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We investigate the many-body level density of gas of non-interacting fermions. We determine its behavior as a function of the temperature and the number of particles. As the temperature increases, and beyond the usual Sommerfeld expansion…

A variational formulation for the calculation of interacting fermion systems based on the density-matrix functional theory is presented. Our formalism provides for a natural integration of explicit many-particle effects into standard…

We present a new quantum field-theoretic definition of fully unintegrated dihadron fragmentation functions (DiFFs) as well as a generalized version for $n$-hadron fragmentation functions. We demonstrate that this definition allows certain…

We propose an improved effective-medium theory to obtain the concentration dependence of the viscosity of particle suspensions at arbitrary volume fractions. Our methodology can be applied, in principle, to any particle shape as long as the…

The problem of asymptotic density of quantum states of fundamental extended objects is revised in detail. We argue that in the near-extremal regime the fundamental $p$-brane approach can yield a microscopic interpretation of the black hole…

We introduce an alternative way to understand the decomposition of a quantum system into interacting parts and show that it is natural in several physical models. This enables us to define a reduced density operator for a working system…

In pursuit of a colloidal analogue to quantum density functional theory (DFT) predictions of atomic crystal structures, we report a new, classical DFT that predicts the relative thermodynamic stability of colloidal crystals of hard, convex…

Motivated by the recent experimental developments on ultracold molecules and atoms, we propose a simplest theoretical model to address the disassociation, reflection and transmission probability of a 1-dimensional cold molecule via quantum…

Real-time perturbation theory is formulated for complex scalar fields away from thermal equilibrium in such a way that dissipative effects arising from the absorptive parts of loop diagrams are approximately resummed into the unperturbed…

The derivative discontinuity is a key concept in electronic structure theory in general and density functional theory in particular. The electronic energy of a quantum system exhibits derivative discontinuities with respect to different…

Numerical algorithms for the integration of stochastic differential equations in the presence of white noise are introduced and compared. Algorithms for the integration of stochastic correlated forces are also briefly reviewed. Finally, a…

Bipartite entanglement entropy is one of the most useful characterizations of universal properties in a many-body quantum system. Far from equilibrium, there exist two highly effective theories describing its dynamics -- the quasiparticle…

Density functional theory (DFT) embedding provides a formally exact framework for interfacing correlated wave-function theory (WFT) methods with lower-level descriptions of electronic structure. Here, we report techniques to improve the…

The quantum optical response of high density ultracold atomic systems is critical to a wide range of fundamentally and technically important physical processes. These include quantum image storage, optically based quantum repeaters and…

This work explores the use of joint density-functional theory, a new form of density-functional theory for the ab initio description of electronic systems in thermodynamic equilibrium with a liquid environment, to describe electrochemical…

In this paper, we study numerical approximations of the ground states in finite temperature density functional theory. We formulate the problem with respect to the density matrices and justify the convergence of the finite dimensional…

Length density is a recently introduced factorization invariant, assigned to each element $n$ of a cancellative commutative atomic semigroup $S$, that measures how far the set of factorization lengths of $n$ is from being a full interval.…

We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and…

Density Functional Theory (DFT) is one of the most widely used methods for "ab initio" calculations of the structure of atoms, molecules, crystals, surfaces, and their interactions. Unfortunately, the customary introduction to DFT is often…

Using the newly introduced theory of finite-temperature reduced density matrix functional theory, we apply the first-order approximation to the homogeneous electron gas. We consider both collinear spin states as well as symmetry broken…