Possibility of the new type phase transition

The scalar field theory and the scalar electrodynamics quantized in the flat gap are considered. The dynamical effects arising due to the boundary presence with two types of boundary conditions (BC) satisfied by scalar fields are studied. It is shown that while the Neumann BC lead to the usual scalar field mass generation, the Dirichlet BC give rise to the dynamical mechanism of spontaneous symmetry breaking. Due to the later, there arises the possibility of the new type phase transition from the normal to spontaneously broken phase. The decreasing in the characteristic size of the quantization region (the gap size here) and increasing in the temperature compete with each other, tending to transport the system in the spontaneously broken and in the normal phase, respectively. The system evolves with a combined parameter, simultaneously reflecting the change in temperature and in the size. As a result, at the critical value of this parameter there occurs the phase transition from the normal phase to the spontaneously broken one. In particular, the usual massless scalar electrodynamics transforms to the Higgs model

Exact results for some Madelung type constants in the finite-size scaling theory

A general formula is obtained from which the madelung type constant: $$C(d|\nu)=\int_0^\infty dx x^{d/2-\nu-1}[(\sum_{l=-\infty}^\infty e^{-xl^2})^d-1-(\frac\pi x)^{d/2}]$$ extensively used in the finite-size scaling theory is computed analytically for some particular cases of the parameters $d$ and $\nu$. By adjusting these parameters one can obtain different physical situations corresponding to different geometries and magnitudes of the interparticle interaction.Comment: IOP- macros, 5 pages, replaced with amended version (1 ref. added

Distribution of quantum states in enclosures of finite size: I

We show that the expression for the density of states of a particle in a three-dimensional rectangular box of finite size can be obtained by using directly the Poisson's summation formula instead of using the Walfisz formula or the generalized Euler formula both of which can be derived from the former. We also derive the expression for the density of states in the case of an enclosure in the form of an infinite rectangular slab and apply it to the problem of the Bose–Einstein condensation of a Bose gas of noninteracting particles confined to a thin-film geometry. </jats:p