The classical model of the spinning particle is analyzed in detail in two versions – with single spinor and two spinors put on the trajectory. Equations of motion of the first version are easily solvable. The system with two spinors becomes nonlinear. Nevertheless, the equations of motion are analyzed in detail and solved analytically and numerically. In either case the trajectories are illustrated

Exactly-solvable confined model of the nonrelativistic quantum harmonic oscillator is proposed. Its position-dependent effective mass Hamiltonian is defined via the von Roos kinetic energy operator. The confinement effect to harmonic oscillator potential is included as a result of certain behaviour of the position-dependent effective mass. The corresponding Schrödinger equation in the canonical approach

The main purpose of this paper is to investigate the relationship between the two order structures of constructing operators for a generalized Riesz system and ( D, ℰ)-quasi bases for two fixed biorthogonal sequences {ϕn} and {Ψn}. In a previous paper, we have studied the order structure of the set Cϕ of all constructing operators for a generalized Riesz system {ϕn}, and furthermore we have shown that

We define the center C(A) of a d0-algebra A as a set of self-mappings on A. The center can be regarded as the set of all possible d0-subdirect factors of A which are subalgebras of A. we show that C(A) is always a Boolean algebra. we also show that C(A) admits an embedding in the power Aκ, where κ is the cofinality of A. In case κ = 1 (i.e. A is a D-lattice) we reobtain the well-known fact that C(A)

In this work we applied the Dirac-Bergmann procedure to establish the Dirac brackets, which have regard to interaction for the light-front Yukawa model in D = 1 + 3 dimensions. We made use of a simple matrix equation leading to solution of the set task, wherein the main problem was to calculate the inverse matrix to the array composed of the constraints for enabled interaction. The proposed device

In this paper we study both analytical and combinatorial properties of solutions of the eigenproblem for the Heisenberg s-1/2 model for two deviations. Our analysis uses Chebyshev polynomials, inverse Bethe Ansatz, winding numbers and rigged string configurations. We show some combinatorial aspects of strings in a geometric way. We discuss some exceptions from the connection between the combinatorial

In classical information theory the conditional probability uniquely defines a classical channel. Introducing a quantum analogue of conditional probability we analyze the mutual information between input and output states of a given quantum channel when the compound state is fully quantum-quantum and classical-quantum. We introduce an analogue of the quantum discord of the channel which measures the

Wave equations on flat Minkowski spacetimes are generalized to curved spacetimes. We present two candidates for generalized wave equation, discuss their legitimacy and consider their applications to Klein–Gordon equation.

In this paper we extend the result of [5] to the quantum version. We present 11 examples of f's and discuss f-deformed quantum mechanics in one dimension for each f which possesses the f-deformed translational symmetry.

Formula for the size of the scatterer is derived explicitly in terms of the scattering amplitude corresponding to this scatterer. By the scatterer either a bounded obstacle D or the support of the compactly supported potential is meant.

Controlled time-decaying harmonic potentials decelerate the velocity of charged particles; however, the particles are never trapped by the harmonic potentials. This physical phenomenon changes the threshold between the short-range and long-range classes of the potential through physical wave operators. We herein report that the threshold is 1/(1 − λ) for some 0 ≤ λ < 1/2, as determined using the mass

We introduce a class of novel ℤ2 × ℤ2-graded color superalgebras of infinite dimension. It is done by realizing each member of the class in the universal enveloping algebra of a Lie superalgebra which is a module extension of the Virasoro algebra. Then the complete classification of central extensions of the ℤ2 × ℤ2-graded color superalgebras is presented. It turns out that infinitely many members

Theoretical study of superluminal sources of electromagnetic radiation boosted after the discovery of Cherenkov–Vavilov radiation. Later, the way to create fictitious sources moving superluminally was suggested. Different approaches have been proposed for the research of the distribution of the potential and the fields radiated by the superluminally moving charges. The simplest idealized cases of uniform

It is well known that Galilean conformal algebras play important roles in the nonrelativistic anti-de Sitter/conformal field theory correspondence. The finite Lie conformal algebras PG(a,b) of planar Galilean type can be viewed as Lie conformal analogues of certain planar Galilean conformal algebras. In this paper, we classify finite irreducible conformal modules over PG(a,b) for all complex numbers

The geometric framework of Double Field Theory (DFT) can be constructed on a para-Hermitian manifold. The canonical, generalized-metric connections and the global expression of the corresponding covariant derivative, a generalization of the kinematical structure of DFT, generalized curvature, a corresponding generalized Lie derivative for the Leibniz algebroid on the tangent bundle are constructed

We derive the Simon–Wolff localization criterion from the spectral averaging using an intuitive measure-theoretic lemma.

We generalize the differential space concept as a tool for developing differential geometry, and enrich this geometry with infinitesimals that allow us to penetrate into the superfine structure of space. This is achieved by Yoneda embedding a ring of smooth functions into the category of loci. This permits us to define a category of functorial differential spaces. By suitably choosing various algebras

A two-dimensional observable is a special kind of a σ-homomorphism defined on the Borel σ-algebra of the real plane with values in a σ-complete MV-algebra or in a monotone σ-complete effect algebra. A two-dimensional spectral resolution is a mapping defined on the real plane with values in a σ-complete MV-algebra or in a monotone σ-complete effect algebra which has properties similar to a two-dimensional

We prove, in this paper, the well-posedness and nonnegativity of the regular solution of the relativistic Boltzmann equation in the presence of a given electromagnetic field, taking as background a Lorentzian space-time which is of type Bianchi I with locally rotational symmetry.

Complex phase factors are viewed not only as redundancies of the quantum formalism but instead as remnants of unitary transformations under which the probabilistic properties of observables are invariant. it is postulated that a quantum observable corresponds to a unitary representation of an abelian Lie group, the irreducible subrepresentations of which correspond to the observable's outcomes. It

The purpose of this article is to give a result of localization in position space of the photons in the ground state for a Hamiltonian describing nuclear magnetic resonance in quantum electrodynamics. We prove that |x|−5 is an upper bound of the photon number density as |x| goes to infinity. We also obtain the asymptotic behaviour of the photon number at infinity and prove in particular that it is

In this paper we consider magnetic Schrödinger operators on the two-dimensional unit disk with a radially symmetric magnetic field which explodes to infinity at the boundary. We prove a bound for the eigenvalue moments and a bound for the number of negative eigenvalues for such operators.

We discuss a few models of quantum universal enveloping algebra Uq(sl(2)) from the q-special matrix functions point of view. These models are in terms of q-dilation operators and matrix q-difference-dilation operators and are connected through a matrix q-integral transformation. In the process, we find new basic matrix function identities involving one and two variable q-special matrix functions.

In this paper we introduce and study three classes of fractional periodic processes. An application to ring polymers is investigated. We obtain closed analytic expressions for the form factors, the Debye functions and their asymptotic decay. The relation between the end-to-halftime and radius of gyration is computed for these classes of periodic processes.

The results for Fisher information of the Morse oscillator have thus far been reported [8] for only the ground state of the system. We make use of the wave functions in [21] to provide a general method for computing Fisher-information values for both bound and excited states of the potential. In order to visualize the effects of anharmonicity, the results of the position- and momentum-space Fisher

We present an application of the Schur–Weyl duality in the one-dimensional Hubbard model in the case of a half-filled system of any number of atoms. We replace the actions of the dual symmetric and unitary groups in the whole 4N-dimensional Hilbert space by the actions of the dual groups in the spin and pseudo-spin spaces. The calculations significantly reduce the dimension of the eigenproblem of the

Based on the general deformation called an f-deformation, the algebraic structure for the f-deformation is investigated. As an example, f-deformed mechanics in one dimension is investigated. The relation between the f-deformed mechanics and the mechanics in a curved space is also investigated.

In this note we obtain sharp Strichartz estimates for the Schrödinger equation associated with the twisted Laplacian on ℂn ≅ ℝ2n. The initial data will be considered in suitable Sobolev spaces associated to the twisted Laplacian.

By using a symmetric generalization of Sturm–Liouville problems in q-difference spaces, we introduce two finite sequences of symmetric q-orthogonal polynomials and obtain their basic properties such as a second-order q-difference equations, the explicit form of the polynomials in terms of basic hypergeometric series, three-term recurrence relations and norm-square values based on a Ramanujan identity

The aim of this work is to treat the time-independent one-dimensional nonlocal Schrödinger equation. The nonlocality is described by a kernel with a noninteger power α between 1 and 2. At first stage, by using Caputo–Fabrizio definition and other known results, we have transformed the nonlocal Schrödinger equation to an ordinary linear differential equation. Secondly, we have applied the last result

We may infer a transition |n〉→|m〉 between energy eigenstates of an open quantum system by observing the emission of a photon of Bohr frequency ωmn=(En−Em)/ℏ. In addition to the “collapses” to the state |m〉, the measurement must also have brought into existence the pre-measurement state |n〉. As quantum trajectories are based on past observations, the condition state will jump to |m〉, but the state |n〉

The three-component Sasa–Satsuma equation associated with the 7 × 7 matrix spectral problem is studied by using the Riemann–Hilbert method. The spectral analysis of the Lax pair is performed for the three-component Sasa–Satsuma equation, from which a Riemann–Hilbert problem is formulated. As applications, N-soliton solutions for the three-component Sasa–Satsuma equation are obtained by solving the

We study mutually unbiased bases (MUBs) in which all the bases are unextendible maximally entangled ones. We first present a necessary and sufficient condition of constructing a pair of MUBs in C2⊗C4. Based on this condition, an analytical and necessary condition for constructing MUBs is given. Moreover we illustrate our approach by some detailed examples in C2⊗C4. The results are generalized to C2⊗Cd(d≥3)

We derive the self-dual equations of the generalized Jackiw-Pi model with the self-dual potential (1.7). We also show that the finite energy solution of the generalized Jackiw-Pi model with special self-dual potential (1.9) satisfies the self-dual system which can be transformed into the Liouville type equation.

We use the method of the Weingarten functions to evaluate SU(N) integrals of the polynomial type. As an application we calculate various one-link integrals for lattice gauge and spin SU(N) theories.

Let S be a set of states of a physical system and p(s) be the probability of the occurrence of an event when the system is in state s ∈ S. A function p: S → [0, 1] is called a numerical event or alternatively an S-probability. If a set P:= {p(s) | s ∈ S} is ordered by the order of real functions such that certain plausible requirements are fulfilled, P becomes an orthomodular poset in which properties

The quantum-mechanical harmonic oscillator is considered in a modified version. The modification consists in the replacement of the operator –d2/dx2 in the Schrödinger equation by the Riesz derivative (–Δx)1/2 (known also as the relativistic operator). The exact solution of the fractional differential equation obtained in this way is presented. A crucial component of the Fourier analysis employed in

By embedding a free function into discrete zero curvature equation, we generalize the original hierarchy of integrable differential-difference equations into a new hierarchy which includes the famous relativistic Toda hierarchy. Infinitely many conservation laws and Darboux transformation for the first nontrivial system in the new hierarchy are constructed with the help of its Lax pair. The exact solutions

We define multiplicative Poisson–Nijenhuis structures on a Lie groupoid which extends the notion of symplectic-Nijenhuis groupoid introduced by Stiénon and Xu. We also introduce a special class of Lie bialgebroid structure on a Lie algebroid A, called PN-Lie bialgebroid, which defines a hierarchy of compatible Lie bialgebroid structures on A. Finally, we show that under some topological assumption

Killing magnetic curves are trajectories of charged particles on a Riemannian manifold under action of a Killing magnetic field. In this paper we study Killing magnetic curves in SL(2, ℝ) geometry.

The paper is concerned with the existence and blow-up behaviour of the minimizers for the 2D attractive Gross-Pitaevskii functional when the interaction strength increases to a critical value. Our results hold for all bounded external potential satisfying some general assumptions.

This paper investigates conformal invariance and conserved quantities of nonmaterial volumes. An infinitesimal transformation group and infinitesimal transformations vectors of generators are proposed. The definition of conformal invariance and the determining equation for the systems are presented. The necessary and sufficient conditions of conformal invariance being Noether symmetrical simultaneously

In this paper, we consider a class of space-time fractional inhomogeneous nonlinear diffusion equations with Riemann-Liouville fractional derivative. Symmetry group method is applied to derive explicit solutions of the governing equation from the reduced fractional ordinary differential equations. Conservation laws admitted by the space-time fractional inhomogeneous nonlinear diffusion equations are

Using an algebraic method for solving the wave equation in quantum mechanics, we encountered new families of orthogonal polynomials on the real line. The properties of the physical system (e.g. energy spectrum, phase shift, density of states, etc.) are obtained from the properties of these polynomials. One of these new families is composed of four-parameter polynomials describing a discrete spectrum

In this paper we analyze the structure of decoherence-free subalgebra N(T) of a uniformly continuous covariant semigroup with respect to a representation π of a compact group G on h. In particular, we obtain that, when π is irreducible, N(T) is isomorphic to (ℬ(k) ⊗ 1m)d for suitable Hilbert spaces k and m, and an integer d related to the connected components of G. We extend this result when π is reducible

A class of vector states on a von Neumann algebra is constructed. These states belong to a deformed exponential family. One specific deformation is considered. It makes the exponential function asymptotically linear. Difficulties arising due to noncommutativity are highlighted.

Spacetimes that include a boundary at infinity have a nontrivial topology. The homology of the background influences gauge fields living on them and leads to topological charges. We investigate the charges and fluxes of fields over a Taub–NUT background in Einstein–Maxwell dilaton-axion gravity, by using the relative homology and de Rham cohomology. It turns out that the electromagnetic sector is devoid

Applying and combining the structures of partial order and of one-parameter strongly continuous semi-module of the family of Lorentz operators, we study nonlinear differential evolution equations in Minkowski space-time.

Some new inequalities of Karamata type are established with a convex function. The methods of our proof allow us to obtain an extended version of the reverse of Jensen inequality given by PečnaričA and MičAičA. Applying the obtained results, we give reverses for information inequality (Shannon inequality) in different types, namely ratio type and difference type, under some conditions. Also, we provide

Through the Kre i⌣bn-Višnik-Birman extension scheme, unlike the classical analysis based on von Neumann’s theory, we reproduce the construction and classification of all self-adjoint realisations of three-dimensional hydrogenoid-like Hamiltonians with singular perturbation supported at the Coulomb centre (the nucleus), as well as of Schrödinger operators with Coulomb potentials on the half-line. These

The mathematical structure of Minkowski space, a consequence of the postulates of the special theory of relativity, is endowed with several physically important non-Euclidean topologies defined using the causal structure of spacetime. The present paper is devoted to the study of the first singular homology group of the Minkowski space with one such topology, namely the t-topology, using the relationship

In the present paper, the notions of similarity and conjugation of two quantum dynamical systems are defined and it is proved that similar quantum dynamical systems are conjugate. Putting forward the concepts of transitivity, minimality, chain-transitivity and equicontinuity in the context, it is proved that these notions are preserved under similarity of quantum dynamical systems. It is obtained that

In this article we construct a large class of interacting Euclidean quantum field theories, over a p-adic space time, by using white noise calculus. We introduce p-adic versions of the Kondratiev and Hida spaces in order to use the Wick calculus on the Kondratiev spaces. The quantum fields introduced here fulfill all the Osterwalder–Schrader axioms, except the reflection positivity.

J. C. Maxwell, B. Riemann and H. Poincaré have proposed the idea that all microscopic particles are sink flows in a fluidic aether. Following this research program, a previous theory of gravitation based on a mechanical model of vacuum and a sink flow model of particles is generalized by methods of special relativistic continuum mechanics. In inertial coordinate systems, we construct a tensorial potential

The self-force of a point charge moving on a rectilinear trajectory is obtained, with no need of any explicit removal of infinities, as the negative of the time rate of change of the momentum of its retarded self-field.

In this article, we prove that there is no timelike Killing vector field K on a timelike or lightlike complete Lorentzian manifold of positive sectional curvature for timelike planes. These results, in addition to the known ones for the spacelike case, provide an obstruction to the existence of such a K under any type of causal completeness.

In this paper, we study some Cauchy matrix type solutions for the nonlocal nonlinear Schrödinger equations, including Cauchy matrix type multisoliton solutions and Cauchy matrix type Jordan block solutions. These solutions are obtained from the Cauchy matrix type solutions of Ablowitz–Kaup–Newell–Segur equation through nonlocal reduction. The reduction procedure developed in this paper can apply to

The aim of the paper is to test on a simple model how impenetrable may be a magnetic shield. We study the time evolution of a single species positive plasma, confined in the half-space x1 > 0. The confinement is the result of a balance between a magnetic field and an external field, both singular at x1 = 0; the magnetic field forbids the entrance of plasma particles in the region x1 ≤ 0, whereas the

This work outlines an exact combinatorial approach to finite coagulating systems through recursive equations and use of generating function method. In the classical approach the mean-field Smoluchowski coagulation is used. However, the assumptions of the mean-field theory are rarely met in real systems which limits the accuracy of the solution. In our approach, cluster sizes and time are discrete,

Let V = ⊗Nk=1 Vk be an N-particle Hilbert space, whose individual single-particle space is the one with spin j and dimension d = 2j + 1. Let V(w) be the subspace of V with constant weight w, consisting of vectors whose total spins are w. We show that the combinatorial properties of the constant weight condition impose strong constraints on the reduced density matrices for any vector |ψ) in the constant