相关论文: Susceptibility Formulation of Density Matrix Pertu…

An expansion method for perturbation of the zero temperature grand canonical density matrix is introduced. The method achieves quadratically convergent recursions that yield the response of the zero temperature density matrix upon variation…

These notes introduce the theory of susceptibilities as developed in [arXiv:2504.18274, arXiv:2601.12703] for interpreting neural networks. The susceptibility of an observable $\phi$ to a data perturbation is defined as a derivative of a…

Density matrix perturbation theory [Phys. Rev. Lett. Vol. 92, 193001 (2004)] provides an efficient framework for the linear scaling computation of response properties [Phys. Rev. Lett. Vol. 92, 193002 (2004)]. In this article, we generalize…

The efficient computation of observables beyond the total energy is a key challenge and opportunity for fault-tolerant quantum computing approaches in quantum chemistry. Here we consider the symmetry-adapted perturbation theory (SAPT)…

We present two analytical formulae for estimating the sensitivity -- namely, the gradient or Jacobian -- at given realizations of an arbitrary-dimensional random vector with respect to its distributional parameters. The first formula…

Time-independent quantum response calculations are performed using Tensor cores. This is achieved by mapping density matrix perturbation theory onto the computational structure of a deep neural network. The main computational cost of each…

This paper studies the problem of recursively estimating the weighted adjacency matrix of a network out of a temporal sequence of binary-valued observations. The observation sequence is generated from nonlinear networked dynamics in which…

We demonstrate the power of a first principle-based and practicable method that allows for the perturbative computation of reduced density matrix elements of an open quantum system without making use of any master equations. The approach is…

Calculating perturbation response properties of materials from first principles provides a vital link between theory and experiment, but is bottlenecked by the high computational cost. Here a general framework is proposed to perform density…

Precision matrix estimation is a fundamental topic in multivariate statistics and modern machine learning. This paper proposes an adversarially perturbed precision matrix estimation framework, motivated by recent developments in adversarial…

We develop convergent variational perturbation theory for quantum statistical density matrices. The theory is applicable to polynomial as well as nonpolynomial interactions. Illustrating the power of the theory, we calculate the…

Density-functional perturbation theory (DFPT) is nowadays the method of choice for the accurate computation of linear and non-linear response properties of materials from first principles. A notable advantage of DFPT over alternative…

We consider the problem of estimating the sparse time-varying parameter vectors of a point process model in an online fashion, where the observations and inputs respectively consist of binary and continuous time series. We construct a novel…

The linear response is investigated in a long-range Hamiltonian system from the view point of dynamics, which is described by the Vlasov equation in the limit of large population. Due to existence of the Casimir invariants of the Vlasov…

Density matrix perturbation theory [Niklasson and Challacombe, Phys. Rev. Lett. 92, 193001 (2004)] is generalized to canonical (NVT) free energy ensembles in tight-binding, Hartree-Fock or Kohn-Sham density functional theory. The canonical…

A linear scaling method for calculation of the static {\em ab inito} response within self-consistent field theory is developed and applied to calculation of the static electric polarizability. The method is based on density matrix…

Most of the fundamental, emergent, and phenomenological parameters of particle and nuclear physics are determined through parametric template fits. Simulations are used to populate histograms which are then matched to data. This approach is…

The self-consistent evaluation of Hubbard parameters using linear-response theory is crucial for quantitatively predictive calculations based on Hubbard-corrected density-functional theory. Here, we extend a recently-introduced approach…

Perturbing a deterministic $n$-dimensional matrix with small Gaussian noise is a cornerstone of smoothed analysis of algorithms [Spielman and Teng, JACM 2004], as it reduces the condition number of the input to $O(n)$, and with it the…

We present a transparent and computationally efficient approach for the first-principles calculation of Hubbard parameters from linear-response theory. This approach is based on density-functional perturbation theory and the use of…