Related papers: Finite Temperature Scaling in Density Functional T…
Finite temperature density functional theory requires representations for the internal energy, entropy, and free energy as functionals of the local density field. A central formal difficulty for an orbital-free representation is…
Finite temperature density functional theory provides, in principle, an exact description of the thermodynamical equilibrium of many-electron systems. In practical applications, however, the functionals must be approximated. Efficient and…
Density scaling has a rich history in density functional theory, providing exact conditions for use in the construction of ever more accurate approximations to the unknown exchange-correlation functional. We define a conjugate potential…
The formalism developed in the first paper of the series [arXiv:0901.1060] is applied to two thermodynamic systems: (i) of three global observables (the energy, the total electron number and the spin number), (ii) of one global observable…
Understanding the thermodynamic properties of many-body quantum systems and their emergence from microscopic laws is a topic of great significance due to its profound fundamental implications and extensive practical applications. Recent…
The self consistent version of the density functional theory is presented, which allows to calculate the ground state and dynamic properties of finite multi-electron systems. An exact functional equation for the effective interaction, from…
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…
A numerical study of finite temperature features of thermodynamical observables is performed for the lattice 2d Ising model. Our results support the conjecture that the Finite Size Scaling analysis employed in the study of integrable…
Density functional theory has made great success in solid state physics, quantum chemistry and in computational material sciences. In this work we show that density functional theory could shed light on phase transitions and entanglement at…
This chapter introduces thermal density functional theory, starting from the ground-state theory and assuming a background in quantum mechanics and statistical mechanics. We review the foundations of density functional theory (DFT) by…
A finite size scaling theory, originally developed only for transitions to absorbing states [Phys. Rev. E {\bf 92}, 062126 (2015)], is extended to distinct sorts of discontinuous nonequilibrium phase transitions. Expressions for quantities…
The self consistent version of the density functional theory (DFT) is presented, which allows to calculate the ground state and dynamic properties of finite multi-electron systems such as atoms, molecules and clusters. The exact functional…
Coordinate scaling of each spin density separately is considered in spin density functional theory. A virial theorem relates the spin-scaled correlation energy to the spin-scaled correlation potentials. An adiabatic connection formula…
The density-functional (DF) theory provides a simple method for calculating the properties of an interacting system under an external potential by associating it with a corresponding non-interacting system. Here, we find some relations in…
The adiabatic connection formula of ground-state density functional theory relates the correlation energy to a coupling-constant integral over a purely potential contribution, and is widely used to understand and improve approximations. The…
We extend to finite temperature a Green's function method that was previously proposed to evaluate ground-state properties of mesoscopic clouds of non-interacting fermions moving under harmonic confinement in one dimension. By calculations…
There has been a trend in the past decade to describe the large-scale structures in the Universe as a (multi)fractal set. However, one of the main objections raised by the opponents of this approach deals with the transition to homogeneity.…
A detailed investigation of the scaling properties of the fully finite ${\cal O}(n)$ systems with long-range interaction, decaying algebraically with the interparticle distance $r$ like $r^{-d-\sigma}$, below their upper critical dimension…
Based on our derivation of finite temperature reduced density matrix functional theory and the discussion of the performance of its first-order functional this work presents several different correlation-energy functionals and applies them…
The density-density correlations of the non-interacting finite temperature electron gas are discussed in detail. Starting from the ideal linear density response function and utilizing general relations from linear response theory, known and…