Self-equilibration theorem in quantum-point contacts of interacting electrons: Time-dependent quantum fluctuations of tunnel transport beyond the Levitov–Lesovik scattering approach

Tunneling maps of interacting electrons in real time: anomalous tunneling in quantum point-contacts beyond the steady state regime

“…Therefore, here we propose the way in which one can solve both these problems providing: i) precise estimation of the small differences in the values of Luttinger liquid correlation parameter g for different tunnel contacts at low temperatures for the situation of strong enough electron-electron repulsion in these QPCs with 0 < g 1/2 and ii) fast enough quantum detection by means of QPC using the statistics of electron tunneling [18,19] on the short-time scales beyond the steady state regime [20]. The key to these results is in the analysis of the probabilities P (N, t) for N electrons (N = 1, 2, 3 .…”

“…to tunnel through given Luttinger liquid QPC by time t as functions of all external parameters such as bias voltage V applied to QPC electrodes, Luttinger liquid correlation parameter g (0 < g ≤ 1) and temperature. This scenario becomes possible due to validity of so-called Stheorem [11,20] for the exact calculation of Keldysh distribution function of interacting electrons which tunnel through a weakly linked QPC.…”

“…Let us consider the quantum point-contact (QPC) between two semi-infinite one-dimensional quantum wires in the weak tunneling limit [6,11,16,20]…”

“…here as well as in all subsequent formulas g is the dimensionless Luttinger liquid correlation parameter de-fined as g = (1 + U s /2E F ) −1/2 (where g = 1 corresponds to Fermi liquid in the QPC leads at U s = 0, while 0 < g < 1 is the case of strong Coulomb repulsion between electrons U s > E F , U is a potential energy of shortrange repulsion between electrons in the QPC leads) and v g = v F /g is the group velocity of collective plasmonic excitations in the leads (here v F is the Fermi velocity (we put = 1 everywhere for simplicity) [9,11,16,20]. In Eq.…”

“…are common phase-and charge quantum bosonic fields with standard commutation relations [θ α (x), ϕ α (x )] = iπ g sgn(x − x )δ α,α (here α, α = L, R) and zero average values with respect to a Luttinger liquid ground state ϕ L(R) (x, t) = θ L(R) (x, t) = 0 [6,11,20].…”