New answers tagged unitarity
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Is Hawking radiation truly random or we just don't know that it is?
The truth is that we just do not know. Hawking radiation is so slow and we do not know everything that it absorbed making it very hard to measure, especially since we dare not go investigate, and if ...
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Proving that a Hamiltonian transformation is canonical - Condensed Matter, Altland and Simons
A quantum canonical transformation is an adjoint group action $\hat{F}\mapsto {\rm Ad}(\hat{U})\hat{F}=\hat{U}\hat{F}\hat{U}^{-1}$ with a unitary operator $\hat{U}$, cf. e.g. this Phys.SE post.
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Connection between Real time evolution and Imaginary time evolution
The eigenvalues of the Pauli matrix $$\sigma_y= \left( \begin{array}{cc} 0 & -i \\ i & 0 \end{array} \right)$$ are $+1$ and $-1$ with associated (normalized) eigenvectors $$\chi_+= \frac{1}{\...
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Time evolution and anti-unitary operators
Ah, I see. It comes down to the fact that $\hat{U}$ is not linear. (It is antilinear, duh!). And it doesn't play well with unitary transformation.
Let's say you define $\hat{U}$ by what it does to ...
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Time evolution and anti-unitary operators
In general if $H$ is symmetric under a unitary or anti-unitary transformation $\hat U$, it implies that if $|\psi(t)\rangle$ is a solution to the Schroedinger equation $i\hbar \frac{d}{dt}|\psi(t)\...
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Transformations on correlation functions
Let $(~,~)$ denote the inner product on a Hilbert space, so that
$$
(\Psi_1,\Psi_2)^* = (\Psi_2 , \Psi_1) , \qquad (\Psi_1,a \Psi_2)= a (\Psi_1,\Psi_2) , \qquad (a \Psi_1,\Psi_2) = a^* (\Psi_1,\Psi_2) ...
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Is there a no-cloning theorem for open quantum dynamics?
A channel $\Phi$ allowing to "clone" any input state would mean $\Phi(\rho)=\rho\otimes\rho$ for all states $\rho$.
Any channel $\Phi$ sending states in $\mathbb{C}^n$ to states in $\mathbb{...
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