Related papers: Generalized Pauli constraints in reduced density m…
Quantum state tomography aims to determine the state of a quantum system as represented by a density matrix. It is a fundamental task in modern scientific studies involving quantum systems. In this paper, we study estimation of…
We study the constraints on low-energy coefficients of the $\nu$SMEFT generalization of the Standard Model effective theory in the simple case of a $\text{U}(1)^\prime$ enlargement of the Standard Model gauge group. In particular, we…
In the constrained minimization method of Gidopoulos and Lathiotakis (J. Chem. Phys. 136, 224109), the Hartree exchange and correlation Kohn-Sham potential of a finite $N$-electron system is replaced by the electrostatic potential of an…
Model-reduction techniques aim to reduce the computational complexity of simulating dynamical systems by applying a (Petrov-)Galerkin projection process that enforces the dynamics to evolve in a low-dimensional subspace of the original…
The partial trace operation is usually considered in composite quantum systems, to reduce the state on a single subsystem. This operation has a key role in the decoherence effect and quantum measurements. However, partial trace operations…
Ensemble density functional theory (EDFT) is a promising alternative to time-dependent density functional theory for computing electronic excitation energies. Using coordinate scaling, we prove several fundamental exact conditions in EDFT…
We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…
We have explained and comprehensively illustrated in Part I that the generalized Pauli constraints suggest a natural extension of the concept of active spaces. In the present Part II, we provide rigorous derivations of the theorems involved…
We have found a (dense) basis for the N-representable, two-electron densities, in which all N-representable two-electron densities can be expanded, using positive coefficients. The inverse problem of finding a representative wavefunction,…
We present a substantial extension of our constraint-based approach for development of orbital-free (OF) kinetic-energy (KE) density functionals intended for the calculation of quantum-mechanical forces in multi-scale molecular dynamics…
The minimum error discrimination problem for ensembles of linearly independent pure states are known to have an interesting structure; for such a given ensemble the optimal POVM is given by the pretty good measurment of another ensemble…
State-of-the-art many-body wave function techniques rely on heuristics to achieve high accuracy at an attainable cost to solve the many-body Schr\"odinger equation. By far the most common property used to assess accuracy has been the total…
Reduced density matrix functional theory for the case of solids is presented and a new exchange correlation functional based on a fractional power of the density matrix is introduced. We show that compared to other functionals, this…
The recently established generalized Gell-Mann--Low theorem is applied in lowest perturbative order to bound-state calculations in a simple scalar field theory with cubic couplings. The approach via the generalized Gell-Mann--Low Theorem…
We consider an electronic bound state of the usual, non-relativistic, molecular Hamiltonian with Coulomb interactions, fixed nuclei, and N electrons (N>1). Near appropriate electronic collisions, we determine the regularity of the…
Physically valid and numerically efficient approximations for the exchange and correlation energy are critical for reduced density-matrix functional theory to become a widely used method in electronic structure calculations. Here we examine…
We show a general phenomenon of the constrained functional value for densities satisfying general convexity conditions, which generalizes the observation in Bobkov and Madiman (2011) that the entropy per coordinate in a log-concave random…
"What are the consequences ... that Fermi particles cannot get into the same state ... " R. P. Feynman wrote of the Pauli exclusion principle, "In fact, almost all the peculiarities of the material world hinge on this wonderful fact." In…
We consider an electron coupled to the quantized radiation field and subject to a slowly varying electrostatic potential. We establish that over sufficiently long times radiation effects are negligible and the dressed electron is governed…
Density functional theory is currently the most widely applied method in electronic structure theory. The Kohn-Sham method, based on a fictitious system of non-interacting particles, is the work horse of the theory. The particular form of…