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The efficient and accurate calculation of how ionic quantum and thermal fluctuations impact the free energy of a crystal, its atomic structure, and phonon spectrum is one of the main challenges of solid state physics, especially when strong…
We provide an accurate calculation of the energy spectrum of three atoms interacting through a contact force in a one-dimensional harmonic trap, considering both spinful fermions and spinless bosons. We use fermionic energies as a benchmark…
In a recent work we have proposed an original analytic expression for the partition function of the quartic oscillator. This partition function, which has a simple and compact form with {\it no adjustable parameters}, reproduces some key…
The properties of crystals consisting of several components can be widely tuned. Often solid solutions are produced, where substitutional or interstitional disorder determines the crystal thermodynamic and mechanical properties. The…
Obtaining the free energy of large molecules from quantum mechanical energy functions is a longstanding challenge. We describe a method that allows us to estimate, at the quantum mechanical level, the harmonic contributions to the…
The thermodynamical properties are calculated for a three-dimensional model of $N$ harmonically interacting spin-polarized fermions in a parabolic potential well. The obtained dependences of the chemical potential and of the internal energy…
Recent investigations show that the statistical mechanics of a finite number of particles in ideal harmonic systems predicts different results for the same physical properties, depending on the ensemble under consideration. Path integral…
We describe a method for the calculation of accurate energy eigenvalues and expectation values of observables of separable quantum-mechanical models. We discuss the application of the approach to one-dimensional anharmonic oscillators with…
We propose an approach to calculate the anharmonic part of the volumetric-strain and temperature dependent free energy of a crystal. The method strikes an effective balance between accuracy and computational efficiency, showing a $\times10$…
The phonon spectrum of the high-pressure simple cubic phase of calcium, in the harmonic approx- imation, shows imaginary branches that make it mechanically unstable. In this letter, the phonon spectrum is recalculated using…
First-principles quasi-harmonic calculations play a very important role in mineral physics because they can accurately predict the structure and thermodynamic properties of materials at pressure and temperature conditions that are still…
The eigenvalue statistics of quantum ideal gases with single particle energies $e_n=n^\alpha$ are studied. A recursion relation for the partition function allows to calculate the mean density of states from the asymptotic expansion for the…
Phonons, quantized vibrations of the atomic lattice, are fundamental to understanding thermal transport, structural stability, and phase behavior in crystalline solids. Despite advances in computational materials science, most predictions…
The approach is developed for the description of isolated Fermi-systems with finite number of particles, such as complex atoms, nuclei, atomic clusters etc. It is based on statistical properties of chaotic excited states which are formed by…
The refraction properties of phononic crystals are revealed by examining the anti-plane shear waves in doubly periodic elastic composites with unit cells containing rectangular and/or elliptical inclusions. The band-structure, group…
We present closed analytical expressions for the particle and kinetic energy spatial densities at finite temperatures for a system of noninteracting fermions (bosons) trapped in a d-dimensional harmonic oscillator potential. For d=2 and 3,…
Molecular crystals often exist in multiple competing polymorphs, showing significantly different physico-chemical properties. Computational crystal structure prediction is key to interpret and guide the search for the most stable or useful…
This article illustrates a completely algebraic method to obtain the energy levels of a massive spin-1 particle moving in a constant magnetic field. In the process to obtain the energy levels the wave function was written by harmonic…
Monte Carlo simulations are performed in classical phase space for a one-dimensional quantum harmonic crystal. Symmetrization effects for spinless bosons and fermions are quantified. The algorithm is tested for a range of parameters against…
An instant homogeneous thermal perturbation in the finite harmonic one-dimensional crystal is studied. Previously it was shown that for the same problem in the infinite crystal the kinetic temperature oscillates with decreasing amplitude…