TY - JOUR

T1 - Density of states of a dissipative quantum dot coupled to a quantum wire

AU - Goldstein, Moshe

AU - Berkovits, Richard

PY - 2010/12/14

Y1 - 2010/12/14

N2 - We examine the local density of states of an impurity level or a quantum dot coupled to a fractional quantum-Hall edge or to the end of a single one-dimensional Luttinger-liquid lead. Effects of an Ohmic dissipative bath are also taken into account. Using both analytical and numerical techniques we show that, in general, the density of states exhibits power-law frequency dependence near the Fermi energy. In a substantial region of the parameter space it simply reflects the behavior of the tunneling density of states at the end of a Luttinger liquid and is insensitive either to the value of the dot-lead interaction or to the strength of dissipation; otherwise it depends on these couplings too. This behavior should be contrasted with the thermodynamic properties of the level, in particular, its occupancy, which were previously shown to depend on the various interactions in the system only through the corresponding Fermi-edge singularity exponent and thus cannot display any Luttinger-liquid specific power law. Hence, we can construct different models, some with and some without interactions in the wire (but with equal Fermi-edge singularity exponents), which would have very different level densities of states, although they all result in the same level population vs energy curves.

AB - We examine the local density of states of an impurity level or a quantum dot coupled to a fractional quantum-Hall edge or to the end of a single one-dimensional Luttinger-liquid lead. Effects of an Ohmic dissipative bath are also taken into account. Using both analytical and numerical techniques we show that, in general, the density of states exhibits power-law frequency dependence near the Fermi energy. In a substantial region of the parameter space it simply reflects the behavior of the tunneling density of states at the end of a Luttinger liquid and is insensitive either to the value of the dot-lead interaction or to the strength of dissipation; otherwise it depends on these couplings too. This behavior should be contrasted with the thermodynamic properties of the level, in particular, its occupancy, which were previously shown to depend on the various interactions in the system only through the corresponding Fermi-edge singularity exponent and thus cannot display any Luttinger-liquid specific power law. Hence, we can construct different models, some with and some without interactions in the wire (but with equal Fermi-edge singularity exponents), which would have very different level densities of states, although they all result in the same level population vs energy curves.

UR - http://www.scopus.com/inward/record.url?scp=78650924653&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.82.235315

DO - 10.1103/PhysRevB.82.235315

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:78650924653

SN - 1098-0121

VL - 82

JO - Physical Review B - Condensed Matter and Materials Physics

JF - Physical Review B - Condensed Matter and Materials Physics

IS - 23

M1 - 235315

ER -