While the Luttinger liquid description of one-dimensional interacting electrons has had many successes, interesting physics appears in situations where it is not applicable. My interest is in identifying how the one-dimensional effects are modified in realistic situations and exploring the novel phenomena that arise.

Quasi-onedimensionality arises either due to coupling between onedimensional systems or due to transverse excitations in the confining potential that defines the onedimensional system. In particular, the second aspect has received surprisingly little attention in the past. Exploring these deviations from onedimensionality has been a central topic of my recent research. Upon increasing the density of electrons in a quantum wire, the system undergoes a transition from a onedimensional to a quasi-onedimensional state. In the absence of interactions between electrons, it corresponds to filling up the second subband of transverse quantization. On the other hand, strongly interacting onedimensional electrons form a Wigner crystal, and the transition corresponds to it splitting into two chains, creating a zigzag crystal. We explored the nature of the phase transition of spinless (spin-polarized) electrons as a function of interaction strength. Furthermore, while the spin properties of the onedimensional Wigner crystal are relatively simple, we showed that they change dramatically in the quasi-onedimensional regime. See the recent review on Wigner crystal physics in quantum wires as well as further references in the list of publications.

Furthermore, the effect of disorder requires novel theoretical approaches. A promising direction is the adaptation of the interacting non-linear sigma-model to the one-dimensional case.