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The evolution of pionium, the $pi^+ pi^-$ hydrogen-like atom, while passing through matter is solved within the density matrix formalism in the first Born approximation. We compare the influence on the pionium break-up probability between the standard probabilistic calculations and the more precise picture of the density matrix formalism accounting for interference effects. We focus our general result in the particular conditions of the DIRAC experiment at CERN.
Chiral Perturbation Theory predicts the lifetime of pionium, a hydrogen-like $pi^+ pi^-$ atom, to better than 3% precision. The goal of the DIRAC experiment at CERN is to obtain and check this value experimentally by measuring the break-up probabilit
In this work, we simulate the electron dynamics in molecular systems with the Time-Dependent Density Matrix Renormalization Group (TD-DMRG) algorithm. We leverage the generality of the so-called tangent-space TD-DMRG formulation and design a computat
We report the progress in the measurement of the pionium lifetime by the DIRAC Collaboration at CERN (PS212). Based on data collected in 2001-2003 on Ni targets we have achieved the precision of 11% in the measurement of the pionium lifetime, which c
We present a method to apply the well-known matrix product state (MPS) formalism to partially separable states in solid state systems. The computational effort of our method is equal to the effort of the standard density matrix renormalisation group
The density matrix formalism and the equation of motion approach are two semi-analytical methods that can be used to compute the non-equilibrium dynamics of correlated systems. While for a bilinear Hamiltonian both formalisms yield the exact result,