International Journal of Modern Physics B

Exploiting the field-amplification effect of a cavity, the possibility of optical nonlinearity by only two photons was indicated experimentally. In the present article, we review our recent analysis of the two-photon dynamics in a cavity quantum electrodynamics (QED) system. Since a cavity-QED system is highly dispersive around its resonances, the shapes of photonic pulses are significantly deformed through interaction with the system. Thus, the present analysis is based on a formalism beyond single-mode approximations. The external photon field is treated rigorously as a continuum, which enables us to handle the two-photon wavefunction in the space representation. The degree of optical nonlinearity in a two-photon state is quantified by comparing the output wavefunction with the linear output wavefunction. It is revealed that the semiclassical optical response theory can be applied for evaluation of the two-photon optical nonlinearity. The two-photon nonlinearity appears not purely as a phase shift in the output wavefunction. The degradation of the fidelity between the output wavefunction and the linear output wavefunction always occurs, which hinders the application of this nonlinear effect as a quantum phase gate. The optimum condition for maximizing the two-photon nonlinearity is clarified, suggesting that pulse shape control is more essential than the Q-value control of the cavity QED system.

In this paper the Galitskii–Migdal–Feynman (GMF) formalism is applied to dilute ³He-HeII mixtures. In particular, the effect of the hole-hole scattering on pairing in these systems is investigated. To this end, the relative phase shifts incorporating many-body effects based on both Brueckner–Bethe–Goldstone (BBG) and GMF formalisms are calculated. In the GMF formalism, the S-wave phase shift at zero relative momentum is –π and has a cusp at the Fermi momentum; while in the BBG formalism, this phase shift has zero values up to the Fermi momentum. From these results we conclude that hole-hole scattering plays a crucial role in any possible fermion-fermion pairing in these systems.

The energy-spectra of nonlinear vibration of molecular crystals such as acetanilide have been calculated by using discrete nonlinear Schrödinger equation appropriate to the systems, containing various interactions. The energy levels including higher excited states are basically consistent with experimental values obtained by infrared absorption and Raman scattering in acetanilide. We further give the features of distribution of the energy-spectra for the acetanilide. Using the energy spectra we also explained well experimental results obtained by Careri et al..

A method of dispersing nanogranules in polymer utilizing the stretching, compression, and shearing effects induced by bubble inflation or oscillation in a polymer melt undergoing foaming is reported. It can be known from theoretical calculation that the bubble inflation is very fast (about μs). The other result of theoretical calculation is that the bubble can oscillate when appearing appropriate condition in polymer. The successful dispersion of nanogranules in a polymer melt by bubble inflation has been shown by experiment. Comparison of a theoretical analysis of the dispersion effect is given by the ISBS method with the results from experimental scanning electron microscope micrographs, given reasonable grounds for support of our hypotheses.

In this study, we investigate magnetic entropy variation and magnetocaloric properties as a function of frustration by considering a spin-1/2 antiferromagnetic Heisenberg model on a square lattice with nearest (J₁) and next-nearest neighbor exchange interaction (J₂). We show that the degree of frustration in the square lattice increases with α=J₂/J₁. While the square lattice is unfrustrated for α = 0, it becomes fully frustrated for α=0.5. Numerical results show that the entropy of the square lattice approaches zero for the unfrustrated case at T=1 K. In contrast, finite entropy can survive in the frustrated case at the same temperature. We also calculate the magnetic entropy change (ΔS_m) in the square lattice and show that the maximum value of ΔS_m increases with increasing α. These results indicate that the magnetic entropy change and consequently the magnetocaloric effect can be enhanced by increasing the degree of frustration. We conclude that the enhanced magnetocaloric effect is related to quantum fluctuations and disordered ground state present in the frustrated square lattice.

We investigate an algebra describing q-deformed Fermion oscillators. We establish the nature of the basic numbers which follow from this algebra, study the Fock space of these generalized Fermions and determine the Jackson Derivative appropriate for these Fermions. The statistical thermodynamics of these Fermions is examined and it is demonstrated that a consistent formulation preserving its full Legendre structure is accomplished by the use of Jackson Derivatives in place of the ordinary thermodynamic derivatives. We determine the important thermodynamic functions and illustrate the thermodynamic properties of q-Fermions.

The paper deals with axial segregation in unsteady diffusion dominated directional solidification from melt of a binary alloy in a finite cylindrical ampoule. The study focuses on the influence of the finite length of the ampoule on the concentration profile in a crystal obtained in a microgravity environment. The results are compared to those reported by Kim et al. [J. Crystal Growth183, 490 (1998)] for an infinite crystal. Numerical simulations are performed for two different situations: the initial transient solidification when the melt is uniform in composition, and the multipass solidification when the crystal is grown from the melt, formed by re-melting a crystal with an initial axial composition profile.

The present work constitutes a guided tour through the mathematics needed for a proper understanding of homotopy perturbation method as applied to various nonlinear problems. It gives a new interpretation of the concept of constant expansion in the homotopy perturbation method.