International Journal of Modern Physics B

We discuss the nature of phase transitions in self-gravitating systems. We show the connection between the binary star model of Padmanabhan, the thermodynamics of stellar systems and the thermodynamics of self-gravitating fermions. We stress the inequivalence of statistical ensembles for systems with long-range interactions, like gravity. In particular, we contrast the microcanonical evolution of stellar systems from the canonical evolution of self-gravitating Brownian particles. At low energies, self-gravitating Hamiltonian systems experience a gravothermal catastrophe in the microcanonical ensemble. At low temperatures, self-gravitating Brownian systems experience an isothermal collapse in the canonical ensemble. For classical particles, the gravothermal catastrophe leads to a binary star surrounded by a hot halo while the isothermal collapse leads to a Dirac peak containing all the mass. For self-gravitating fermions, the collapse stops when quantum degeneracy comes into play through the Pauli exclusion principle. The end-product of the collapse is a fermion ball, resembling a cold white dwarf star, surrounded by a halo. We can thus describe a phase transition from a gaseous phase to a condensed phase. At high energies or high temperatures, the condensate can experience an explosion, reverse to the collapse, and return to the gaseous phase. Due to the existence of long-lived metastable states, the points of collapse and explosion differ. This leads to a notion of hysteretic cycle in microcanonical and canonical ensembles.

The electronic band structure of AlN, AlSb, AlAs and their ternary alloys with In has been investigated by ETB. The ETB method has been formulated for sp³d² basis and nearest neighbor interactions of the compounds and its energy parameters have been derived from the results of the present first principles calculations carried on AlN, AlSb and AlAs. It has been found that the present ETB energy parameters can produce the band structure of the compounds and their ternary alloys with In successfully.

By considering the effects of the space charges and domain boundaries in ferroelectric thin films, the thickness dependence of coercive field (E_c) is numerically simulated based on the four-state Potts model with the nearest-neighbor interactions between dipole moments. For large thickness, experimental results where E_c decreases with thickness can be produced from our Monte-Carlo simulation. On the other hand, when the thickness is very small, our simulation gets that E_c increases with thickness by the study of the polarization switching in the film. This gives an explanation of the experimental result by Zhu et al. in J. Appl. Phys.83, 1 (1998) for SBT-BTN film, and a similar report by Bune et al. in Nature391, 874 (1998) for the crystalline film. The critical temperature of the thin film is also discussed.

With the help of a mapping approach, a new type of variable separation solution with two arbitrary functions to (2+1)-dimensional Boiti–Leon–Pempinelli system (BLP) is derived. Based on the derived variable separation solution, some single valued and multiple valued localized excitations such as dromions, peakons and foldons, etc. with novel evolutional properties are revealed by introducing appropriate initial conditions in this paper.

We propose a photon correlation theory for ferroelectrics especially focused on KDP-type where we consider a photon field from its constituent electrons and ions. We derive a Curie–Weiss type dielectric susceptibility from the microscopic Hamiltonian and we obtain the ferroelectric transition temperature, T_c. We calculate the free energy by applying the bosonic operator formalism to the Hamiltonian. A linear temperature-dependent specific heat C_v conforming with experimental data for some ferroelectric materials is obtained. We calculate the isotope exponent, α, on T_c. We also derive phonon dispersion relations in the presence of electron-phonon interactions to show soft modes at T_c.

The recent quantum Hall experiments in graphene have confirmed the theoretically well-understood picture of the quantum Hall (QH) conductance in fermion systems with continuum Dirac spectrum. In this paper we take into account the lattice and perform an exact diagonalization of the Landau problem on the hexagonal lattice. At very large magnetic fields the Dirac argument fails completely and the Hall conductance, given by the number of edge states present in the gaps of the spectrum, is dominated by lattice effects. As the field is lowered, the experimentally observed situation is recovered through a phenomenon which we call band collapse. As a corollary, for low magnetic fields, graphene will exhibit two qualitatively different QHE's: at low filling, the QHE will be dominated by the "relativistic" Dirac spectrum and the Hall conductance will be odd-integer; above a certain filling, the QHE will be dominated by a non-relativistic spectrum, and the Hall conductance will span all integers, even and odd.