相关论文: New sum rules for an electron in a periodic or nea…
PT-symmetric potentials $V({x}) = -{x}^4 +\j B {x}^3 + C {x}^2+\j D {x} +\j F/{x} +G/{x}^2$ are quasi-exactly solvable, i.e., a specific choice of a small $G=G^{(QES)}= integer/4$ is known to lead to wave functions $\psi^{(QES)}(x)$ in…
The motion of an electron in an image field and a blocking electric field is considered in semiclassical approximation. An exact analytical expression is found for the density of the energy spectrum of states. The dependence of spectral…
It is shown that the Coulomb correlation problem for a system of two electrons (two charged particles) in an external oscillator potential possesses a hidden $sl_2$-algebraic structure being one of recently-discovered quasi-exactly-solvable…
This work revisits the classical concept of electric energy and suggests that the common definition is likely to generate large errors when dealing with nanostructures. For instance, deriving the electrostatic energy in semiconductors using…
In-medium sum rules following from the chiral charge algebra of QCD are reviewed, and new sum rules are derived. The new sum rules relate the I^G(J^{PC})=1^-(0^{++}) excitations (quantum numbers of a_0(980)) to the scalar and isovector…
After discussing alternative scenarios for the origins of the electroweak symmetry breaking, I briefly review the experimental status of the Standard Model. I explore further both the hints for, and constraints on, supposing that that a…
In this paper we derive an expression for the dynamic electric polarizability of a particle bound by a double delta potential for frequencies below and above the absolute value of the particle's ground state energy. The derived expression…
This paper presents a novel design of an electronic circuit that is equivalent to a mechanical discontinuous impact oscillator exhibiting hard impacts. The governing equations of the electronic circuit are derived to demonstrate its…
This paper investigates a novel mechanism for quasi-singularity formation in both linear and nonlinear hyperbolic wave equations in two and three dimensions. We prove that over any finite time interval, there exist inputs such that the…
Lattice sum rules are checked using lattice perturbation theory. The action sum rule gives a relation between the quark-antiquark potential, its logarithmic derivative with respect to distance and the expectation value of the action; the…
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…
Based on Gauss's law for the electric field, new integral formulas are deduced. Although the applications are not limited within the physics realm, an application is also presented, for the sake of practicability, specifically in the area…
Sum rules for the total- and scissors-mode M1 strength in odd-A nuclei are derived within the single-j interacting boson-fermion model. We discuss the physical content and geometric interpretation of these sum rules and apply them to…
In recent years some near-optimal estimates have been established for certain sum-product type estimates. This paper gives some first extremal results which provide information about when these bounds may or may not be tight. The main tool…
Relations between particle and wave properties for charge carriers in periodic potentials of crystalline metals and semiconductors are derived. The particle aspects of electrons and holes in periodic potentials are considered using…
Photonic bound states in the continuum are spatially localised modes with infinitely long lifetimes that exist within a radiation continuum at discrete energy levels. These states have been explored in various systems where their emergence…
Using unitarity, analyticity and crossing symmetry, we derive universal sum rules for scattering amplitudes in theories invariant under an arbitrary symmetry group. The sum rules relate the coefficients of the energy expansion of the…
A generalized Friedel sum rule is derived for a quantum dot with internal orbital and spin degrees of freedom. The result is valid when all many-body correlations are taken into account and it links the phase shift of the scattered electron…
The sum rule for the first moment of the polarised (virtual) photon structure function $g_1^\gamma(x,Q^2;K^2)$ is revisited in the light of proposals for future $e^+ e^-$ colliders. The sum rule exhibits an array of phenomena characteristic…
Two interacting electrons in a harmonic oscillator potential under the influence of a perpendicular homogeneous magnetic field are considered. Analytic expressions are obtained for the energy spectrum of the two- and three-dimensional…