Mean-field dynamics for mixture condensates via Fock space methods

Abstract

We consider a mean-field model to describe the dynamics of $N_1$ bosons of species one and $N_2$ bosons of species two in the limit as $N_1$ and $N_2$ go to infinity. We embed this model into Fock space and use it to describe the time evolution of coherent states which represent two-component condensates. Following this approach, we obtain a microscopic quantum description for the dynamics of such systems, determined by the Schrödinger equation. Associated to the solution to the Schrödinger equation, we have a reduced density operator for one particle in the first component of the condensate and one particle in the second component. In this paper, we estimate the difference between this operator and the projection onto the tensor product of two functions that are solutions of a system of equations of Hartree type. Our results show that this difference goes to zero as $N_1$ and $N_2$ go to infinity. Our hypotheses allow the Coulomb interaction.

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Cited by in corpus (3)

• Rate of convergence towards equations of Hartree type for mixture condensates with factorized initial data
• On the characterisation of fragmented Bose-Einstein condensation and its emergent effective evolution
• Uniform in Time Convergence to Bose-Einstein Condensation for a Weakly Interacting Bose Gas with an External Potential