Related papers: Generalized $f$-Sum Rules and Kohn formulas on Non…
Generalising a result of classical mechanics an infinite set of conserved quantities can be found for the bare equations of motion describing the evolution of a scalar field in out of equilibrium quantum field theory, in the large N…
We display an interesting sum rule for the dynamical thermal conductivity for many standard models of condensed matter in terms of the expectation of a thermal operator. We present the thermal operator for several model systems of current…
Friedel's sum rule provides an explicit expression for a conductance functional, $\mathcal{G}[n]$, valid for the single impurity Anderson model at zero temperature. The functional is special because it does not depend on the interaction…
We construct the most general form of our previously proposed nonlinear extension of quantum mechanics that possesses three basic properties. Unlike the simpler model, the new version is not completely integrable, but it has an underlying…
Various sum rules accounting for the coupling between density and particle excitations and emphasizing in an explicit way the role of the Bose-Einstein condensation are discussed. Important consequences on the fluctuations of the particle…
We formulate a Born rule for families of quantum systems parametrized by a noncommutative space of control parameters. The resulting formalism may be viewed as a generalization of quantum mechanics where overlaps take values in a…
A generalized formalism of the so-called non-adiabatic quantum molecular dynamics is presented, which applies for atomic many-body systems in external laser fields. The theory treats the nuclear dynamics and electronic transitions…
We derive the first two moment sum rules of the conduction electron retarded self-energy for both the Falicov-Kimball model and the Hubbard model coupled to an external spatially uniform and time-dependent electric field (this derivation…
In this work, the existence, uniqueness and regularity of solutions to the time-dependent Kohn-Sham equations are investigated. The Kohn-Sham equations are a system of nonlinear coupled Schr\"odinger equations that describe multi-particle…
We show that a recently introduced generalized scheme of quantum mechanics has connections to Li\'{e}nard and Levinson-Smith classes of nonlinear systems. For the Li\'{e}nard type, which has coefficients of odd and odd symmetry, we…
We derive a closed equation of motion for the current density of an inhomogeneous quantum many-body system under the assumption that the time-dependent wave function can be described as a geometric deformation of the ground-state wave…
The Kramers-Kronig relations and various oscillator strength sum rules represent strong constraints on the physical response of materials. In this work, taking inspiration from the well-established equivalence between $f-$sum rules and…
The $f$ sum rule is derived in a non-relativistic frame and connected, via Ward Identities, to the low energy Thomson scattering. A generalisation to isospin symmetry in the nuclear case is discussed and linked to the Meson Exchange…
The quantum regression formula for an open quantum system consists in an infinite hierarchy of conditions for its multi-time correlation functions, thus requiring full access to the total "system+environment" evolution, and providing a…
Quantum criticality provides an important route to revealing universal non-equilibrium behaviour. A canonical example of a quantum critical point is the Bose-Hubbard model, which we study under the application of an electric field. A…
Generalizations of the three main equations of quantum physics, namely, the Schr\"odinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear terms, characterized by exponents depending on an index $q$, are considered in such a way…
The adiabatic theorem states that when the time evolution of the Hamiltonian is "infinitely slow", a system, when started in the ground state, remains in the instantaneous ground state at all times. This, however, does not mean that the…
We propose a list of conditions that consistency with thermodynamics imposes on linear and nonlinear generalizations of standard unitary quantum mechanics that assume a set of true quantum states without the restriction $\rho^2=\rho$ even…
The emergence of macroscopic coherence in a many-body quantum system is a ubiquitous phenomenon across different physical systems and scales. This Chapter reviews key concepts characterizing such systems (correlation functions,…
Recently, Son and Stephanov have considered an "open moose" as a possible dual model of a QCD-like theory of chiral symmetry breaking. In this note we demonstrate that although the Weinberg sum rules are satisfied in any such model, the…