Abstract
We analytically study quantum dissipative dynamics described by the Caldirola-Kanai model with inter-particle interactions. We have found that the dissipative quantum dynamics of the Caldirola-Kanai model can be exactly mapped to a dissipationless quantum dynamics under a negative external harmonic potential, even when the particles are strongly interacting. In particular, we show that the mapping is valid for the unitary Fermi gas, which is relevant for cold atoms and nuclear matters.
Highlights
Dissipation plays essential roles in the non-equilibrium dynamics of quantum matters
We have studied a quantum dissipative dynamics of the Caldirola-Kanai model, and shown that it can be rigorously mapped to a dissipationless quantum dynamics under an inverted-harmonic potential
We have found that the dissipative dynamics of the unitary Fermi gas can be exactly mapped to a dissipationless dynamics of the unitary Fermi gas under an inverted harmonic potential
Summary
Dissipation plays essential roles in the non-equilibrium dynamics of quantum matters. While the Caldirola-Kanai model has usually been applied to a singleparticle motion regarding U as an external potential as in the original setting [12, 13], we can consider the dynamics of interacting quantum particles under the dissipation regarding U as inter-particle interactions. We analytically study the quantum dissipative motion of interacting particles with the Caldirola-Kanai model. We show that this dissipative system can be exactly mapped to a dissipationless system with an inverted harmonic potential. We see that the mapping between the dissipative and dissipationless dynamics can be understood as a transformation of the coordinate from one system to the other We find that the mapping can formally remain true even in the presence of inter-particle interactions
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