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Dive into the research topics where Alexandre G.M. Schmidt is active.

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Featured researches published by Alexandre G.M. Schmidt.


Journal of The Optical Society of America B-optical Physics | 2013

Vector vortex implementation of a quantum game

A. R. C. Pinheiro; C. E. R. Souza; D. P. Caetano; J. A. O. Huguenin; Alexandre G.M. Schmidt; A. Z. Khoury

The concept of nonseparability between spin and orbital degrees of freedom of laser modes is applied in the implementation of the quantum prisoners dilemma. The quantum version of the game brings novel features with a richer universe of strategies and is one of the basic examples to illustrate the concepts of game theory. Exploiting the classical paraxial spin–orbit modes, we implemented the most important strategies that can be achieved in the quantum version of the game.


Journal of Physics A | 2009

Squeezing a wave packet with an angular-dependent mass

Alexandre G.M. Schmidt

We present a new effect of position-dependent mass (PDM) systems: the possibility of creating squeezed wave packets at the partial revival times. We solve exactly the PDM Schrodinger equation for the two-dimensional quantum rotor with two effective masses μ(θ), both free and interacting with a uniform electric field, and present their energy eigenvalues and eigenfunctions in terms of Mathieu functions. For the first one, in order to squeeze the wave packet it is necessary to apply an electric field; for the second one such an effect can be achieved without the field.


Journal of Physics A | 2012

Quantum duel revisited

Alexandre G.M. Schmidt; Milena M Paiva

We revisit the quantum two-person duel. In this problem, both Alice and Bob each possess a spin-1/2 particle which models dead and alive states for each player. We review the Abbott and Flitney result—now considering non-zero α1 and α2 in order to decide if it is better for Alice to shoot or not the second time—and we also consider a duel where players do not necessarily start alive. This simple assumption allows us to explore several interesting special cases, namely how a dead player can win the duel shooting just once, or how can Bob revive Alice after one shot, and the better strategy for Alice—being either alive or in a superposition of alive and dead states—fighting a dead opponent.


Journal of Physics B | 2015

Experimental realization of the quantum duel game using linear optical circuits

W. F. Balthazar; M H M Passos; Alexandre G.M. Schmidt; D. P. Caetano; J. A. O. Huguenin

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.


Journal of Mathematical Physics | 2015

Quantum systems with position-dependent mass and spin-orbit interaction via Rashba and Dresselhaus terms

Alexandre G.M. Schmidt; L. Portugal; Anderson L. de Jesus

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.


Journal of Mathematical Physics | 2018

Mapping between charge-monopole and position-dependent mass systems

Alexandre G.M. Schmidt; Anderson L. de Jesus

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.


conference on lasers and electro optics | 2013

Playing a quantum game on polarization vortices

Antonio Pinheiro; C. E. R. Souza; Dilson Caetano; J. A. O. Huguenin; Alexandre G.M. Schmidt; A. Z. Khoury

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.


Physics Letters A | 2006

Wave-packet revival for the Schrödinger equation with position-dependent mass

Alexandre G.M. Schmidt


Physica A-statistical Mechanics and Its Applications | 2013

Quantum Russian roulette

Alexandre G.M. Schmidt; Ladário da Silva


Physics Letters A | 2008

Quantum wave packet revival in two-dimensional circular quantum wells with position-dependent mass

Alexandre G.M. Schmidt; Abel D. Azeredo; A. Gusso

Collaboration


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J. A. O. Huguenin

Federal Fluminense University

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A. Z. Khoury

Federal Fluminense University

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Anderson L. de Jesus

Federal Fluminense University

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C. E. R. Souza

Federal Fluminense University

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D. P. Caetano

Federal Fluminense University

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A. R. C. Pinheiro

Federal Fluminense University

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A.O. Castro

Federal Fluminense University

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Abel D. Azeredo

Federal University of Roraima

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Antonio Pinheiro

Federal Fluminense University

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Dilson Caetano

Federal Fluminense University

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