DOCSLIB.ORG

Think Different from Particle-Wave Duality Simulation of Nature Using Quantum Software and Hardware (Original Ideas from Richard Feynman)

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Think Different from Particle-Wave Duality Simulation of Nature Using Quantum Software and Hardware (Original Ideas from Richard Feynman) Revolution in Physics PHYS 342 Modern Physics Revolution in Physics must unifies seemingly unrelated phenomena. Ultracold Atoms and Trappe Ions Mechanical Revolution: EM Revolution: Relativity Revolution: Unified falling apples on Unified electricity, Unified space, time and earth and the planets magnetism, and light gravity Today and Mar.23 Contents: motions in sky a) Revolution in physics –2nd Quantum revolution b) Quantum simulation, measurement, and information c) Atomic ensemble and quantum statistical (refer to Charpter10) d) Cooling and trapping of 6Li fermions e) Quantum simulation with ultracold atoms f) Quantum measurement with ultracold atoms Quantum Revolution: Unified particle and wave g) Quantum Information Basis h) Cooling and Trapping Charged Particles i) Preparation, Manipulation and Detection of 171Yb+ What is the second j) Trapped Ion Quantum Computers quantum revolution? k) Quantum Network Think different from Particle-Wave Duality Simulation of Nature using Quantum Software and Hardware (original ideas from Richard Feynman) “wave-like” : flying in the ” Nature isn’t classical, if you want to make a simulation of nature, space, messenger of the you’d better make it quantum mechanical.” world------ Information Software from quantum principles (quantum information) “How can we simulate the quantum mechanics?….Can you do it with a new kind of computer - a quantum computer? “ Hardware from quantum devices (quantum matter) “particle-like” : localized in the space, elements for Second Quantum Revolution the world------ Matter unifies Matter and Information at Quantum Level ! Particle-Wave duality Matter – Information duality Need Quantum Computer! Toys for Second Quantum Revolution My Favorite Toys : Trapped Atoms and Ions “We can create states of quantum coherent or entangled matter and energy that likely existed nowhere else in the Universe. These new man-made quantum states have wide application to the development of computers, communications systems, sensors and compact metrological devices.“ ---- by J.P.Dowling and G.J.Milburn 6Li Atom: Fermi Condensation 40Ca+ Ion: Ground State Interaction, Spin, Dimensionality, Filling, Impurity, Coherence … All Tunable ! Developed to: Atomic Matter Physics, Quantum Simulator, Quantum Sensors, Atomtronics … Trapped Quantum Particles (Historical) Trapped Atoms and Ions 1989 Nobel Prize: 1997 Nobel Prize: Ion trap isolating Laser cooling and single quantum trapping atoms. particle. Steven Chu Hans Dehmelt Claude Cohen-Tannoudji Wolfgang Paul William Daniel Phillips 2001 Nobel Prize: 2012 Nobel Prize: Bose-Einstein condensation in dilute gases Manipulation of individual quantum systems Degenerate Fermi Gas Hybrid Atom-photon Ion Trap Quantum Computer Eric Cornell, Carl Wieman, Wolfgang Ketterle Serge Haroche and David J. Wineland and Condensation Interferometer And Network 7 US Physicists (4 from NIST/JILA), 2 France, 1 Germany Pauli Exclusion Principle Today and Mar.23 Contents: Fundamental principle -- Pauli Exclusion Principle a) Revolution in physics –2nd Quantum revolution Any fundamental particles with Odd/2 spin can not have the b) Quantum simulation, measurement, and information same set of quantum numbers in a quantum system. c) Atomic ensemble and quantum statistical (refer to Charpter10) d) Cooling and trapping of 6Li fermions e) Quantum simulation with ultracold atoms f) Quantum measurement with ultracold atoms g) Quantum Information Basis h) Cooling and Trapping Charged Particles spin=0,1,2,3,4.. i) Preparation, Manipulation and Detection of 171Yb+ j) Trapped Ion Quantum Computers k) Quantum Network spin=1/2,3/2,5/2... How to Label an Atomic State Mixture of Spin Up/Down 6Li Atoms Now we have seven quantum numbers for a certain atomic state. ( n, l , ml, s , ms, j, mj,I , mI, F, m F) Hyperfine Structure in a Magnetic Field e‐orbital e‐spin e‐total nuclei‐spin total 2p B 0 6 # 5 (for all electrons):1 2 670 nm 4 E 3 2 (for the outer electrons): 2 / 2s 1 2 1 1 Ground State(1s 2s ):J=1/2 Level 1 Spin ½ Up 1 = ,1 Now I =1, what is F, m ? 2 F Nuclear Spin: I=1 1 Level 2 Spin ½ Down 2 = ,0 2 1,2 States High B-Field Seeking----Requires Optical Trap 6Li Atoms for Fermionic Condensation Strong Interacting Systems in Nature Black Holes in String Theory High-Tc Neutron Supercond uctor Stars Universal Properties Ultracold Quark- Fermi Gas Gluon Plasma No Interaction (idea gas) Strong Interaction Scaling Invariance All fundamental material particles are fermions: Universal Properties ?? Fermionic condensation plays more significant roles in many-body physics Trivial Universality (PV=nRT) Many-body Strong Interaction From103 K to 10-7 K George Bertsch’s Problem L MOT Beam ( a problem for neutron star) T=700 K R -V 0 T=150 μK Slowing Zeeman Slower N=500 Million | a | L R 0 MOT Beam R -V0 The only length scale is the interparticle spacing L (n,T). Free and Forced Optical Trap Evaporative U = 0.7mK Cooling I =2MW/cm2 All thermodynamic and L T < 1 μK Size ~ 50 μm dynamic properties are N=200,000 Two spin component interacting only determined by density via s-wave quantum collisions. and temperature Optical Dipole Trapped Fermi Gas S-wave scattering Feshbach Resonance 1 g 3 3 3 u u agnet coils u B B B 1 1 = ,1 = ,0 2 2 electron spin, nuclear spin Optical Trap Loading Forced Evaporation Force Evaporative Cooling Weakly Interacting Regime cooling@ 330 G for weakly interacting Fermi Gas Strongly Interacting Regime cooling@ 834 G for strongly interacting Fermi Gas High-Field Imaging Phase Diagram for 6Li Ultracold Fermi Gas BEC Unitary BCS Strongly Interacting Degenerate Fermi Gases BEC-BCS crossover: A pure theoretical problem in condensed matter physics before 2002. Become real experiments in atomic physic after 2002 0.01 U0， T/TF = 0.45 0.001 U0， T/TF = 0.18 Ballistic Expansion – Gas dynamics Hydrodynamic Expansion- Fluid Dynamics Noninteracting Fermi Gas Fermi Condensation or Strongly interacting Fermi gas.
Load more

Recommended publications
  • Optical Trapping of Objects Is Among the Most Exciting Applications of a Laser
    Reg. No: 2016/23/P/ST3/02156; Principal Investigator: dr inż. Paweł Karpiński Optical trapping of objects is among the most exciting applications of a laser. Started by Arthur Ashkin in 1970s it brought manifold of intriguing discoveries in physics, chemistry and biology. Among the most exciting applications in physics one can point out the laser induced cooling and realization of Bose-Einstein condensation in atomic vapors (Nobel prize in 1997 for Stephen Chou, Claude Cohen-Tannoudji and William Daniel Phillips). In chemistry and biology one can mention a single molecule force spectroscopy, with studies of a single DNA being the one of the most recognizable achievements. More than 30 years after realization of the first optical tweezers there are still a lot of exciting effects and basic studies realized today. The nonequilibrium thermodynamics and Brownian motion of single particle trapped with highly intense laser light is not fully described and its understanding may potentially lead to very interesting new discoveries such as microscopic engines with efficiency higher than the Carnot engine. In standard optical tweezers a single Gaussian laser beam is used to trap and manipulate objects. The degree of control of optical forces can be greatly increased by controlling both the key parameters of the beam and the particles. The alignment and light induced motion of a particle can be better controlled in an optical trap when beam shape, phase or polarization are not trivial, e.g. using cylindrical vector beams known also as structured light. Three dimensional vector structure of an optical field can carry momentum, spin and orbital angular momentum which might be transferred from light to the trapped object.
    [Show full text]
  • 2007-2008 Physics at Brown Newsletter
    Physics at Brown NEWS FOR ALUM N I an D FRIE N DS 2007 ISSUE GREETINGS FROM THE CHAIR - SP RING 2008 elcome to another issue of the Brown Physics newsletter. the rank of Associate Professor with tenure. We also report on WI wrote three years ago, during my first term as the some notable faculty achievements for the past year. department chair--with a committed faculty, dedicated staff, enthusiastic students, supportive administration, and engaged e continue the tradition of highlighting the research of alumni and friends--that the future of physics at Brown looked Wour 2007 Galkin Foundation Fellow on page 2. Also bright. Many things have taken place since then. Here we the effort in enriching our physics instruction continues. Three highlight some of the activities of the past year. new courses are offered this year and proposals for three new physics concentrations are under way. Other noteworthy 007 marked the 50th anniversary of the BCS Theory activities include WiSE, Poster Session, UTRA Awards, 2of Superconductivity. We honored Prof. Leon Resource Center, etc. In addition, community outreach Cooper with a two-day symposium on April remains a priority for the Department with a weekly 12-13. A brief description of this event is open house at Ladd and a greatly expanded five- provided on page 3. year NSF supported GK-12 program. e also report on the establishment hanks to a generous gift from his family, an Wof the Institute for Molecular and TAnthony Houghton Prize will be awarded Nanoscale Innovation, which represents an annually for the best theoretical thesis.
    [Show full text]
  • Wolfgang Pauli Niels Bohr Paul Dirac Max Planck Richard Feynman
    Wolfgang Pauli Niels Bohr Paul Dirac Max Planck Richard Feynman Louis de Broglie Norman Ramsey Willis Lamb Otto Stern Werner Heisenberg Walther Gerlach Ernest Rutherford Satyendranath Bose Max Born Erwin Schrödinger Eugene Wigner Arnold Sommerfeld Julian Schwinger David Bohm Enrico Fermi Albert Einstein Where discovery meets practice Center for Integrated Quantum Science and Technology IQ ST in Baden-Württemberg . Introduction “But I do not wish to be forced into abandoning strict These two quotes by Albert Einstein not only express his well­ more securely, develop new types of computer or construct highly causality without having defended it quite differently known aversion to quantum theory, they also come from two quite accurate measuring equipment. than I have so far. The idea that an electron exposed to a different periods of his life. The first is from a letter dated 19 April Thus quantum theory extends beyond the field of physics into other 1924 to Max Born regarding the latter’s statistical interpretation of areas, e.g. mathematics, engineering, chemistry, and even biology. beam freely chooses the moment and direction in which quantum mechanics. The second is from Einstein’s last lecture as Let us look at a few examples which illustrate this. The field of crypt­ it wants to move is unbearable to me. If that is the case, part of a series of classes by the American physicist John Archibald ography uses number theory, which constitutes a subdiscipline of then I would rather be a cobbler or a casino employee Wheeler in 1954 at Princeton. pure mathematics. Producing a quantum computer with new types than a physicist.” The realization that, in the quantum world, objects only exist when of gates on the basis of the superposition principle from quantum they are measured – and this is what is behind the moon/mouse mechanics requires the involvement of engineering.
    [Show full text]
  • Laser Cooling of Atoms
    Information sheet 2 Laser cooling of atoms In 1985, Alain Aspect joined Claude Cohen-Tannoudji, professor at the Collège de France (Chair of atomic and molecular physics), at the Laboratoire Kastler-Brossel (ENS Paris/CNRS/Université Paris VI), and embarked on research into the laser cooling of atoms with Jean Dalibard, and later with Christophe Salomon, physicists at CNRS. The aim is to control the movement of atoms, by using the force of radiation pressure exerted by lasers. It turns out to be possible to reduce the speed of atoms down to extremely low values, in the region of a few centimeters per second. The gas thus obtained has an extraordinarily low temperature: around one microkelvin, which is only a millionth of a degree above absolute zero. Among the many results obtained at ENS and which were rewarded in particular by the 1997 Nobel prize awarded to Claude Cohen-Tannoudji2, Alain Aspect especially contributed to the development of the first cooling method which made it possible to slow down the speed at which atoms move to below the “photon recoil”. This is the speed gained by an atom which emits a photon, rather like a gun recoiling when it is fired. The photon recoil was considered at that time to be an unsurmountable barrier. Note that the process used to obtain this result (dubbed “velocity-selective black resonance”) Cooling of atoms to “below photon recoil”. This leads to each atom being placed into a quantum shows the tracks left on a fluorescent screen by superposition where it is simultaneously present in several hundred atoms which were cooled and several areas of space that are a few centimeters released above the screen.
    [Show full text]
  • World's Leading Scientists and Technologists to Gather at the Global
    MEDIA RELEASE WORLD’S LEADING SCIENTISTS AND TECHNOLOGISTS TO GATHER AT THE GLOBAL YOUNG SCIENTISTS SUMMIT 2021 Summit will host 21 eminent scientists including Nobel Laureates, who will engage and share first-hand insights in science and research with over 500 young scientists from 30 countries 6 JANUARY 2021, SINGAPORE – The National Research Foundation Singapore (NRF) will host the ninth edition of the Global Young Scientists Summit (GYSS), which will see the gathering of the world’s foremost scientists and technologists engage and inspire aspiring young scientists. Held virtually from 12 to 15 January 2021, the eminent scientists will also discuss the latest advances in research and how they can be used to develop solutions to address major global challenges. The Summit will be graced by Singapore’s Deputy Prime Minister and Chairman of NRF, Mr Heng Swee Keat, who will deliver the opening address. The GYSS is a multi-disciplinary event covering the disciplines of chemistry, physics, biology, mathematics, computer science, and engineering. During the event, luminary scientists and technologists will share details of their discoveries by delivering plenary addresses, participating in panel discussions, and engaging with the young scientists in small group discussions. They will also provide mentorship to over 500 young researchers from more than 30 countries. Star-studded panel speaking on a wide range of subjects and issues This year, the GYSS sees 21 speakers, the highest number since the start of the Summit, of whom 17 are speaking at the Summit for the first time. The list includes Nobel Laureates, Fields Medallists, Millennium Technology Prize and the Turing Award winners.
    [Show full text]
  • Ion Trap Nobel
    The Nobel Prize in Physics 2012 Serge Haroche, David J. Wineland The Nobel Prize in Physics 2012 was awarded jointly to Serge Haroche and David J. Wineland "for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems" David J. Wineland, U.S. citizen. Born 1944 in Milwaukee, WI, USA. Ph.D. 1970 Serge Haroche, French citizen. Born 1944 in Casablanca, Morocco. Ph.D. from Harvard University, Cambridge, MA, USA. Group Leader and NIST Fellow at 1971 from Université Pierre et Marie Curie, Paris, France. Professor at National Institute of Standards and Technology (NIST) and University of Colorado Collège de France and Ecole Normale Supérieure, Paris, France. Boulder, CO, USA www.college-de-france.fr/site/en-serge-haroche/biography.htm www.nist.gov/pml/div688/grp10/index.cfm A laser is used to suppress the ion’s thermal motion in the trap, and to electrode control and measure the trapped ion. lasers ions Electrodes keep the beryllium ions inside a trap. electrode electrode Figure 2. In David Wineland’s laboratory in Boulder, Colorado, electrically charged atoms or ions are kept inside a trap by surrounding electric fields. One of the secrets behind Wineland’s breakthrough is mastery of the art of using laser beams and creating laser pulses. A laser is used to put the ion in its lowest energy state and thus enabling the study of quantum phenomena with the trapped ion. Controlling single photons in a trap Serge Haroche and his research group employ a diferent method to reveal the mysteries of the quantum world.
    [Show full text]
  • Bose-Einstein Condensation
    Low Dimensional Systems and Nanostructures Jon Ander Arregi Bose-Einstein Condensation A Bose-Einstein condensate is a state of a dilute gas, sometimes also called fifth state of matter, of weakly interacting bosons (i.e., particles with integer spin) confined by an external potential and cooled down to temperatures very near to the absolute zero. At low enough temperatures the system undergoes a transition to a state with a large fraction of the bosons occupying the lowest energy level, corresponding to a zero momentum state, at which quantum effects become apparent on a macroscopic scale. In 1924, the indian physicist Satyendra Nath Bose was working on the quantum statistics of light quanta (nowadays called photons) but he had troubles getting people to accept his ideas. He sent his results to Albert Einstein, who realised of the importance of his work and he translated and sent Bose's paper for publication [1]. Einstein extended the description for massive particles and he found out that something very unusual was supposed to happen at very low temperatures [2]. It was not until 1995, after decades of huge efforts seeking for the experimental evidence, that the first realization of the Bose-Einstein condensate of a gas of around two thousand 87Rb atoms cooled down to 170 nanokelvin (nK) was made by Eric Cornell, Carl Wieman and co-workers at the University of Colorado at Boulder [3]. Four months later, the group led by Wolfgang Ketterle at MIT created a condensate of 23Na with a hundred times more atoms [4], allowing him to observe important effects such as quantum mechanical interference between different condensates [5].
    [Show full text]
  • Nobel 2012: Trapped Ions and Photons
    FEATURES Nobel 2012: Trapped ions and photons l Michel Brune1, Jean-Michel Raimond1, Claude Cohen-Tannoudji 1,2 - DOI: 10.1051/epn/2012601 l 1 Laboratoire Kastler Brossel, ENS, CNRS, UMPC Paris 6, 24 rue Lhomond, 75005 Paris, France l 2 Collège de France, 11 place Marcelin Berthelot, 75005 Paris, France m This colorized The 2012 Nobel prize in physics has been awarded jointly to Serge Haroche image shows the fluorescence from three (Collège de France and Ecole Normale Supérieure) and David Wineland (National trapped beryllium ions illuminated with Institute for Standards and Technology, USA) “for ground-breaking experimental an ultraviolet laser methods that enable measuring and manipulation of individual quantum systems”. beam. Black and blue areas indicate lower intensity, and red and white higher intensity. hat are these methods, why are they For instance, Einstein and Bohr once imagined weighing NIST physicists used jointly recognized? a photon trapped forever in a box, covered by perfect three beryllium ions to demonstrate a crucial The key endeavour in the last century mirrors. These gedankenexperiments and their “ridicu- step in a procedure that of quantum physics has been the explo- lous consequences”, as Schrödinger once stated, played could enable future ration of the coupling between matter and electromag- a considerable role in the genesis of quantum physics quantum computers W to break today's netic radiation. For a long time, the available experimental interpretation. The technical progress made these most commonly used techniques were limited to a large number of atoms and experiments possible. One can now realize some of the encryption codes.
    [Show full text]
  • Decoherence and the Transition from Quantum to Classical—Revisited
    Decoherence and the Transition from Quantum to Classical—Revisited Wojciech H. Zurek This paper has a somewhat unusual origin and, as a consequence, an unusual structure. It is built on the principle embraced by families who outgrow their dwellings and decide to add a few rooms to their existing structures instead of start- ing from scratch. These additions usually “show,” but the whole can still be quite pleasing to the eye, combining the old and the new in a functional way. What follows is such a “remodeling” of the paper I wrote a dozen years ago for Physics Today (1991). The old text (with some modifications) is interwoven with the new text, but the additions are set off in boxes throughout this article and serve as a commentary on new developments as they relate to the original. The references appear together at the end. In 1991, the study of decoherence was still a rather new subject, but already at that time, I had developed a feeling that most implications about the system’s “immersion” in the environment had been discovered in the preceding 10 years, so a review was in order. While writing it, I had, however, come to suspect that the small gaps in the landscape of the border territory between the quantum and the classical were actually not that small after all and that they presented excellent opportunities for further advances. Indeed, I am surprised and gratified by how much the field has evolved over the last decade. The role of decoherence was recognized by a wide spectrum of practic- 86 Los Alamos Science Number 27 2002 ing physicists as well as, beyond physics proper, by material scientists and philosophers.
    [Show full text]
  • Eindhoven University of Technology BACHELOR Creating Rydberg
    Eindhoven University of Technology BACHELOR Creating Rydberg crystals in ultra-cold gases using stimulated Raman adiabatic passage schemes Plantz, N.W.M.; van der Wurff, E.C.I. Award date: 2012 Link to publication Disclaimer This document contains a student thesis (bachelor's or master's), as authored by a student at Eindhoven University of Technology. Student theses are made available in the TU/e repository upon obtaining the required degree. The grade received is not published on the document as presented in the repository. The required complexity or quality of research of student theses may vary by program, and the required minimum study period may vary in duration. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain Eindhoven University of Technology Department of Applied Physics Coherence and Quantum Technology group CQT 2012-08 Creating Rydberg crystals in ultra-cold gases using Stimulated Raman Adiabatic Passage Schemes N.W.M. Plantz & E.C.I. van der Wurff July 2012 Supervisors: ir. R.M.W. van Bijnen dr. ir. S.J.J.M.F. Kokkelmans dr. ir. E.J.D. Vredenbregt Abstract This report is the result of a bachelor internship of two applied physics students.
    [Show full text]
  • VITA for WOLFGANG PAUL MENZEL Personal
    VITA for WOLFGANG PAUL MENZEL Personal: Birth: 5 October 1945 Marital Status: Married Citizenship: United States Education: Ph.D. 1974 University of Wisconsin - Madison (Theoretical Solid State Physics) M.S. 1968 University of Wisconsin - Madison B.S. 1967 University of Maryland - College Park (with high honors, Omicron Delta Kappa, Phi Beta Kappa) Experience: 2007 – present UW Senior Scientist Currently, I am pursuing research interests in remote sensing of atmospheric temperature and moisture profiles, ozone, carbon dioxide, cloud properties, and surface properties. The current focus of my research is improving the synergy of leo sounders (CrIS, IASI) and geo imagers (ABI, AHI) as well as studying cloud and moisture properties derived from HIRS data over the past four decades. For additional information see http://www.ssec.wisc.edu/~paulm/research.html. 2007 – 2011 Verner Suomi Distinguished Professor In the University of Wisconsin Department of Atmospheric and Oceanic Sciences, I was honored to be selected as the first Suomi Professor. I conducted research, taught students, and peformed public service in the socially relevant environmental and climate sciences in the spirit of the inquisitive approach pioneered by Verner Suomi. In the classroom I used my textbook titled “Remote Sensing Applications with Meteorological Satellites” that has been published as a World Meteorological Organization technical document. 1999 – 2007 Chief Scientist for the Office of Research and Applications As the Chief Scientist for the NOAA Office of Research and Applications, I was responsible for providing guidance on science issues and initiating major science programs for the Director of the Office. This included conducting and stimulating research on environmental remote sensing systems, fostering expanded utilization locally and globally, assisting in evolution of NOAA polar orbiting and geostationary satellite holdings, and guiding ORA science resources into the future.
    [Show full text]
  • El Premio Nobel De Fısica De 2012
    El premio Nobel de f´ısica de 2012 Jose´ Mar´ıa Filardo Bassalo* Abstract Palabras clave: Premio nobel de f´ısica de 2012; Haroche y In this article we will talk about the 2012 Nobel Prize in Phy- Wineland, manipulacion´ cuantica.´ sics, awarded to the physicists, the frenchman Serge Haroche and the north-american David Geffrey Wineland for ground- Serge Haroche breaking experimental methods that enable measuring and ma- El premio nobel de f´ısica (PNF) de 2012 fue con- nipulation of individual quantum systems. cedido a los f´ısicos, el frances´ Serge Haroche (n. 1944) y el norteamericano David Geffrey Wine- Keywords: 2012 Physics Nobel Prize; Haroche and Wineland; Quantum Manipulation. land (n. 1944) por el desarrollo de tecnicas´ experimen- tales capaces de medir y manipular sistemas qu´ımi- Resumen cos individuales por medio de la optica´ cuanti-´ En este art´ıculo trataremos del premio nobel de f´ısica de 2012 ca. Con todo, emplearon tecnicas´ distintas y comple- concedido a los f´ısicos, el frances´ Serge Haroche y al norteame- mentarias: Haroche utilizo´ fotones de atomos´ carga- ricano David Geffrey Wineland por el desarrollo de tecnicas´ ex- dos (iones) entrampados; Wineland entrampo´ los io- perimentales capaces de medir y manipular sistemas cuanticos´ nes y empleo´ fotones para modificar su estado individuales. cuantico.´ *http://www.amazon.com.br Recibido: 16 de abril de 2013. Comencemos viendo algo de la vida y del trabajo de es- Aceptado: 09 de octubre de 2013. tos premiados, as´ı como la colaboracion´ en estos temas 5 6 ContactoS 92, 5–10 (2014) por algunas f´ısicos brasilenos,˜ por ejemplo Nicim Za- gury (n.
    [Show full text]