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| :''For the ball used in [[billiards]], see [[cue ball]].''<br>''"Q ball" is also the name of the [[Dynamic pressure|Q]] sensor module in the [[Apollo spacecraft]] [[launch escape system]].''<br>''"Q-Ball" is a colloquialism for [[quetiapine]]''
| | == but getting thicker == |
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| In [[theoretical physics]], '''Q-ball''' refers to a type of [[non-topological soliton]]. A soliton is a localized field configuration that is stable—it cannot spread out and dissipate. In the case of a non-topological soliton, the stability is guaranteed by a conserved charge: the soliton has lower energy per unit charge than any other configuration. (In physics, charge is often represented by the letter "Q", and the soliton is spherically symmetric, hence the name.)
| | Animals eye suddenly opened his eyes,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_41.htm テニス サングラス オークリー], eyes glowing golden light.<br><br>Boom,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_10.htm オークリー サングラス 野球]!<br><br>a teleport directly into the kingdom of God to go. Then sent through the kingdom of God,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_40.htm サングラス オークリー 人気], towards the goal of the land rush!<br><br>......<br><br>Luo Feng could not simply ignore the short distance to disturb their ancestral dream demon,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_40.htm ゴルフ オークリー サングラス], ghost holding a knife,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_61.htm オークリー ゴルフ サングラス], once again hit!<br><br>'Wow ......'<br><br>wins breathtaking beauty,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_10.htm オークリーサングラス一覧].<br><br>Daoguang onwards,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_40.htm オークリー サングラス イチロー], at first just a hint, but getting thicker,[http://www.alleganycountyfair.org/_vti_cnf/rakuten_oakley_56.htm オークリーサングラス画像], the then mighty draped canopy, the endless Daoguang directly converging a huge black miniature universe. The Lord of the universe who Yaozu crowd again completely wrapped up. TV drama will be followed by a black mini-universe split ...... a thin bright golden fleeting.<br><br>crack has appeared in the sky around a very thin space, the channel space crack, even cutting a myriad of space debris 'Space caught' inside ......<br><br>'dark, close the net!' Luo Feng acoustic |
| | | 相关的主题文章： |
| == Intuitive explanation ==
| | <ul> |
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| A Q-ball arises in a theory of [[boson]]ic particles, when there is an attraction between the particles. Loosely speaking, the Q-ball is a finite-sized "blob" containing a large number of particles. The blob is stable against fission into smaller blobs, and against "evaporation" via emission of individual particles, because, due to the attractive interaction, the blob is the lowest-energy configuration of that number of particles. (This is analogous to the fact that [[Nickel-62]] is the most stable nucleus because it is the most stable configuration of neutrons and protons. However, Nickel-62 is not a Q-ball, in part because neutrons and protons are [[fermion]]s, not bosons.)
| | <li>[http://www.xxga.gov.cn/plus/feedback.php?aid=1187 http://www.xxga.gov.cn/plus/feedback.php?aid=1187]</li> |
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| For there to be a Q-ball, the number of particles must be conserved (i.e. the particle number is a conserved "charge", so the particles are described by a complex-valued field <math>\phi</math>), and the interaction potential <math>V(\phi)</math> of the particles must have a negative (attractive) term.
| | <li>[http://www.iflip4.com/member/56901 http://www.iflip4.com/member/56901]</li> |
| For non-interacting particles, the potential would be just a mass term <math>V_{\rm free}(\phi)=m^2|\phi|^2</math>, and there would be no Q-ball. But if one adds an attractive <math>-\lambda |\phi|^4</math> term (and positive higher powers of <math>\phi</math> to ensure that the potential has a lower bound) then there are values of <math>\phi</math> where <math>V(\phi)<V_{\rm free}(\phi)</math>, i.e. the energy of these field values is ''less'' than the energy of a free field. This corresponds to saying that one can create blobs of non-zero field (i.e. clusters of many particles) whose energy is lower than the same number of individual particles far apart. Those blobs are therefore stable against evaporation into individual particles.
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| | | <li>[http://www.80xingui.com/home.php?mod=space&uid=68147 http://www.80xingui.com/home.php?mod=space&uid=68147]</li> |
| ==Constructing a Q-ball==
| | |
| | | </ul> |
| In its simplest form, a Q-ball is constructed in a field theory of a complex scalar field <math>\phi</math>, in which Lagrangian is invariant under a global <math> U(1) </math> symmetry. The Q-ball solution is a state which minimizes energy while keeping the charge Q associated with the global <math>U(1)</math> symmetry constant. A particularly transparent way of finding this solution is via the method of [[Lagrange multipliers]]. In particular, in three spatial dimensions we must minimize the functional
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| :<math> E_{\omega} = E + \omega \left[ Q - \frac{1}{2i} \int d^{3} x(\phi^{*} \partial_{t} \phi - \phi \partial_{t} \phi^{*}) \right], </math>
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| where the energy is defined as
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| :<math> E = \int d^{3} x \left[ \frac{1}{2} \dot{\phi}^{2} + \frac{1}{2} |\nabla \phi|^{2} + U(\phi, \phi^{*}) \right], </math> | |
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| and <math>\omega</math> is our Lagrange multiplier. The time dependence of the Q-ball solution can be obtained easily if one rewrites the functional <math>E_{\omega}</math> as
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| :<math> E_{\omega} = \int d^{3} x \left[ \frac{1}{2} |\dot{\phi} - i \omega \phi|^{2} + \frac{1}{2} |\nabla \phi|^{2} + \hat{U}_{\omega}(\phi, \phi^{*}) \right] </math>
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| where <math> \hat{U}_{\omega} = U - \frac{1}{2} \omega^{2} \phi^{2} </math>. Since the first term in the functional is now positive, minimization of this terms implies
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| :<math> \phi(\vec{r},t) = \phi_{0}(\vec{r}) e^{i\omega t}. </math> | |
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| We therefore interpret the Lagrange multiplier <math>\omega</math> as the frequency of oscillation of the field within the Q-ball.
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| The theory contains Q-ball solutions if there are any values of <math>\phi^*\phi</math> at which the potential is less than <math>m^2\phi^*\phi</math>. In this case, a volume of space with the field at that value can have an energy per unit charge that is less than <math>m</math>, meaning that it cannot decay into a gas of individual particles. Such a region is a Q-ball. If it is large enough, its interior is uniform, and is called "Q-matter". (For a review see Lee ''et al.'' (1992).<ref>
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| {{cite journal
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| |author=T. D. Lee, Y. Pang
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| |year=1992
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| |title=Nontopological solitons
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| |journal=[[Physics Reports]]
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| |volume=221 |pages=251–350
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| |doi=10.1016/0370-1573(92)90064-7
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| |bibcode = 1992PhR...221..251L
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| |issue=5–6 }}</ref>
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| === Thin-wall Q-balls ===
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| The thin-wall Q-ball was the first to be studied, and this pioneering work was carried out by [[Sidney Coleman]] in 1986.<ref name="S. Coleman 1985">
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| {{cite journal
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| |author=S. Coleman
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| |year=1985
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| |title=Q-Balls
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| |journal=[[Nuclear Physics B]]
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| |volume=262 |pages=263
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| |doi=10.1016/0550-3213(85)90286-X
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| |bibcode = 1985NuPhB.262..263C
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| |issue=2 }} and erratum in {{cite journal
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| |author=
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| |year=1986
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| |title=Fourth order supergravity S. Theisen, Nucl. Phys. B263 (1986) 687
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| |journal=Nuclear Physics B
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| |volume=269 |pages=744
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| |doi=10.1016/0550-3213(86)90519-5
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| |bibcode = 1986NuPhB.269Q.744.
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| |issue=3–4 }}</ref> For this reason, Q-balls of the thin-wall variety are sometimes called "Coleman Q-balls".
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| We can think of this type of Q-ball a spherical ball of nonzero [[vacuum expectation value]]. In the thin-wall approximation we take the spatial profile of the field to be simply
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| <math> \phi_{0}(r) = \theta(R-r) \phi_{0}. </math>
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| In this regime the charge carried by the Q-ball is simply <math> Q = \omega \phi_{0}^{2} V </math>. Using this fact we can eliminate <math> \omega </math> from the energy, such that we have
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| <math> E = \frac{1}{2} \frac{Q^{2}}{\phi_{0}^{2} V} + U(\phi_{0}) V. </math>
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| Minimization with respect to <math> V </math> gives
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| <math> V = \sqrt{\frac{Q^{2}}{2 U(\phi_{0}) \phi_{0}^{2}}}. </math>
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| Plugging this back into the energy yields
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| <math> E = \sqrt{ \frac{2 U(\phi_{0})}{\phi_{0}^{2}}}~ Q .</math>
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| Now all that remains is to minimize the energy with respect to <math> \phi_{0} </math>. We can therefore state that a Q-ball solution of the thin-wall type exists if and only if
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| <math> min = \frac{2 U(\phi)}{\phi^{2}}, </math> for <math> \phi > 0</math>.
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| When the above criterion is satisfied the Q-ball exists and by construction is stable against decays into scalar quanta. The mass of the thin-wall Q-ball is simply the energy
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| <math> M(Q) = \omega_{0} Q. </math>
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| It should be pointed out that while this kind of Q-ball is stable against decay into scalars, it is not stable against decay into fermions if the scalar field <math> \phi </math> has nonzero [[Yukawa]] couplings to some fermions. This decay rate was calculated in 1986 by Andrew Cohen, Sidney Coleman, Howard Georgi, and Aneesh Manohar.<ref>
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| {{cite journal
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| |author=A. Cohen, S. Coleman, H. Georgi, A. Manohar
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| |year=1986
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| |title=The Evaporation of Q-balls
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| |journal=[[Nuclear Physics B]]
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| |volume=272 |pages=301
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| |doi=10.1016/0550-3213(86)90004-0
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| |bibcode = 1986NuPhB.272..301C
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| |issue=2 }}</ref>
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| ==History==
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| Configurations of a charged scalar field that are classically stable (stable against small perturbations) were constructed by Rosen
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| in 1968.<ref>
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| {{cite journal
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| |author=G. Rosen
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| |year=1968
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| |title=Particlelike Solutions to Nonlinear Complex Scalar Field Theories with Positive-Definite Energy Densities
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| |journal=[[Journal of Mathematical Physics]]
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| |volume=9 |pages=996
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| |doi=10.1063/1.1664693
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| |bibcode = 1968JMP.....9..996R
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| |issue=7 }}</ref> Stable configurations of multiple scalar fields were studied by Friedberg, Lee, and Sirlin in 1976.<ref>
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| {{cite journal
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| |author=R. Friedberg, T. D. Lee, A. Sirlin
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| |year=1976
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| |title=Class of scalar-field soliton solutions in three space dimensions
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| |journal=[[Physical Review D]]
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| |volume=13 |pages=2739
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| |doi=10.1103/PhysRevD.13.2739
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| |bibcode = 1976PhRvD..13.2739F
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| |issue=10 }}</ref> The name "Q-ball" and the proof of quantum-mechanical stability
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| (stability against tunnelling to lower energy configurations) come from [[Sidney Coleman]].<ref name="S. Coleman 1985"/>
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| ==Occurrence in nature==
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| It has been theorized that [[dark matter]] might consist of Q-balls (Frieman ''et al.''. 1988,<ref>
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| {{cite journal
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| |author=J. Frieman, G. Gelmini, M. Gleiser, E. Kolb | |
| |year=1988
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| |title=Solitogenesis: Primordial Origin Of Nontopological Solitons
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| |url=http://lss.fnal.gov/archive/test-preprint/fermilab-pub-88-013-a.shtml
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| |journal=[[Physical Review Letters]]
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| |volume=60 |pages=2101
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| |doi=10.1103/PhysRevLett.60.2101
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| |bibcode=1988PhRvL..60.2101F
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| |issue=21
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| }}</ref> Kusenko ''et al.''. 1997<ref>
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| {{cite journal
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| |author=A. Kusenko, M. Shaposhnikov
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| |year=1998
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| |title=Supersymmetric Q balls as dark matter
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| |journal=[[Physics Letters B]]
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| |volume=418 |pages=46–54
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| |doi=10.1016/S0370-2693(97)01375-0
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| |id=
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| |arxiv=hep-ph/9709492
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| |bibcode = 1998PhLB..418...46K }}</ref>) and that Q-balls might play a role in [[baryogenesis]], i.e. the origin of the matter that fills the universe (Dodelson ''et al.''. 1990,<ref>
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| {{cite journal
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| |author=S. Dodelson, L. Widrow
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| |year=1990
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| |title=Baryon Symmetric Baryogenesis
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| |journal=[[Physical Review Letters]]
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| |volume=64 |pages=340–343
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| |doi=10.1103/PhysRevLett.64.340
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| |pmid=10041955
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| |bibcode=1990PhRvL..64..340D
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| |issue=4
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| }}</ref> Enqvist ''et al.''. 1997<ref>
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| {{cite journal
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| |author=K. Enqvist, J. McDonald
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| |year=1998
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| |title=Q-Balls and Baryogenesis in the MSSM
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| |journal=[[Physics Letters B]]
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| |volume=425 |pages=309–321
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| |doi=10.1016/S0370-2693(98)00271-8
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| |id=
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| |arxiv=hep-ph/9711514
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| |bibcode = 1998PhLB..425..309E
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| |issue=3–4 }}</ref>). Interest in Q-balls was stimulated by the
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| suggestion that they arise generically in [[supersymmetry|supersymmetric]] field theories (Kusenko 1997)<ref>
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| {{cite journal
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| |author=A. Kusenko
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| |year=1997
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| |title=Solitons in the supersymmetric extensions of the Standard Model
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| |journal=[[Physics Letters B]]
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| |volume=405 |pages=108
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| |doi=10.1016/S0370-2693(97)00584-4
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| |id=
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| |arxiv=hep-ph/9704273
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| |bibcode = 1997PhLB..405..108K }}</ref>), so if
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| nature really is fundamentally supersymmetric then Q-balls might have been created in the early universe, and still exist in the cosmos today.
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| ==Fiction==
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| * In the movie ''[[Sunshine (2007 film)|Sunshine]]'', the [[Sun]] is undergoing a premature death. The movie's science adviser, scientist [[Brian Cox (physicist)|Brian Cox]], proposed "infection" with a Q-ball as the mechanism for this death, but this is mentioned only in the commentary tracks and not in the movie itself.
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| * In the fictional universe of [[Orion's Arm]], Q-balls are one of the speculated sources for the large amounts of antimatter used by certain groups.
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| ==References==
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| {{Reflist}}
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| ==External links==
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| *[http://www.physics.ucla.edu/~kusenko/new_sci_qballs.html Cosmic anarchists], by Hazel Muir. A popular account of the proposal of Alexander Kusenko.
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| {{DEFAULTSORT:Q-Ball}}
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| [[Category:Particle physics]]
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| [[Category:Quantum field theory]]
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