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For a hydrogen atom subject to a constant magnetic field, we report a numerical realization of the two-dimensional Non-Linearization Procedure (NLP) to estimate the accuracy of the variational energy associated with a given trial function. Relevant equations of the NLP, which resemble those describing a dielectric medium with a space-dependent permittivity and charge distribution, are solved numerically with high accuracy by using an orthogonal collocation method. As an illustration, we consider three different trial functions including the one proposed in Phys. Rev. A 103, (2021) 032820. For a magnetic field strength of $\gamma = 1$ a.u., we establish the accuracy of the variational energy as well as the local accuracy of the trial function. Additionally, the accuracy of the cusp parameter and the quadrupole moment, found by means of the trial function, is investigated, Comment: 18 pages, 2 figures

Following up on a recent paper [Bharti et al., Phys. Rev. A 109 (2024) 023110], we compare the predictions from severalR-matrix with time-dependence calculations for a modified three-sideband version of the "reconstruction of attosecond beating by interference of two-photon transitions" (RABBITT) configuration applied to helium. Except for the special case of the threshold sideband, which appears to be very sensitive to the details of coupling to the bound Rydberg states, increasing the number of coupled states in the close-coupling expansion used to describe the ejected-electron--residual-ion interaction hardly changes the results. Consequently, the remaining discrepancies between the experimental data and the theoretical predictions are likely due to uncertainties in the experimental parameters, particularly the detailed knowledge of the laser pulse.

We report a detailed study of high-order harmonic generation (HHG) in helium. When comparing predictions from a single-active-electron model with those from all-electron simulations, such as ATTOMESA and R-matrix with time-dependence, which can include different numbers of states in the close-coupling expansion, it seems imperative to generate absolute numbers for the HHG spectrum in a well-defined framework. While qualitative agreement in the overall frequency dependence of the spectrum, including the cut-off frequency predicted by a semi-classical model, can be achieved by many models in arbitrary units, only absolute numbers can be used for benchmark comparisons between different approaches.

Following our previous study of the Bohr-Sommerfeld (B-S) quantization condition for one-dimensional case (del Valle \& Turbiner (2021) \cite{First}), we extend it to $d$-dimensional power-like radial potentials. The B-S quantization condition for $S$-states of the $d$-dimensional radial Schr\"odinger equation is proposed. Based on numerical results obtained for the spectra of power-like potentials, $V(r)=r^m$ with $m \in [-1, \infty)$, the correctness of the proposed B-S quantization condition is established for various dimensions $d$. It is demonstrated that by introducing the {\it WKB correction} $\gamma$ (supposedly coming from the higher order WKB terms) into the r.h.s. of the B-S quantization condition leads to the so-called {\it exact WKB quantization condition}, which reproduces the exact energies, while $\gamma$ remains always very small. For $m=2$ (any integer $d$) and for $m=-1$ (at $d=2$) the WKB correction $\gamma=0$: for $S$ states the B-S spectra coincides with the exact ones. Concrete calculations for physically important cases of linear, cubic, quartic, and sextic oscillators, as well as Coulomb and logarithmic potentials in dimensions $d=2,3,6$ are presented. Radial quartic anharmonic oscillator is considered briefly., Comment: 15 pages, 4 figures, 4 tables; extended, some typos fixed, to be published in IJMPA

Assuming a logarithmic interaction between constituent particles, compact and locally accurate wave functions that describe bound states of the two-particle neutral and three-particle charged complexes in two dimensions are designed. Prime examples of these complexes are excitons and trions that appear in monolayers of Transition-Metal DichalCogenides (TMDCs). In the case of excitons, these wave functions led to 5-6 correct decimal digits in the energy and the diamagnetic shifts. In addition, it is demonstrated that they can be used as zero-order approximations to study magnetoexcitons via perturbation theory in powers of the magnetic field strength. For the trion, making a comparison with experimental data for concrete TMDCs, we established that the logarithmic potential leads to binding energies $\lesssim 25\%$ greater than experimental ones. Finally, the structure of the wave function at small distances is established for excitons whose carriers interact via the Rytova-Keldysh potential., Comment: 21 pages, 4 figures

In order to find the spectrum associated with the one-dimensional Schr\"oodinger equation, we discuss the Lagrange Mesh method (LMM) and its numerical implementation for bound states. After presenting a general overview of the theory behind the LMM, we introduce the LagrangeMesh package: the numerical implementation of the LMM in Mathematica. Using few lines of code, the package enables a quick home-computer computation of the spectrum and provides a practical tool to study a large class of systems in quantum mechanics. The main properties of the package are (i) the input is basically the potential function and the interval on which is defined; and (ii) the accuracy in calculations and final results is controllable by the user. As illustration, a highly accurate spectrum of some relevant quantum systems is obtained by employing the commands that the package offers. In fact, the present work can be regarded as a user guide based on worked examples., Comment: File LagrangeMesh.wl can be provided to the interested reader, just contact the author via email. Alternatively, it can be found at https://github.com/JuanCarlosdelValle/LagrangeMesh-Package

As a continuation of Part I, dedicated to the ground state of He-like and Li-like isoelectronic sequences for nuclear charges $Z \leq 20$, and Part II, dedicated to two excited states of He-like sequence, two ultra-compact wave functions in the form of generalized Guevara-Harris-Turbiner functions are constructed for Li-like sequence. They describe accurately the domain of applicability of the Quantum Mechanics of Coulomb Charges (QMCC) for energies (2-3 significant digits (s.d.)) of the spin-quartet state $1^40^+$ of Li-like ions (in static approximation with point-like, infinitely heavy nuclei). Variational parameters are fitted in $Z$ by 2nd degree polynomials. The most accurate ultra-compact function leads to the absolute accuracy $\sim 10^{-3}$\,a.u. for energy, and $\sim 10^{-4}$ for the normalized electron-nuclear cusp parameter for $Z \leq 20$. Critical charge $Z=Z_B$, where the ultra-compact trial function for the $1^40^+$ state looses its square-integrability, is estimated, $Z_B(1^4\,0^+) \sim 1.26 - 1.30$. As a complement to Part I, square integrability for the compact functions constructed for the {\it ground, spin-doublet state} $1^2\,0^+$ of the Li-like sequence is discussed. The critical charge, for which these functions stop to be normalizable, is estimated as $Z_B( 1^2\,0^+) = 1.62 - 1.65$. It implies that at $Z=2$ - the negative helium ion He${}^-$ - both states $1^2\,0^+$ and $1^4\,0^+$ exist as states embedded to continuum., Comment: 29 pages, 5 figures, 2 tables

It is already known that the quantum quartic single-well anharmonic oscillator $V_{ao}(x)=x^2+g^2 x^4$ and double-well anharmonic oscillator $V_{dw}(x)= x^2(1 - gx)^2$ are essentially one-parametric, their eigenstates depend on a combination $(g^2 \hbar)$. Hence, these problems are reduced to study the potentials $V_{ao}=u^2+u^4$ and $V_{dw}=u^2(1-u)^2$, respectively. It is shown that by taking uniformly-accurate approximation for anharmonic oscillator eigenfunction $\Psi_{ao}(u)$, obtained recently, see JPA 54 (2021) 295204 [1] and Arxiv 2102.04623 [2], and then forming the function $\Psi_{dw}(u)=\Psi_{ao}(u) \pm \Psi_{ao}(u-1)$ allows to get the highly accurate approximation for both the eigenfunctions of the double-well potential and its eigenvalues., Comment: 7 pages, extended, two figures added, to be published at Acta Polytechnica

As a continuation of Part I \cite{Part-1:2020} (Int. Journal of Quantum Chem. 2021; 121: qua.26586), dedicated to the ground state of He-like and Li-like isoelectronic sequences for nuclear charges $Z \leq 20$, a few ultra-compact wave functions in the form of generalized Hylleraas-Kinoshita functions are constructed, which describe the domain of applicability of the Quantum Mechanics of Coulomb Charges (QMCC) for the energies (4-5 significant digits (s.d.)) of two excited states of He-like ions: the spin-singlet (first) excited state $2^1 S$ and the lowest spin-triplet $1^3 S$ state. For both states it provides absolute accuracy for energy $\sim 10^{-3}$\,a.u., exact values for cusp parameters and also for 6 expectation values the relative accuracy $\sim 10^{-2}$. The Bressanini-Reynolds observation about the special form of the nodal surface of the $2^1 S$ state of Helium is confirmed and extended to He-like ions with $Z > 2$. Critical charges $Z=Z_B$, where ultra-compact trial functions lose their square-integrability, are estimated: $Z_B(1^1 S)\approx Z_B(2^1 S)\sim 0.905$ and $Z_B(1^3 S)\sim 0.902$. For both states the Majorana formula - the energy as a second degree polynomial in $Z$ - provides accurately 4-5 significant digits for $Z \leq 20$., Comment: 27 pages, 6 figures, 4 tables: typos fixed, 8 extra references added, the text essentially extended, to be published at Int Journ Quantum Chemistry

For one-dimensional power-like potentials $|x|^m, m > 0$ the Bohr-Sommerfeld Energies (BSE) extracted explicitly from the Bohr-Sommerfeld quantization condition are compared with the exact energies. It is shown that for the ground state as well as for all positive parity states the BSE are always above the exact ones contrary to the negative parity states where BSE remain above the exact ones for $m>2$ but they are below them for $m < 2$. The ground state BSE as the function of $m$ are of the same order of magnitude as the exact energies for linear $(m=1)$, quartic $(m=4)$ and sextic $(m=6)$ oscillators but relative deviation grows with $m$ reaching the value 4 at $m=\infty$. For physically important cases $m=1,4,6$ for the $100$th excited state BSE coincide with exact ones in 5-6 figures. It is demonstrated that modifying the right-hand-side of the Bohr-Sommerfeld quantization condition by introducing the so-called {\it WKB correction} $\gamma$ (coming from the sum of higher order WKB terms taken at the exact energies) to the so-called exact WKB condition one can reproduce the exact energies. It is shown that the WKB correction is small, bounded function $|\gamma| < 1/2$ for all $m \geq 1$, it is slow growing with increase in $m$ for fixed quantum number, while it decays with quantum number growth at fixed $m$. For the first time for quartic and sextic oscillators the WKB correction and energy spectra (and eigenfunctions) are written explicitly in closed analytic form with high relative accuracy $10^{-9 \ -11}$ (and $10^{-6}$)., Comment: 16 pages, 4 figures, 3 tables; typos corrected, extended version, new formulas added, several new references and footnotes

It is shown that for the one-dimensional quantum quartic anharmonic oscillator the numerical results obtained by Okun-Burke in Ref.2 are easily reproduced and can be significantly improved in Lagrange Mesh Method (based on non-uniform lattice)., Comment: 8 pages, 3 Tables; several footnotes added, typos corrected, Ref.7 updated, Acknowledgements added

A simple locally accurate uniform approximation for the nodeless wavefunction is constructed for a {\it neutral} system of two Coulomb charges of different masses $(-q,m_1)$ and $(q,m_2)$ at rest in a constant uniform magnetic field for the states of positive and negative parity, ${(1s_0)}$ and ${(2p_0)}$, respectively. It is shown that by keeping the mass and charge of one of the bodies fixed, all systems with different second body masses are related. This allows one to consider the second body as infinitely-massive and to take such a system as basic. Three physical systems are considered in details: the Hydrogen atom with (in)-finitely massive proton (deuteron, triton) and the positronium atom $(-e,e)$. We derive the Riccati-Bloch and Generalized-Bloch equations, which describe the domains of small and large distances, respectively. Based on the interpolation of the small and large distance behavior of the logarithm of the wavefunction, a compact 10-parametric function is proposed. Taken as a variational trial function it provides accuracy of not less than 6 significant digits (s.d.) ($\lesssim 10^{-6}$ in relative deviation) for the total energy in the whole domain of considered magnetic fields $[0\,,\,10^4]$ a.u. and not less than 3 s.d. for the quadrupole moment $Q_{zz}$. In order to get reference points the Lagrange Mesh Method with 16K mesh points was used to get from 10 to 6 s.d. in energy from small to large magnetic fields. Based on the Riccati-Bloch equation the first 100 perturbative coefficients for the energy, in the form of rational numbers, are calculated and, using the Pad\'e-Borel re-summation procedure, the energy is found with not less than 10 s.d. at magnetic fields $\leq 1$\,a.u., Comment: post-publication version: 51 pages, 8 tables (one new), 5 figures, 3 appendices; several important typos corrected, extra table, clarifications added -- all is published in erratum: Phys.Rev.A 105, 049901 (2022)

Several ultra-compact accurate wave functions in the form of generalized Hylleraas-Kinoshita functions and Guevara-Harris-Turbiner functions, which describe the domain of applicability of the Quantum Mechanics of Coulomb Charges (QMCC), or, equivalently, the Non-Relativistic QED (NRQED), for the ground state energies (4-5 significant digits (s.d.)) of He-like and Li-like iso-electronic sequences in the static approximation with point-like, infinitely heavy nuclei are constructed. It is shown that for both sequences the obtained parameters can be fitted in $Z$ by simple smooth functions: in general, these parameters differ from the ones emerging in variational calculations. For the He-like two-electron sequence the approximate expression for the ground state function, which provides absolute accuracy for the energy $\sim 10^{-3}$\,a.u. and the same relative accuracies $\sim 10^{-2}-10^{-3}$ for both the cusp parameters and the six expectation values, is found. For the Li-like three-electron sequence the most accurate ultra-compact function taken as the variational trial function provides absolute accuracy for energy $\sim 10^{-3}$\,a.u., 2-3 s.d. for the electron-nuclear cusp parameter for $Z \leq 20$ and 3 s.d. for the two expectation values for $Z=3$., Comment: post-publication, extended version, 43 pages, 4 figures, 7 tables: perturbation theory view added, Tables dramatically extended, Appendix with interpolated parameters vs Z added, published at IJQC (early view)

The optical properties of a spherical topological insulator embedded concentrically in a single-electron system consisting of a core-shell GaAs quantum dot are analyzed, when the system is under a uniform external magnetic field. The topological insulator's magnetoelectric response is computed in the effective framework of $\theta$-electrodynamics, which allows analytical calculations for the induced electric and magnetic potentials by Green's Function method. The GaAs Hamiltonian is constructed in the effective-mass approximation, and its corresponding Schr\"odinger equation is numerically solved through the Lagrange-mesh method. We compute the total absorption coefficients and refractive index changes given by the non-linear iterative density matrix formalism up to third order. Our results show that the presence of the magnetoelectric material causes new dipolar transitions otherwise not allowed. Also, an enhancement of the photon absorption is found when the incident light polarization is oriented parallel to the external magnetic field, in comparison with perpendicular polarization. Moreover, we report an appreciable blue shift in the optical functions when the values of the $\theta$-parameter are increased. These results can be useful for indirect experimental measures of the magnetoelectric polarizability which is proportional to the QED fine-structure constant $\alpha$., Comment: 17 pages, 9 figures

In our previous paper I (del Valle--Turbiner, Int. J. Mod. Phys. A34, 1950143, 2019) it was developed the formalism to study the general $D$-dimensional radial anharmonic oscillator with potential $V(r)= \frac{1}{g^2}\,\hat{V}(gr)$. It was based on the Perturbation Theory (PT) in powers of $g$ (weak coupling regime) and in inverse, fractional powers of $g$ (strong coupling regime) in both $r$-space and in $(gr)$-space, respectively. As the result it was introduced - the Approximant - a locally-accurate uniform compact approximation of a wave function. If taken as a trial function in variational calculations it has led to variational energies of unprecedented accuracy for cubic anharmonic oscillator. In this paper the formalism is applied to both quartic and sextic, spherically-symmetric radial anharmonic oscillators with two term potentials $V(r)= r^2 + g^{2(m-1)}\, r^{2m}, m=2,3$, respectively. It is shown that a two-parametric Approximant for quartic oscillator and a five-parametric one for sextic oscillator for the first four eigenstates used to calculate the variational energy are accurate in 8-12 figures for any $D=1,2,3\ldots $ and $g \geq 0$, while the relative deviation of the Approximant from the exact eigenfunction is less than $10^{-6}$ for any $r \geq 0$., Comment: 52 pages, 17 figures, 3 appendices

A controlled local enhancement of superconductivity yields unexpected modifications in the vortex dynamics. This local enhancement has been achieved by designing an array of superconducting Nb nanostructures embedded in a V superconducting film. The most remarkable findings are: i) vanishing of the main commensurability effect between the vortex lattice and the array unit cell, ii) hysteretic behavior in the vortex dynamics, iii) broadening of the vortex liquid phase and iv) strong softening of the vortex lattice. These effects can be controlled and they can be quenched by reducing the Nb array superconducting performance applying an in-plane magnetic field. These results can be explained by taking into account the repulsive potential landscape created by the superconducting Nb nanostructures on which vortices move., Comment: 16 pages, 8 figures

For the general $D$-dimensional radial anharmonic oscillator with potential $V(r)= \frac{1}{g^2}\,\hat{V}(gr)$ the Perturbation Theory (PT) in powers of coupling constant $g$ (weak coupling regime) and in inverse, fractional powers of $g$ (strong coupling regime) is developed constructively in $r$-space and in $(gr)$ space, respectively. The Riccati-Bloch (RB) equation and Generalized Bloch (GB) equation are introduced as ones which govern dynamics in coordinate $r$-space and in $(gr)$-space, respectively, exploring the logarithmic derivative of wavefunction $y$. It is shown that PT in powers of $g$ developed in RB equation leads to Taylor expansion of $y$ at small $r$ while being developed in GB equation leads to a new form of semiclassical expansion at large $(g r)$: it coincides with loop expansion in path integral formalism. In complementary way PT for large $g$ developed in RB equation leads to an expansion of $y$ at large $r$ and developed in GB equation leads to an expansion at small $(g r)$. Interpolating all four expansions for $y$ leads to a compact function (called the {\it Approximant}), which should uniformly approximate the exact eigenfunction at $r \in [0, \infty)$ for any coupling constant $g \geq 0$ and dimension $D > 0$. Free parameters of the Approximant are fixed by taking it as a trial function in variational calculus. As a concrete application the low-lying states of the cubic anharmonic oscillator $V=r^2+gr^3$ are considered. It is shown that the relative deviation of the Approximant from the exact ground state eigenfunction is $\lesssim 10^{-4}$ for $r \in [0, \infty)$ for coupling constant $g \geq 0$ and dimension $D=1,2,\ldots$. In turn, the variational energies of the low-lying states are obtained with unprecedented accuracy 7-8 s.d. for $g \geq 0$ and $D=1,2,\ldots$., Comment: 49 pages, 7 figures, 8 tables, 44 references: one figure (3 subfigures) added, typos corrected, formulas rectified, to be published at Intern Journal Mod Phys A

Despite decades of experimental and theoretical efforts, the origin of metal-insulator transitions (MIT) in strongly-correlated materials is one of the main longstanding problems in condensed matter physics. An archetypal example is V2O3, where electronic, structural and magnetic phase transitions occur simultaneously. This remarkable concomitance makes the understanding of the origin of the MIT a challenge due to the many degrees of freedom at play. In this work, we demonstrate that magnetism plays the key dominant role. By acting on the magnetic degree of freedom, we reveal an anomalous behaviour of the magnetoresistance of V2O3, which provides strong evidence that the origin of the MIT in V2O3 is the opening of an antiferromagnetic gap in the presence of strong electronic correlations., Comment: 7 pages, 4 figures

Using three different approaches, Perturbation Theory (PT), the Lagrange Mesh Method (Lag-Mesh) and the Variational Method (VM), we study the low-lying states of the Yukawa potential $V(r)=-(\lambda/r)e^{-\alpha r}\,$. First orders in PT in powers of $\alpha$ are calculated in the framework of the Non-Linerization Procedure. It is found that the Pad\'e approximants to PT series together with the Lag-Mesh provide highly accurate values of the energy and the positions of the radial nodes of the wave function. The most accurate results, at present, of the critical screening parameters ($\alpha_c$) for some low-lying states and the first coefficients in the expansion of the energy at $\alpha_c$ are presented. A locally-accurate and compact approximation for the eigenfunctions of the low-lying states for any $r\in [ 0,\infty)$ is discovered. This approximation used as a trial function in VM eventually leads to energies as precise as those of PT and Lag-Mesh. Finally, a compact analytical expression for the energy as a function of $\alpha$, that reproduce at least $6$ decimal digits in the entire physical range of $\alpha$, is found., Comment: 28 pages, 4 figures

We have studied two nanomagnet systems with strong (Co/Pd multilayers) and weak (NdCo alloy films) stray magnetic fields by probing the out-of-plane magnetic states with superconducting vortices. The hybrid samples are made of array of nanomagnets embedded in superconducting Nb thin films. The vortex motion detects relevant magnetic state features, since superconducting vortices are able to discriminate between different magnetic stray field strengths and directions. The usual matching effect between the superconducting vortex lattice and the periodic pinning array can be quenched by means of disorder magnetic potentials with strong stray fields at random. Ordered stray fields retrieve the matching effect and yield asymmetry and shift in the vortex dissipation signal. Furthermore vortices can discriminate the sizes of the nanomagnet magnetic domains, detecting magnetic domain sizes as small as 70 nm. In addition, we observe that the vortex cores play the crucial role instead of the supercurrents around the vortex., Comment: 22 pages, 8 figures

Superconducting 2H-NbSe2 single crystals show intrinsic low pinning values. Therefore, they are ideal materials with which to explore fundamental properties of vortices. (V, I) characteristics are the experimental data we have used to investigate the dissipation mechanisms in a rectangular shape 2H-NbSe2 single crystal. Particularly, we have studied dissipation behavior with magnetic fields applied in the plane of the crystal and parallel to the injected currents, i.e. in the force-free state where the vortex helical instability governs the vortex dynamics. In this regime, the data follow the elliptic critical state model and the voltage dissipation shows an exponential dependence.Moreover, this exponential dependence can be observed for in-plane applied magnetic fields up to 40 degrees off the current direction, which implies that the vortex helical instability plays a role in dissipation even out of the force-free configuration., Comment: 13 pages, 6 figures

Superconducting films in contact with non-superconducting regular arrays can exhibit commensurability effects between the vortex lattice and the unit cell of the pinning array. These matching effects yield a slowdown of the vortex flow and the corresponding dissipation decrease. The superconducting samples are Nb films grown on Si substrates. We have studied these matching effects with the array on top, embedded or threading the Nb superconducting films and using different materials (Si, Cu, Ni, Py dots and dots fabricated with Co/Pd multilayers). These hybrids allow studying the contribution of different pinning potentials to the matching effects. The main findings are: i) Periodic roughness induced in the superconducting film is enough to generate resistivity minima; ii) A minor effect is achieved by magnetic pinning from periodic magnetic field potentials obtained by dots with out of plane magnetization grown on top of the superconducting film, iii) In the case of array of magnetic dots embedded in the films vortex flow probes the magnetic state; i.e. magnetoresistance measurements detect the magnetic state of very small nanomagnets. In addition, we have studied the role played by the local order in the commensurability effects. This was attained using an array that mimics a smectic crystal. We have found that preserving the local order is crucial. If the local order is not retained the magnetoresistance minima vanish., Comment: 11 pages, 7 figures

In order to compare magnetic and non-magnetic pinning we have nanostructured two superconducting films with regular arrays of pinning centers: Cu (non-magnetic) dots in one case, and Py (magnetic) dots in the other. For low applied magnetic fields, when all the vortices are pinned in the artificial inclusions, magnetic dots prove to be better pinning centers, as has been generally accepted. Unexpectedly, when the magnetic field is increased and interstitial vortices appear, the results are very different: we show how the stray field generated by the magnetic dots can produce an effective reduction of the penetration length. This results in strong consequences in the transport properties, which, depending on the dot separation, can lead to an enhancement or worsening of the transport characteristics. Therefore, the election of the magnetic or non-magnetic character of the pinning sites for an effective reduction of dissipation will depend on the range of the applied magnetic field., Comment: 10 pages, 3 figures

Smectic order has been generated in superconducting Nb films with two-fold symmetry arrays of symmetric pinning centers. Magnetic fields applied perpendicularly to the films develop a vortex matter smectic phase that is easily detected when the vortices commensurate with the pinning center array. The smectic phase can be turned on and off with external parameters., Comment: 15 pages, 5 figures

We present a simple nanodevice that can operate in two modes: i) three-state memory and ii) reading device. The nanodevice is fabricated with an array of ordered triangular-shaped nanomagnets embedded in a superconducting thin film. The input signal is ac current and the output signal is dc voltage. Vortex ratchet effect in combination with out of plane magnetic anisotropy of the nanomagnets is the background physics which governs the nanodevice performance., Comment: 10 pages, 4 figures

Hybrid magnetic arrays embedded in superconducting films are ideal systems to study the competition between different physical (such as the coherence length) and structural length scales such as available in artificially produced structures. This interplay leads to oscillation in many magnetically dependent superconducting properties such as the critical currents, resistivity and magnetization. These effects are generally analyzed using two distinct models based on vortex pinning or wire network. In this work, we show that for magnetic dot arrays, as opposed to antidot (i.e holes) arrays, vortex pinning is the main mechanism for field induced oscillations in resistance R(H), critical current Ic(H), magnetization M(H) and ac-susceptibility Xac(H) in a broad temperature range. Due to the coherence length divergence at Tc, a crossover to wire network behavior is experimentally found. While pinning occurs in a wide temperature range up to Tc, wire network behavior is only present in a very narrow temperature window close to Tc. In this temperature interval, contributions from both mechanisms are operational but can be experimentally distinguished.