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Remove indentation from align envs
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thangleiter committed May 14, 2024
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4 changes: 2 additions & 2 deletions doc/source/examples/calculating_quantum_processes.ipynb
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"The decay amplitudes $\\Gamma$ can be calculated from the generalized filter function and are thus amenable to the concatenation property of the control matrices. As the second order of the Magnus expansion involves a double time integral, such a simplification is not possible in the case of the frequency shifts $\\Delta$. However, we can define a filter function for them just the same:\n",
"\n",
"\\begin{align}\n",
" \\Gamma_{\\alpha\\beta,kl} &= \\int\\frac{\\mathrm{d}\\omega}{2\\pi}S_{\\alpha\\beta}(\\omega) F_{\\alpha\\beta,kl}^{(\\Gamma)}(\\omega) \\\\\n",
" \\Delta_{\\alpha\\beta,kl} &= \\int\\frac{\\mathrm{d}\\omega}{2\\pi}S_{\\alpha\\beta}(\\omega) F_{\\alpha\\beta,kl}^{(\\Delta)}(\\omega)\n",
"\\Gamma_{\\alpha\\beta,kl} &= \\int\\frac{\\mathrm{d}\\omega}{2\\pi}S_{\\alpha\\beta}(\\omega) F_{\\alpha\\beta,kl}^{(\\Gamma)}(\\omega) \\\\\n",
"\\Delta_{\\alpha\\beta,kl} &= \\int\\frac{\\mathrm{d}\\omega}{2\\pi}S_{\\alpha\\beta}(\\omega) F_{\\alpha\\beta,kl}^{(\\Delta)}(\\omega)\n",
"\\end{align}\n",
"\n",
"### Performance considerations\n",
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6 changes: 3 additions & 3 deletions doc/source/examples/getting_started.ipynb
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"The central object of this package is the `PulseSequence` class. It is used to represent the control operation implementing a certain Hamiltonian ${H}_c$ and the sensitivities of the noise afflicting the system. More concisely, the total Hamiltonian of the system is modelled as\n",
"\n",
"\\begin{align*}\n",
" {H} &= {H}_c + {H}_n \\\\\n",
" {H}_c &= \\sum_i a_i(t) A_i \\\\\n",
" {H}_n &= \\sum_\\alpha s_\\alpha(t) b_\\alpha(t) B_\\alpha \\\\\n",
"{H} &= {H}_c + {H}_n \\\\\n",
"{H}_c &= \\sum_i a_i(t) A_i \\\\\n",
"{H}_n &= \\sum_\\alpha s_\\alpha(t) b_\\alpha(t) B_\\alpha \\\\\n",
"\\end{align*}\n",
"\n",
"where $A_i$ and $B_\\alpha$ are the control and noise operators, respectively, $a_i(t)$ the control strength of $A_i$ at time $t$, $s_\\alpha(t)$ a deterministic time dependence of the noise operators to model, for instance, non-linear coupling to the noise sources, and $b_\\alpha(t)$ classically fluctuating noise variables. Since the noise is captured in a spectral density function that accounts for different realizations of the random noise, the $b_\\alpha(t)$ are not required at instantiation of a `PulseSequence` instance. Note that we always calculate in units where $\\hbar\\equiv 1$.\n",
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