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Hawking–Penrose Black Hole Model. Large Emission Regime Rep. Math. Phys. (IF 0.86) Pub Date : 2021-02-17 E. Pechersky; S. Pirogov; A. Yambartsev
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
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Gauge Transformations of a Relativistic Field of Quantum Harmonic Oscillators Rep. Math. Phys. (IF 0.86) Pub Date : 2021-02-17 Jan Naudts
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
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Multi-Species Stochastic Model and Related Effective Site-Dependent Transition Rates Rep. Math. Phys. (IF 0.86) Pub Date : 2021-02-17 Mohammad Ghadermazi
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
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Geodesic Compatibility: Goldfish Systems Rep. Math. Phys. (IF 0.86) Pub Date : 2021-02-17 Worapat Piensuk; Sikarin Yoo-Kong
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
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Fractional Diffusion with Time-Dependent Diffusion Coefficient Rep. Math. Phys. (IF 0.86) Pub Date : 2021-02-17 F.S. Costa; E. Capelas de Oliveira; Adrian R.G. Plata
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
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Automorphisms of Effect Algebras with Respect to Convex Sequential Product Rep. Math. Phys. (IF 0.86) Pub Date : 2021-02-17 Jinhua Zhang; Guoxing Ji
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
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Invariants in Quantum Geometry Rep. Math. Phys. (IF 0.86) Pub Date : 2021-02-17 Adrian P.C. Lim
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
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W★ Dynamics of Infinite Dissipative Quantum Systems Rep. Math. Phys. (IF 0.86) Pub Date : 2021-02-17 Geoffrey L. Sewell
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
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Two-Qutrit Entangled f-Coherent States Rep. Math. Phys. (IF 0.86) Pub Date : 2021-02-17 A. Dehghani; B. Mojaveri; R. Jafarzadeh Bahrbeig
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
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Fractional Schrödinger Equation with Singular Potentials of Higher Order Rep. Math. Phys. (IF 0.86) Pub Date : 2021-02-17 Arshyn Altybay; Michael Ruzhansky; Mohammed Elamine Sebih; Niyaz Tokmagambetov
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
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New Dynamics of the Classical and Nonlocal Gross-Pitaevskii Equation with a Parabolic Potential Rep. Math. Phys. (IF 0.86) Pub Date : 2020-12-02 Shimin Liu; Wu Hua; Da-Jun Zhang
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
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Uniqueness of Gibbs Measures for an Ising Model with Continuous Spin Values on a Cayley Tree Rep. Math. Phys. (IF 0.86) Pub Date : 2020-12-02 Farhod Halimjonovich Haydarov; Shamshod A. Akhtamaliyev; Madalixon A. Nazirov; Behzod Boyxonovich Qarshiyev
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.
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Thermal Equilibrium Distribution in Infinite-Dimensional Hilbert Spaces Rep. Math. Phys. (IF 0.86) Pub Date : 2020-12-02 Roderich Tumulka
The thermal equilibrium distribution over quantum-mechanical wave functions is a so-called Gaussian adjusted projected (GAP) measure, GAP(ρβ), for a thermal density operator ρβ at inverse temperature β. More generally, GAP(ρ) is a probability measure on the unit sphere in Hilbert space for any density operator ρ (i.e. a positive operator with trace 1). In this note, we collect the mathematical details
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Non-Translation-Invariant Gibbs Measures of an SOS Model on a Cayley Tree Rep. Math. Phys. (IF 0.86) Pub Date : 2020-12-02 Muzaffar M. Rahmatullaev; B.U. Abraev
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
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Matrix Spectral Problems and Integrability Aspects of the Błaszak-Marciniak Lattice Equations Rep. Math. Phys. (IF 0.86) Pub Date : 2020-12-02 Deng-Shan Wang; Qian Li; Xiao-Yong Wen; Ling Liu
A method to derive the matrix spectral problems of the Błaszak–Marciniak lattice equations is proposed, and the matrix Lax representations of all the three-field and four-field Błaszak-Marciniak lattice equations are given explicitly. The integrability aspects of a three-field Błaszak–Marciniak lattice equation is studied as an example. To be specific, an integrable lattice hierarchy is constructed
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Isomorphism Between the Local Poincaré Generalized Translations Group and the Group of Spacetime Transformations (⊗ LB1)4 Rep. Math. Phys. (IF 0.86) Pub Date : 2020-12-02 Alcides Garat
We will prove that there is a direct relationship between the Poincaré 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
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Double-Graded Quantum Superplane Rep. Math. Phys. (IF 0.86) Pub Date : 2020-12-02 Andrew James Bruce; Steven Duplij
A ℤ2 × ℤ2-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 superplane admits a natural
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Symmetries, Explicit Solutions and Conservation Laws for Some Time Space Fractional Nonlinear Systems Rep. Math. Phys. (IF 0.86) Pub Date : 2020-11-01 Komal Singla; M. Rana
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
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⋆-Cohomology, Connes–Chern Characters, and Anomalies in General Translation-Invariant Noncommutative Yang–Mills Rep. Math. Phys. (IF 0.86) Pub Date : 2020-11-01 Amir Abbass Varshovi
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.
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Stateless Quantum Structures and Extremal Graph Theory Rep. Math. Phys. (IF 0.86) Pub Date : 2020-11-01 Václav Voràček
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
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Flat Gauge Fields and the Riemann-Hilbert Correspondence Rep. Math. Phys. (IF 0.86) Pub Date : 2020-11-01 Andrés Viña
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 on a complex manifold X, so that such a field on a B-brane turns it into an object of the category of constructible sheaves on X.
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Positively Subexpansive Dynamical Systems Rep. Math. Phys. (IF 0.86) Pub Date : 2020-11-01 Alessandro Fedeli
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.
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The Coupled Yang–Mills–Boltzmann System in Bianchi Type I Space-Time Rep. Math. Phys. (IF 0.86) Pub Date : 2020-11-01 David Dongo; Abel Kenfack Nguelemo; Norbert Noutchegueme
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.
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Spinor Covariant Derivative on Degenerate Manifolds Rep. Math. Phys. (IF 0.86) Pub Date : 2020-11-01 Gülşah Aydin Şekercı; Abdılkadır Ceylan Çöken
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
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Nonlocal Phenomena in Quantum Mechanics with Fractional Calculus Rep. Math. Phys. (IF 0.86) Pub Date : 2020-11-01 Kazim Gökhan Atman; Hüseyin Şirin
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
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The Spinning Particles – Classical Description Rep. Math. Phys. (IF 0.86) Pub Date : 2020-09-02 Cezary J. Walczyk, Zbigniew Hasiewicz
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
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Quantum-Mechanical Explicit Solution for the Confined Harmonic Oscillator Model with the Von Roos Kinetic Energy Operator Rep. Math. Phys. (IF 0.86) Pub Date : 2020-09-02 E.I. Jafarov, S.M. Nagiyev, A.M. Jafarova
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
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Order Structures of ( D, ℰ)-Quasi-Bases and Constructing Operators for Generalized Riesz Systems Rep. Math. Phys. (IF 0.86) Pub Date : 2020-09-02 Hiroshi Inoue
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
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The Center of a d0-Algebra Rep. Math. Phys. (IF 0.86) Pub Date : 2020-09-02 Anna Avallone, Paolo Vitolo
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)
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Dirac-Bergmann Procedure Having Regard to Interaction for Light-Front Yukawa Model Rep. Math. Phys. (IF 0.86) Pub Date : 2020-09-02 Jan Żochowski
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
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Analytical and Combinatorial Aspects of the Eigenproblem for the Two-Magnon Sector of XXX Heisenberg Rings Rep. Math. Phys. (IF 0.86) Pub Date : 2020-09-02 P. Krasoń, M. Łabuz, J. Milewski
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
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Quantum Conditional Probability and Measurement Induced Disturbance of a Quantum Channel Rep. Math. Phys. (IF 0.86) Pub Date : 2020-09-02 Dariusz Chruściński, Takashi Matsuoka
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
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On a Generalized Wave Equation and its Application Rep. Math. Phys. (IF 0.86) Pub Date : 2020-09-02 Do-Hyung Kim
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.
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The f-Deformation II: f-Deformed Quantum Mechanics in One Dimension Rep. Math. Phys. (IF 0.86) Pub Date : 2020-06-30 Won Sang Chung, Hassan Hassanabadi
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.
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Estimating the Size of the Scatterer Rep. Math. Phys. (IF 0.86) Pub Date : 2020-06-30 Alexander G. Ramm
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.
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Existence and Nonexistence of Wave Operators for Time-Decaying Harmonic Oscillators Rep. Math. Phys. (IF 0.86) Pub Date : 2020-06-30 Atsuhide Ishida, Masaki Kawamoto
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
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ℤ2 × ℤ2-Generalizations of Infinite-Dimensional Lie Superalgebra of Conformal Type with Complete Classification of Central Extensions Rep. Math. Phys. (IF 0.86) Pub Date : 2020-06-30 N. Aizawa, P.S. Isaac, J. Segar
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
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Stationary Phase Approximation for the Mach Surface of Superluminally Moving Source Rep. Math. Phys. (IF 0.86) Pub Date : 2020-06-30 V.V. Achkasov, M. Ye. Zhuravlev
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
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Irreducible Representations of Finite Lie Conformal Algebras of Planar Galilean Type Rep. Math. Phys. (IF 0.86) Pub Date : 2020-06-30 Xiu Han, Dengyin Wang, Chunguang Xia
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
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Generalized Kinematics on ρ-Commutative Algebras Rep. Math. Phys. (IF 0.86) Pub Date : 2020-06-30 E. Peyghan, Z. Bagheri, I. Gultekin, A. Gezer
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
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A Real-Analytic Proof of the Simon-Wolff Theorem Rep. Math. Phys. (IF 0.86) Pub Date : 2020-06-30 Alexander Y. Gordon, Oleg Safronov
We derive the Simon–Wolff localization criterion from the spectral averaging using an intuitive measure-theoretic lemma.
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Functorial Differential Spaces and the Infinitesimal Structure of Space-Time Rep. Math. Phys. (IF 0.86) Pub Date : 2020-06-30 Leszek Pysiak, Wiesław Sasin, Michael Heller, Tomasz Miller
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
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Two-Dimensional Observables and Spectral Resolutions Rep. Math. Phys. (IF 0.86) Pub Date : 2020-04-20 Anatolij Dvurečenskij, Dominik Lachman
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
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Nonnegativity and Well-Posedness of the Regular Solution of the Magnetized Boltzmann Equation Rep. Math. Phys. (IF 0.86) Pub Date : 2020-04-20 David Dongo, Francis Etienne Djiofack
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.
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Born's Rule from the Principle of Unitary Equivalence Rep. Math. Phys. (IF 0.86) Pub Date : 2020-04-20 Fritiof Wallentin
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
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Ground State Photon Number at Large Distance Rep. Math. Phys. (IF 0.86) Pub Date : 2020-04-20 L. Amour, L. Jager, J. Nourrigat
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
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Eigenvalue Bound for Schrödinger Operators with Unbounded Magnetic Field Rep. Math. Phys. (IF 0.86) Pub Date : 2020-04-20 Diana Barseghyan, Baruch Schneider
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.
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On q-Special Matrix Functions Using Quantum Algebraic Techniques Rep. Math. Phys. (IF 0.86) Pub Date : 2020-04-20 Ravi Dwivedi, Vivek Sahai
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.
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Fractional Periodic Processes: Properties and an Application of Polymer Form Factors Rep. Math. Phys. (IF 0.86) Pub Date : 2020-04-20 Wolfgang Bock, Jose Luis da Silva, Ludwig Streit
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.
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Fisher Information for the Morse Oscillator Rep. Math. Phys. (IF 0.86) Pub Date : 2020-04-20 Supriya Chatterjee, Golam Ali Sekh, Benoy Talukdar
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
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Application of the Schur–Weyl Duality in the One-Dimensional Hubbard Model Rep. Math. Phys. (IF 0.86) Pub Date : 2020-04-20 Dorota Jakubczyk
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
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The f-Deformation I: f-Deformed Classical Mechanics Rep. Math. Phys. (IF 0.86) Pub Date : 2020-02-28 Won Sang Chung, Hassan Hassanabadi
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.
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Sharp Estimates for the Schrödinger Equation Associated with the Twisted Laplacian Rep. Math. Phys. (IF 0.86) Pub Date : 2020-02-28 Duván Cardona Sánchez
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.
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Two Finite Sequences of Symmetric q-Orthogonal Polynomials Generated by Two q-Sturm–Liouville Problems Rep. Math. Phys. (IF 0.86) Pub Date : 2020-02-28 Mohammad Masjed-Jamei, Fatemeh Soleyman, Wolfram Koepf
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
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Solutions of Nonlocal Schrödinger Equation via the Caputo-Fabrizio Definition for Some Quantum Systems Rep. Math. Phys. (IF 0.86) Pub Date : 2020-02-28 Fatma El-Ghenbazia Bouzenna, Zineb Korichi, Mohammed Tayeb Meftah
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
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The Collapse Before a Quantum Jump Transition Rep. Math. Phys. (IF 0.86) Pub Date : 2020-02-28 John E. Gough
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〉
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Riemann–Hilbert Method for the Three-Component Sasa–Satsuma Equation and Its N-Soliton Solutions Rep. Math. Phys. (IF 0.86) Pub Date : 2020-02-28 Siqi Xu, Ruomeng Li, Xianguo Geng
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
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Constructing Mutually Unbiased Bases from Unextendible Maximally Entangled Bases Rep. Math. Phys. (IF 0.86) Pub Date : 2020-02-28 Hui Zhao, Lin Zhang, Shao-Ming Fei, Naihuan Jing
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)
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Remarks on Solutions of the Generalized Jackiw-Pi Model with Self-Dual Potential Rep. Math. Phys. (IF 0.86) Pub Date : 2020-02-28 Hyungjin Huh
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.
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Su(N) Polynomial Integrals and Some Applications Rep. Math. Phys. (IF 0.86) Pub Date : 2020-02-28 O. Borisenko, S. Voloshyn, V. Chelnokov
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.
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