Related papers: An effective solution to convex $1$-body $N$-repre…
We employ projective Fra\"iss\'e theory to define the "generic combinatorial $n$-simplex" as the pro-finite, simplicial complex that is canonically associated with a family of simply defined selection maps between finite triangulations of…
We prove a new kind of quantum de Finetti theorem for representations of the unitary group U(d). Consider a pure state that lies in the irreducible representation U_{mu+nu} for Young diagrams mu and nu. U_{mu+nu} is contained in the tensor…
A previous study of diatomic molecules revealed that variational second-order density matrix theory has serious problems in the dissociation limit when the N-representability is imposed at the level of the usual two-index (P, Q, G) or even…
In the Onsager model of one-component hard-particle systems, the entire phase behaviour is dictated by a function of relative orientation, which represents the amount of space excluded to one particle by another at this relative…
It is commonly claimed in the recent literature that certain solutions to wave equations of positive energy of Dirac-type with internal variables are characterized by a non-thermal spectrum. As part of that statement, it was said that the…
We investigate the thermodynamics at finite density of a generalized $(2 + 1)$-dimensional Gross-Neveu model of $N$ fermion species with various types of four-fermion interactions. The motivation for considering such a generalized schematic…
We use Arveson's notion of strongly peaking representation to generalize uniqueness theorems for free spectrahedra and matrix convex sets which admit minimal presentations. A fully compressed separable operator system necessarily generates…
The quantum de Finetti theorem asserts that the k-body density matrices of a N-body bosonic state approach a convex combination of Hartree states (pure tensor powers) when N is large and k fixed. In this note we review a construction due to…
We establish one-body reduced density-matrix functional theory for the canonical ensemble in a finite basis set at an elevated temperature. Including temperature guarantees differentiability of the universal functional by occupying all…
This work studies the problem of maximizing a higher degree real homogeneous multivariate polynomial over the unit sphere. This problem is equivalent to finding the leading eigenvalue of the associated symmetric tensor of higher order,…
A new distribution for systems of particles in equilibrium obeying exclusion of correlated states is presented following the Haldane's state counting. It relies upon an ansatz to deal with the multiple exclusion that takes place when the…
One-electron reduced density matrices (1RDMs) from equation-of-motion (EOM) coupled-cluster with single and double excitations (CCSD) calculations are analyzed to assess their N-representability ({\em i.e.}, whether they are derivable from…
We use the Thomas-Fermi method to examine the thermodynamics of particles obeying Haldane exclusion statistics. Specifically, we study Calogero-Sutherland particles placed in a given external potential in one dimension. For the case of a…
Starting with the homogeneous Bethe-Salpeter equation for two fermions, we perform a 3D reduction using a series expansion around an unspecified positive-energy instantaneous approximation of the kernel. A second series expansion is made,…
We investigate two simple prescriptions to account for the Pauli principle in a three-body cluster model employing a new method based on an adiabatic hyperspherical expansion to solve the Faddeev equations in coordinate space. The resulting…
Inspired by a question of Lov\'asz, we introduce a hierarchy of nested semidefinite relaxations of the convex hull of real solutions to an arbitrary polynomial ideal, called theta bodies of the ideal. For the stable set problem in a graph,…
We generalize Bohr's complementarity principle for wave and particle properties to arbitrary quantum systems. We begin by noting that a particle-like state is represented by a spatially-localized wave function and its narrow probability…
Finite-temperature, grand-canonical computations based on field theory are widely applied in areas including condensed matter physics, ultracold atomic gas systems, and lattice gauge theory. However, these calculations have computational…
We revisit the issue of interpreting the results of large volume cosmological simulations in the context of large scale general relativistic effects. We look for simple modifications to the nonlinear evolution of the gravitational potential…
This work discusses the main analogies and differences between the deterministic approach underlying most cosmological N-body simulations and the probabilistic interpretation of the problem that is often considered in mathematics and…