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arXiv 1902.06491nucl-th
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两个超流系统(II)之间对转移的微观描述:含时Hartree-Fock Bogolyubov轨道的量子混合

Microscopic description of pair transfer between two superfluid systems (II): a quantum mixing of Time-Dependent Hartree-Fock Bogolyubov trajectories

D. Regnier, D. Lacroix

摘要:

虽然超流性可以用一个明确打破粒子数对称性的状态来准确地把握,但对重离子反应过程中粒子转移等现象的精确描述只能通过考虑具有良好粒子数的系统来实现。研究了通过混合多个含时Hartree-Fock Bogolyubov(TDHFB)轨迹来恢复多体动力学问题中粒子数的可能性。在我们的方法中,每个轨道是独立的,从变分原理推导出轨道之间的量子混合。相关理论可以被看作是多配置TDHFB(MC-TDHFB)理论的简化版本。它的准确性,以解决问题的对称性恢复动力学问题的情况下,两个超流系统,交换粒子在短时间内。在参考文献[Phys. Rev. C 97,034627(2018)]中,使用一个示意性模型,其中最初由配对哈密顿算子描述的两个系统在短接触时间内耦合,证明了TDHFB轨迹的统计混合只能定性地描述转移过程,并且必须进行完全量子处理。我们在这里表明,目前的MC-TDHFB方法给出了一个很好的协议与精确解时,两种超流体是相同的(对称的情况下)或不同的(不对称的情况下)和从弱到强相互作用强度。最后,我们讨论了这种方法的优点和瓶颈,鉴于其应用于现实系统。

英文摘要:

While superfluidity is accurately grasped with a state that explicitly breaks the particle number symmetry, a precise description of phenomena like the particle transfer during heavy-ion reactions can only be achieved by considering systems with good particle numbers. We investigate the possibility to restore particle number in many-body dynamical problems by mixing-up several Time-Dependent Hartree-Fock Bogolyubov (TDHFB) trajectories. In our approach, each trajectory is independent from the others and the quantum mixing between trajectories is deduced from a variational principle. The associated theory can be seen as a simplified version of the Multi-Configuration TDHFB (MC-TDHFB) theory. Its accuracy to tackle the problem of symmetry restoration in dynamical problems is illustrated for the case of two superfluid systems that exchange particles during a short time. In Ref. [Phys. Rev. C 97, 034627 (2018)], using a schematic model where two systems initially described by a pairing Hamiltonians are coupled during a short contact time, it was demonstrated that statistical mixing of TDHFB trajectories can only qualitatively describe the transfer process and that a fully quantum treatment is mandatory. We show here that the present MC-TDHFB approach gives an excellent agreement with the exact solution when the two superfluids are the same (symmetric case) or different (asymmetric case) and from weak to strong interaction strength. Finally, we discuss the benefits and bottleneck of this method in view of its application to realistic systems.

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