Related papers: Friedel sum rule for an interacting multiorbital q…
The transmission phase through a quantum dot with few electrons shows a complex, non-universal behavior. Here we combine configuration-interaction calculations ---treating rigorously Coulomb interaction--- and the Friedel sum rule to…
We illustrate the relation between the scattering phase appearing in the Friedel sum rule and the phase of the transmission amplitude for quantum scatterers connected to two one-dimensional leads. Transmission zero points cause abrupt phase…
We study the relationship between the spectral shift function and the excess charge in potential scattering theory. Although these quantities are closely related to each other, they have been often formulated in different settings so far.…
We examine the Friedel sum rule which states that the "excess charge" due to a single impurity potential in a metal is equal to a sum of phase shifts for scatterings of electrons by the impurity. For finite volume, the ``excess charge" is…
When an atomic-size break junction is mechanically stretched, the total conductance of the contact remains approximately constant over a wide range of elongations, although at the same time the transmissions of the individual channels…
In Quantum Field Theory, scattering amplitudes are computed from propagators which, for internal lines, are built upon spin/polarization-sum relationships. In turn, these are normally constructed upon plane-wave solutions of the free field…
The Gerasimov-Drell-Hearn sum rule and related dispersive integrals connect real and virtual Compton scattering to inclusive photo- and electroproduction. Being based on universal principles as causality, unitarity, and gauge invariance,…
In this work, the generalization of Friedel formula and Krein's theorem in complex potential scattering theory is presented. The consequence of various symmetry constraints on dynamical system are discussed. In addition,…
The Gerasimov-Drell-Hearn sum rule is one of several dispersive sum rules that connect the Compton scattering amplitudes to the inclusive photoproduction cross sections of the target under investigation. Being based on such universal…
Elastic scattering in a quantum wire has several novel features not seen in 1D, 2D or 3D. In this work we consider a single channel quantum wire as its application is inevitable in making devices based on quantum interference effects. We…
The validity of the Luttinger sum rule is considered for finite systems of interacting electrons, where the Fermi volume is determined by location of zeroes of Green's function. It is shown that the sum rule in the paramagnetic state is…
Considering a quench process in which an electric field pulse is applied to the system, "$f$-sum rule" for the conductivity for general quantum many-particle systems is derived. It is furthermore extended to an infinite series of sum rules,…
In the wake of a new kind of phase generally occurring in mesoscopic transport phenomena, we discuss the validity of Friedel sum rule in the presence of this phase. We find that the general Friedel sum rule may be violated.
The properties of scattering phases in quantum dots are analyzed with the help of lattice models. We first derive the expressions relating the different scattering phases and the dot Green functions. We analyze in detail the Friedel sum…
We discuss a sum rule satisfied by the correlation function of two particles with small relative momenta. The sum rule, which results from the completeness condition of the quantum states of the two particles, is first derived and then we…
Analytical expressions are derived for sums of matrix elements and their squared moduli over many-body states with given total spin --- the states built from spin and spatial wavefunctions belonging to multidimensional irreducible…
We study correlated two-level quantum dots, coupled in effective 1-channel fashion to metallic leads; with electron interactions including on-level and inter-level Coulomb repulsions, as well as the inter-orbital Hund's rule exchange…
We study the coherent transport in multi-terminal mesoscopic Aharonov-Bohm ring with a quantum dot embedded in an arm. Employing the Friedel sum rule for the effective single-particle levels in the quantum dot, we explain some anomalous…
We formulate real-space dynamical mean-field theory within scattering theory. Thereby the Friedel sum rule is derived for interacting lattice fermions at zero temperature.
The $f$-sum rule and the Kohn formula are well-established general constraints on the electric conductivity in quantum many-body systems. We present their generalization to non-linear conductivities at all orders of the response in a…