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Abstract We propose the superintegrable generalization of Smorodinsky–Winternitz system on the N -dimensional complex Euclidian space which is specified by the presence of constant magnetic field. We find out that in addition to 2 N Liouville integrals the system has additional functionally independent constants of motion, and compute their symmetry algebra. We perform the Kustaanheimo–Stiefel transformation of C 2 -Smorodinsky–Winternitz system to the (three-dimensional) generalized MICZ-Kepler problem and find the symmetry algebra of the latter one. We observe that constant magnetic field appearing in the initial system has no qualitative impact on the resulting system. Highlights • We review the properties of (RN-)Smorodinsky–Winternitz system, presenting expressions of its symmetry generators, symmetry algebra, wavefunctions and Energy spectrum. • We present CN-Smorodinsky–Winternitz system in a constant magnetic field, find the expressions of its constants of motion, compute their algebra and quantize the system. • We perform Kustaanheimo–Stieffel transformation of the C2-Smorodinsky–Winternitz system and obtain, in this way, the so-called "generalized MICZ-Kepler system". • We discuss the obtained results and possibilities of generalizations, namely supersymmetrization and quaternionic and curved background generalizations. [ABSTRACT FROM AUTHOR]

A relevant problem in the statistical and mathematical physics literature is to derive numerically accurate expressions to calculate Lévy α -stable distributions P α ( x ; β ) . On the formal side, important exact results rely on special functions, such as Meijer- G , Fox- H and finite sums of hypergeometric functions, with only a few exceptional cases expressed in terms of elementary functions. Hence, from a more practical point of view, methods such as series expansions are in order, e.g., to allow for the estimation of the Lévy distribution with high numerical precision, even though most of the existing approaches are restricted to a subset of the distribution parameters and/or usually demand relatively time-consuming sophisticated algorithms. Here we present a rather simple truncated expansion for the case of symmetric Lévy distributions P α ( x ) ( β = 0 ). This is achieved by dividing the full range of integration into windows, performing proper series expansion inside each, and then calculating the integrals term by term. The obtained representation is convergent for any 0 < α ≤ 2 . Moreover, its accuracy is directly controlled by the number of terms in the truncated expression, being straightforward to implement numerically. As we show with different examples, for almost all allowable α 's the calculations lead to P α ( x ) with reasonable low absolute error for computationally inexpensive simulations. [ABSTRACT FROM AUTHOR]

Under inquisition in this paper is a ( 2 + 1 ) -dimensional Breaking Soliton equation, which can describe various nonlinear scenarios in fluid dynamics. Using the Bell polynomials, some proficient auxiliary functions are offered to apparently construct its bilinear form and corresponding soliton solutions which are different from the previous literatures. Moreover, a direct method is used to construct its rogue wave and solitary wave solutions using particular auxiliary function with the assist of bilinear formalism. Finally, the interactions between solitary waves and rogue waves are offered with a complete derivation. These results enhance the variety of the dynamics of higher dimensional nonlinear wave fields related to mathematical physics and engineering. [ABSTRACT FROM AUTHOR]

In this study the flow rate in a quasi-2D hopper with two symmetric outlets was investigated numerically. When two outlets merge into one, the flow rate is obviously bigger than that with a large enough distance between them. To explain the influence of the interaction between these two outlets, it was found that the velocity field above one outlet will be affected by the neighboring outlet by reducing the stagnant zone. With increasing distance, this interaction becomes weaker. Finally the formula of flow rate considering various outlet sizes and distances is fitted to the simulation data. [ABSTRACT FROM AUTHOR]

In this paper we revise the classical analog of f -oscillators, a generalization of q -oscillators given in Man'ko et al. (1997) [8] , in the framework of classical spectrum generating algebras (SGA) introduced in Kuru and Negro (2008) [9] . We write down the deformed Poisson algebra characterizing the entire family of non-linear oscillators and construct its general solution algebraically. The latter, covering the full range of f -deformations, shows an energy dependence both in the amplitude and the frequency of the motion. [ABSTRACT FROM AUTHOR]

We study the existence of analytic first integrals of the complex Hamiltonian systems of the form H = 1 2 ∑ i = 1 2 p i 2 + V l ( q 1 , q 2 ) with the homogeneous polynomial potential V l ( q 1 , q 2 ) = α ( q 2 − i q 1 ) l ( q 2 + i q 1 ) k − l , l = 0 , … , k , α ∈ C ∖ { 0 } of degree k called exceptional potentials . In Remark 2.1 of Ref. [7] the authors state: The exceptional potentials V 0 , V 1 , V k − 1 , V k and V k / 2 when k is even are integrable with a second polynomial first integral. However nothing is known about the integrability of the remaining exceptional potentials . Here we prove that the exceptional potentials with k even different from V 0 , V 1 , V k − 1 , V k and V k / 2 , have no independent analytic first integral different from the Hamiltonian one. [ABSTRACT FROM AUTHOR]

We consider quantum brachistochrone evolution for a spin- s system on rotational manifolds. Such manifolds are determined by the rotation of the eigenstates of the operator of projection of spin- s on some direction. The Fubini–Study metrics of these manifolds are those of spheres with radii dependent on the value of the spin and on the value of the spin projection. The conditions for optimal evolution of the spin- s system on rotational manifolds are obtained. [ABSTRACT FROM AUTHOR]

We derive asymptotic expansion for the spectrum of Hamiltonians with a strong attractive δ′ interaction supported by a smooth surface in R3, either infinite and asymptotically planar, or compact and closed. Its second term is found to be determined by a Schrödinger type operator with an effective potential expressed in terms of the interaction support curvatures. [ABSTRACT FROM AUTHOR]

The Whitham equation was proposed as an alternate model equation for the simplified description of unidirectional wave motion at the surface of an inviscid fluid. An advantage of the Whitham equation over the KdV equation is that it provides a more faithful description of short waves of small amplitude. Recently, Ehrnström and Kalisch [19] established that the Whitham equation admits periodic traveling-wave solutions. The focus of this work is the stability of these solutions. The numerical results presented here suggest that all large-amplitude solutions are unstable, while small-amplitude solutions with large enough wavelength L are stable. Additionally, periodic solutions with wavelength smaller than a certain cut-off period always exhibit modulational instability. The cut-off wavelength is characterized by k[sub h0] = 1.145, where k = 2π/L is the wave number and [sub h0] is the mean fluid depth. [ABSTRACT FROM AUTHOR]

The second of the two proofs of the Wigner theorem on symmetry in quantum mechanics given in Simon et al. (2008) [1] is reexamined and refined to remove a possible gap in the argument presented there. [ABSTRACT FROM AUTHOR]

Abstract: We unify two long-memory Fokker–Planck mechanisms. Stationary solutions of the equation (; ) exist for a wide class of systems, namely for , (A, B, θ, η) being constants. We obtain that, for and arbitrary confining potential , , where . [Copyright &y& Elsevier]

Abstract: We investigate the formation of high-order polarization vortex spatial solitons. The high-order polarization vortex solitons have novel polarization states which are different from fundamental polarization vortex solitons and have rotational symmetry only in intensity. It is proved that the polarization vortex solitons cannot carry vortex phase. The existence domain and dynamical characteristic of these high-order polarization vortex solitons in Bessel optical lattices are discussed in detail. [Copyright &y& Elsevier]

Abstract: The idea of a Larmor clock is reexamined in the relativistic regime. We propose a concept of proper time for quantum theoretical particles. The Larmor clock can measure, under some relevant conditions, the proper time that passes while the particle stays in a space region. Our approach to Larmor clock is different than those of other researchers in the following two aspects: our concept of Larmor clock does not distinguish whether the particle is transmitted or reflected at the end of its stay, and pointer of our Larmor clock is not the spin but the total angular momentum. [Copyright &y& Elsevier]

Abstract: In terms of geometric discord, we study quantum correlations between two qubits interacting with a common heat bath. A necessary and sufficient condition for zero discord for arbitrary two-qubit density matrix is derived. With this condition, we show that a common heat bath can always induce two-qubit quantum correlations if both qubits are initially prepared in arbitrary superposition of “pointer basis”. [Copyright &y& Elsevier]

Abstract: The Redfield theory-based model of excitation energy transfer in chromophore ensembles within dissipative environment is proposed. Application of the multipole expansion to an operator of interaction between the chromophore molecules and the environment together with some assumptions about the latter led to the closed-form expressions for the elements of the dissipation tensor. These expressions relate the rates of transition between eigenstates of a chromophore ensemble with the spectral and electronic properties of an environment and the chromophore molecules. For several model cases the exact solution of the Redfield equations was obtained. [Copyright &y& Elsevier]

Abstract: In this Letter, a three-dimensional three-wave equation with self-consistent sources (3D3W ESCS) is constructed via the source generation procedure. The corresponding Grammian determinant solutions are then derived. As a simple case, the -lump solution is subsequently examined. A new feature of this 3D3W ESCS is that we allow -dependence of the arbitrary constants in the determinant solution for the three-dimensional three-wave equation while applying the source generation procedure. Finally, we show how this new system is reduced to other systems with self-consistent sources. [Copyright &y& Elsevier]

Abstract: This Letter considers the curvature conditions of AW(k)-type null Cartan curves, and investigates null Cartan Bertrand curves. We show that null Cartan Bertrand curves are AW(k)-type curves in Minkowski 4-space. [Copyright &y& Elsevier]

Abstract: A fundamental length (or time) is conjectured in many contexts. The “stability of physical theories principle” provides an unambiguous derivation of the stable structures that Nature might have chosen for its algebraic framework. and ℏ are the deformation parameters that stabilize the Galilean and Poisson algebras. The stability principle applied to the Poincaré–Heisenberg algebra, yields two deformation parameters defining two length (or time) scales. One of the scales is probably related to Planckʼs length but the other might be much larger. This is used as working hypothesis to compute deviations from c in speed measurements of massless particles. [Copyright &y& Elsevier]

Abstract: The Zhdanov–Trubnikov equation describing wrinkled premixed flames is studied, using pole decompositions as starting points. Its one-parameter () nonlinearity generalises the Michelson–Sivashinsky equation () to a stronger Darrieus–Landau instability. The shapes of steady flame crests (or periodic cells) are deduced from Laguerre (or Jacobi) polynomials when , which numerical resolutions confirm. Large wrinkles are analysed via a pole density: adapting results of Dunkl relates their shapes to the generating function of Meixner–Pollaczek polynomials, which numerical results confirm for (reduced stabilisation). Although locally ill-behaved if (over-stabilisation) such analytical solutions can yield accurate flame shapes for . Open problems are invoked. [Copyright &y& Elsevier]

Abstract: Here we present analytic results for the Slater sum and the magnetic moment for arbitrary magnetic field strengths for an assembly of harmonically confined, but initially free, electrons. The relevance of the results to the generalized Landau diamagnetism of such confined electrons is emphasized. [Copyright &y& Elsevier]

Abstract: We analyze the sensitivity of gravitational-wave antenna with stable double optical spring created by two independent pumps. We investigate regime of three close eigen frequencies (roots of characteristic equation) which appears to provide more wide frequency band in which sensitivity of antenna can beat Standard Quantum Limit (SQL) than previously considered regime with two close eigen frequencies. We take into account optical losses and show that they do not degrade sensitivity significantly. We also demonstrate possible application of considered regime to Einstein Telescope. [Copyright &y& Elsevier]

Abstract: Grid-based discretizations of the time dependent Schrödinger equation coupled to an external magnetic field are converted to manifest gauge invariant discretizations. This is done using generalizations of ideas used in classical lattice gauge theory, and the process defined is applicable to a large class of discretized differential operators. In particular, popular discretizations such as pseudospectral discretizations using the fast Fourier transform can be transformed to gauge invariant schemes. Also generic gauge invariant versions of generic time integration methods are considered, enabling completely gauge invariant calculations of the time dependent Schrödinger equation. Numerical examples illuminating the differences between a gauge invariant discretization and conventional discretization procedures are also presented. [Copyright &y& Elsevier]

Abstract: We present explicit formulas for the Faddeev eigenfunctions and related generalized scattering data for point (delta-type) potentials in two dimensions. In particular, we obtain the first explicit examples of such eigenfunctions with contour singularity in spectral parameter at a fixed real energy. [Copyright &y& Elsevier]

Abstract: The entanglement backflow of two qubits coupled to two independent reservoirs is investigated. It is found that under the collective effects of the two independent reservoirs, the entanglement backflow of the qubits does not always increase with the increase of the non-Markovianity of one of the reservoirs but demonstrates an intricate behavior. Interestingly, the action of one reservoir can affect the other reservoirʼs contribution to the entanglement backflow even when the two reservoirs are independent. [Copyright &y& Elsevier]

Abstract: Trace distance and superfidelity play an important role in quantum information theory. The aim of this Letter is to consider an inequality involving trace distance and superfidelity in infinite dimension and give a necessary and sufficient condition for equality of this inequality. In addition, some related results involving trace distance and superfidelity are obtained. [Copyright &y& Elsevier]

Abstract: The interaction of a charged particle with a nanosphere is studied based on the dielectric response theory. We obtain the analytical expressions of the induced potential and stopping power, as the charged particle moving outside the nanosphere with a constant velocity. From our results, since the spherical shape limitation, the well-known V-shaped wake effect tracing the particle cannot be observed clearly no matter at the nanosphere surface or in the bulk. Besides, we also find that the particle can even gain energy from the electron polarization as the particle moves to the nanosphere at relatively low velocity. [Copyright &y& Elsevier]

Using first-principles calculations, we study the electronic transport properties in Au一(C20)2 lar junctions with different contact interface configurations: point contact and bond contact. We observe that the transmission through the bond contact is considerably higher than that of point contact. Furthermore, the I–V characteristics are rather different. For the bond contact, we get a metallic behavior followed by a varistor-type behavior. While as for the point contact, the current increases very slowly in a nonlinear way and is one order of magnitude smaller than that of bond contact. We attribute these obvious differences to the distinct contact configurations. [Copyright &y& Elsevier]

Abstract: An interaction of vector solitons in the frame of coupled third-order nonlinear Schrödinger equations taking into account third-order linear dispersion, nonlinear dispersion, and cross-phase modulation terms is considered. Phase nature of the solitonsʼ interaction is shown. In particular, dependence of solitonsʼ trajectories on initial distance between solitons is shown. Conditions of reflection and propagation of solitons through each other are obtained. [Copyright &y& Elsevier]

Abstract: We explore the results of [V. Coffman, et al., Phys. Rev. A 61 (2000) 052306] derived for general tripartite states in a dynamical context. We study a class of physically motivated tripartite systems. We show that whenever entanglement sudden death occurs in one of the partitions residual entanglement will appear. For fourpartite systems however, the appearance of residual entanglement is not conditioned by sudden death of entanglement. We can only say that if sudden death of entanglement occurs in some partition there will certainly be residual entanglement. [Copyright &y& Elsevier]

Abstract: For Adlerʼs equation in the Viallet form and Yamilovʼs discretisation of the Krichever–Novikov equation we present new recursion and Hamiltonian operators. This new recursion operator and the recursion operator found in [A.V. Mikhailov, et al., Theor. Math. Phys. 167 (2011) 421, arXiv:1004.5346] satisfy the spectral curve associated with the equation. [Copyright &y& Elsevier]

Abstract: The dynamics of fluid particles in the vicinity of a self-propagating vortex pair, embedded in a nonstationary shear flow, is studied. When the shear flow is steady, the vicinity of the pair, which is called as a vortex atmosphere, consists of closed stream-lines, which coincide with fluid particlesʼ trajectories. When the shear flow is nonstationary, the trajectoriesʼ behaviour changes drastically, then chaotic advection occurs. It is shown in the Letter that the vortex pair propagation velocity varies with the parameters (amplitude, and frequency) of the nonstationary shear flow. It is demonstrated, that changing of the mean velocity leads to changing of the size of the atmosphere. [Copyright &y& Elsevier]

Abstract: We study the nonlinear incompressible non-viscous fluid flows within a thin rotating atmospheric shell that serve as a simple mathematical description of an atmospheric circulation caused by the temperature difference between the equator and the poles. The model is also superimposed by a particular stationary flow which, under the assumption of no friction and a distribution of temperature dependent only upon latitude, models the zonal west-to-east flows in the upper atmosphere between the Ferrel and Polar cells. Owing to the Coriolis effects, the resulting achievable meteorological flows correspond to the asymptotical stable flows that are being translated along the equatorial plane. The exact solutions in terms of elementary functions are found by using Lie group methods. [Copyright &y& Elsevier]

Abstract: We construct non-radially symmetry solutions for the compressible 1-dimensional adiabatic Euler equations in this Letter. In detail, we perturb the linear velocity with a drifting term: to seek new solutions. Then, we transform the problem into the analysis of ordinary differential equations. By investigating the corresponding ordinary differential equations, a new class of blowup or global solutions can be given. Here, our constructed solutions can provide the mathematical explanations for the drifting phenomena of some propagation wave like Tsunamis. And when we adopt the Galilean-like transformation to a drifting frame, the constructed solutions are self-similar. [Copyright &y& Elsevier]

Abstract: We analyze decoherence properties of entangled coherent states due to channel losses. Employing the concept of “entanglement of formation”, degradation of fidelity and degree of entanglement are calculated. We have obtained an explicit expression of concurrence concerning the symmetric noise channel and found our result is just incompatible with that of [K. Park, H. Jeong, Phys. Rev. A 82 (2010) 062325] measured by negativity in the limit of . We demonstrate that entangled coherent states with sufficient small amplitudes are more robust against channel decoherence than Bell states. [Copyright &y& Elsevier]

Abstract: We put forward a new nontrivial three-step strategy to execute joint remote state preparation via Einstein–Podolsky–Rosen pairs deterministically. At variance with all existing protocols, in ours the receiver contributes actively in both preparation and reconstruction steps, although he knows nothing about the quantum state to be prepared. [Copyright &y& Elsevier]

Abstract: The Painlevé property for the coupled Zakharov–Kuznetsov equation is verified with the WTC approach and new exact solutions of bell-type are constructed from standard truncated expansion. A symmetry transformation group theorem is also given out from a simple direct method. [Copyright &y& Elsevier]

Abstract: In this Letter, a variable-coefficient discrete -expansion method is proposed to seek new and more general exact solutions of nonlinear differential–difference equations. Being concise and straightforward, this method is applied to the -dimension Toda equation. As a result, many new and more general exact solutions are obtained including hyperbolic function solutions, trigonometric function solutions and rational solutions. It is shown that the proposed method provides a very effective and powerful mathematical tool for solving a great many nonlinear differential–difference equations in mathematical physics. [Copyright &y& Elsevier]

Abstract: We demonstrate that it is possible to discern the way that has been followed to measure a quantum observable that can be expressed in terms of different products of observables, whereas no such discrimination is possible by assigning predetermined values. Specifically we show how to distinguish different routes (contexts) to measure , when and commute with each other, but A and B do not commute with and . [Copyright &y& Elsevier]

Abstract: The asymptotic behavior of loop-soliton solution and periodic loop solutions is studied for the equation. The results show that both of them consist of two or more branches of non-smooth solutions. [Copyright &y& Elsevier]

Abstract: We indicate that the proof of theorem is incorrect in Letter [Y. Xu, W. Zhou, J. Fang, W. Sun, Phys. Lett. A 374 (2010) 1673]. For correcting the mistakes, a correct version of the proof of theorem is given in this Letter. [Copyright &y& Elsevier]

Abstract: We study dynamics of populations of resonantly coupled oscillators having different frequencies. Starting from the coupled van der Pol equations we derive the Kuramoto-type phase model for the situation, where the natural frequencies of two interacting subpopulations are in relation . Depending on the parameter of coupling, ensembles can demonstrate fully synchronous clusters, partial synchrony (only one subpopulation synchronizes), or asynchrony in both subpopulations. Theoretical description of the dynamics based on the Watanabe–Strogatz approach is developed. [Copyright &y& Elsevier]

Abstract: We present a generalization of a compact form, due to Baker, for quadratic identities satisfied by the three-index ℘-functions on curves of genus , and a further generalization of a new result in genus . The compact forms involve a bordered determinant containing free parameters. [Copyright &y& Elsevier]

Abstract: We consider the generalized Stäckel systems, the broadest class of integrable Hamiltonian systems that admit separation of variables and possess separation relations affine in the Hamiltonians. For these systems we construct in a systematic fashion hierarchies of basic separable potentials. Moreover, we show how the equations of motion for the systems under study are related through appropriately chosen reciprocal transformations and how the respective constants of motion are related through generalized Stäckel transforms. [Copyright &y& Elsevier]

Abstract: We study the dynamical Casimir effect in the presence of a finite coherence time, which is associated with a finite quality factor of the optical cavity. We use the time refraction model, where a fixed cavity with a modulated optical medium, replaces the empty cavity with a vibrating mirror. Temporal coherence is described with the help of cavity quasi-mode operators. Asymptotic expressions for the number of photon pairs generated from vacuum are derived. [Copyright &y& Elsevier]

Abstract: Including a random component of a magnetic field parallel to an ambient field introduces a mean perpendicular motion to the average field line. This effect is normally not discussed because one customarily chooses at the outset to ignore such a field component in discussing random walk and diffusion of field lines. A discussion of the basic effect is given, indicating that any random magnetic field with a non-zero helicity will lead to such a non-zero perpendicular mean motion. Several exact analytic illustrations are given of the effect as well as a simple numerical illustration. [Copyright &y& Elsevier]

Abstract: Some properties of minimal and nonminimal vector interactions in the Duffin–Kemmer–Petiau (DKP) formalism are discussed. The conservation of the total angular momentum for spherically symmetric nonminimal potentials is derived from its commutation properties with each term of the DKP equation and the proper boundary conditions on the spinors are imposed. It is shown that the space component of the nonminimal vector potential plays a crucial role for the confinement of bosons. The exact solutions for the vector DKP oscillator (nonminimal vector coupling with a linear potential which exhibits an equally spaced energy spectrum in the weak-coupling limit) for spin-0 bosons are presented in a closed form and it is shown that the spectrum exhibits an accidental degeneracy. [Copyright &y& Elsevier]

Abstract: Using first-principles density functional theory and non-equilibrium Greenʼs function formalism for quantum transport calculation, we have investigated the electronic transport properties of the unsymmetrical C121-based molecular junction. Our results show that the current–voltage curve displays a negative differential resistance phenomenon in a certain bias voltage range. The mechanism for the negative differential resistance phenomenon is suggested. The present findings could be helpful for the application of the C121 molecule in the field of single molecular devices or nanometer electronics. [Copyright &y& Elsevier]

Abstract: We discuss alternatives to the usual quantization of a relativistic particle which result in discrete spectra for position and time operators. [Copyright &y& Elsevier]

Abstract: Finite dimensional representations of extended Weyl–Heisenberg algebra are studied both from mathematical and applied viewpoints. They are used to define unitary phase operator and the corresponding eigenstates (phase states). It is also shown that the unitary depolarizers can be constructed in a general setting in terms of phase operators. Generation of generalized Bell states using the phase operator is presented and their expressions in terms of the elements of mutually unbiased bases are given. [Copyright &y& Elsevier]

Abstract: In this Letter, we investigate the dynamics of Bose–Einstein Condensates (BECs) with spatially inhomogeneous interaction and generate bright solitons for the condensates by solving the associated mean field description governed by the Gross–Pitaevskii (GP) equation. We then investigate the properties of BECs in an optical lattice and periodic potential. We show that the GP equation in an optical lattice potential is integrable provided the interaction strength between the atoms varies periodically in space. The model discussed in the Letter offers the luxury of choosing the form of the lattice without destroying the integrability. Besides, we have also brought out the possible ramifications of the integrable model in the condensates of quasi-particles. [Copyright &y& Elsevier]