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| {{Standard model of particle physics}}
| | Andrew Berryhill is what his wife loves to contact him and he totally digs that title. Kentucky is exactly where I've usually been living. One of the issues she loves most is canoeing and she's been performing it for quite a while. I am an invoicing officer and I'll be promoted soon.<br><br>My site :: free online tarot card readings ([http://cspl.postech.ac.kr/zboard/Membersonly/144571 http://cspl.postech.ac.kr]) |
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| A '''Majorana fermion''', also referred to as a '''Majorana particle''', is a [[fermion]] that is its own [[antiparticle]]. They were hypothesised by [[Ettore Majorana]] in 1937. The term is sometimes used in opposition to a [[Dirac fermion]], which describes fermions that are not their own antiparticles. No elementary fermions are known to be their own antiparticle, though the nature of the [[neutrino]] is not settled and it might be a Majorana fermion. By contrast, it is common that [[bosons]] are their own antiparticle, such as the [[photon]].
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| In condensed matter physics, Majorana fermions exist as [[quasiparticle]] excitations in [[superconductors]] and can be used to form Majorana bound states possessing [[Anyon#Non-abelian_anyons|non-abelian statistics]].
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| ==Theory==
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| The concept goes back to [[Ettore Majorana]]'s 1937 suggestion<ref>{{cite journal|author=E. Majorana|title=Teoria simmetrica dell’elettrone e del positrone|journal=Nuovo Cimento|volume=14|page=171|year=1937|language=Italian|postscript=. [http://www2.phys.canterbury.ac.nz/editorial/Majorana1937-Maiani2.pdf English translation].}}</ref> that neutral spin-1/2 particles can be described by a real [[relativistic wave equations|wave equation]] (the [[Majorana equation]]), and would therefore be identical to their antiparticle (since the wave function of particle and antiparticle are related by [[complex conjugate|complex conjugation]]).
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| The difference between Majorana fermions and Dirac fermions can be expressed mathematically in terms of the [[creation and annihilation operators]] of [[second quantization]]. The creation operator <math>\gamma^{\dagger}_j</math> creates a fermion in quantum state <math>j</math> (described by a ''real'' wave function), while the annihilation operator <math>\gamma_j</math> annihilates it (or, equivalently, creates the corresponding antiparticle). For a Dirac fermion the operators <math>\gamma^{\dagger}_j</math> and <math>\gamma_j</math> are distinct, while for a Majorana fermion they are identical.
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| ==Elementary particle==
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| No elementary particle in the [[Standard Model]] is known to be a Majorana fermion. However, the nature of the [[neutrino]] is not yet definitely settled; it might be a Majorana fermion or it might be a [[Dirac fermion]]. Gauge theories suggest that neutrinos are Majorana fermions{{clarify|date=December 2013}}, so [[lepton number]] is violated in nature, which could be verified in both low and high energy experiments. At low energies, [[double beta decay|neutrinoless double beta decay]], where two neutrons decay into two protons and two electrons only, is possible; experiments are underway to search for this type of decay.<ref>{{cite journal|author=W. Rodejohann
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| |title=Neutrino-less Double Beta Decay and Particle Physics|journal=[[International Journal of Modern Physics]]|volume=E20|page=1833|year=2011|doi=10.1142/S0218301311020186|arxiv=1106.1334|bibcode = 2011IJMPE..20.1833R }}</ref> The significance of neutrinoless double beta decay stems from the fact
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| that, in any gauge theory like the [[Standard Model]] the observation of neutrinoless double beta decay necessarily implies Majorana nature of neutrinos, a result known as the [[Black Box theorem]] <ref>{{cite journal|author= J. Schechter, J.W.F. Valle.|title=Neutrinoless Double beta Decay in SU(2) x U(1) Theories|journal=[[Physical Review]]|volume=D25|page=2951|year=1982|doi=10.1103/PhysRevD.25.2951|bibcode = 1982PhRvD..25.2951S }}</ref>
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| The high energy analog of the neutrinoless double beta decay process is the production of same sign charged lepton pairs at hadron colliders;<ref>{{cite journal|author=W.-Y. Keung and G. Senjanovic|title=Majorana Neutrinos and the Production of the Right-Handed Charged Gauge Boson|journal=[[Physical Review Letters]]|volume=50|page=1427|year=1983|bibcode = 1983PhRvL..50.1427K|doi=10.1103/PhysRevLett.50.1427}}</ref> it is being searched for by both the [[ATLAS]] and [[Compact Muon Solenoid|CMS]] experiments at the [[Large Hadron Collider]]. In theories based on [[left–right symmetry]], there is a deep connection between these processes.<ref>{{cite journal|author= V. Tello, M. Nemevsek, F. Nesti and G. Senjanovic
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| |title=Left-Right Symmetry: from LHC to Neutrinoless Double Beta Decay|journal=[[Physical Review Letters]]|volume=106|page=151801|year=2011|doi=10.1103/PhysRevLett.106.151801|arxiv=1011.3522|bibcode = 2011PhRvL.106o1801T }}</ref>
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| In the most accepted explanation of the smallness of [[neutrino mass]], the [[seesaw mechanism]], the neutrino is naturally a Majorana fermion.
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| Majorana fermions cannot possess intrinsic electric or magnetic moments, only [[toroidal moment]]s.<ref>{{Citation
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| | last = Kayser
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| | first = Boris
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| | last2 = Goldhaber
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| | first2 = Alfred S.
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| | title = CPT and CP properties of Majorana particles, and the consequences
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| | journal = Phys. Rev. D
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| | volume = 28
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| | pages = 2341–2344
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| | year = 1983
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| | doi = 10.1103/PhysRevD.28.2341 |bibcode = 1983PhRvD..28.2341K }}</ref><ref>{{Citation
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| | last = Radescu
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| | first = E. E.
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| | title = On the electromagnetic properties of Majorana fermions
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| | journal = Phys. Rev. D
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| | volume = 32
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| | pages = 1266–1268
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| | year = 1985
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| | doi = 10.1103/PhysRevD.32.1266 |bibcode = 1985PhRvD..32.1266R }}</ref><ref>{{Citation
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| | last = Boudjema
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| | first = F.
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| | last2 = Hamzaoui
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| | first2 = C.
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| | last3 = Rahal
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| | first3 = V.
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| | last4 = Ren
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| | first4 = H. C.
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| | title = Electromagnetic Properties of Generalized Majorana Particles
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| | journal = Phys. Rev. Lett.
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| | volume = 62
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| | issue = 8
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| | pages = 852–854
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| | year = 1989
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| | doi = 10.1103/PhysRevLett.62.852 |bibcode = 1989PhRvL..62..852B }}</ref> Such minimal interaction with electromagnetic fields makes them potential candidates for [[cold dark matter]].<ref>{{Citation
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| | last = Pospelov
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| | first = Maxim
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| | last2 = ter Veldhuis
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| | first2 = Tonnis
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| | title = Direct and indirect limits on the electro-magnetic form factors of WIMPs
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| | journal = Phys. Lett. B
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| | volume = 480
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| | pages = 181–186
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| | year = 2000
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| | arxiv = hep-ph/0003010
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| | doi = 10.1016/S0370-2693(00)00358-0 |bibcode = 2000PhLB..480..181P }}</ref><ref>{{Citation
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| | last = Ho
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| | first = C. M.
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| | last2 = Scherrer
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| | first2 = R. J.
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| | title = Anapole Dark Matter
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| | journal = Phys. Lett. B
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| | volume = 722
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| | issue = 8
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| | pages = 341-346
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| | year = 2013
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| | arxiv = 1211.0503
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| | doi = 10.1103/PhysRevLett.62.852 |bibcode = 1989PhRvL..62..852B }}</ref> The hypothetical [[neutralino]] of [[supersymmetry|supersymmetric]] models is a Majorana fermion.
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| ==Majorana bound states==
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| In [[Superconductivity|superconducting materials]], Majorana fermions can emerge as (non-fundamental) [[quasiparticle]]s. This becomes possible because a quasiparticle in a superconductor is its own antiparticle. Mathematically, the superconductor imposes [[electron hole]] "symmetry" on the quasiparticle excitations, relating the creation operator <math>\gamma(E)</math> at energy <math>E</math> to the annihilation operator <math>{\gamma^{\dagger}(-E)}</math> at energy <math>-E</math>. Majorana fermions can be bound to a defect at zero energy, and then the combined objects are called Majorana bound states or Majorana zero modes.<ref>{{cite journal|author=F. Wilczek|title=Majorana returns|journal=[[Nature Physics]]|volume=5|page=614|year=2009|doi=10.1038/nphys1380|url=http://ctp.lns.mit.edu/Wilczek_Nature/Majorana_return434.pdf|issue=9|bibcode=2009NatPh...5..614W}}</ref> This name is more appropriate than Majorana fermion (although the distinction is not always made in the literature), since the statistics of these objects is no longer [[Quantum_field_theory#Fermions|fermionic]]. Instead, the Majorana bound states are an example of [[Anyon#Non-abelian_anyons|non-abelian anyons]]: interchanging them changes the state of the system in a way which depends only on the order in which exchange was performed. The non-abelian statistics that Majorana bound states possess allows to use them as a building block for a [[topological quantum computer]].<ref name=nayak2008>{{cite journal|title=Non-Abelian anyons and topological quantum computation|journal=[[Reviews of Modern Physics]]|volume=80|page=1083|year=2008|author=C. Nayak, S. Simon, A. Stern, M. Freedman, and S. Das Sarma|bibcode = 2008RvMP...80.1083N |doi = 10.1103/RevModPhys.80.1083 |arxiv = 0707.1889 }}</ref>
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| A [[quantum vortex]] in certain superconductors or superfluids can trap midgap states, so this is one source of Majorana bound states.<ref>{{cite journal|author1=N.B. Kopnin|author2=M.M. Salomaa|title=Mutual friction in superfluid <sup>3</sup>He: Effects of bound states in the vortex core|journal=[[Physical Review B]]|volume=44|page=9667|year=1991|bibcode=1991PhRvB..44.9667K|doi=10.1103/PhysRevB.44.9667|issue=17}}</ref><ref>{{cite journal|author=G.E. Volovik|title=Fermion zero modes on vortices in chiral superconductors|journal=[[JETP Letters]]|volume=70|page=609|year=1999|bibcode=1999JETPL..70..609V|doi=10.1134/1.568223|issue=9|arxiv = cond-mat/9909426 }}</ref><ref>{{cite journal|author1=N. Read|author2=D. Green|title=Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect|journal=[[Physical Review B]]|volume=61|page=10267|year=2000|bibcode=2000PhRvB..6110267R|doi=10.1103/PhysRevB.61.10267|issue=15|arxiv = cond-mat/9906453 }}</ref> [[Surface_states#Shockley_states|Shockley states]] at the end points of superconducting wires or line defects are an alternative, purely electrical, source.<ref>{{cite journal|author=A. Yu. Kitaev|title=Unpaired Majorana fermions in quantum wires|journal=[[Physics-Uspekhi]] (supplement)|volume=44|issue=131|year=2001|bibcode=2001PhyU...44..131K|pages=131|doi=10.1070/1063-7869/44/10S/S29|arxiv = cond-mat/0010440 }}</ref> An altogether different source uses the [[fractional quantum Hall effect]] as a substitute for the superconductor.<ref>{{cite journal|author1=G. Moore|author2=N. Read|title=Nonabelions in the fractional quantum Hall effect|journal=[[Nuclear Physics B]]|volume=360|page=362|year=1991|bibcode=1991NuPhB.360..362M|doi=10.1016/0550-3213(91)90407-O|issue=2–3}}</ref>
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| ===Experiments in superconductivity===
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| In 2008 Fu and Kane provided a groundbreaking development by theoretically predicting that Majorana bound states can appear at the interface between topological insulators and superconductors.<ref>{{cite journal|author1=L. Fu|author2=C. L. Kane|title=Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator|journal=[[Physical Review Letters]]|volume=10|page=096407|year=2008|url=http://link.aps.org/doi/10.1103/PhysRevLett.100.096407|doi=10.1103/PhysRevLett.100.096407|issue=9|bibcode = 2008PhRvL.100i6407F |arxiv = 0707.1692 }}</ref><ref>{{cite journal|author1=L. Fu|author2=C. L. Kane|title=Josephson current and noise at a superconductor/quantum-spin-Hall-insulator/superconductor junction|journal=[[Physical Review B]]|volume=79|page=161408|year=2009|url=http://link.aps.org/doi/10.1103/PhysRevB.79.161408|doi=10.1103/PhysRevB.79.161408|issue=16|bibcode = 2009PhRvB..79p1408F |arxiv = 0804.4469 }}</ref> Many proposals of a similar spirit soon followed, where it was shown that Majorana bound states can appear even without topological insulator. An intense search to provide experimental evidence of Majorana bound states in superconductors<ref>{{cite journal|author=J. Alicea|title=New directions in the pursuit of Majorana fermions in solid state systems|arxiv=1202.1293|bibcode = 2012RPPh...75g6501A |doi = 10.1088/0034-4885/75/7/076501 }}</ref><ref>{{cite journal|author=C. W. J. Beenakker|title=Search for Majorana fermions in superconductors|arxiv=1112.1950|bibcode = 2011arXiv1112.1950B }}</ref> first produced some positive results in 2012.<ref>{{cite journal|author=E. S. Reich|title=Quest for quirky quantum particles may have struck gold|journal=[[Nature News]]|date=28 February 2012|doi=10.1038/nature.2012.10124|url=http://www.nature.com/news/quest-for-quirky-quantum-particles-may-have-struck-gold-1.10124}}</ref><ref>{{cite news|author=Jonathan Amos|url=http://www.bbc.co.uk/news/science-environment-17695944|title=Majorana particle glimpsed in lab|work=[[BBC News]]|date=13 April 2012|accessdate=15 April 2012}}</ref> A team from the [[Kavli Institute of Nanoscience]] at [[Delft University of Technology]] in the Netherlands reported an experiment involving [[indium antimonide]] nanowires connected to a circuit with a gold contact at one end and a slice of superconductor at the other. When exposed to a moderately strong magnetic field the apparatus showed a peak electrical conductance at zero voltage that is consistent with the formation of a pair of Majorana bound states, one at either end of the region of the nanowire in contact with the superconductor.<ref>{{cite journal|author1=V. Mourik|author2=K. Zuo|author3=S.M. Frolov|author4=S.R. Plissard|author5=E.P.A.M. Bakkers|author6=L.P. Kouwenhoven|title=Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices|journal=[[Science (journal)|Science]]|date=12 April 2012|doi=10.1126/science.1222360|arxiv=1204.2792|bibcode = 2012Sci...336.1003M }}</ref>
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| This experiment from Delft marks a possible verification of independent theoretical proposals from two groups<ref>{{cite journal|author1=R. Lutchyn|author2=J. Sau|author3=S. Das Sarma|title=Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures|journal=[[Physical Review Letters]]|volume=105|page=077001|year=2010|url=http://prl.aps.org/abstract/PRL/v105/i7/e077001|bibcode=2010PhRvL.105g7001L|doi=10.1103/PhysRevLett.105.077001|issue=7|arxiv = 1002.4033 }}</ref><ref>{{cite journal|author1=Y. Oreg|author2=G. Refael|author3=F. von Oppen|title=Helical Liquids and Majorana Bound States in Quantum Wires|journal=[[Physical Review Letters]]|volume=105|page=177002|year=2010|url=http://link.aps.org/doi/10.1103/PhysRevLett.105.177002|doi=10.1103/PhysRevLett.105.177002|issue=17|bibcode = 2010PhRvL.105q7002O |arxiv = 1003.1145 }}</ref> predicting the solid state manifestation of Majorana bound states in semiconducting wires.
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| ==References==
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| {{reflist|colwidth=25em}}
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| ==Further reading==
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| * Palash B. Pal: ''Dirac, Majorana and Weyl fermions'', [http://arxiv.org/abs/1006.1718 arXiv:1006.1718], 24 June / 17 July 2009 (introductory article)
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| {{Particles}}
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| [[Category:Particle physics]]
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| [[Category:Quantum field theory]]
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| [[Category:Subatomic particles]]
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| [[Category:Fermions]]
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| [[Category:Concepts in physics]]
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Andrew Berryhill is what his wife loves to contact him and he totally digs that title. Kentucky is exactly where I've usually been living. One of the issues she loves most is canoeing and she's been performing it for quite a while. I am an invoicing officer and I'll be promoted soon.
My site :: free online tarot card readings (http://cspl.postech.ac.kr)