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Yes tensor network algorithms have been developed to describe braiding of anyons, Abelian and non-Abelian. The networks are constructed from tensors that explicitly conserve topological charge and the braiding, fusion, and recoupling data are taken as input to the algorithms. This reference: http://arxiv.org/pdf/1311.0967.pdf describes how to use the Time ...

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Correlation energy is generally defined as the difference between the true total energy and the Hartree-Fock limit. There are mainly two reasons for HF not being exact. Firstly, it approximates the many-body wavefunction as a single Slater determinant, while the exact result must be taken as a combination of many Slater determinants. This leads to a ...

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It's thirty-five (!) years since I last did an HF/SCF calculation, but in those days our code worked by minimising the energy: $$E_{HF} = \langle \Psi_{HF} | H | \Psi_{HF} \rangle$$ where $\Psi_{HF}$ is the approximate wavefunction expressed as a sum of some convenient basis set of functions. Once you'd done the HF/SCF calculation you'd do a CI ...

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Bulirsch–Stoer like algorithms may work better than the Runge-Kutta like methods here. You can consider any arbitrary scheme for approximating the function at the next time step, but instead of modeling the deviation as a function of the time step $h$ by power series, you consider the asymptotic behavior valid for large $h$. A rational function approximation ...

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There are two ways I can think of that can improve run times (outside of using a compiled language like C/C++ or Fortran). Use a hybrid RK2 + RK4/5 integration method. Here, you use an RK2 method first and test the truncation error. If it's sufficiently small, accept the value & move on. If the error is too large, move to an adaptive 4-5 RK method (or ...

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Don't do it that way. You have what is called a "Change Point". Run it up until the time when the change should occur. Then stop the solver. Perform the instantaneous state change. Then restart the solver. So much silliness happens when people try to run ODE solvers over discontinuities.

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RK 4th order is a good numerical approach - but it is only accurate up to fourth order terms in the Taylor expansion of your series. As long as the fifth (and higher) order derivatives of the function are small, you are fine. But when you introduce a step function, or even a piecewise linear approximation, that assumption is violated. I would recommend, as ...

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Use the fact that force is equal to the rate of change of momentum. The rain is accelerated to the same velocity as the train, so if you know the mass of rain per second you can calculate the momentum change per second. This is equal to the force required.

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If you plot the path of the moon with respect to the star you should get a cycloid pattern averaging around the path of the planet. That's what our moon does. The planet and the moon are doing a gyrating dance about their center of mass, with the moon doing the most motion (because it has the smallest mass), while the planet/moon duo orbit the star. I've ...

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A full introduction to the DMRG algorithm definitely does not fit here, and you can find many well-written introductory materials online. DMRG has been applied to simulate perturbed toric code model, which is the simplest example of string-net model, see http://arxiv.org/pdf/1205.4289.pdf. Generally speaking, DMRG for 2D spin models is indeed much more ...

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For start of conversation, there are infinite quantity of process (functions) of physics that are not computable. The match of a physical process and computability lies in the degree of precision for measurements. The scale of measure defines a basis for computable numbers. e.g. $$\alpha^{-1} \cong 137.035\,999\,173(35)$$ \pi \cong ...

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