Related papers: The Effects of Geometry on the Hyperpolarizability
Certain many-particle Hardy inequalities are derived in a simple and systematic way using the so-called ground state representation for the Laplacian on a subdomain of $\mathbb{R}^n$. This includes geometric extensions of the standard Hardy…
It is shown here that symmetric hyperbolicity, which guarantees well-posedness, leads to a set of two inequalities for matrices whose elements are determined by a given theory. As a part of the calculation, carried out in a mostly-covariant…
We have analytically investigated the effects of non-linearity on the free energy and thermodynamic geometry of holographic superconductors in $2+1 -$dimensions. The non-linear effect is introduced by considering the coupling of the massive…
Topology and nonlinearity are deeply connected. However, whether topological effects can arise solely from the structure of nonlinear interaction terms, and the nature of the resulting topological phases, remain to large extent open…
The high-energy non-thermal universe is dominated by power law-like spectra. Therefore results in high-energy astronomy are often reported as parameters of power law fits, or, in the case of a non-detection, as an upper limit assuming the…
New ray-optical elements allow generalized refraction of light rays, but geometry imposes limitations on possible mappings between the positions of an object and its geometric image. Here I study the case of an infinite, planar,…
Several cellular activities, such as directed cell migration, are coordinated by an intricate network of biochemical reactions which lead to a polarised state of the cell, in which cellular symmetry is broken, causing the cell to have a…
The pattern of radiation energy deposition in substances at the microscopic level of lattice, molecule size, or the cell's nucleus is not uniform. The energy of radiation is transferred to the substance medium in the form of discrete,…
What is nuclear symmetry energy? Why is it important? What do we know about it? Why is it so uncertain especially at high densities? Can the total symmetry energy or its kinetic part be negative? What are the effects of three-body and/or…
The optical properties of solids are governed not only by their energy band dispersions but also by the quantum geometry of Bloch states. While the role of energy bands in determining the perceived optical appearance of materials, such as…
Background: Spectroscopic factors, overlaps, and isospin symmetry are often used in conjunction with single-particle wave functions for the phenomenological analysis of nuclear structure and reactions. Many differing prescriptions for…
When it is polarised, a cell develops an asymmetric distribution of specific molecular markers, cytoskeleton and cell membrane shape. Polarisation can occur spontaneously or be triggered by external signals, like gradients of signalling…
In the standard treatment of heterogeneous nucleation on a surface, the energy of the surface is assumed to be homogeneous. Often its value is obtained from some macroscopic measurement. We ask the question what happens if we consider the…
Nonlinear optical phenomena are typically local. Here we predict the possibility of highly nonlocal optical nonlinearities for light propagating in atomic media trapped near a nano-waveguide, where long-range interactions between the atoms…
We analyze the consequences of models of structure formation for higher-order ($n$-point) galaxy correlation functions in the mildly non-linear regime. Several variations of the standard $\Omega=1$ cold dark matter model with…
We present a practical roadmap to achieve optical cycling and laser cooling of asymmetric top molecules (ATMs). Our theoretical analysis describes how reduced molecular symmetry, as compared to diatomic and symmetric non-linear molecules,…
We consider membranes as fluid deformable surface and allow for higher order geometric terms in the bending energy. The evolution equations are derived and numerically solved using surface finite elements. The higher order geometric terms…
We isolate a geometric mechanism that complements the dynamical suppression of macroscopic interference: In a high-dimensional Hilbert space, almost all state vectors are nearly orthogonal, accommodating an exponentially large reservoir of…
We construct the geometric quantization of a compact surface using a singular real polarization coming from an integrable system. Such a polarization always has singularities, which we assume to be of nondegenerate type. In particular, we…
A geometrical model for tri-nuclear molecules is presented. An analytical solution is obtained provided the nuclei, which are taken to be prolately deformed, are connected in line to each other. Furthermore, the tri-nuclear molecule is…