Exact space-time propagator for the wave (second-order in time) equation in a layered ysstem, made up of a layer sandwiched between two other different semi-infinite layers, is obtained by means of the multiple scattering theory (MST) approach. The MST approach is made possible due to obtained effective potentials localized at interfaces and responsible for reflection from and propagation through them

The present paper aims at developing a theory of logical entropy for p-preserving systems (L, p, ψ), where p is a Bayesian gs-map on a bounded lattice L and ψ is a p-preserving lattice homomorphism. Having proved several desirable properties, we construct a Rokhlin-type metric involving logical conditional entropy of p-partitions of a Bayesian gs-space (L,p), and use it to establish a logical entropy

It is proved that if the Navier-Stokes problem is considered in ℝ3, then the initial velocity has to be zero. This is the paradox. The consequences of this paradox are: a) The NSP is contradictory physically and mathematically; it is not a correct formulation of the problem of motion of the incompressible viscous fluid. b) The solution to the NSP does not exist on [0, ∞). This solves one of the millennium

We consider magnetic Schrödinger operator H = (i ∇ + A)2 - αδΓ with an attractive singular interaction supported by a piecewise smooth curve Γ being a local deformation of a straight line. Such a Hamiltonian describes a charged particle confined to a leaky quantum wire and exposed to the magnetic field B which is supposed to be nonzero and local. We show that the essential spectrum of this system is

In this paper we study diagonal quantum channels and their structure by proving some results and giving the most applicable instances of them. It is shown that the action of every diagonal quantum channel on a pure state from a computational basis is a convex combination of pure states determined by some transition probabilities. Finally, by using the Cholesky decomposition it is presented an algorithmic

In order to highlight time-varying constants such as the universal gravitation constant and to elucidate the effects of higher dimensions on cosmological parameters in the universe, we developed a toy cosmological model based upon an anisotropic n-dimensional spatial universe within an (n + 1)-dimensional spacetime. A dynamical power law model for dark energy is considered. The observational parameters

For this work, we studied a finite system of discrete-size aggregating particles for two types of kernels with arbitrary parameters, a condensation (or branched-chain polymerization) kernel, K(i, j) = (A + i)(A + j), and a linear combination of the constant and additive kernels, K(i, j) = A + i + j. They were solved under monodisperse initial conditions in the combinatorial approach with the assumption

The present paper is a follow-up of our previous paper that derives a slightly simplified model equation for the Klein-Gordon equation, describing the propagation of a scalar field of mass μ in the background of a rotating black hole and, among others, supports the instability of the field down to a/M ≈ 0.97. The latter result was derived numerically. This paper gives corresponding rigorous results

In the present article, we construct the super fuzzy Dirac and chirality operators on super fuzzy sphere SF(2|2). Using the super fuzzy Ginsparg-Wilson algebra, we study the super gauged fuzzy Dirac and chirality operators in instanton sector. We show that they have correct commutative limit in the limit case when noncommutative parameter l tends to infinity.

We construct a class of generalized q-deformed coherent states (Gq-CS) and we introduce a generalization of the Euler probability distribution for which we write down the probability generating function. As application, we discuss the statistics of a q-deformed number operator in these Gq-CS with respect to many parameters.

We obtain a class of exact solutions for a Bessel-type differential equation, which is a five-parameter linear ordinary differential equation of the second order with irregular (essential) singularity at the origin. The solutions are obtained using the Tridiagonal Representation Approach (TRA) as bounded series of square-integrable functions written in terms of a quasirational Laguerre function (Laguerre

The paper deals with the Caldirola–Kanai Hamiltonian in which the potential energy is defined as a linear function of the position variable. The exact solution of the Schrödinger equation using this Hamiltonian is presented. It is shown that this solution can be utilized in the theory of electric conduction of metals and semiconductors. The main idea of this paper is that if the Caldirola–Kanai Hamiltonian

Dynamical systems with dissipative behaviour can be described in terms of contact manifolds and a modified version of Hamilton's equations. Dissipation terms can also be added to field equations, as showed in a recent paper where we introduced the notion of k-contact structure, and obtained a modified version of the De Donder–Weyl equations of covariant Hamiltonian field theory. In this paper we continue

We characterize all spacelike and spherically symmetric constant mean curvature hypersurfaces in the maximally extended Reissner–Nordström spacetimes. These characterizations also provide a proof of the existence and uniqueness of the initial value problem for the spacelike and spherically symmetric constant mean curvature equation in the maximally extended Reissner–Nordström spacetimes.

The electromagnetic self-force of a point charge moving arbitrarily on a rectilinear trajectory is calculated by averaging its retarded electric self-field over a sphere of infinitesimal radius centred on the charge's present position. The finite part of the self-force obtained is the well-established relativistic radiation reaction, while its divergent part implies the pre-relativistic longitudinal

The object of the present paper is to investigate D-homothetically deformed (CS)4-spacetime (or GRW-spacetime) satisfying different semi-symmetric conditions, based on the equivalence, proved by Shaikh and Kundu, of the mentioned above structures.

Generalized eigenvectors are key tools in the theory of rigged Hilbert spaces. Let H be a Hilbert space and let Φ be a dense subspace of H. Let A be a densely defined linear operator in H such that Φ ⊂ DA and AΦ ⊂ Φ. The generalized eigenvectors of A are the eigenvectors of the algebraic dual of A |Φ. In the case where Φ is endowed with a topology τ finer than the norm topology inherited from H, generalized

We show that the approximate quasi-orthogonality of two operator algebras is equivalent to the algebras being approximately private relative to their conditional expectation quantum channels. Our analysis is based on a characterization of the measure of orthogonality in terms of Choi matrices and Kraus operators for completely positive maps. We present examples drawn from different areas of quantum

When solving Einstein's equations for an isolated system of masses, V. Fock introduced a harmonic reference frame and obtained an unambiguous solution. Further, he concluded that there existed a harmonic reference frame which was determined uniquely apart from a Lorentz transformation if suitable supplementary conditions were imposed. It is known that wave equations keep the same form under Lorentz

In this article, we consider and study the order topology in Minkowski spacetime of the special theory of relativity, i.e. the finest locally convex topology τ on spacetime for which every order bounded subset of spacetime is τ-bounded. This order topology that is introduced into spacetime as an ordered vector space proves to be Hausdorff and differs from Zeeman's order topology. Applying the order

In an attempt to generalize Hamilton's principle, an action functional is proposed which, unlike the standard version of the principle, accounts properly for all initial data and the possible presence of dissipation. To this end, the convolution is used instead of the L2 inner product so as to eliminate the undesirable end temporal condition of Hamilton's principle. Also, fractional derivatives are

Motivated by the theory of Painlevé equations and associated hierarchies, we study nonautonomous Hamiltonian systems that are Frobenius integrable. We establish sufficient conditions under which a given finite-dimensional Lie algebra of Hamiltonian vector fields can be deformed into a time-dependent Lie algebra of Frobenius integrable vector fields spanning the same distribution as the original algebra

In this note we prove some new results about the application of Wright functions of the first kind to solve fractional differential equations with variable coefficients. Then, we consider some applications of these results in order to obtain some new particular solutions for nonlinear fractional partial differential equations.

In this paper, we propose a stochastic version of the Hawking–Penrose black hole model. We describe the dynamics of the stochastic model as a continuous-time Markov jump process of quanta out and in the black hole. The average of the random process satisfies the deterministic picture accepted in the physical literature. Assuming that the number of quanta is finite the proposed Markov process consists

A set of gauge transformations of a relativistic field of quantum harmonic oscillators is studied in a mathematically rigorous manner. Each wave function in the domain of the number operator of a single oscillator generates a Fréchet-differentiable field of wave functions. Starting from a coherent wave function one obtains a two-dimensional differentiable manifold of coherent vector states. As an illustration

The dynamical rules in an auxiliary stochastic process that generate the biased ensemble of rare events are nonlocal. For the systems with one type of particles, it is shown that one can find special cases for which the transition rates of the auxiliary stochastic generator can be local. In this paper, we investigate this possibility for a system of classical hard-core particles with more than one

To capture a multidimensional consistency feature of integrable systems in terms of geometry, we give a condition called geodesic compatibility implying the existence of integrals in involution of the geodesic flow. The geodesic compatibility condition is constructed from a concrete example namely the integrable Calogero's goldfish system through the Poisson structure and the variational principle

In this paper we propose and discuss the fractional diffusion equation with time-dependent diffusion coefficient, considering the Hilfer-type and Weyl fractional derivatives in the time-variable and space-variable, respectively. We apply the similarity method and Mellin transform methodology to find an explicit solution in terms of Fox H-function. We illustrate graphically the diffusive behaviour described

Let ℌ be a complex Hilbert space with dim ℌ ≥ 3 and ℬ(ℋ) the algebra of all bounded linear operators on ℌ. The effect algebra E (ℌ) on ℌ is the set of all positive contractions in ℬ(ℋ). We consider the automorphism of E(ℌ) with respect to convex sequential product ox on E(ℌ) for some λ ∈ [0, 1] defined by A∘λB=λA12BA12+(1−λ)B12AB12,∀A,B∈E(ℋ). We show that an automorphism of E (ℌ) with respect to convex

In quantum geometry, we consider a set of loops, a compact orientable surface and a solid compact spatial region, all inside ℝ × ℝ3 = ℝ4, which forms a triple. We want to define an ambient isotopic equivalence relation on such triples, so that we can obtain equivalence invariants. These invariants describe how these submanifolds are causally related to or ‘linked’ with each other, and they are closely

We formulate the dynamics of an infinitely extended open dissipative quantum system, Σ, in the Schroedinger picture. The generic model on which this is based comprises a C★-algebra, A, of observables, a folium, ℱ, of states on this algebra and a one-parameter semigroup, τ, of linear transformations of ℱ that represents its dynamics and is given by a natural infinite-volume limit of the corresponding

Nonlinear coherent states or f -coherent states are one of the important class of quantum states of light attached to the f -deformed oscillators. They have been introduced in a pioneering work by Manko et al. and have been realized physically as the stationary states of the centre of mass motion of a trapped ion by de Matos Filho et al. To gain insight into the effectiveness of these states in quantum

In this paper the space-fractional Schrödinger equations with singular potentials are studied. Delta like or even higher-order singularities are allowed. By using the regularising techniques, we introduce a family of ‘weakened’ solutions, calling them very weak solutions. The existence, uniqueness and consistency results are proved in an appropriate sense. Numerical simulations are done, and a particles

Solutions of the classical and nonlocal Gross-Pitaevskii (GP) equation with a parabolic potential and a gain term are derived by using a second order nonisospectral Ablowitz-Kaup-Newell-Segur system and reduction technique of double Wronskians. Solutions of the classical GP equation show typical space-time localized characteristics. An interesting dynamics, solitons carrying an oscillating wave, are

In this paper we consider an Ising model with nearest-neighbour interactions with spin space [0, 1] on a Cayley tree. We present a sufficient condition under which the Ising model has a unique splitting Gibbs measure.

The thermal equilibrium distribution over quantum-mechanical wave functions is a so-called Gaussian adjusted projected (GAP) measure, $GAP(\rho_\beta)$, for a thermal density operator $\rho_\beta$ at inverse temperature $\beta$. More generally, $GAP(\rho)$ is a probability measure on the unit sphere in Hilbert space for any density operator $\rho$ (i.e., a positive operator with trace 1). In this note

In this paper we consider an SOS model with nearest-neighbour interactions and with three spin values, on a Cayley tree of k ≥ 3. For this model, using the well-known translation-invariant Gibbs measures, some non-translation-invariant Gibbs measures are constructed

A method to derive the matrix spectral problems of the Blaszak–Marciniak lattice equations is proposed, and the matrix Lax representations of all the three-field and four-field Blaszak-Marciniak lattice equations are given explicitly. The integrability aspects of a three-field Blaszak–Marciniak lattice equation is studied as an example. To be specific, an integrable lattice hierarchy is constructed

We will prove that there is a direct relationship between the Poincare subgroup of translations, and the group of tetrad transformations LB1 introduced in a previous paper. LB1 is the group composed of SO(1, 1) plus two kinds of discrete transformations. Translations have been extensively studied under the scope of gauge theories. By using the geometric structures built to prove this elementary result

A $\mathbb{Z}_2 \times \mathbb{Z}_2$-graded generalisation of the quantum superplane is proposed and studied. We construct a bicovariant calculus on what we shall refer to as the double-graded quantum superplane. The commutation rules between the coordinates, their differentials and partial derivatives are explicitly given. Furthermore, we show that an extended version of the double-graded quantum

In this work, two space-time fractional nonlinear systems named Drinfeld–Sokolov–Satsuma–Hirota system and Broer Kaup system are considered with fractional derivatives in Riemann–Liouville type. The symmetry approach and power series expansion technique are applied to derive the explicit solutions of both the systems. In addition, the nontrivial conserved vectors are reported using the nonlinear self-adjointness

Topological structure of translation-invariant noncommutative Yang–Mills theories are studied by means of a cohomology theory, the so-called ⋆-cohomology, which plays an intermediate role between de Rham and cyclic (co)homology theory for noncommutative algebras and gives rise to a cohomological formulation comparable to Seiberg–Witten map.

We study hypergraphs which represent finite quantum event structures. We contribute to results of graph theory, regarding bounds on the number of edges, given the number of vertices. We develop a missing one for 3-graphs of girth 4. As an application of the graph-theoretical approach to quantum structures, we show that the smallest orthoalgebra with an empty state space has 10 atoms. Optimized constructions

The geometric phase that appears in the effects of Aharonov-Bohm type is interpreted in the frame of Deligne's version of the Riemann-Hilbert correspondence. We extend also the concept of flat gauge field to $B$-branes which are coherent sheaves, so that such a field on a sheaf turns it into a holonomic regular $D$-module.

In this paper we start the investigation of a metric-related weakening of positive expansiveness. We will show some of its fundamental properties and relation to notions such as weak positive expansiveness and cover expansiveness. Finally, we will see how to use the Bing–Hanner modification to produce examples of positively subexpansive dynamical systems with nonmetrizable phase space.

We prove a local in time existence theorem to a Cauchy problem for the coupled Yang–Mills–Boltzmann system in Bianchi type 1 space-time background.

In this work, we define a spinor covariant derivative for degenerate manifolds with 4-dimensions. To perform this, we have found the principal bundle by using a degenerate spin group. Then, we benefit from a covering map to establish a relationship between the local connection forms of principal bundles. After that, we define a covariant derivative on a degenerate spinor bundle which is an associated

In this study, nonlocal phenomena in quantum mechanics are investigated by making use of fractional calculus. in this context, fractional creation and annihilation operators are introduced and quantum mechanical harmonic oscillator has been generalized as an important tool in quantum field theory. Therefore wave functions and energy eigenvalues of harmonic oscillator are obtained with respect to the

The classical model of spinning particle is analyzed in details 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 non-linear. Nevertheless the equations of motion are analyzed in details and solved numerically. In either case the trajectories are ilustrated and their properties

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 Schrodinger 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

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. Proposed device comes down

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 the charged particle but the particle never be trapped by this harmonic potentials. This physical phenomena changes threshold between the short range class of potential and long-range class of potential in the sense of the existence of physical wave operators. In this paper, we reveal such a threshold is $1/(1-\lambda)$ for some

We introduce a class of novel $\mathbb{Z}_2 \times \mathbb{Z}_2$-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 $\mathbb{Z}_2 \times \mathbb{Z}_2$-graded color superalgebras is