Related papers: Fermionic Phonons: Exact Analytic Results and Quan…
We consider a two-dimensional layer of dipolar particles in the regime of strong dipole moments. Here we can describe the system using classical methods and determine the crystal structure that minimizes the total energy. The dipoles are…
The ongoing discussion whether thermodynamic properties can be extracted from a (possibly approximate) quantum mechanical time evolution using time averages is fed with an instructive example. It is shown for the harmonic oscillator how the…
The dynamics of quasicrystals is characterized by the existence of phason excitations in addition to the usual phonon modes. In order to investigate their interplay on an elementary level we resort to various one-dimensional model systems.…
We establish an analytical criterion for dynamical thermalization within harmonic systems, applicable to both classical and quantum models. Specifically, we prove that thermalization of various observables, such as particle energies in…
One-particle properties of non-interacting Fermions in a one-dimensional harmonic trap and at zero temperature are studied. Exact expressions and asymptotic results for large Fermion number N are given for the particle density distribution…
The most important recent results in the theory of phase transitions and quantum effects in quantum anharmonic crystals are presented and discussed. In particular, necessary and sufficient conditions for a phase transition to occur at some…
In this work, the energy eigenvalues are calculated for the quadratic ($\frac{g^2 x^2}{2}$), pure quartic ($\lambda x^4 $), and quartic anharmonic oscillators ($\frac{g^2 x^2}{2} + \lambda x^4 $) by applying variational method. For this,…
Standard procedures for local crystal-structure optimisation involve numerous energy and force calculations. It is common to calculate an energy-volume curve, fitting an equation of state around the equilibrium cell volume. This is a…
Free energy, internal energy, and specific heat for each of the three phonon spectrum branches of a magnetized Coulomb crystal with body-centered cubic lattice are calculated by numerical integration over the Brillouin zone in the range of…
Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…
I develop simple thermodynamic relations for a collection of noninteracting classical particles confined in a harmonic trap. The volume of such a trap is not a good thermodynamic variable, so conventional expressions of the first law of…
In the present communication we consider the one-dimensional (1D) isotopically disordered lattice with the harmonic potential. Our analytical method is adequate for any 1D lattice where potential energy can be presented as the quadratic…
The free energy and other thermodynamic properties of hexagonal-close-packed iron are calculated by direct {\em ab initio} methods over a wide range of pressures and temperatures relevant to the Earth's core. The {\em ab initio}…
The kinetic energy is estimated for the ground-state of liquid $^3$He at equilibrium density. The obtained value for this quantity, $10.16\pm0.05$ K/atom at density $0.0163~\mbox{\AA}$, is in agreement with most of the experimental data…
A statistical approach to the description of the thermodynamic properties of the Fermi particle system occupying a half-space over a plane of finite size in a uniform external field is proposed. The number of particles per unit area is…
The non-extensive self-consistent theory describing the thermodynamics of hadronic systems at high temperatures is used to derive some thermodynamical quantities, as pressure, entropy, speed of sound and trace-anomaly. The calculations are…
A normal ordered exponential parametrization is used to obtain equations for thermal one-and two-particle reduced density matrices, as well as free energies, partition functions and entropy for both Fermionic (electronic) and Bosonic…
The multifractal scaling exponents are calculated for the critical wave function of a two-dimensional Dirac fermion in the presence of a random magnetic field. It is shown that the problem of calculating the multifractal spectrum maps into…
For the reliable analysis and modelling of astrophysical, laser-produced and fusion plasmas, atomic data are required for a number of parameters, including energy levels, radiative rates and electron impact excitation rates. Such data are…
The thermodynamic properties of bosons moving in a harmonic trap in an arbitrary number of dimensions are investigated in the grand canonical, canonical and microcanonical ensembles by applying combinatorial techniques developed earlier in…