The HVT Technique and the "Uncertainty" Relation for Central

The quantum mechanical hypervirial theorems (HVT) technique is used to treat the so-called "uncertainty" relation for quite a wide class of central potential wells, including the (reduced) Poeschl-Teller and the Gaussian one.It is shown that this technique is quite suitable in deriving an approximate analytic expression in the form of a truncated power series expansion for the dimensionless product $P_{nl}\equiv <r^2>_{nl}<p^2>_{nl}/\hbar^2$, for every (deeply) bound state of a particle moving non-relativistically in the well, provided that a (dimensionless) parameter s is sufficiently small. Numerical results are also given and discussed.

About the quantum Fisher information of nearly pure quantum statistical models

We address nearly pure quantum statistical models, i.e. situations where the information about a parameter is encoded in pure states weakly perturbed by the mixing with a parameter independent state, mimicking a weak source of noise. We show that the symmetric logarithmic derivative is left unchanged, and find an approximate analytic expression for the quantum Fisher information (QFI) which provides bounds on how much a weak source of noise may degrade the QFI.

A new Λ- nucleus potential for the Λ- particle energies in hypernuclei

A new single particle Λ− nucleus potential is considered for the study of the Λ−particle energies in hypernuclei. This potential belongs to the class of potentials for which the formalism of the s−power series expansions of the Hypervirial Theorems technique is applicable. The numbers d_k (k = 0, 1, 2, 3, 4) related to the derivatives of the potential form factor f , determining the potential shape, are obtained and therefore the approximate analytic expression of the energy level Enl (including third-order terms in the small parameter s). Preliminary numerical results are also given and a discussion is made.

Theoretical Expressions for the Ascent Rate of Moist Deep Convective Thermals

An approximate analytic expression is derived for the ratio λ of the ascent rate of moist deep convective thermals and the maximum vertical velocity within them; λ is characterized as a function of two nondimensional buoyancy-dependent parameters y and h and is used to express the thermal ascent rate as a function of the buoyancy field. The parameter y characterizes the vertical distribution of buoyancy within the thermal, and h is the ratio of the vertically integrated buoyancy from the surface to the thermal top and the vertical integral of buoyancy within the thermal. Theoretical λ values are calculated using values of y and h obtained from idealized numerical simulations of ascending moist updrafts and compared to λ computed directly from the simulations. The theoretical values of [Formula: see text] 0.4–0.8 are in reasonable agreement with the simulated λ (correlation coefficient of 0.86). These values are notably larger than the [Formula: see text] from Hill’s (nonbuoyant) analytic spherical vortex, which has been used previously as a framework for understanding the dynamics of moist convective thermals. The relatively large values of λ are a result of net positive buoyancy within the upper part of thermals that opposes the downward-directed dynamic pressure gradient force below the thermal top. These results suggest that nonzero buoyancy within moist convective thermals, relative to their environment, fundamentally alters the relationship between the maximum vertical velocity and the thermal-top ascent rate compared to nonbuoyant vortices. Implications for convection parameterizations and interpretation of the forces contributing to thermal drag are discussed.

Approximate analytic expression for the Skyrmions crystal

We find approximate solutions for the two-dimensional nonlinear [Formula: see text]-model with Dzyalioshinkii–Moriya term, representing magnetic Skyrmions. They are built in an analytic form, by pasting different approximate solutions found in different regions of space. We verify that our construction reproduces the phenomenology known from numerical solutions and Monte Carlo simulations, giving rise to a Skyrmion lattice at an intermediate range of magnetic field, flanked by spiral and spin-polarized phases for low and high magnetic fields, respectively.