Showing papers in "Journal of Mathematical Physics in 2015"
TL;DR: In this article, the finite part of the two-loop sunrise integral with unequal masses in four space-time dimensions in terms of the O(e0)-part and the O (e1)-part of the sunrise integral around two space time dimensions were given in terms elliptic generalisations of Clausen and Glaisher functions.
Abstract: We present the result for the finite part of the two-loop sunrise integral with unequal masses in four space-time dimensions in terms of the O(e0)-part and the O(e1)-part of the sunrise integral around two space-time dimensions. The latter two integrals are given in terms of elliptic generalisations of Clausen and Glaisher functions. Interesting aspects of the result for the O(e1)-part of the sunrise integral around two space-time dimensions are the occurrence of depth two elliptic objects and the weights of the individual terms.
192 citations
TL;DR: For a number of nonlocal nonlinear equations such as nonlocal, nonlinear Schrodinger equation (NLSE), nonlocal Ablowitz-Ladik (AL), non-local, saturable discrete NLSE (DNLSE) and coupled nonlocal AL (CNLSE, AL, DNLSE and AL), this article obtained periodic solutions in terms of Jacobi elliptic functions as well as the corresponding hyperbolic soliton solutions.
Abstract: For a number of nonlocal nonlinear equations such as nonlocal, nonlinear Schrodinger equation (NLSE), nonlocal Ablowitz-Ladik (AL), nonlocal, saturable discrete NLSE (DNLSE), coupled nonlocal NLSE, coupled nonlocal AL, and coupled nonlocal, saturable DNLSE, we obtain periodic solutions in terms of Jacobi elliptic functions as well as the corresponding hyperbolic soliton solutions. Remarkably, in all the six cases, we find that unlike the corresponding local cases, all the nonlocal models simultaneously admit both the bright and the dark soliton solutions. Further, in all the six cases, not only the elliptic functions dn(x, m) and cn(x, m) with modulus m but also their linear superposition is shown to be an exact solution. Finally, we show that the coupled nonlocal NLSE not only admits solutions in terms of Lame polynomials of order 1 but also admits solutions in terms of Lame polynomials of order 2, even though they are not the solution of the uncoupled nonlocal problem. We also remark on the possible integrability in certain cases.
137 citations
TL;DR: In this paper, the Katugampola fractional derivative, Dα[y]=t1−αdydt, and the associated differential operator Dα = t 1−αD1.
Abstract: Katugampola [e-print arXiv:1410.6535] recently introduced a limit based fractional derivative, Dα (referred to in this work as the Katugampola fractional derivative) that maintains many of the familiar properties of standard derivatives such as the product, quotient, and chain rules. Typically, fractional derivatives are handled using an integral representation and, as such, are non-local in character. The current work starts with a key property of the Katugampola fractional derivative, Dα[y]=t1−αdydt, and the associated differential operator, Dα = t1−αD1. These operators, their inverses, commutators, anti-commutators, and several important differential equations are studied. The anti-commutator serves as a basis for the development of a self-adjoint operator which could potentially be useful in quantum mechanics. A Hamiltonian is constructed from this operator and applied to the particle in a box model.
135 citations
TL;DR: In this paper, the pseudospectrum is given a central role in quantum mechanics with non-Hermitian operators, and the concept of pseudo-spectral properties is linked to quasi-hermiticity, similarity to self-adjoint operators and basis properties of eigenfunctions.
Abstract: We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT-symmetric quantum mechanics.
132 citations
TL;DR: A two-parameter family of Renyi relative entropies Dα,z(ρ ∥ σ) that are quantum generalisations of the classical Renyi divergence Dα(p ∥ q) are considered, obtaining explicit formulas for each one of them.
Abstract: We consider a two-parameter family of Renyi relative entropies Dα,z(ρ ∥ σ) that are quantum generalisations of the classical Renyi divergence Dα(p ∥ q). This family includes many known relative entropies (or divergences) such as the quantum relative entropy, the recently defined quantum Renyi divergences, as well as the quantum Renyi relative entropies. All its members satisfy the quantum generalizations of Renyi’s axioms for a divergence. We consider the range of the parameters α, z for which the data-processing inequality holds. We also investigate a variety of limiting cases for the two parameters, obtaining explicit formulas for each one of them.
127 citations
TL;DR: A direct and systematic algorithm is proposed to find one- dimensional optimal system for the group invariant solutions, which is attributed to the classification of its corresponding one-dimensional Lie algebra.
Abstract: A direct and systematic algorithm is proposed to find one-dimensional optimal system for the group invariant solutions, which is attributed to the classification of its corresponding one-dimensional Lie algebra. Since the method is based on different values of all the invariants, the process itself can both guarantee the comprehensiveness and demonstrate the inequivalence of the optimal system, with no further proof. To leave the algorithm clear, we illustrate each stage with a couple of well-known examples: the Korteweg-de Vries equation and the heat equation. Finally, we apply our method to the Novikov equation and use the found optimal system to investigate the corresponding invariant solutions.
98 citations
TL;DR: The conditional quantum mutual information (CMI) of a tripartite state ρABC is an information quantity which lies at the center of many problems in quantum information theory as mentioned in this paper.
Abstract: The conditional quantum mutual information I(A; B|C) of a tripartite state ρABC is an information quantity which lies at the center of many problems in quantum information theory. Three of its main properties are that it is non-negative for any tripartite state, that it decreases under local operations applied to systems A and B, and that it obeys the duality relation I(A; B|C) = I(A; B|D) for a four-party pure state on systems ABCD. The conditional mutual information also underlies the squashed entanglement, an entanglement measure that satisfies all of the axioms desired for an entanglement measure. As such, it has been an open question to find Renyi generalizations of the conditional mutual information, that would allow for a deeper understanding of the original quantity and find applications beyond the traditional memoryless setting of quantum information theory. The present paper addresses this question, by defining different α-Renyi generalizations I α (A; B|C) of the conditional mutual information, some of which we can prove converge to the conditional mutual information in the limit α → 1. Furthermore, we prove that many of these generalizations satisfy non-negativity, duality, and monotonicity with respect to local operations on one of the systems A or B (with it being left as an open question to prove that monotonicity holds with respect to local operations on both systems). The quantities defined here should find applications in quantum information theory and perhaps even in other areas of physics, but we leave this for future work. We also state a conjecture regarding the monotonicity of the Renyi conditional mutual informations defined here with respect to the Renyi parameter α. We prove that this conjecture is true in some special cases and when α is in a neighborhood of one.
96 citations
TL;DR: Geracie et al. as discussed by the authors constructed a Bargmann spacetime in complete generality without any prior restrictions on the fields specifying the geometry, and used it to investigate the details of matter couplings, including the Noether-Ward identities and transport phenomena and thermodynamics of non-relativistic fluids.
Abstract: There is significant recent work on coupling matter to Newton-Cartan spacetimes with the aim of investigating certain condensed matter phenomena. To this end, one needs to have a completely general spacetime consistent with local non-relativistic symmetries which supports massive matter fields. In particular, one cannot impose a priori restrictions on the geometric data if one wants to analyze matter response to a perturbed geometry. In this paper, we construct such a Bargmann spacetime in complete generality without any prior restrictions on the fields specifying the geometry. The resulting spacetime structure includes the familiar Newton-Cartan structure with an additional gauge field which couples to mass. We illustrate the matter coupling with a few examples. The general spacetime we construct also includes as a special case the covariant description of Newtonian gravity, which has been thoroughly investigated in previous works. We also show how our Bargmann spacetimes arise from a suitable non-relativistic limit of Lorentzian spacetimes. In a companion paper [M. Geracie et al., e-print arXiv:1503.02680], we use this Bargmann spacetime structure to investigate the details of matter couplings, including the Noether-Ward identities, and transport phenomena and thermodynamics of non-relativistic fluids.
83 citations
TL;DR: The classical Schrodinger bridge is characterised by an automorphism on the space of endpoints probability measures, which has been studied by Fortet, Beurling, and others as mentioned in this paper.
Abstract: The classical Schrodinger bridge seeks the most likely probability law for a diffusion process, in path space, that matches marginals at two end points in time; the likelihood is quantified by the relative entropy between the sought law and a prior. Jamison proved that the new law is obtained through a multiplicative functional transformation of the prior. This transformation is characterised by an automorphism on the space of endpoints probability measures, which has been studied by Fortet, Beurling, and others. A similar question can be raised for processes evolving in a discrete time and space as well as for processes defined over non-commutative probability spaces. The present paper builds on earlier work by Pavon and Ticozzi and begins by establishing solutions to Schrodinger systems for Markov chains. Our approach is based on the Hilbert metric and shows that the solution to the Schrodinger bridge is provided by the fixed point of a contractive map. We approach, in a similar manner, the steering of a quantum system across a quantum channel. We are able to establish existence of quantum transitions that are multiplicative functional transformations of a given Kraus map for the cases where the marginals are either uniform or pure states. As in the Markov chain case, and for uniform density matrices, the solution of the quantum bridge can be constructed from the fixed point of a certain contractive map. For arbitrary marginal densities, extensive numerical simulations indicate that iteration of a similar map leads to fixed points from which we can construct a quantum bridge. For this general case, however, a proof of convergence remains elusive.
73 citations
TL;DR: A 4-parameter polynomial family of equations generalizing the Camassa-Holm and Novikov equations that describe breaking waves is introduced in this article, where a classification of low-order conservation laws, peaked travelling wave solutions, and Lie symmetries is presented for this family.
Abstract: A 4-parameter polynomial family of equations generalizing the Camassa-Holm and Novikov equations that describe breaking waves is introduced. A classification of low-order conservation laws, peaked travelling wave solutions, and Lie symmetries is presented for this family. These classifications pick out a 1-parameter equation that has several interesting features: it reduces to the Camassa-Holm and Novikov equations when the polynomial has degree two and three; it has a conserved H1 norm and it possesses N-peakon solutions when the polynomial has any degree; and it exhibits wave-breaking for certain solutions describing collisions between peakons and anti-peakons in the case N = 2.
67 citations
TL;DR: In this article, a variant of the Kochen-specker theorem has been shown to imply value indefiniteness in quantum mechanical observables, under the assumption of noncontextuality.
Abstract: The Kochen-Specker theorem proves the inability to assign, simultaneously, noncontextual definite values to all (of a finite set of) quantum mechanical observables in a consistent manner. If one assumes that any definite values behave noncontextually, one can nonetheless only conclude that some observables (in this set) are value indefinite. In this paper, we prove a variant of the Kochen-Specker theorem showing that, under the same assumption of noncontextuality, if a single one-dimensional projection observable is assigned the definite value 1, then no one-dimensional projection observable that is incompatible (i.e., non-commuting) with this one can be assigned consistently a definite value. Unlike standard proofs of the Kochen-Specker theorem, in order to localise and show the extent of value indefiniteness, this result requires a constructive method of reduction between Kochen-Specker sets. If a system is prepared in a pure state ψ, then it is reasonable to assume that any value assignment (i.e., hidd...
TL;DR: In this article, a class of real spectral triples that are similar in structure to a Riemannian manifold but have a finite-dimensional Hilbert space is defined and investigated, determining a general form for the Dirac operator.
Abstract: A class of real spectral triples that are similar in structure to a Riemannian manifold but have a finite-dimensional Hilbert space is defined and investigated, determining a general form for the Dirac operator. Examples include fuzzy spaces defined as real spectral triples. Fuzzy 2-spheres are investigated in detail, and it is shown that the fuzzy analogues correspond to two spinor fields on the commutative sphere. In some cases, it is necessary to add a mass mixing matrix to the commutative Dirac operator to get a precise agreement for the eigenvalues.
TL;DR: In this paper, the adjacency matrix of the ensemble of Erdős-Renyi random graphs is considered and it is shown that in the regime pN ≫ 1, these matrices exhibit bulk universality in the sense that both the averaged n-point correlation functions and distribution of a single eigenvalue gap coincide with the GOE.
Abstract: We consider the adjacency matrix of the ensemble of Erdős-Renyi random graphs which consists of graphs on N vertices in which each edge occurs independently with probability p. We prove that in the regime pN ≫ 1, these matrices exhibit bulk universality in the sense that both the averaged n-point correlation functions and distribution of a single eigenvalue gap coincide with those of the GOE. Our methods extend to a class of random matrices which includes sparse ensembles whose entries have different variances.
TL;DR: The equations governing anti-self-dual and Einstein-Weyl conformal geometries can be regarded as "master dispersionless systems" in four and three dimensions, respectively as mentioned in this paper.
Abstract: The equations governing anti-self-dual and Einstein-Weyl conformal geometries can be regarded as “master dispersionless systems” in four and three dimensions, respectively. Their integrability by twistor methods has been established by Penrose and Hitchin. In this note, we present, in specially adapted coordinate systems, explicit forms of the corresponding equations and their Lax pairs. In particular, we demonstrate that any Lorentzian Einstein-Weyl structure is locally given by a solution to the Manakov-Santini system, and we find a system of two coupled third-order scalar partial differential equations for a general anti-self-dual conformal structure in neutral signature.
TL;DR: In this paper, the authors propose an alternative formulation in which the potential function does not appear, and obtain a set of analytically realizable systems, which is larger than in the standard formulation and may or may not be associated with any given or previously known potential functions.
Abstract: In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schrodinger equation, which is solved for the wavefunction, bound states energy spectrum, and/or scattering phase shift. In this work, however, we propose an alternative formulation in which the potential function does not appear. The aim is to obtain a set of analytically realizable systems, which is larger than in the standard formulation and may or may not be associated with any given or previously known potential functions. We start with the wavefunction, which is written as a bounded infinite sum of elements of a complete basis with polynomial coefficients that are orthogonal on an appropriate domain in the energy space. Using the asymptotic properties of these polynomials, we obtain the scattering phase shift, bound states, and resonances. This formulation enables one to handle not only the well-known quantum systems but also previously untreated ones. Illustrative examples are given for two- and three-parameter systems.
TL;DR: In this article, the theory of irregular conformal blocks of the Virasoro algebra was developed, and the definition of irregular vertex operators of two types was presented, and a conjectural formula for series expansions of the tau functions of the fifth and fourth Painleve equations was proposed.
Abstract: We develop the theory of irregular conformal blocks of the Virasoro algebra. In previous studies, expansions of irregular conformal blocks at regular singular points were obtained as degeneration limits of regular conformal blocks; however, such expansions at irregular singular points were not clearly understood. This is because precise definitions of irregular vertex operators had not been provided previously. In this paper, we present precise definitions of irregular vertex operators of two types and we prove that one of our vertex operators exists uniquely. Then, we define irregular conformal blocks with at most two irregular singular points as expectation values of given irregular vertex operators. Our definitions provide an understanding of expansions of irregular conformal blocks and enable us to obtain expansions at irregular singular points. As an application, we propose conjectural formulas of series expansions of the tau functions of the fifth and fourth Painleve equations, using expansions of irregular conformal blocks at an irregular singular point.
TL;DR: In this paper, it was shown that braidings of the metaplectic anyons Xϵ in SO(3)2 = SU(2)4 with their total charge equal to Y supplemented with projective measurements of the total charge of two metaplectric anyons are universal for quantum computation.
Abstract: We show that braidings of the metaplectic anyons Xϵ in SO(3)2 = SU(2)4 with their total charge equal to the metaplectic mode Y supplemented with projective measurements of the total charge of two metaplectic anyons are universal for quantum computation. We conjecture that similar universal anyonic computing models can be constructed for all metaplectic anyon systems SO(p)2 for any odd prime p ≥ 5. In order to prove universality, we find new conceptually appealing universal gate sets for qutrits and qupits.
TL;DR: In this article, the authors consider the problem of minimally coupled scalar fields with quadratic potential in flat Friedmann-Lemaitre-Robertson-Walker cosmology and present a global and regular dynamical systems description that yields a global understanding of the solution space, including asymptotic features.
Abstract: We consider the familiar problem of a minimally coupled scalar field with quadratic potential in flat Friedmann-Lemaitre-Robertson-Walker cosmology to illustrate a number of techniques and tools, which can be applied to a wide range of scalar field potentials and problems in, e.g., modified gravity. We present a global and regular dynamical systems description that yields a global understanding of the solution space, including asymptotic features. We introduce dynamical systems techniques such as center manifold expansions and use Pade approximants to obtain improved approximations for the “attractor solution” at early times. We also show that future asymptotic behavior is associated with a limit cycle, which shows that manifest self-similarity is asymptotically broken toward the future and gives approximate expressions for this behavior. We then combine these results to obtain global approximations for the attractor solution, which, e.g., might be used in the context of global measures. In addition, we elucidate the connection between slow-roll based approximations and the attractor solution, and compare these approximations with the center manifold based approximants.
TL;DR: In this paper, the complete set of orbits for neutral and weakly charged test particles is discussed, including for neutral particles the extreme and over-extreme metric, and analytical solutions for the equation of motion of neutral test particles in a parametric form are derived.
Abstract: We consider the motion of test particles in the regular black hole space-time given by Ayon-Beato and Garcia [Phys. Rev. Lett. 80, 5056 (1998)]. The complete set of orbits for neutral and weakly charged test particles is discussed, including for neutral particles the extreme and over-extreme metric. We also derive the analytical solutions for the equation of motion of neutral test particles in a parametric form and consider a post-Schwarzschild expansion of the periastron shift to second order in the charge.
TL;DR: In this paper, the authors derived novel dark-bright soliton solutions for the three-component defocusing nonlinear Schrodinger equation with nonzero boundary conditions, and obtained these solutions within the framework of a recently developed inverse scattering transform for the underlying nonlinear integrable partial differential equation, and unlike darkbright solitons in the two component (Manakov) system in the same dispersion regime, their interactions display non-trivial polarization shift for the two bright components.
Abstract: We derive novel dark-bright soliton solutions for the three-component defocusing nonlinear Schrodinger equation with nonzero boundary conditions. The solutions are obtained within the framework of a recently developed inverse scattering transform for the underlying nonlinear integrable partial differential equation, and unlike dark-bright solitons in the two component (Manakov) system in the same dispersion regime, their interactions display non-trivial polarization shift for the two bright components.
TL;DR: In this paper, the authors derived several fundamental inequalities about the eigenvalues of 2n × 2n real positive definite matrices, such as the relation between the symplectic eigenvalue of A and those of At, between the Riemannian mean of m matrices A1, A2, Am, and Am and their mean of their mean, a perturbation theorem, and some variational principles.
Abstract: If A is a 2n × 2n real positive definite matrix, then there exists a symplectic matrix M such that MTAM=DOOD where D = diag(d1(A), …, dn(A)) is a diagonal matrix with positive diagonal entries, which are called the symplectic eigenvalues of A. In this paper, we derive several fundamental inequalities about these numbers. Among them are relations between the symplectic eigenvalues of A and those of At, between the symplectic eigenvalues of m matrices A1, …, Am and of their Riemannian mean, a perturbation theorem, some variational principles, and some inequalities between the symplectic and ordinary eigenvalues.
TL;DR: In this article, a two-component asymmetric simple exclusion process (ASEP) with second-class particles was studied and self-duality with respect to a family of duality functions was shown to arise from reversible measures of the process and the symmetry of the generator under the quantum algebra.
Abstract: We study a two-component asymmetric simple exclusion process (ASEP) that is equivalent to the ASEP with second-class particles. We prove self-duality with respect to a family of duality functions which are shown to arise from the reversible measures of the process and the symmetry of the generator under the quantum algebra Uq[𝔤𝔩3]. We construct all invariant measures in explicit form and discuss some of their properties. We also prove a sum rule for the duality functions.
TL;DR: In this article, the authors present a path-sum formulation for the time-ordered exponential of a time-dependent matrix and establish a super-exponential decay bound for the magnitude of entries of the entries of sparse matrices.
Abstract: We present the path-sum formulation for the time-ordered exponential of a time-dependent matrix. The path-sum formulation gives the time-ordered exponential as a branched continued fraction of finite depth and breadth. The terms of the path-sum have an elementary interpretation as self-avoiding walks and self-avoiding polygons on a graph. Our result is based on a representation of the time-ordered exponential as the inverse of an operator, the mapping of this inverse to sums of walks on a graphs, and the algebraic structure of sets of walks. We give examples demonstrating our approach. We establish a super-exponential decay bound for the magnitude of the entries of the time-ordered exponential of sparse matrices. We give explicit results for matrices with commonly encountered sparse structures.
TL;DR: In this article, an alternative method to solve second order differential equations which have at most four singular points was reported, which was developed by changing the degrees of the polynomials in the basic equation of NU method.
Abstract: We report an alternative method to solve second order differential equations which have at most four singular points. This method is developed by changing the degrees of the polynomials in the basic equation of Nikiforov-Uvarov (NU) method. This is called extended NU method for this paper. The eigenvalue solutions of Heun equation and confluent Heun equation are obtained via extended NU method. Some quantum mechanical problems such as Coulomb problem on a 3-sphere, two Coulombically repelling electrons on a sphere, and hyperbolic double-well potential are investigated by this method.
TL;DR: In this article, the authors considered a chemotaxis system with consumption of chemoattractant under homogeneous Neumann boundary conditions and proved that the global classical solution converges to (u, v) exponentially as t → ∞, where u0≔1|Ω|∫Ωu(x, 0)dx.
Abstract: We consider chemotaxis system with consumption of chemoattractant {vt=Δv−uv,ut=Δu−χ∇⋅(u∇v), under homogeneous Neumann boundary conditions. It is proved that if either n ≤ 2 or 0<χ≤16(n+1)‖v(x,0)‖L∞(Ω), n ≥ 3, the global classical solution (u, v) of this problem converges to (u0,0) exponentially as t → ∞, where u0≔1|Ω|∫Ωu(x,0)dx.
TL;DR: In this article, the conditions for invariance of Pfaff action and conserved quantities are presented under the special infinitesimal transformations and general infiniteimal transformations, respectively.
Abstract: Birkhoff equations on time scales and Noether theorem for Birkhoffian system on time scales are studied. First, some necessary knowledge of calculus on time scales are reviewed. Second, Birkhoff equations on time scales are obtained. Third, the conditions for invariance of Pfaff action and conserved quantities are presented under the special infinitesimal transformations and general infinitesimal transformations, respectively. Fourth, some special cases are given. And finally, an example is given to illustrate the method and results.
TL;DR: In this paper, the authors considered a family of translation-invariant quantum spin chains with nearest-neighbor interactions and derived necessary and sufficient conditions for these systems to be gapped in the thermodynamic limit.
Abstract: We consider a family of translation-invariant quantum spin chains with nearest-neighbor interactions and derive necessary and sufficient conditions for these systems to be gapped in the thermodynamic limit. More precisely, let ψ be an arbitrary two-qubit state. We consider a chain of n qubits with open boundary conditions and Hamiltonian H_n (ψ) which is defined as the sum of rank-1 projectors onto ψ applied to consecutive pairs of qubits. We show that the spectral gap of H_n (ψ) is upper bounded by 1/(n − 1) if the eigenvalues of a certain 2 × 2 matrix simply related to ψ have equal non-zero absolute value. Otherwise, the spectral gap is lower bounded by a positive constant independent of n (depending only on ψ). A key ingredient in the proof is a new operator inequality for the ground space projector which expresses a monotonicity under the partial trace. This monotonicity property appears to be very general and might be interesting in its own right. As an extension of our main result, we obtain a complete classification of gapped and gapless phases of frustration-free translation-invariant spin-1/2 chains with nearest-neighbor interactions.
TL;DR: In this paper, a generalization of the quantum entropy power inequality involving conditional entropies is proposed for the special case of Gaussian states, and a proof based on perturbation theory for symplectic spectra is given.
Abstract: We propose a generalization of the quantum entropy power inequality involving conditional entropies. For the special case of Gaussian states, we give a proof based on perturbation theory for symplectic spectra. We discuss some implications for entanglement-assisted classical communication over additive bosonic noise channels.
TL;DR: In this paper, first order integrals of motion for Schrodinger equations with position dependent masses are classified as integrable, superintegrably, and maximally super-integrable.
Abstract: First order integrals of motion for Schrodinger equations with position dependent masses are classified. Eighteen classes of such equations with non-equivalent symmetries are specified. They include integrable, superintegrable, and maximally superintegrable systems. Among them is a system invariant with respect to the Lie algebra of Lorentz group and a system whose integrals of motion form algebra so(4). Three of the obtained systems are solved exactly.
TL;DR: In this paper, the quantum dynamics of a moving particle with a magnetic quadrupole moment that interacts with electric and magnetic fields is introduced, where an analogue of the Coulomb potential can be generated and bound state solutions can be obtained.
Abstract: The quantum dynamics of a moving particle with a magnetic quadrupole moment that interacts with electric and magnetic fields is introduced. By dealing with the interaction between an electric field and the magnetic quadrupole moment, it is shown that an analogue of the Coulomb potential can be generated and bound state solutions can be obtained. Besides, the influence of the Coulomb-type potential on the harmonic oscillator is investigated, where bound state solutions to both repulsive and attractive Coulomb-type potentials are achieved and the arising of a quantum effect characterized by the dependence of the harmonic oscillator frequency on the quantum numbers of the system is discussed.