crucial for grasping the behavior of various quantum systems.
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Does Bose Einsteine Condesate violate the Pauli Exclusion Principle?
 
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No, because Bosons are not under it. Fermions are however, and they cannot form a BEC.
 
Fermions can form superfluids and superconductors.
The superconducting ground state is formed by a collection of Cooper pairs that are again bosonic. So you could say that it is sort of a BEC but the mechanism is very different.
 
Ahh, of course. Thanks for refreshing my memory.
 

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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