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In this work, we analyze the Dirac-Morse problem with spin and pseudo-spin symmetries in deformed nuclei. So, we consider the Dirac equation with the scalar U (r) and vector V (r) Morse-type potentials and tensor Hellmann-type potential in curved space-time whose line element is of type ds2 = (1 + α2 U (r))2 (dt2 − dr2 )− r2 dθ2 − r2 sin2θdφ2 . From the effective tensor potential Aeff(r) = λ/r + α2 λU(r)/r + A(r), that contain terms of spin-orbit coupling, line element and electromagnetic field, we analyze dirac’s spinor in two ways: (i) in the first, we solve the problem approximately considering A ef f (r) not null; (ii) in the second analysis, we obtain exact solutions of radial spinor and eigenenergies considering Aeff(r) = 0. In both cases, we consider two types of coupling of vector and scalar potentials, with spin symmetry for V (r) = U (r) and pseudo-spin symmetry for V (r) = −U (r). We analyzed the effect of coupling the electromagnetic field with the curvature of space in eigenenergies and radial spinor.

We present exact solutions of the Schrodinger equation for a charged particle constrained to move along a toroidal surface in the presence of uniform electric and magnetic fields.

We study the modified Dirac oscillator with spin and pseudo-spin symmetries in deformed nuclei. For that, we consider the Dirac equation in curved space-time which line element is $$ds^2 = (1+\alpha ^2 U(r))^2(dt^2- dr^2) - r^2d\theta ^2-r^2\sin ^2\theta d\phi ^2$$ and electromagnetic field $$A_{\mu } = (V(r), cA_r(r),0,0)$$ . From this coupling of $$ A_{\mu } $$ with the curved space-time emerged two symmetries: Spin symmetry with $$ V (r) = U (r) $$ and pseudo-spin symmetry with $$V(r)= -U(r)$$ . In both cases, we solve the Dirac equation exactly and get the energy spectrum. We also analyze the probability density and some energy spectra for both cases.

We present an exact solution to the Lippmann-Schwinger equation for a two-dimensional elliptic billiard modeled as a boundary-wall. Using a property of the Green function — which is a zeroth order Hankel function of the first kind — we managed to separate the integral equation Kernel. This approach allows us to study the problem analytically for four representative potential coupling strength γ(s), namely: (i) γ ( s ) = γ 0 / cosh 2 μ 0 − cos 2 s ; (ii) γ(s) = γ0; (iii) γ(s) being a 2π−periodic even function; and (iv) γ(s) being a 2π−periodic odd function, where γ0 is a real constant. Also, we find the condition which needs to be verified in order to the incident plane wave to produce a resonance inside the barrier.

We solve analytically the Pauli equation for a charged spin 1∕2 particle constrained to move along a toroidal surface and interacting with a uniform magnetic field . The two-component spinorial wavefunction can only be realized if the applied magnetic field has certain special values.

In this work we study the Dirac equation in a curved static space–time, where the metric depends on two arbitrary functions f ( r ) and g ( r ) , namely the line element is d s 2 = e 2 f ( r ) d t 2 − e 2 g ( r ) d r 2 − r 2 d θ 2 − r 2 sin 2 θ d ϕ 2 . We exactly solve the angular equation for arbitrary f ( r ) and g ( r ) . Then, we uncouple the radial component of the spinor for a metric model defined by f = g and find the exact solutions for three quantum systems: Hydrogen atom, Dirac–Morse oscillator and a linear radial potential by V ( r ) = a r .

We investigate the scattering of a plane wave in the hyperbolic plane. We formulate the problem in terms of the Lippmann-Schwinger equation and solve it exactly for barriers modeled as Dirac delta functions running along: (i) N − horizontal lines in the Poincaré upper half-plane; (ii) N − concentric circles centered at the origin; and, (iii) a hypercircle in the Poincaré disk.

In this paper we solve the Dirac equation with the Coulomb scalar U(r) and vector V(r) potentials and type-Mie tensor potential in curved space-time whose metric is of type ds 2 = ( 1 + α 2 U ( r ) ) 2 ( dt 2 − dr 2 ) − r 2 d θ 2 − r 2 sin 2 θ d ϕ 2 with spherical symmetry. For this we consider two types of symmetry in the system, first spin symmetry with V(r) = U(r) and then with pseudo-spin symmetry V(r) = − U(r). In both cases we have a tensor potential A(r) that coupling through the electromagnetic field A μ = (V(r), cA(r), 0, 0). We find, quasi-exactly, the Dirac spinor and the energy spectrum of the system, and we sketch the probability densities and some energy spectra.

We present exact solutions for the Lippmann–Schwinger equation in two dimensions for circular boundary walls in three cases: (i) a finite number N of concentric barriers; (ii) a single barrier with Dirac delta derivatives, in the sense of distribution theory, namely, angular, normal, and along the curve; and (iii) a single barrier with an arbitrary distribution. As an application of this last result, we obtain conditions that must be fulfilled in order for the barrier to become invisible.

We present exact solutions to the Lippmann-Schwinger equation for the scattering of a plane wave by an oblate spheroidal barrier modeled as a boundary-wall with coupling strength γ = γ ( η , ϕ ) . We study analytically two representative potential strengths: (i) γ ( η , ϕ ) = γ 0 / ξ 0 2 + η 2 , that is a coupling strength which compensates the variation of the spheroid surface element; and (ii) a constant potential γ ( η , ϕ ) = γ 0 . In the first case, we present a condition that must be satisfied in order to a resonance effect to take place inside the barrier. We use this result as a basis to obtain the solution for the scattering of a plane wave by Nspheroidal barriers.

In this work a new analysis of the 010-010 and 000–010 bands in the A 2 Σ + - X2Π electronic transition of the N2O + molecule is performed by high resolution Fourier transform spectroscopy. Two sets of spectra of the N2O + molecule at different temperatures are analysed, one at 30 K and the other at 340 K approximately, which made possible an unambiguous assignment of the spectral lines. Due to this fact and from a “natural” advantage of the Fourier transform spectroscopy since, being an interferential spectrometry, the obtained spectrum provides absolute wavenumbers and no further calibration is required, the more accurate wavenumber allowed new and improved molecular constants and band origins, making it possible to obtain more reliable values for previously reported molecular constants. With these new constants, a new set of spin-vibronic term values was determined and compared to the values already reported in the literature.

We exactly solve the Schrodinger equation written on a spherical surface and interacting with the Poschl-Teller double-ring-shaped (PTDRS) potential and calculate their eigenenergies. We also solve the Pauli equation in a spherical surface and interacting with the same PTDRS potential. We find that the coupling constants of the potential must obey certain constraints for the spinor to be realized.

We present a quantum mechanical version of the Colonel Blotto game, where two players, Blotto and Enemy, collocate their soldiers (resources) sequentially in a finite number of territories. We analyse the representative classical cases of this game as well as the trivial case—which on its turn has no interest at all in the point of view of classical game theory—where, surprisingly, a player that could control a single parameter can win the game even if he/she is greatly outnumbered by his/her opponent. Besides the theoretical study we present an experimental realization of classical game by using linear optics circuits as well as a proposal of an experimental investigation of the quantized game. Finally, in order to check our quantization scheme we also present computer simulation results.

In this work we report on a study of entropic threshold of digital speckle patterns images produced by rough surfaces using Tsallis entropy. The speckle pattern images were obtained in the diffraction plane at the normal direction and they are the outcome of the incidence of a laser beam in the rough metallic surfaces. The speckle pattern images were segmented in order to verify the sensitivity of the optimal Tsallis entropic threshold value as a function of the surface roughness. We show that the surface roughness can be sensed and tuned by this method.

We solve analytically the Lippmann-Schwinger equation for a linear potential. As an application of this result, we investigate the two-dimensional scattering of a scalar particle by a linear potential and by an arbitrary barrier modeled as a boundary-wall.

We generalize the concept of quantum Russian roulette introduced in Schmidt and da Silva (2013). Our model coincides with the previous one in the case of the game with two players and gives the suitable quantum description for any finite number of players. As an example, we provide a detailed study of the three and four-person case.

The main purpose of this work is to reproduce a quantum system charge-monopole utilizing position-dependent effective mass (PDM) system in the nonrelativistic regime via the Pauli equation. In this case, we substitute the exact charge-monopole wavefunction into the free PDM Pauli equation and then solve it for the mass distribution considering a radial dependence only, i.e., M = M(r). The resulting equations are nonlinear, and in such cases, we were able to numerically solve them, fixing θ0 and considering specific values of μ and m satisfying a given condition. The mapping was studied for eigenvalues starting from the minimal value j = μ − 1/2.The main purpose of this work is to reproduce a quantum system charge-monopole utilizing position-dependent effective mass (PDM) system in the nonrelativistic regime via the Pauli equation. In this case, we substitute the exact charge-monopole wavefunction into the free PDM Pauli equation and then solve it for the mass distribution considering a radial dependence only, i.e., M = M(r). The resulting equations are nonlinear, and in such cases, we were able to numerically solve them, fixing θ0 and considering specific values of μ and m satisfying a given condition. The mapping was studied for eigenvalues starting from the minimal value j = μ − 1/2.

The primary purpose of this work is to reproduce the scenario composed of a charge-dyon system utilizing position-dependent effective mass (PDM) background in the non-relativistic and in the relativistic regimes. In the non-relativistic case we substitute the exact charge-dyon eigenfunction into PDM Schrödinger equation, in the Zhu-Kroemer parametrization, and then solve it for the mass distribution considering M = M(r). Analogously, in the relativistic case we study the Klein-Gordon equation for a position-dependent mass, and in this case, we are able to analytically solve the equation for M = M(r,θ).

We calculate exact solutions of the Schrodinger equation for a particle constrained to move along a spherical surface and interacting with non-central potentials, namely, (i) Makarov, (ii) ring-shaped pseudo-harmonic oscillatory, and (iii) Kratzer potentials. We also study exact solutions of the Pauli equation in the same geometrical setting for a charged particle in the presence of a uniform magnetic field. In this case, the two-component spinor can adhere to the surface only if the magnetic field intensity has certain special values. The solutions of Schrodinger equations allow us to obtain exact Pauli spinors and their corresponding energy eigenvalues for the same non-central potentials.

We quantize the gamble known as Russian roulette and we study it in two versions for two- and three-persons when: (i) players use a fully loaded quantum gun; (ii) the quantum gun has only one quantum bullet.

We present exact solutions for the position-dependent mass Schrodinger equation (PDMSE) in an annular billiard with impenetrable walls where the mass is allowed to depend on the radial position, i.e., μ = μ ( r ) . Exact wavefunctions are calculated explicitly for four mass distributions.

We present an exact solution to the Lippmann-Schwinger equation for a two-dimensional circular billiard. After diagonalizing an integral operator whose kernel is a zeroth order Hankel function of first kind, we use its eigenfunctions and eigenvalues to obtain in a straightforward way the exact wavefunctions of the referred Lippmann-Schwinger equation.

We study the non-relativistic charge-monopole system when the charged particle has a position-dependent mass written as M(r) = m0rw. The angular wave functions are the well-known monopole harmonics, and the radial ones are ordinary Bessel functions which depend on the magnetic and electric charge product as well as on the w parameter. We investigate mappings—approximate and exact—between the charge-monopole system with constant mass and the charge with a position-dependent mass solving the position-dependent mass Schrodinger equation for the mass distribution.We study the non-relativistic charge-monopole system when the charged particle has a position-dependent mass written as M(r) = m0rw. The angular wave functions are the well-known monopole harmonics, and the radial ones are ordinary Bessel functions which depend on the magnetic and electric charge product as well as on the w parameter. We investigate mappings—approximate and exact—between the charge-monopole system with constant mass and the charge with a position-dependent mass solving the position-dependent mass Schrodinger equation for the mass distribution.

We study the possibility of controlling a quantum rotor interacting with a time-dependent external field, namely, using a continuous or a piecewise continuous (bang-bang control) magnetic flux. Using the exact eigenfunctions we show how to steer a wave-packet constructed as a superposition of these eigenstates. In the first case we show how to steer a Gaussian wave-packet (GWP) to two other positions: one of them which would not be realized if the evolution were free, and the second is the one where wave-packet revival takes place. In the piecewise approach we implement a kind of tracking control, i.e. before steering it to the final target we achieve another given GWP.

We study quantum wave packet revivals on two-dimensional infinite circular quantum wells (CQWs) and circular quantum dots with position-dependent mass (PDM) envisaging a possible experimental realization. We consider CQWs with radially varying mass, addressing particularly the cases where M ( r ) ∝ r w with w = 1 , 2 , or −2. The two PDM Hamiltonians currently allowed by theory were analyzed and we were able to construct a strong theoretical argument favoring one of them.

Here we review the many aspects and distinct phenomena associated to quantum dynamics on general graph structures. For so, we discuss such class of systems under the energy domain Green's function ($G$) framework. This approach is particularly interesting because $G$ can be written as a sum over classical-like paths, where local quantum effects are taking into account through the scattering matrix amplitudes (basically, transmission and reflection amplitudes) defined on each one of the graph vertices. Hence, the {\em exact} $G$ has the functional form of a generalized semiclassical formula, which through different calculation techniques (addressed in details here) always can be cast into a closed analytic expression. It allows to solve exactly arbitrary large (although finite) graphs in a recursive and fast way. Using the Green's function method, we survey many properties for open and closed quantum graphs as scattering solutions for the former and eigenspectrum and eigenstates for the latter, also considering quasi-bound states. Concrete examples, like cube, binary trees and Sierpi\'{n}ski-like topologies are presented. Along the work, possible distinct applications using the Green's function methods for quantum graphs are outlined., Comment: 54 pages, 24 figures, 1 table. Two sections expanded + minor modifications. One appendix added. References added. To appear in Physics Reports

We study the time evolution of a one-dimensional harmonic oscillator with position-dependent mass. The results obtained for three distinct cases are compared with the constant mass case.

We study the temporal evolution of solutions of 1D Schrodinger equation with position-dependent mass inside an infinite well. Revival of wave-packet is shown to exist and partial revivals are different from the usual ones.

We show that at one-loop order, negative-dimensional, Mellin-Barnes' (MB) and Feynman parametrization (FP) approaches to Feynman loop integrals calculations are equivalent. Starting with a generating functional, for two and then for $N$-point scalar integrals we show how to reobtain MB results, using negative-dimensional and FP techniques. The $N-$point result is valid for different masses, arbitrary exponents of propagators and dimension., 11 pages, LaTeX. To be published in J.Phys.A

We present a recursive prescription to calculate the exact Green function for general quantum graphs. For the closed case, the expression for the poles of G—which gives the individual eigenstates—has the structure of a semiclassical formula, where the sum over the periodic orbit is already performed. As applications we discuss eigenstate localization for a three-arm closed star and filter-like mechanisms for transmission throughout an open trident graph.

We apply negative dimensional integration method (NDIM) to three outstanding gauges: Feynman, light-cone and Coulomb gauges. Our aim is to show that NDIM is a very suitable technique to deal with loop integrals, being them originated from any gauge choice. In Feynman gauge we perform scalar two-loop four-point massless integrals; in the light-cone gauge we calculate scalar two-loop integrals contributing for two-point functions without any kind of prescriptions, since NDIM can abandon such devices -- this calculation is the first test of our prescriptionless method beyond one-loop order; finally, for the Coulomb gauge we consider a four propagator massless loop integral, in the split dimensional regularization context., Comment: 12 pages, 2 figures, style files included

The only calculations performed beyond one-loop level in the light-cone gauge make use of the Mandelstam-Leibbrandt (ML) prescription in order to circumvent the notorious gauge dependent poles. Recently we have shown that in the context of negative dimensional integration method (NDIM) such prescription can be altogether abandoned, at least in one-loop order calculations. We extend our approach, now studying two-loop integrals pertaining to two-point functions. While previous works on the subject present only divergent parts for the integrals, we show that our prescriptionless method gives the same results for them, besides finite parts for arbitrary exponents of propagators., 6 pages, revtex. Version 2: paragraph added below eq.(3). To be published in Physics Letters B

One of the main difficulties in studying Quantum Field Theory, in the perturbative regime, is the calculation of D-dimensional Feynman integrals. In general, one introduces the so-called Feynman parameters and associated with them the cumbersome parametric integrals. Solving these integrals beyond the one-loop level can be a difficult task. Negative dimensional integration method (\ndim{}) is a technique whereby such problem is dramatically reduced. In this work we present the calculation of two-loop integrals in three diferent cases: scalar ones with three diferent masses, massless with arbitrary tensor rank, with N-insertions of a 2-loop diagram., 7 pages, 4 figures, RevTex. To be published in JPA

Feynman integrals in the physical light-cone gauge are harder to solve than their covariant counterparts. The difficulty is associated with the presence of unphysical singularities due to the inherent residual gauge freedom in the intermediate boson propagators constrained within this gauge choice. In order to circumvent these non-physical singularities, the headlong approach has always been to call for mathematical devices --- prescriptions --- some successful ones and others not so much so. A more elegant approach is to consider the propagator from its physical point of view, that is, an object obeying basic principles such as causality. Once this fact is realized and carefully taken into account, the crutch of prescriptions can be avoided altogether. An alternative third approach, which for practical computations could dispense with prescriptions as well as prescinding the necessity of careful stepwise watching out of causality would be of great advantage. And this third option is realizable within the context of negative dimensions, or as it has been coined, negative dimensional integration method, NDIM for short., 9 pages, PTPTeX (included)

Perturbative quantum gauge field theory seen within the perspective of physical gauge choices such as the light-cone entails the emergence of troublesome poles of the type $(k\cdot n)^{-\alpha}$ in the Feynman integrals, and these come from the boson field propagator, where $\alpha = 1,2,...$ and $n^{\mu}$ is the external arbitrary four-vector that defines the gauge proper. This becomes an additional hurdle to overcome in the computation of Feynman diagrams, since any graph containing internal boson lines will inevitably produce integrands with denominators bearing the characteristic gauge-fixing factor. How one deals with them has been the subject of research for over decades, and several prescriptions have been suggested and tried in the course of time, with failures and successes. However, a more recent development in this front which applies the negative dimensional technique to compute light-cone Feynman integrals shows that we can altogether dispense with prescriptions to perform the calculations. An additional bonus comes attached to this new technique in that not only it renders the light-cone prescriptionless, but by the very nature of it, can also dispense with decomposition formulas or partial fractioning tricks used in the standard approach to separate pole products of the type $(k\cdot n)^{-\alpha}[(k-p)\cdot n]^{-\beta}$, $(\beta = 1,2,...)$. In this work we demonstrate how all this can be done., Comment: 6 pages, no figures, Revtex style, reference [2] corrected

Feynman diagrams are the best tool we have to study perturbative quantum field theory. For this very reason the development of any new technique that allows us to compute Feynman integrals is welcome. By the middle of the 1980s, Halliday and Ricotta suggested the possibility of using negative-dimensional integrals to tackle the problem. The aim of this work is to revisit the technique as such and check on its possibilities. For this purpose, we take a box diagram integral contributing to the photon-photon scattering amplitude in quantum electrodynamics using the negative-dimensional integration method. Our approach enables us to quickly reproduce the known results as well as six other solutions as yet unknown in the literature. These six new solutions arise quite naturally in the context of negative-dimensional integration method, revealing a promising technique to handle Feynman integrals.

In this work we calculate two two-loop massless Feynman integrals pertaining to self-energy diagrams using NDIM (Negative Dimensional Integration Method). We show that the answer we get is 36-fold degenerate. We then consider special cases of exponents for propagators and the outcoming results compared with known ones obtained via traditional methods., Comment: LaTeX, 10 pages, 2 figures, styles included

The quantum mechanical approach to the well known prisoners dilemma, one of the basic examples to illustrate the concepts of Game Theory, is implemented with a classical optical resource, nonquantum entanglement between spin and orbital degrees of freedom of laser modes. The concept of entanglement is crucial in the quantum version of the game, which brings novel features with a richer universe of strategies. As we show, this richness can be achieved in a quite unexpected context, namely that of paraxial spin-orbit modes in classical optics.

We quantize the classical game of simultaneous two-person duel. In this game, the players Alice and Bob, have a two level system, for example, a spin 1/2 particle, which models alive and dead states. Through physical considerations we write up the unitary operator which represents the classical action of firing, which quantum mechanically is represented by flipping the opponent’s spin and test its classical limits. We study three representative special cases of such duel where players start the duel: both alive; in a Bell state; and when one of them has her skills decreasing along the duel. We also present a proposal of experimental realization of this quantum game using twin photons produced by spontaneous parametric down conversion.

We report on the experimental realization of the quantum duel game for two players, Alice and Bob. Using an all optical approach, we have encoded Alice and Bob states in transverse modes and polarization degrees of freedom of a laser beam, respectively. By setting Alice and Bob input states and considering the possibility of Alice performing two shots, we demonstrated the quantum features of the game as well as we recovered the classical version of the game.

We perform a theoretical analysis of a setup intended to measure the repulsive (outward) Casimir forces predicted to exist inside of perfectly conducting rectangular cavities. We consider the roles of the conductivity of the real metals, of the temperature and surface roughness. The use of this repulsive force to reduce friction and wear in micro and nanoelectromechanical systems (MEMS and NEMS) is also considered., Changed content, RevTex4, two column, 10 pages, 5 figures. Accepted for publication in the Brazilian Journal of Physics

Here we study a one-dimensional finite lattice formed by generalized contact interactions in a circular setup, i.e., under periodic boundary conditions. Considering only four such potentials, we show the emergence of different behaviors as revivals, bouncing, and trapping for the time evolution of wave packets. This is done by properly choosing the parameters that characterize the contact interactions. We also discuss possible physical applications for this type of system, such as using it to split an initially localized state into spatially separated and dynamically independent parts.

We consider a particle with spin 1/2 with position-dependent mass moving in a plane. Considering separately Rashba and Dresselhaus spin-orbit interactions, we write down the Hamiltonian for this problem and solve it for Dirichlet boundary conditions. Our radial wavefunctions have two contributions: homogeneous ones which are written as Bessel functions of non-integer orders—that depend on angular momentum m—and particular solutions which are obtained after decoupling the non-homogeneous system. In this process, we find non-homogeneous Bessel equation, Laguerre, as well as biconfluent Heun equation. We also present the probability densities for m = 0, 1, 2 in an annular quantum well. Our results indicate that the background as well as the spin-orbit interaction naturally splits the spinor components.

Recently, general point interactions in one dimension has been used to model a large number of different phenomena in quantum mechanics. Such potentials, however, require some sort of regularization to lead to meaningful results. The usual ways to do so rely on technicalities that may hide important physical aspects of the problem. In this work we present a method to calculate the exact Green functions for general point interactions in one dimension. Our approach differs from previous ones because it is based only on physical quantities, namely, the scattering coefficients R and T to construct G. Renormalization or particular mathematical prescriptions are not invoked. The simple formulation of the method makes it easy to extend to more general contexts, such as for lattices of N general point interactions, on a line, on a half-line, under periodic boundary conditions, and confined in a box.

In this article we present the complete massless and massive one-loop triangle diagram results using the negative dimensional integration method (NDIM). We consider the following cases: massless internal fields; one massive, two massive with the same mass m and three equal masses for the virtual particles. Our results are given in terms of hypergeometric and hypergeometric-type functions of external momenta (and masses for the massive cases) where the propagators in the Feynman integrals are raised to arbitrary exponents and the dimension of the space-time D. Our approach reproduces the known results as well as other solutions as yet unknown in the literature. These new solutions occur naturally in the context of NDIM revealing a promising technique to solve Feynman integrals in quantum field theories.