Related papers: Matching Conditions in Effective-Mass Theory
We improve the upper bounds of the following inequalities proved in [H. Alzer and N. Batir, Monotonicity properties of the gamma function, Appl. Math. Letters, 20(2007), 778-781]. \begin{equation*}…
The Standard Model (SM) of particle physics is both incredibly successful and glaringly incomplete. Among the questions left open is the striking imbalance of matter and antimatter in the observable universe which inspires experiments to…
We consider a loop mixing of two fermion fields of opposite parities whereas the parity is conserved in a Lagrangian. Such kind of mixing is specific for fermions and has no analogy in boson case. Possible applications of this effect may be…
We present a critical analysis of Pade-based methods for the unitarization of low energy amplitudes. We show that the use of certain Pade Approximants to describe the resonance region may lead to inaccurate determinations. In particular, we…
The classical limit of wave quantum mechanics is analyzed. It is shown that the general requirements of continuity and finiteness to the solution $\psi(x)=Ae^{i\phi(x)}+ Be^{-i\phi(x)}$, where $\phi(x)=\frac 1\hbar W(x)$ and $W(x)$ is the…
Partial dynamical symmetry describes a situation in which some eigenstates have a symmetry which the quantum Hamiltonian does not share. This property is shown to have a classical analogue in which some tori in phase space are associated…
We show that electronic wave functions Psi of atoms and molecules have a representation Psi=F*phi, where F is an explicit universal factor, locally Lipschitz, and independent of the eigenvalue and the solution Psi itself, and phi has…
It is often argued that measurable predictions of Bohmian mechanics cannot be distinguished from those of a theory with arbitrarily modified particle velocities satisfying the same equivariance equation. By considering the wave function of…
n a recent paper we proposed the expansion of the space of variations in energy calculations by considering the approximate wave function $\psi$ to be a functional of functions $\chi: \psi = \psi[\chi]$ rather than a function. For the…
Four problematic circumstances are considered, involving models which describe dynamical wavefunction collapse toward energy eigenstates, for which it is shown that wavefunction collapse of macroscopic objects does not work properly. In one…
With the discoveries of very close star-planet systems with planet orbiting sometimes at several star radius but also with well-known situations in our solar system where natural satellites are very close to their parent planet the validity…
In the context of stationary $\mathbb{Z}^d$ nearest-neighbour Gibbs measures $\mu$ satisfying strong spatial mixing, we present a new combinatorial condition (the topological strong spatial mixing property (TSSM)) on the support of $\mu$…
We obtained the order $\rho$ and the type $\sigma$ of wave function with power-law potentials, and found that the order and the type are compatible with the condition $|\sigma|\rho =\sqrt{v_m}$ except to $m=-2$. At the same time, we ansatz…
A new class of matching condition between the atomistic and continuum regions is presented for the multi-scale modeling of crystals. They ensure the accurate passage of large scale information between the atomistic and continuum regions and…
The multi-wave exact resonance condition is a fundamental principle for understanding energy transfer in condensed matter systems, yet the dynamical evolution of waves satisfying this condition remains unexplored. Here, we reveal that the…
Sources of energy errors resulting from the replacement of the physical Coulomb interaction by its long-range $\mathrm{erfc}(\mu r)/r$ approximation are explored. It is demonstrated that the results can be dramatically improved and the…
In a two-part system the "collapse of the wavefunction" of one part can put the other part in a state which would be difficult or impossible to achieve otherwise, in particular one sensitive to small effects in the `collapse' interaction.…
Taking into account the negative results of direct searches for beyond the Standard Model fields and the consequent mass gap between Standard Model and possible unknown states, the use of electroweak effective theories is justified. Whereas…
We give a necessary and sufficient condition for the incompatibility of a pair of effects in a general probabilistic model in which the state space is a total convex space, which can be obtained by minimising a real parameter. This has an…
This paper establishes new common fixed point theorems for weakly compatible mappings in metric spaces, relaxing traditional requirements such as continuity, compatibility, and reciprocal continuity. We present a unified framework for three…