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We present a theoretical analysis of the dynamics of a one-dimensionalspin-1/2 fermionic gas subject to weak two-body losses. Our approach highlightsthe crucial role played by spin conservation in the determination of the fulltime evolution. We focus in particular on the dynamics of a gas that isinitially prepared in a Dicke state with fully-symmetric spin wavefunction, ina band insulator, or in a Mott insulator. In the latter case, we investigatethe emergence of a steady symmetry-resolved purification of the gas. Ourresults could help the modelisation and understanding of recent experimentswith alkaline-earth(-like) gases like ytterbium or fermionic molecules.

One-dimensional spin-1/2 fermionic gases with two-body losses: weak dissipation and spin conservation