Related papers: Thermodynamic Limit of Crystal Defects with Finite…
We consider atomistic geometry relaxation in the context of linear tight binding models for point defects. A limiting model as Fermi-temperature is sent to zero is formulated, and an exponential rate of convergence for the nuclei…
We consider an isolated point defect embedded in a homogeneous crystalline solid. We show that, in the harmonic approximation, a periodic supercell approximation of the formation free energy as well as of the transition rate between two…
The semi-classical approach leading to the Thomas-Fermi (TF) model provides a simple universal thermodynamic description of the electronic cloud surrounding the nucleus in an atom. This model is known to be exact at the limit of…
We review thermodynamic limits and scaling limits of electronic structure models for condensed matter. We discuss several mathematical ways to implement these limits in three models of increasing chemical complexity and mathematical…
I present a theoretical model of a quantum statistical ensemble for which, unlike in conventional physics, the total number of particles is extremely small. The thermodynamical quantities are calculated by taking a small $N$ by virtue of…
The tight binding model is a minimalistic electronic structure model for predicting properties of materials and molecules. For insulators at zero Fermi-temperature we show that the potential energy surface of this model can be decomposed…
Precise thermometry is of wide importance in science and technology in general and in quantum systems in particular. Here, we investigate fundamental precision limits for thermometry on cold quantum systems, taking into account constraints…
A finite temperature model of strongly correlated nucleons with underlying isospin symmetries is developed. The model can be used to study the role of bound states and Feshbach resonances on the thermal properties of a spin 1/2, isospin 1/2…
We study a system of $N$ interacting fermions at positive temperature in a confining potential. In the regime where the intensity of the interaction scales as $1/N$ and with an effective semi-classical parameter $\hbar=N^{-1/d}$ where $d$…
We study systems containing electrons and nuclei. Based on the fact that the thermodynamic limit exists for systems with Dirichlet boundary conditions, we prove that the same limit is obtained if one imposes other boundary conditions such…
We introduce a quantum Monte Carlo method at finite temperature for interacting fermionic models in the canonical ensemble, where the conservation of the particle number is enforced. Although general thermodynamic arguments ensure the…
An analysis is made of the particle composition in the final state of $pp$ collisions at 7 TeV as a function of the charged particle multiplicity ($dN_{ch}/d\eta$). The thermal model is used to determine the chemical freeze-out temperature…
Warm dense matter is one of the most active frontiers in plasma physics due to its relevance for dense astrophysical objects as well as for novel laboratory experiments in which matter is being strongly compressed e.g. by high-power lasers.…
The present paper aims at developing a theory of computation of crystalline defects at finite temperature. In a one-dimensional setting we introduce Gibbs distributions corresponding to such defects and rigorously establish their asymptotic…
We briefly review the Thomas-Fermi statistical model of atoms in the classical non-relativistic formulation and in the generalised finite-nucleus relativistic formulation. We then discuss the classical generalisation of the model to finite…
While the ability to measure low temperatures accurately in quantum systems is important in a wide range of experiments, the possibilities and the fundamental limits of quantum thermometry are not yet fully understood theoretically. Here we…
The various thermodynamic functions dependence on degree of energy band occupation and temperature was studied. The one-band tight binding approximation for the electron energy spectrum was used. The Fermi energy, density of states,…
We investigate QCD in the canonical ensemble with respect to the quark number. We reveal that the canonical description in which the quark number is fixed would be reduced to the grand canonical description under the thermodynamic limit.…
In a previous paper, we have developed a general theory of thermodynamic limits. We apply it here to three different Coulomb quantum systems, for which we prove the convergence of the free energy per unit volume. The first system is the…
The pair correlations in mesoscopic systems such as $nm$-size superconducting clusters and nuclei are studied at finite temperature for the canonical ensemble of fermions in model spaces with a fixed particle number: i) a degenerate…