Collective neutrino oscillations with tensor networks using a time-dependent variational principle
Collective neutrino oscillations with tensor networks using a time-dependent variational principle
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DOI：
10.1103/physrevd.105.123025
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发表时间：
2022-02
影响因子：
5
通讯作者：
Michael J. Cervia;P. Siwach;A. Patwardhan;A. Balantekin;S. Coppersmith;C. Johnson
中科院分区：
文献类型：
--
作者：
Michael J. Cervia;P. Siwach;A. Patwardhan;A. Balantekin;S. Coppersmith;C. Johnson
如果一个味振荡中微子系统的密度足够高，以至于中微子-中微子相干前向散射不可忽略，那么这个系统就变成了一个含时多体问题。一个重要的和开放的问题是味道的演变是充分描述的平均场的方法，或者可以强烈影响的相关性所产生的两体相互作用的中微子哈密顿量，测量的非平凡的量子纠缠。多体量子系统的时间演化的数值计算是具有挑战性的，因为希尔伯特空间的大小与系统中粒子的数量N成指数关系。因此，重要的是研究近似的，但超出平均场的数值处理在较大的N值。在这里，我们调查的张量网络方法的有效性，以计算在更大的N值的相互作用中微子的时间演化比传统的方法是可能的。特别是，我们介绍了使用时间相关的变分原理方法来解决远程（在动量空间）的中微子哈密顿相互作用时，包括许多不同的真空振荡频率。我们还定义了新的误差测量的基础上瞬时保守的电荷算符已知的这个哈密顿量，以确定大N张量网络计算的有效性。
If a system of flavor-oscillating neutrinos is at high enough densities that neutrino-neutrino coherent forward scatterings are non-negligible, the system becomes a time-dependent many-body problem. An important and open question is whether the flavor evolution is sufficiently described by a mean-field approach or can be strongly affected by correlations arising from two-body interactions in the neutrino Hamiltonian, as measured by nontrivial quantum entanglement. Numerical computations of the time evolution of many-body quantum systems are challenging because the size of the Hilbert space scales exponentially with the number of particles N in the system. Thus, it is important to investigate approximate but beyond-mean-field numerical treatments at larger values of N. Here we investigate the efficacy of tensor network methods to calculate the time evolution of interacting neutrinos at larger values of N than are possible with conventional methods. In particular, we introduce the use of time-dependent variational principle methods to address the long-range (in momentum space) interactions of the neutrino Hamiltonian when including many distinct vacuum oscillation frequencies. We also define new error measures based upon the instantaneously conserved charge operators known for this Hamiltonian to determine validity of large-N tensor network calculations.