Tensor Networks Algorithms to Describe Strong Correlations in Heterogeneous, Non-ideal Plasmas

Inertial fusion energy plasmas involve highly heterogeneous and nonequilibrium plasmas. Standard simulation techniques for obtaining transport and equation of state properties, such as the hypernetted-chain approximation, typically assume slowly varying conditions far from boundaries; such bulk homogeneous calculations can be a poor approximation for highly transient high energy density plasmas. Incorporating complex boundary conditions in a highly heterogeneous environment can be achieved using the Yvon-Born-Green hierarchy with Salpeter closure. In the fully heterogeneous limit, even the pair correlation function, g(r), becomes a six dimensional function, g(r,r'), which is further coupled to even higher order correlation functions, g⁽ⁿ⁾(r₁, ..., r_n) generating the hierarchy, and making obtaining these correlations intractable with standard techniques. This high dimensionality make these equations perfect candidates for tensor network techniques, which decompose high-dimensional objects into a series of tensor products of lower-dimensional objects.