Related papers: Fermions in a random medium
We consider field theory formulation for directed polymers and interfaces in the presence of quenched disorder. We write a series representation for the averaged free energy, where all the integer moments of the partition function of the…
We derive exact relations that connect the universal $C/k^4$-decay of the momentum distribution at large $k$ with both thermodynamic properties and correlation functions of two-component Fermi gases in one dimension with contact…
Quasi-one-dimensional (quasi-1d) two-component Fermi gases with effectively attractive and repulsive interactions are characterized for arbitrary interaction strength. The ground-state properties of the gas confined in highly elongated…
The universal relations for spin-$1/2$ fermions with contact interaction in the presence of quenched disorder are discussed. The disorder is modeled by a random external potential with the Gaussian distribution and $\delta$-like two-point…
Inspired by the renewed experimental activities on $p$-wave resonantly interacting atomic Fermi gases, we theoretically investigate some experimental observables of such systems at zero temperature in two dimensions, using both mean-field…
We study directed polymers subject to a quenched random potential in d transversal dimensions. This system is closely related to the Kardar-Parisi-Zhang equation of nonlinear stochastic growth. By a careful analysis of the perturbation…
We consider a pair of identical fermions with a short-range attractive interaction on a finite lattice cluster in the presence of strong site disorder. This toy model imitates a low density regime of the strongly disordered Hubbard model.…
Dynamical conductivity in a disordered one-dimensional model of interacting fermions is studied numerically at high temperatures and in the weak-interaction regime in order to find a signature of many-body localization and vanishing d.c.…
Motivated by the realization of hard-wall boundary conditions in experiments with ultracold atoms, we investigate the ground-state properties of spin-1/2 fermions with attractive interactions in a one-dimensional box. We use lattice Monte…
We study the $1+1$-dimensional random directed polymer problem, i.e., an elastic string $\phi(x)$ subject to a Gaussian random potential $V(\phi,x)$ and confined within a plane. We mainly concentrate on the short-scale and…
We study fermions in two dimensions interacting via a long-ranged 1/r potential for small particle separations and a short-ranged 1/r^3 potential for larger separations in comparison to a length scale \xi. We compute the energy of the…
Stretched polymers with attractive interaction are studied in two and three dimensions. They are described by biased self-avoiding random walks with nearest neighbour attraction. The bias corresponds to opposite forces applied to the first…
A density functional theory is developed for fermions in one dimension, interacting via a delta-function. Such systems provide a natural testing ground for questions of principle, as the local density approximation should work well for…
We consider directed polymers in 1+1 spatial dimension under action of an external repulsive potential along a line. Using the exact mapping onto imaginary time evolution of free fermions we find that for sufficiently strong potential the…
We investigate the particle and kinetic energy densities of harmonically trapped fermion gases at zero temperature in arbitrary dimensions. We derive analytically a differential equation connecting these densities, which so far have been…
We study a two-component mixture of fermionic dipoles in two dimensions at zero temperature, interacting via a purely repulsive $1/r^3$ potential. This model can be realized with ultracold atoms or molecules, when their dipole moments are…
We apply Dynamical Mean-Field Theory to strongly interacting fermions in an inhomogeneous environment. With the help of this Real-Space Dynamical Mean-Field Theory (R-DMFT) we investigate antiferromagnetic states of repulsively interacting…
We analyze, via Imry-Ma scaling arguments, the strong disorder phases that exist in low dimensions at all temperatures for directed polymers and interfaces in random media. For the uncorrelated Gaussian disorder, we obtain that the optimal…
We describe some recent results concerning the statistical properties of a self-interacting polymer stretched by an external force. We concentrate mainly on the cases of purely attractive or purely repulsive self-interactions, but our…
The canonical thermodynamic properties of a one-dimensional system of interacting spin-1/2 fermions with an attractive zero-range pseudo-potential are investigated within an exact approach. The density operator is evaluated as the…