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In the framework of the LDA+U approximation we propose the direct way of calculation of crystal-field excitation energy and apply it to La and Y titanates. The method developed can be useful for comparison with the results of spectroscopic…
Spin space groups, formed by operations where the rotation of the spins is independent of the accompanying operation acting on the crystal structure, are appropriate groups to describe the symmetry of magnetic structures with null…
Starting from the idea of realising constant roll inflation in string theory we develop the constant roll formalism for two scalar fields. We derive the two-field potential which is compatible with a constant roll regime and discuss…
It is well known how to define the operator $Q$ for the total charge (i.e., positron number minus electron number) on the standard Hilbert space of the second-quantized Dirac equation. Here we ask about operators $Q_A$ representing the…
The paper aims to explore the impact of composite operators containing a few physical quantities on the gravitational and electromagnetic fields, studying the influencing factors and physical properties of octonion field equations. J. C.…
We introduce a notion of smooth fields of operators following the notion of smooth fields of Hilbert spaces recently defined by L. Lempert and R. Sz\H{o}oke arXiv:1004.4863(2) . Formally, if $\nabla$ is the connection of a smooth field of…
We present molecular-dynamic simulations of memory resistors (memristors) including the crystal field effects on mobile ionic species such as oxygen vacancies appearing during operation of the device. Vacancy distributions show different…
Many studies have been conducted on statistical convergence, and it remains an area of active research. Since its introduction, statistical convergence has found applications many fields. Nevertheless, there is a shortage of research…
Reducible representations of CAR and CCR are applied to second quantization of Dirac and Maxwell fields. The resulting field operators are indeed operators and not operator-valued distributions. Examples show that the formalism may lead to…
The problem of extending quantum-mechanical formal scattering theory to a more general class of models that also includes quantum field theories is discussed, with the aim of clarifying certain aspects of the definition of scattering…
We introduce a family or Herz type spaces considering rectangles instead of balls and we study continuity properties of some average operators acting on them
The $H^\infty$-functional calculus is a two-step procedure, introduced by A. McIntosh, that allows the definition of functions of sectorial operators in Banach spaces. It plays a crucial role in the spectral theory of differential…
We present a new phase field crystal model for structural transformations in multi-component alloys. The formalism builds upon the two-point correlation kernel developed in Greenwood et al. for describing structural transformations in pure…
New phenomenological approach for the description of elementary collective excitations is proposed. The crystal is considered to be an anisotropic space-time vacuum with a prescribed metric tensor in which the information on electromagnetic…
Inspired by the spin geometry theorem, two operators are defined which measure angles in the quantum theory of geometry. One operator assigns a discrete angle to every pair of surfaces passing through a single vertex of a spin network. This…
Relations between two definitions of (total) angular momentum operator, as a generator of rotations and in the Lagrangian formalism, are explored in quantum field theory. Generally, these definitions result in different angular momentum…
We give a tentative definition of the recently introduced Root-$T\bar{T}$ operator in a generic, two dimensional quantum conformal field theory with continuous spectrum of scaling weights. The definition assumes certain factorization…
Crystals are paradigms of ordered structures. While order was once seen as synonymous with lattice periodic arrangements, the discoveries of incommensurate crystals and quasicrystals led to a more general perception of crystalline order,…
One can introduce so-called {\em Plain Mechanics} having an {\bf operator realization}. Then the set of one-dimension representations of this operator realization may be identified with the Classical Mechanics. Different irreducible…
In the problem of entanglement there exist two different notions. One is the entanglement of a quantum state, characterizing the state structure. The other is entanglement production by quantum operators, describing the action of operators…