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We summarize recent developments in the field of higher dimensional bosonization made by the authors and collaborators and propose a general formula for the field operator in terms of currents and densities in one dimension using a new…
The linear Boltzmann equation with constant coefficients in the three-dimensional infinite space is revisited. It is known that the Green's function can be calculated via the Fourier transform in the case of isotropic scattering. In this…
We determine the nonperturbative anisotropic parameter of the gauge action in the quenched approximation with less than 1% accuracy using the Sommer scale measured by the L\"uscher-Weisz algorithm or smearing technique. We also study the…
The scattering phase, defined as $ \log \det S ( \lambda ) / 2\pi i $ where $ S ( \lambda ) $ is the (unitary) scattering matrix, is the analogue of the counting function for eigenvalues when dealing with exterior domains and is closely…
We present a method for precisely measuring the tunnel splitting in single-molecule magnets using electron-spin resonance, and use these measurements to precisely and independently determine the underlying transverse anisotropy parameter,…
This is a review of theoretical results from the three-dimensional equations of anisotropic elasticity or linear piezoelectricity on waves and vibrations in quartz crystal plates. It covers both the classical results on acoustic wave…
To calculate the magnetic ground state of nanoparticles we present a self-consistent first principles method in terms of a fully relativistic embedded cluster multiple scattering Green's function technique. Based on the derivatives of the…
The Wigner function of a finite-dimensional system can be constructed via dual pairing of a density matrix with the Stratonovich-Weyl kernel. Following Kenfack and $\dot{\text{Z}}$yczkowski, we consider the indicator of nonclassicality of a…
A numerical method for calculation electronic structure of a nanosystem composed of a pseudoisocyanine (PIC) molecule assembled on a silver nanoparticle is developed. The electronic structure of the silver nanoparticle containing 125 atoms…
In this article, we consider a theoretical model for a type I Weyl semimetal, under the presence of a diluted uniform concentration of torsional dislocations. By a mathematical analysis for partial wave scattering (phase-shift) for the…
We examine the possibility of using negative refraction stemming from the phonon response in an anisotropic crystal to create a simple slab lens with plane parallel sides, and show that imaging from such a lens should be possible at room…
We present here a set of lecture notes on tomography. The Radon transform and some of its generalizations are considered and their inversion formulae are proved. We will also look from a group-theoretc point of view at the more general…
We study the potential energy surface of the ozone molecule by means of Quantum Monte Carlo simulations based on the resonating valence bond concept. The trial wave function consists of an antisymmetrized geminal power arranged in a…
We investigate the inversion phenomenon between the XXZ anisotropies of the Hamiltonian and the wave function in quantum spin chains, mainly focusing on the S=1/2 trimerized XXZ model with the next-nearest-neighbor interactions. We have…
Acoustic room modes and the Green's function mode expansion are well-known for rectangular rooms with perfectly reflecting walls. First-order approximations also exist for nearly rigid boundaries; however, current analytical methods fail to…
We study Weyl elements in isotropic reductive groups over commutative rings. Our main result in an explicit formula for squares of such elements. We also classify these elements in rank one groups and prove basic properties of their loci.
We obtain an estimate for the main term of the counting function for numerical monoids.
Magnetocrystalline anisotropy is a fundamental property of magnetic materials that determines the dynamics of magnetic precession, the frequency of spin waves, the thermal stability of magnetic domains, and the efficiency of spintronic…
We formulate the conformal mapping between $R^3$ and $S^3$, the 3 sphere. This mapping is applied to the critical Ising model. From this mapping, we calculate the second and fourth moments of the magnetization density, and using those…
The performance of permanent magnets YCo$_5$ can be improved by replacing cobalt with other elements, such as iron, copper, and nickel. In order to determine its optimum composition, it is necessary to perform systematic theoretical…