Thermodynamical dimensional reduction in a UV & IR-deformed Snyder space

We study a formulation of statistical mechanics in the context of symplectic structures of the IR and also UV & IR-deformed Snyder phase-spaces. We derive the corresponding invariant Liouville volume and by using it we obtain the deformed partition function. We then study the thermodynamical properties of the 3-dimensional harmonic oscillator in this set-up. By using the equipartition theorem, we show that two of the six degrees of freedom for a 3-dimensional harmonic oscillator will be frozen as the temperature increases. Also, at a constant temperature, whatever is the increase in oscillator length, this reduction of the number of degrees of freedom gets more and more appreciable and it offers an effective dimensional reduction of space from [Formula: see text] to [Formula: see text] when it is close to the IR-length scale.

New possibilities of harmonic oscillator basis application for calculation of the ground state energy of a Coulomb non-identical three-particle system

A new harmonic oscillator (HO) expansion method for calculation of the non-relativistic ground state energy of the Coulomb non-identical three-particle systems is presented. The HO expansion basis with different size parameters in the Jacobi coordinates instead of only one unique oscillator length parameter in the traditional treatment is introduced. This method is applied to calculate the ground state energy of a number of Coulomb three-particle systems for up to 28 excitation HO quanta. The obtained results suggest that the HO basis with different size parameters in the Jacobi coordinates could lead to significant increasing of the rate of convergence for the ground state energy than in the traditional approach.

THERMODYNAMICS OF A BOSE GAS TRAPPED IN A BOUNDED HARMONIC POTENTIAL

Some thermodynamic features of an assembly of a finite number of bosons trapped in a bounded harmonic potential are investigated. P–V isotherms are drawn for both the degenerate and the non-degenerate phases. At any temperature, the pressure is a decreasing function of volume, unlike the free Bose gas for which the pressure becomes independent of volume in the degenerate phase. At the absolute zero of temperature the quantum pressure for a spherical enclosure of radius r0 equal to aho, aho being the characteristic harmonic oscillator length, is found to be of order 10-10 Torr while for [Formula: see text] it is of order 10-12 Torr. The isothermal compressibility has a sharp drop near the critical point and becomes negligibly small for temperatures above the critical temperature, irrespective of the size of the trap. The coefficient of thermal expansion also shows a sudden drop at the critical temperature. The specific heat at constant pressure shows a peak and is well-defined in the degenerate phase, in contradistinction to the ideal Bose gas. Results recently derived by Singh on the basis of local equilibrium theory are found to be in good agreement with our numerical computations.

Shell-model calculations in the 4He system

Structure calculations for the 4He system are performed in both [Formula: see text] and [Formula: see text] model spaces. The results of these calculations suggest that a reasonable level spectrum can be obtained with the Sussex interaction if binding energy considerations are neglected. Imposing binding energy requirements leads to distortions in the level spectrum. The T = 1 levels and selected T = 0 levels are reasonably described by the bare Sussex interaction (b = 1.4 fm). The (0+, 0) 20.1 MeV level and (2−, 0) 22.1 MeV level are best described by the b = 1.80 fm and b = 1.60 fm Sussex interactions, respectively. Attempts to arbitrarily vary individual relative matrix elements do not improve the (0+, 0) spectrum. The resulting calculations suggest that an adequate description of the 4He level spectrum is not possible if a single oscillator length parameter is used for all levels. The results also emphasize the difficulty of performing structure and reaction calculations in a consistent manner, because different b values are required for binding, rms radius, or level considerations. The choice of b is not obvious and should be determined by solution criteria.