Attractive Self-interaction Research Articles

Spontaneous symmetry breaking of Bose-Fermi mixtures in double-well potentials

We study the spontaneous symmetry breaking (SSB) of a superfluid Bose-Fermi (BF) mixture in a double-well potential (DWP). The mixture is described by the Gross-Pitaevskii equation (GPE) for the bosons, coupled to an equation for the order parameter of the Fermi superfluid, which is derived from the respective density functional in the unitarity limit (a similar model applies to the BCS regime too). Straightforward SSB in the degenerate Fermi gas loaded into a DWP is impossible, as it requires an attractive self-interaction, while the intrinsic nonlinearity in the Fermi gas is repulsive. Nonetheless, we demonstrate that the symmetry breaking is possible in the mixture with attraction between fermions and bosons, like 40K and 87Rb. Numerical results are represented by dependencies of asymmetry parameters for both components on particle numbers of the mixture, N_F and N_B, and by phase diagrams in the (N_F,N_B) plane, which displays regions of symmetric and asymmetric ground states. The dynamical picture of the SSB, induced by a gradual transformation of the single-well potential into the DWP, is reported too. An analytical approximation is proposed for the case when GPE for the boson wave function may be treated by means of the Thomas-Fermi (TF) approximation. Under a special linear relation between N_F and N_B, the TF approximation allows us to reduce the model to a single equation for the fermionic function, which includes competing repulsive and attractive nonlinear terms. The latter one directly displays the mechanism of the generation of the effective attraction in the Fermi superfluid, mediated by the bosonic component of the mixture.

Symbiotic bright solitary wave solutions of coupled nonlinear Schrödinger equations

Conventionally, bright solitary wave solutions can be obtained in self-focusing nonlinear Schrödinger equations with attractive self-interaction. However, when self-interaction becomes repulsive, it seems impossible to have bright solitary wave solutions. Here we show that there exist symbiotic bright solitary wave solutions of coupled nonlinear Schrödinger equations with repulsive self-interaction but strongly attractive interspecies interaction. For such coupled nonlinear Schrödinger equations in two- and three-dimensional domains, we prove the existence of least energy solutions and study the location and configuration of symbiotic bright solitons. We use Nehari's manifold to construct least energy solutions and derive their asymptotic behaviour by some techniques of singular perturbation problems.

Dynamics of a Wavefunction for the Attractive Nonlinear Schrödinger Equation under Isotropic Harmonic Confinement Potential

We study dynamics of a wavefunction for the nonlinear Schrodinger equation with attractive self-interaction under a harmonic potential. By use of the variance identity and a rigorous inequality, we obtain a sufficient condition for the collapse of the wavefunction. By applying this method, we investigate the dynamic stability of a trapped Bose–Einstein condensate and its dependence on the initial shape of the condensate. The result agrees qualitatively well with the results of the time-dependent variational method. We find that the anisotropy introduced in the initial state has a significant effect on the stabilization.

NOVEL PHENOMENA IN CHARGED BOSE LIQUID

We investigate charged Bose liquid immersed in uniform background charge at zero temperature. Novel phenomena, such as oscillatory shielding of external localized electric charge, rotons and charge density waves (charge stripes in two dimensions), occur in any dimensions. Oscillatory shielding is caused by mixing between scalar boson exchange and Coulomb interactions, which mediate opposite forces. On the other hand, rotons and charge density waves are due to attractive local self-interaction of bosons. Rotons can be regarded as a finite size charge density wave packet without any back flow. We also comment on charge stripes observed recently in cuprates and nickelates.

Even Grassmann fields in momentum space

We extend previous results about fields whose Fourier components are even elements of a Grassmann algebra. Their main interest is related to the possibility that they describe fermionic composites. We evaluate the free propagators for arbitrary index of nilpotency and investigate to one loop a φ 4 model. Due to the nature of the integral over even Grassmann fields such a model exists for repulsive as well as attractive selfinteraction. In the first case the β -function is equal to that of the ordinary theory while in the second one the model is asymptotically free. The renormalized mass has a peculiar dependence on the cut off, being quadratically increasing/decreasing for attractive/repulsive selfinteraction.

Nonlinear axion dynamics and the formation of cosmological pseudosolitons.

The $(3+1)$-dimensional evolution of an inhomogeneous axion field configuration around the QCD epoch is studied numerically, including important non-linear effects due to the attractive self-interaction. It is found that axion perturbations on scales corresponding to causally disconnected regions at $T \sim 1 \, {\rm GeV}$ can lead to very dense pseudo-soliton configurations we call axitons. These configurations evolve to axion miniclusters with present density $\rho_a \ga 10^{-8}\,{\rm g \, cm^{-3}}$. This is high enough for the collisional $2a \rightarrow 2a$ process to lead to Bose--Einstein relaxation in the gravitationally bound clumps of axions, forming Bose stars.