Related papers: The Oblique Basis Method from an Engineering Point…
This paper extends sliding-mode control theory to nonlinear systems evolving on smooth manifolds. Building on differential geometric methods, we reformulate Filippov's notion of solutions, characterize well-defined vector fields on quotient…
The nuclear many-body problem for medium-mass systems is commonly addressed using wave-function expansion methods that build upon a second-quantized representation of many-body operators with respect to a chosen computational basis. While…
The notion of optical geometry, introduced more than twenty years ago as a formal tool in quantum field theory on a static background, has recently found several applications to the study of physical processes around compact objects. In…
Broyden's method, widely used in quantum chemistry electronic-structure calculations for the numerical solution of nonlinear equations in many variables, is applied in the context of the nuclear many-body problem. Examples include the…
We identify the maximal chiral algebra of conformal cyclic orbifolds. In terms of this extended algebra, the orbifold is a rational and diagonal conformal field theory, provided the mother theory itself is also rational and diagonal. The…
We explore the robustness of the correlation matrix Hamiltonian reconstruction technique with respect to the choice of operator basis, studying the effects of bases that are undercomplete and over-complete -- too few or too many operators…
We introduce a four-dimensional quantum model for describing the torsional control of $\rm G_{16}$-type molecules in the electronic ground state, based on the symmetry-adapted variational method. We define conditions for which…
A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely…
The nuclear wobbling motion is studied from a microscopic viewpoint. It is shown that the expressions not only of the excitation energy but also of the electromagnetic transition rate in the microscopic RPA framework can be cast into the…
In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as ``why mathematicians are/should be interested in…
A perturbation method is presented which can be applied to the description of a wide range of physical problems that deal with dynamics of dipolar coupled spins in solids. The method is based on expansion of the operator exponent in a…
Lie-algebraic and quantum-algebraic techniques are used in the analysis of thermodynamic properties of molecules and solids. The local anharmonic effects are described by a Morse-like potential associated with the $su(2)$ algebra. A…
A novel form of quantum control is proposed by applying twisted-light also known as optical vortex beams to drive ultra-narrow atomic transitions in neutral Ca, Mg, Yb, Sr, Hg and Cd bosonic isotopes. This innovative all-optical…
A multidimensional basis of p-adic wavelets is constructed. The relation of the constructed basis to a system of coherent states (i.e. orbit of action) for some $p$-adic group of linear transformations is discussed. We show that the set of…
Excitations of a relativistic geometry are used to represent the theory of quantum electrodynamics. The connection excitations and the frame excitations reduce, respectively, to the electromagnetic field operator and electron field…
We estimate locations of the regions of the percolation and of the non-percolation in the plane $(\lambda,\beta)$: the Poisson rate -- the inverse temperature, for interacted particle systems in finite dimension Euclidean spaces. Our…
We consider the problem of finding paths of shortest transit time between two points (popularly known as Brachistochrone) for cylinders with off-centered center of mass, rolling down without slip, subject solely to the force of gravity.…
In this paper, we consider several geometric inverse problems for linear elliptic systems. We prove uniqueness and stability results. In particular, we show the way that the observation depends on the perturbations of the domain. In some…
The mechanical influence on objects due to their interaction with light has been a central topic in atomic physics for decades. Thus, one finds that many concepts developed to describe cavity optomechanical systems with solid-state…
The one-dimensional harmonic oscillator in a box problem is possibly the simplest example of a two-mode system. This system has two exactly solvable limits, the harmonic oscillator and a particle in a (one-dimensional) box. Each of the two…