How does a non-linear Schrodinger equation implies non-unitary evolution?

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SUMMARY

The discussion centers on the implications of a non-linear Schrödinger equation (SE) for wave-function collapse and unitarity. Participants argue that while non-linearities can describe wave-function collapse, they may not necessarily lead to non-unitary evolution if the Hamiltonian remains Hermitian. The conversation references the works of Mostafazadeh and Bender, highlighting that non-Hermitian Hamiltonians can still exhibit unitary behavior. Ultimately, the breakdown of superposition is identified as a key factor in understanding non-unitary evolution.

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Hi,

I several times heard that one way to describe the collapse of the wave-function is to add non linearities in the Schrödinger equation (I know that this approaches are not convincing but that's not my point), however, I don't see why a non linear SE would imply loss of unitarity? As long as the Hamiltonian is hermitean, or real if you see it as a function of \psi and \psi^*, we can derive an equation of probability conservation.
 
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you call, loss of unitarity, to the breakdown of the superposition ?
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and apart there are non hermitian hamiltonians that are unitary.
Mostafazadeh, Bender.
 
Well, I would call loss of unitarity any loss of unitarity, but as I heard of using non-linearities to describe wave-function collapse, and the breakdown of a superposition is non unitary evolution, I'd say maybe =)
 

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