From Spinach Documentation Wiki
This page contains the list of misprints discovered so far in Ilya Kuprov's "SPIN: from Basic Symmetries to Quantum Optimal Control".
| Location |
Printed |
Should be
|
| Page 44, under Eq 2.5 |
"physical meaning of oscillation frequency" |
"physical meaning of frequency"
|
| Page 54, under Eq 2.52 |
"meV" |
"MeV"
|
| Page 83, Eq 3.42 |
\[ - {\mu _{\rm{N}}}{g_n}\left( {{\bf{1}} - {\sigma }} \right)\] |
\[ - {\mu _{\rm{N}}}{g_n}\left( {{\bf{1}} - {\bf{σ}}} \right)\]
|
| Page 114, under Eq 4.31 |
"up to a phase" |
"up to an overall phase"
|
| Page 123 (Eqs 4.66, 4.69, 4.70), Page 126 (Eqs 4.80, 4.81), Page 130 (Eq 4.102) |
\[l\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}
\over n} \] |
\[{\rm{l\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}
\over n} }}\]
|
| Page 123, Eq 4.69 |
\[\begin{array}{c}
\exp \left( { - i{\bf{\bar H}}T} \right) - \exp \left( { + i{{\bf{H}}_0}T} \right)\exp \left( { - i\left( {{{\bf{H}}_0} + {{\bf{H}}_1}} \right)T} \right)\\
\Downarrow \\
{\bf{\bar H}} - \frac{i}{T}l\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}
\over n} \left[ {\exp \left( { + i{{\bf{H}}_0}T} \right)\exp \left( { - i\left( {{{\bf{H}}_0} + {{\bf{H}}_1}} \right)T} \right)} \right]
\end{array}\] |
\[\begin{array}{c}
\exp \left( { - i{\bf{\bar H}}T} \right) = \exp \left( { + i{{\bf{H}}_0}T} \right)\exp \left( { - i\left( {{{\bf{H}}_0} + {{\bf{H}}_1}} \right)T} \right)\\
\Downarrow \\
{\bf{\bar H}} = \frac{i}{T}l\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}
\over n} \left[ {\exp \left( { + i{{\bf{H}}_0}T} \right)\exp \left( { - i\left( {{{\bf{H}}_0} + {{\bf{H}}_1}} \right)T} \right)} \right]
\end{array}\]
|
| Page 172, Eq 4.248 |
\(\frac{i\sqrt{3}}{12}\) |
\(\frac{i}{6}\)
|
| Page 207, Item 4 |
rth (two instances) |
rth
|
| Page 250, top of Fig 6.2 |
\[ \downarrow \] |
\[ \times \]
|
| Page 250, top of Fig 6.2 |
\[ \to \] |
\[ - \]
|
| Page 257, Eq 6.149 |
\[\left[ {\bf{V}}_k,{\bf{ρ}} V_k^\dagger \right]\] |
\[{\left[ {{{\bf{V}}_k},{\bf{ρV}}_k^\dagger } \right]}\]
|
| Page 291, under Eq 7.1 |
"the state of the other spin" |
"the state of the other system"
|
| Page 294, under Eq 7.7 |
"where the ISTs are now indexed by ascending rank l and within ranks by ascending projection number m" |
"where the ISTs are now indexed by ascending rank l and within ranks by descending projection number m"
|
| Page 295, Eq 7.9 |
\[\begin{array}{c}
{c_{ijk}} = {\rm{Tr}}\left[ {\left( {\mathop \otimes \limits_{n = 1}^N {{\bf{T}}_{l_n^{\left( i \right)}m_n^{\left( i \right)}}}} \right)\left( {\mathop \otimes \limits_{n = 1}^N {{\bf{T}}_{l_n^{\left( j \right)}m_n^{\left( j \right)}}}} \right){{\left( {\mathop \otimes \limits_{n = 1}^N {{\bf{T}}_{l_n^{\left( k \right)}m_n^{\left( k \right)}}}} \right)}^\dagger }} \right] = \\
= {\rm{Tr}}\left[ {\mathop \otimes \limits_{n = 1}^N \left( {{{\bf{T}}_{l_n^{\left( i \right)}m_n^{\left( i \right)}}}{{\bf{T}}_{l_n^{\left( j \right)}m_n^{\left( j \right)}}}{\bf{T}}_{l_n^{\left( k \right)}m_n^{\left( k \right)}}^\dagger } \right)} \right] = \prod\limits_{n = 1}^N {{\rm{Tr}}\left( {{{\bf{T}}_{l_n^{\left( i \right)}m_n^{\left( i \right)}}}{{\bf{T}}_{l_n^{\left( j \right)}m_n^{\left( j \right)}}}{\bf{T}}_{l_n^{\left( k \right)}m_n^{\left( k \right)}}^\dagger } \right)} = \prod\limits_{n = 1}^N {f_{ijk}^{\left( n \right)}}
\end{array}\] |
\[\begin{array}{c}
{\rm{Tr}}\left[ {\left( {\mathop \otimes \limits_{n = 1}^N {{\bf{T}}_{l_n^{\left( i \right)}m_n^{\left( i \right)}}}} \right)\left( {\mathop \otimes \limits_{n = 1}^N {{\bf{T}}_{l_n^{\left( j \right)}m_n^{\left( j \right)}}}} \right){{\left( {\mathop \otimes \limits_{n = 1}^N {{\bf{T}}_{l_n^{\left( k \right)}m_n^{\left( k \right)}}}} \right)}^\dagger }} \right] = \\
= {\rm{Tr}}\left[ {\mathop \otimes \limits_{n = 1}^N \left( {{{\bf{T}}_{l_n^{\left( i \right)}m_n^{\left( i \right)}}}{{\bf{T}}_{l_n^{\left( j \right)}m_n^{\left( j \right)}}}{\bf{T}}_{l_n^{\left( k \right)}m_n^{\left( k \right)}}^\dagger } \right)} \right] = \prod\limits_{n = 1}^N {{\rm{Tr}}\left( {{{\bf{T}}_{l_n^{\left( i \right)}m_n^{\left( i \right)}}}{{\bf{T}}_{l_n^{\left( j \right)}m_n^{\left( j \right)}}}{\bf{T}}_{l_n^{\left( k \right)}m_n^{\left( k \right)}}^\dagger } \right)}
\end{array}\]
|
| Page 295, under Eq 7.9 |
"in terms of the structure coefficients \(f_{ijk}\) of" |
"in terms of the structure coefficients of"
|
| Page 295, above Eq 7.10 |
"given incomplete basis" |
"given orthogonal basis"
|
| Page 295, under Eq 7.14 |
\[{c_{ijk}} = {\rm{Tr}}\left( {{{\bf{O}}_i}{{\bf{O}}_j}{\bf{O}}_k^\dagger } \right)\] |
\[{c_{ijk}} = \frac{{{\rm{Tr}}\left( {{{\bf{O}}_i}{{\bf{O}}_j}{\bf{O}}_k^\dagger } \right)}}{{{\rm{Tr}}\left( {{{\bf{O}}_k}{\bf{O}}_k^\dagger } \right)}}\]
|
| Page 296, above Eq 7.17 |
kth |
kth
|
| Page 296, Eq 7.18 |
\[{\left[ {H_n^{\left( {\rm{L}} \right)}} \right]_{jk}} = \left\langle {{{\bf{O}}_j}} \right|H_n^{\left( {\rm{L}} \right)}\left| {{{\bf{O}}_k}} \right\rangle = {\rm{Tr}}\left( {{\bf{O}}_j^\dagger {{\bf{H}}_n}{{\bf{O}}_k}} \right) = \ldots = {\omega _n}\prod\limits_{m = 1}^N {{\rm{Tr}}\left( {{\bf{S}}_{j,m}^\dagger {{\bf{S}}_{n,m}}{{\bf{S}}_{k,m}}} \right)} \] |
\(\begin{matrix} {{\left[ H_{n}^{\left( \text{L} \right)} \right]}_{jk}}=\frac{\left\langle {{\mathbf{O}}_{j}} \right|H_{n}^{\left( \text{L} \right)}\left| {{\mathbf{O}}_{k}} \right\rangle }{\sqrt{\text{Tr}\left( \mathbf{O}_{j}^{\dagger }{{\mathbf{O}}_{j}} \right)}\sqrt{\text{Tr}\left( \mathbf{O}_{k}^{\dagger }{{\mathbf{O}}_{k}} \right)}}= \\ \frac{\text{Tr}\left( \mathbf{O}_{j}^{\dagger }{{\mathbf{H}}_{n}}{{\mathbf{O}}_{k}} \right)}{\sqrt{\text{Tr}\left( \mathbf{O}_{j}^{\dagger }{{\mathbf{O}}_{j}} \right)}\sqrt{\text{Tr}\left( \mathbf{O}_{k}^{\dagger }{{\mathbf{O}}_{k}} \right)}}=\ldots ={{\omega }_{n}}\prod\limits_{m=1}^{N}{\frac{\text{Tr}\left( \mathbf{S}_{j,m}^{\dagger }{{\mathbf{S}}_{n,m}}{{\mathbf{S}}_{k,m}} \right)}{\sqrt{\text{Tr}\left( \mathbf{S}_{j,m}^{\dagger }{{\mathbf{S}}_{j,m}} \right)}\sqrt{\text{Tr}\left( \mathbf{S}_{k,m}^{\dagger }{{\mathbf{S}}_{k,m}} \right)}}} \end{matrix}\)
|
| Page 362, Eq 9.16 |
\[\left[ math \right]\] |
\[ math \]
|
