particlematrix

The particlematrix is a term used in physics and computational modeling to describe a matrix representation of multi-particle systems, encoding either occupancy, correlations, or transition amplitudes among single-particle states. It is not a single established object but a family of related constructs.

In practice, a particlematrix may be defined as the matrix with elements P_{ab} representing the amplitude or probability that a particle initially in state a occupies state b, or more generally as a representation of two-point correlations between single-particle states. It overlaps with concepts such as the one-particle reduced density matrix (1-RDM) and the adjacency or coupling matrices in tight-binding models.

Construction approaches vary: from quantum many-body theory, where P_{ab} = ⟨Ψ| c_a† c_b |Ψ⟩, to lattice simulations where entries encode hopping amplitudes or interaction strengths; machine learning applications may use particle matrices as feature representations of particle configurations or as kernel matrices.

Applications include analysis of energy spectra, particle number fluctuations, coherence properties, and transport in quantum materials; it supports methods like diagonalization, spectral decomposition, and correlation studies.

Terminology and standardization: particlematrix is not a widely formalized term; users should define basis, normalization, and interpretation clearly to avoid ambiguity. See also density matrix, reduced density matrices, adjacency matrices, and tight-binding Hamiltonians.