We discuss the issues with tentative generalisations of the process matrix formalism from finite-dimensional mechanical systems all the way to quantum field theory. We present a detailed overview of possible open problems that arise when one attempts to move from particle ontology into the realm of field ontology, i.e., when one transitions from mechanics to field theory framework. These issues need to be addressed, and problems solved, if one aims to expand the scope of applicability of the process matrix formalism, and therefore its usefulness. This is far from a trivial and straightforward endeavour, but rather a task for a whole future research programme.
Downfolding of many-body Hamiltonians using active-space models: extension of the sub-system embedding sub-algebras approach to unitary coupled cluster formalisms
Motivated by cosmological Hartle-Hawking and microcanonical density matrix prescriptions for the quantum state of the Universe we develop Schwinger-Keldysh in-in formalism for generic nonequilibrium dynamical systems with the initial density matrix. We build the generating functional of in-in Green's functions and expectation values for a generic density matrix of the Gaussian type and show that the requirement of particle interpretation selects a distinguished set of positive/negative frequency basis functions of the wave operator of the theory, which is determined by the density matrix param…
We present an extension of Nelson's stochastic quantum mechanics to finite temperature. Utilizing the formulation of Thermo Field Dynamics (TFD), we can show that Ito's stochastic equations for tilde and non-tilde particle positions reproduce the TFD-type Schrödinger equation which is equivalent to the Liouville-von Neumann equation. In our formalism, the drift terms in the Ito's stochastic equation have the temperature dependence and the thermal fluctuation is induced through the correlation of the non-tilde and tilde particles. We show that our formalism satisfy the position-momentum uncerta…
An efficient Multiple Scattering method based on partitioning of scattering matrix by angular momentum and approximations of matrix elements
我们提出了一个数值上有效和精确的多重散射形式，它是一个推广的多重散射方法与截断基集[X。-G. Zhang和W. H. Butler，Phys.Rev.B46，7433（1992）]。与后一种方法相比，我们保留了高角动量的相移，但对散射矩阵的元素进行了近似，即用单位矩阵减去转移算子矩阵和结构常数矩阵的乘积。详细的行为，我们的形式主义为不同类型的计算，其中不完全信息的格林函数是必要的，进行了讨论。我们应用我们的方法研究了面心立方Cu和Si的态密度以及石墨烯的C K边X射线吸收谱，以检验我们的方法的效率和准确性。我们发现，与张的方法相比，我们的方法的精度大大提高。
