One-dimensional interacting electrons in a quantum wire connected to reservoirs are studied theoretically. The difference in the Tomonaga-Luttinger interaction constants between the wire

(g)

and reservoirs

{(g}_{\ensuremath{\infty}})

produces the cross correlation between the right- and left-going chiral components of the charge-density wave field. The low-energy asymptotics of this field correlator, which is determined by

(g)

and

{(g}_{\ensuremath{\infty}}),

specifies renormalization of physical quantities. We have found that charge of the carriers in the shot noise is determined by

{g}_{\ensuremath{\infty}}

(no renormalization for the Fermi liquid reservoirs) at any energy, meanwhile the factor g renormalizing the charge and spin susceptibilities emerges in the threshold structures at some rational fillings.

DOI: 10.1103/physrevb.60.16865

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One-dimensional interacting electrons in a quantum wire connected to reservoirs are studied theoretically. The difference in the Tomonaga-Luttinger interaction constants between the wire

(g)

and reservoirs

{(g}_{\ensuremath{\infty}})

produces the cross correlation between the right- and left-going chiral components of the charge-density wave field. The low-energy asymptotics of this field correlator, which is determined by

(g)

and

{(g}_{\ensuremath{\infty}}),

specifies renormalization of physical quantities. We have found that charge of the carriers in the shot noise is determined by

{g}_{\ensuremath{\infty}}

(g_{\infty})

produces the cross-correlation between the right- and left-going chiral components of the charge density wave field. The low energy asymptotics of this field correlator, which is determined by (g) and

(g_{\infty})

, specifies renormalization of physical quantities. We have found that charge of the carriers in the shot noise is determined by

g_\infty

(g_{\infty})

(g_{\infty})

, specifies renormalization of physical quantities. We have found that charge of the carriers in the shot noise is determined by

g_\infty

{G}_{\mathrm{SD}}^{(2)}{=e}^{2}/h

and

{G}_{\mathrm{SD}}^{(2)}{=ge}^{2}/h,

where g is the TLL charge interaction parameter. We find that under these two boundary conditions for the end contacts the 3T SD conductance

{G}_{\mathrm{SD}}^{(3)}

shows an UV-relevant deviation from the above two values, suggesting new fixed points in the Ohmic limit. Nontrivial scaling exponents are predicted as a result of electron fractionalization.

G_{\rm SD}^{(2)}=e^2/h

and

G_{\rm SD}^{(2)}=ge^2/h

, where

g

is the TLL charge interaction parameter. We find that under these two boundary conditions for the {\it end} contacts the 3T SD conductance

G_{\rm SD}^{(3)}

shows an UV-relevant deviation from the above two values, suggesting new fixed points in the ohmic limit. Non-trivial scaling exponents are predicted as a result of electron fractionalization.

Transport between two Fermi liquid reservoirs through a one channel wire of length

L

is examined when the 1D electron system has an energy gap $2M\ensuremath{\gg}{v}_{c}/L$ (

{v}_{c}

is the charge velocity in the wire). In the spinless case transformation of reservoir electrons into solitons of fractional charge entails a crossover from a Fermi liquid regime of integer charge transfer below the crossover energy ${T}_{x}\ensuremath{\ll}{T}_{L}$ to an insulating regime of the fractional charge transfer in the current vs voltage, conductance vs temperature, and the shot noise. Similar behavior is predicted for a spin Mott insulator of filling factor $\ensuremath{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}n/({2m}^{\ensuremath{'}})$ ( ${n,m}^{\ensuremath{'}}$ are positive integers).

The finiteness of the length of a one-channel wire results in a crossover from Tomonaga-Luttinger to Fermi-liquid behavior with lowering energy scale. Under the condition that the voltage drop

(V)

mostly occurs across a tunnel barrier inside the wire, we determined the coefficients of temperature and voltage expansion for low-energy conductance as a function of the interaction strength and the right and left traversal times. At higher voltage, the finite-length contribution exhibits oscillations related to both traversal times and becomes a slowly decaying correction to the scale-invariant ${V}^{1/g\ensuremath{-}1}$ dependence of the conductance.