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Quadratica package

Alexander E. Teretenkov
Organization: Dept. of Physics, Moscow State University
Revision date


Quantum generators which are quadratic in bosonic or fermionic creation and annihilation operators play very important role in quantum physics and quantum field theory because they are exactly solvable. This is true both for unitary evolution with quadratic Hamiltonians and for non-unitary evolution with quadratic Gorini-Kossakowski-Sudarshan-Lindblad generator. The Cauchy problems with quadratic generators have explicit solutions in case of Gaussian initial conditions (including coherent and squeezed states). Thus, it useful to develop a Wolfram Mathematica package to deal with quadratic generators and Gaussian states. We have implement it in our package called "Quadratica". Since we are still improving our package we uploaded it at GitHub:


This package is based on our articles: [1] A. E. Teretenkov, "Quadratic Fermionic Dynamics with Dissipation", Math. Notes, 102:6 (2017), 846-853 [2] A. E. Teretenkov, "Quadratic Dissipative Evolution of Gaussian States with Drift", Math. Notes, 101:2 (2017), 341-351 [3] A. E. Teretenkov, "Quadratic Dissipative Evolution of Gaussian States", Math. Notes, 100:4 (2016), 642-646 [4] A. M. Chebotarev, A. E. Teretenkov, "Singular value decomposition for the Takagi factorization of symmetric matrices", Applied Mathematics and Computation (New York), 234 (2014), 380-384

*Science > Physics > Quantum Physics