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arXiv 1802.00524physics.plasm-ph
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用实时晶格标量QED模拟相对论量子等离子体

Simulations of relativistic-quantum plasmas using real-time lattice scalar QED

Yuan Shi, Jianyuan Xiao, Hong Qin, Nathaniel J. Fisch

摘要:

实时晶格量子电动力学(QED)提供了一个独特的工具,模拟等离子体在强场制度,集体等离子体尺度没有很好地从相对论量子尺度分离。作为一个玩具模型,我们研究标量QED,它描述了带电玻色子和电磁场之间的自洽相互作用。为了在计算机上求解这个模型,我们首先将标量QED作用量离散到格点上,以尊重外部微积分和U(1)-规范对称性的几何结构的方式。在经典统计体系中,格点标量QED可以通过在时间上推进一个统计等价的初始条件的系综来求解,使用通过使离散作用量极值化而获得的经典场方程。为了证明我们的数值方案的能力,我们将其应用到两个例子的问题。第一个例子是线性波的传播,我们使用数值谱恢复解析波色散关系。第二个例子是一个强激光与一维等离子体板相互作用,在那里我们演示了自然过渡从尾场加速对生产时,波的振幅超过Schwinger阈值。我们的实时格子方案是完全明确的,并尊重当地的守恒律,使其可靠的长期动态。该算法很容易使用区域分解并行化,并且在未来可以使用量子并行来计算系综。

英文摘要:

Real-time lattice quantum electrodynamics (QED) provides a unique tool for simulating plasmas in the strong-field regime, where collective plasma scales are not well-separated from relativistic-quantum scales. As a toy model, we study scalar QED, which describes self-consistent interactions between charged bosons and electromagnetic fields. To solve this model on a computer, we first discretize the scalar-QED action on a lattice, in a way that respects geometric structures of exterior calculus and U(1)-gauge symmetry. The lattice scalar QED can then be solved, in the classical-statistics regime, by advancing an ensemble of statistically equivalent initial conditions in time, using classical field equations obtained by extremizing the discrete action. To demonstrate the capability of our numerical scheme, we apply it to two example problems. The first example is the propagation of linear waves, where we recover analytic wave dispersion relations using numerical spectrum. The second example is an intense laser interacting with a 1D plasma slab, where we demonstrate natural transition from wakefield acceleration to pair production when the wave amplitude exceeds the Schwinger threshold. Our real-time lattice scheme is fully explicit and respects local conservation laws, making it reliable for long-time dynamics. The algorithm is readily parallelized using domain decomposition, and the ensemble may be computed using quantum parallelism in the future.

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