Related papers: Exploring the equivalence of causality-based and q…
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…
Uncertainties $(\Delta x)^2$ and $(\Delta p)^2$ are analytically derived in an $N$-coupled harmonic oscillator system when spring and coupling constants are arbitrarily time-dependent and each oscillator is in an arbitrary excited state.…
Strong light-matter coupling within electromagnetic environments provides a promising path to modify and control chemical and physical processes. The origin of the enhancement of nonlinear optical processes such as second-harmonic and…
Optical coherence encodes information about the correlations of the electromagnetic field. In combination with quantum optical approaches, it allows for the study of the correlations between photons. Since the pioneering papers of Glauber,…
Truncated sum rules have been used to calculate the fundamental limits of the nonlinear susceptibilities; and, the results have been consistent with all measured molecules. However, given that finite-state models result in inconsistencies…
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,…
Nonlinear processes are at the core of many optical technologies including lasers, information processing, sensing, and security, and require optimised materials suitable for nanoscale integration. Here we demonstrate the emergence of a…
We study the nonlinear process of second harmonic generation in photonic time-crystals, materials with refractive index that varies abruptly and periodically in time, and obtain the phase matching condition for this process. We find…
We present a Gedankenexperiment that leads to a violation of detailed balance if quantum mechanical transition probabilities are treated in the usual way by applying Fermi's "golden rule". This Gedankenexperiment introduces a collection of…
Sum rules have played an important role in the development of many branches of physics since the earliest days of quantum mechanics. We present examples of one-dimensional quantum mechanical sum rules and apply them in two familiar systems,…
The theory of Bloembergen and Pershan for the light waves at the boundary of nonlinear media is extended to a nonlinear two-dimensional atomic crystal, i.e. a single planar atomic lattice, placed in between linear bulk media. The crystal is…
We investigate the efficacy of boosting the nonlinear-optical response by using novel systems such as those in an excited state or with a degenerate ground state. By applying the Three Level Ansatz (TLA) and using the Thomas-Reiche-Kuhn…
We consider an ionic fluid made with two species of mobile particles carrying either a positive or a negative charge. We derive a sum rule for the fourth moment of equilibrium charge correlations. Our method relies on the study of the…
We consider the dominant $c\bar{c}$ contribution to $\Delta \Gamma$ for the $B_s^0$-$\bar{B}_s^0$ system in the heavy quark limit for both $b$ and $c$ quarks. In analogy with the Bjorken-Isgur-Wise sum rule in semileptonic heavy hadron…
Competition and cooperation among orders is at the heart of many-body physics in strongly correlated materials and leads to their rich physical properties. It is crucial to investigate what impact many-body physics has on extreme nonlinear…
We revisit the photo-absorption sum rule for real Compton scattering from the proton and from nuclear targets. In analogy with the Thomas-Reiche-Kuhn sum rule appropriate at low energies, we propose a new "constituent quark model" sum rule…
Inspired by the work of Pratt and coworkers on a sum rule for the polarization correlations in electron bremsstrahlung when the outgoing electron is not observed, we derive the corresponding sum rule for the elementary process of…
New relations between Bjorken polarized, Gross-Llewellyn Smith and Bjorken unpolarized sum rules are proposed. They are based on the ``universality'' of the perturbative and non-perturbative $\rm{1/Q^2}$ contributions to these sum rules.…
The principle of causality leads to linear Kramers-Kronig relations (KKR) that relate the real and imaginary parts of the complex modulus $G^{*}$ through integral transforms. Using the multiple integral generalization of the Boltzmann…
We consider the optical Hall conductivity of a general electronic medium and prove that the optical Hall angle obeys a new sum rule. This sum rule governs the response of an electronic fluid to a Lorentz electric field and can thought of as…