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We show that a simple one-dimensional model of spinless fermions with pair hopping displays a phase in which a Luttinger liquid of paired fermions coexists with a Luttinger liquid of unpaired fermions. Our results are based on extensive…
We study the existence of energy minimizers for a Bose-Einstein condensate with dipole-dipole interactions, tightly confined to a plane. The problem is critical in that the kinetic energy and the (partially attractive) interaction energy…
We consider the Ginzburg-Landau functional with a variable applied magnetic field in a bounded and smooth two dimensional domain. The applied magnetic field varies smoothly and is allowed to vanish non-degenerately along a curve. Assuming…
The objective of the present paper is to study 4-dimensional weakly Ricci symmetric spacetimes $(WRS)_4$ with non-zero constant Ricci scalar. We prove that such a $(WRS)_4$ satisfying $F(R)$-gravity field equations represents a perfect…
In a recent paper [arXiv:1601.02165], Tao Li claimed that a gapped $\mathbb{Z}_2$ spin liquid, obtained using projected Gutzwiller fermionic wave functions, can be stabilized in the Heisenberg model on the kagome lattice. We perform very…
We investigate separations of trapped balanced two-component atomic Fermi gases with repulsive contact interaction. Candidates for ground-state densities are obtained from the imaginary-time evolution of a nonlinear pseudo-Schr\"odinger…
A new transverse mode in a two-stream magnetized quantum plasma is studied by means of a quantum hydrodynamic model, under non-relativistic and ideal Fermi gas assumptions. It is found that Fermi pressure effects induce a minimum cutoff…
Replacing linear diffusion by a degenerate diffusion of porous medium type is known to regularize the classical two-dimensional parabolic-elliptic Keller-Segel model. The implications of nonlinear diffusion are that solutions exist globally…
We study the nonlinear Schr\"odinger equation arising in dipolar Bose-Einstein condensate in the unstable regime. Two cases are studied: the first when the system is free, the second when gradually a trapping potential is added. In both…
We investigate the kinetic theory of two-temperature plasmas for reactive polyatomic gas mixtures. The Knudsen number is taken proportional to the square root of the mass ratio between electrons and heavy-species, and thermal…
We use a new approach that we call unification to prove that standard weighted double bubbles in $n$-dimensional Euclidean space minimize immiscible fluid surface energy, that is, surface area weighted by constants. The result is new for…
We study in this paper the general properties of a many body system of fermions in arbitrary dimensions assuming that the {\em momentum} of individual fermions are good quantum numbers of the system. We call these systems $k$-Fermi liquids.…
Paralleling a previous paper, we examine single- and many-body states of relativistic electrons in an intense, rotating magnetic dipole field. Single-body orbitals are derived semiclassically and then applied to the many-body case via the…
The purpose of this article is to extend the work by Anantharaman and Canc\`es [1], and prove the existence of minimizers for the spin-polarized Kohn-Sham model in the presence of a magnetic field within the local spin density…
Using molecular dynamics simulations we study the temperature-density phase diagram of a simple model system of particles in two dimensions. In addition to translational degrees of freedom, each particle has two internal states and…
The accompanying Comment by A. Holas and N. H. March [Phys. Rev. A {\bf 66}, 066501 (2002)] is concerned with the issue of whether or not kinetic energy can be represented by an effective local potential, as required for an exact…
We perform a thorough analysis of the dynamic and thermodynamic stability for the charged perfect fluid star by applying the Wald formalism to the Lagrangian formulation of Einstein-Maxwell-charged fluid system. As a result, we find that…
Two-component, ideal, self-gravitating fluids are conceived as macrogases, and the related equation of state is expressed using the virial theorem for subsystems, under the restriction of homeoidally striated density profiles. Shallower…
We consider the 3d cubic nonlinear Schr\"odinger equation (NLS) with a strong 2d harmonic potential. The model is physically relevant to observe the lower-dimensional dynamics of the Bose-Einstein condensate, but its ground state cannot be…
We show how the stability conditions for a system of interacting fermions that conventionally involve variations of thermodynamic potentials can be rewritten in terms of one- and two-particle correlators. We illustrate the applicability of…