Strongly Interacting Quantum Systems in Low Dimensions.

We demonstrate that scattering of particles strongly interacting in three dimensions (3D) can be suppressed at low energies in a quasi-one-dimensional (1D) confinement. The underlying mechanism is the interference of the s- and p-wave scattering contributions with large s- and p-wave 3D scattering lengths being a necessary prerequisite. This low-dimensional quantum scattering effect might be useful in "interacting" quasi-1D ultracold atomic gases, guided atom interferometry, and impurity scattering in strongly confined quantum wire-based electronic devices.We demonstrate that scattering of particles strongly interacting in three dimensions (3D) can be suppressed at low energies in a quasi-one-dimensional (1D) confinement. The underlying mechanism is the interference of the s- and p-wave scattering contributions with large s- and p-wave 3D scattering lengths being a necessary prerequisite. This low-dimensional quantum scattering effect might be useful in "interacting" quasi-1D ultracold atomic gases, guided atom interferometry, and impurity scattering in strongly confined quantum wire-based electronic devices.

arXiv:quant-ph/0610265Physical Review LettersNov 10, 200664 citations

Non-Perturbative Approaches for Strongly Interacting Quantum Systems.

Sandi Tsu-Shiang Lieu

Aug 1, 19750 citations

Exotic quantum order in low-dimensional systems

S. M. Girvin

arXiv:cond-mat/9711233Solid State CommunicationsAug 1, 19984 citations

Quantum Coulomb gap in low dimensions

M. Pino, A. M. Somoza, M. Ortuño

We study the single-particle density of states of one- and two-dimensional quantum disordered systems in the strongly localized regime with long-range interactions. We consider a $1/\sqrt{r}$ interaction in one dimension and a Coulomb interaction in two dimensions, which produce linear gaps in the density of states in both cases. We use an exact diagonalization technique for small system sizes and a perturbation approach for larger sizes. With both methods, the inclusion of a finite hopping contribution does not change the linear character of the gap, but reduces its slope, widening the gap.We study the single-particle density of states of one- and two-dimensional quantum disordered systems in the strongly localized regime with long-range interactions. We consider a $1/\sqrt{r}$ interaction in one dimension and a Coulomb interaction in two dimensions, which produce linear gaps in the density of states in both cases. We use an exact diagonalization technique for small system sizes and a perturbation approach for larger sizes. With both methods, the inclusion of a finite hopping contribution does not change the linear character of the gap, but reduces its slope, widening the gap.

arXiv:1205.5186Physical Review BSep 17, 20127 citations

We study the single-particle density of states of one- and two-dimensional quantum disordered systems in the strongly localized regime with long-range interactions. We consider a

1/\sqrt{r}

interaction in one dimension and a Coulomb interaction in two dimensions, which produce linear gaps in the density of states in both cases. We use an exact diagonalization technique for small system sizes and a perturbation approach for larger sizes. With both methods, the inclusion of a finite hopping contribution does not change the linear character of the gap, but reduces its slope, widening the gap.