TY - JOUR

T1 - Scattering of hole excitations in a one-dimensional spinless quantum liquid

AU - Matveev, K. A.

AU - Andreev, A. V.

PY - 2012/7/30

Y1 - 2012/7/30

N2 - Luttinger liquid theory accounts for the low-energy boson excitations of one-dimensional quantum liquids, but disregards the high-energy excitations. The most important high-energy excitations are holes, which have infinite lifetime at zero temperature. At finite temperatures, they can be scattered by thermally excited bosons. We describe the interaction of a hole with the bosons by treating it as a mobile impurity in a Luttinger liquid. This approach enables us to evaluate the scattering probability at arbitrary interaction strength. In general, the result is expressed in terms of the hole spectrum, its dependence on the density and momentum of the fluid, and the parameters of the Luttinger liquid Hamiltonian. In the special case of Galilean invariant systems, the scattering probability is expressed in terms of only the hole spectrum and its dependence on the fluid density. We apply our results to the problem of equilibration of one-dimensional quantum liquids.

AB - Luttinger liquid theory accounts for the low-energy boson excitations of one-dimensional quantum liquids, but disregards the high-energy excitations. The most important high-energy excitations are holes, which have infinite lifetime at zero temperature. At finite temperatures, they can be scattered by thermally excited bosons. We describe the interaction of a hole with the bosons by treating it as a mobile impurity in a Luttinger liquid. This approach enables us to evaluate the scattering probability at arbitrary interaction strength. In general, the result is expressed in terms of the hole spectrum, its dependence on the density and momentum of the fluid, and the parameters of the Luttinger liquid Hamiltonian. In the special case of Galilean invariant systems, the scattering probability is expressed in terms of only the hole spectrum and its dependence on the fluid density. We apply our results to the problem of equilibration of one-dimensional quantum liquids.

UR - http://www.scopus.com/inward/record.url?scp=84864591352&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.86.045136

DO - 10.1103/PhysRevB.86.045136

M3 - Article

AN - SCOPUS:84864591352

VL - 86

JO - Physical Review B - Condensed Matter and Materials Physics

JF - Physical Review B - Condensed Matter and Materials Physics

SN - 1098-0121

IS - 4

M1 - 045136

ER -