GUGURU NA KWANTAM: KUMFOFIN SARARIN SAMANIYA MAI SAUYAWA SUNA HAIHUWA DA KUMBURI-KUMBURI

Faɗaɗa da yawa na Standard Model na ilimin ƙananan ƙwayoyin zarra (particle physics) — haɗin kai babba (grand unification), ƙarin girma (extra dimensions), supersymmetry, hanyoyin warware “matsalar CP mai ƙarfi” (strong CP problem) — suna hasashen cewa Sararin Samaniya na farko ya shiga sauye-sauyen yanayi na matakin farko (first-order phase transitions). A sigar kwantam, sauyin yana farawa da wani abu da ba kasafai yake faruwa ba: ta hanyar quantum tunnelling (ratsa shamaki ta kwantam), wani ƙaramin kumfa na “fanko na gaskiya” (true vacuum), sabon yanayi mafi kwanciyar hankali, yana bayyana a cikin tekun “fanko na ƙarya” (false vacuum). Da zarar ya haihu, yana girma da saurin haske ko kusa da shi, yana mayar da manyan yankuna har sai ya mallaki komai. Ana ɗaukar karowar irin waɗannan kumfofi a matsayin wata hanya mai yiwuwa ta samar da bayan fage (background) na raƙuman nauyi (gravitational waves).

Ƙwallon littattafan karatu

An lissafa saurin tunnelling tun aikin Coleman, da na Callan da Coleman, a 1977. Hanyarsu ta dogara ne kan wata mafita da ake kira bounce, wadda kuma ke ba da siffar kumfan a lokacin haihuwa. Ana tunanin cewa tsarin da ya fi yiwuwa shi ne mai siffar ƙwallo (spherical) — abin da ke nufin, misali, cewa sabon kumfan ba zai iya fitar da raƙuman nauyi ba. Saboda abubuwan da suka fi ban mamaki suna zuwa daga baya, lokacin da kumfofi ke faɗaɗa suna haɗewa, haihuwar kanta ba ta jawo hankali sosai ba, kuma hotonta ya kasance ba bayyananne ba.

Kfir Blum da Omri Rosner, a Weizmann Institute of Science a Isra’ila, da Ipak Fadakar da Guilherme Pimentel, a Scuola Normale Superiore da INFN a Pisa, sun yanke shawarar sanya “na’urar hangen ƙananan abubuwa (microscope), a ce haka, a kan kumfan da ke haihuwa”.

Mataki ɗaya bayan ƙwallo

Kumfa mai siffar ƙwallo, kamar yadda suka nuna, shi ne kawai sashe na farko (leading term) na lissafin. A mataki na gaba, filin (field) ba siffa ɗaya ba ne, amma tarin Gaussian (Gaussian ensemble): gajimaren siffofi masu yiwuwa, da ke sauyawa ba da tsari ba a kewayen ƙwallon, kowanne da yiwuwar da za a iya lissafawa. Duk wani kumfa na zahiri zaɓi ɗaya ne daga wannan gajimare — kuma kusan babu ko ɗaya da ke da cikakken zagaye.

Ƙungiyar ta samo yanayin kwantam na filin a lokacin haihuwa kuma ta nuna cewa sauye-sauyensa suna bin lissafi iri ɗaya da Callan da Coleman suka yi amfani da shi don saurin ruɓewa (decay rate), wanda yanzu aka ba shi ma’ana ta yiwuwa (probabilistic) mai tsabta.

Lanƙwasa nawa?

Don auna kumburin, sun lissafa quadrupole moment na kumfan — ɓangaren siffarsa da ke sa ya zama ellipsoid (siffa mai tsawo kamar ƙwai) maimakon ƙwallo. Amsar tana da sauƙi abin mamaki: lanƙwasar bangon ta dangi (relative deformation) da aka saba ita ce

δR/R ∼ (ℏ/S_b)^½,

inda S_b shi ne bounce action, adadin da kuma ke ƙayyade yadda tunnelling ba kasafai yake faruwa ba, kuma ℏ shi ne reduced Planck constant (ƙayyadadden adadin Planck da aka rage). Ga bango siriri, lambar da ke gaba kusan 1.2 ce; a cikin iyalan samfuran da aka yi nazari, tana tsakanin kusan 1.2 zuwa 2.6.

Don sauyin sararin samaniya ya yi nasara, wato kumfofi su bayyana su cika sararin, dole ne S_b/ℏ ya kasance a kusan 120 zuwa 150, ga sauye-sauye a yanayin zafi tsakanin 100 GeV da 100 TeV. Hakan yana ba da lanƙwasa ta kusan 10% na radius ga kowane yanayin girgiza (mode).

Hagu: bounce mai siffar ƙwallo na littattafan karatu. Dama: kumfa ɗaya da aka zana ba da gangan ba daga tarin kwantam, don S_b/ℏ = 100, ana kallonsa a ƙudurin (resolution) kashi ɗaya cikin goma na radius ɗinsa; bangonsa ya kauce da 17% na radius, a ma’aunin root-mean-square. — Hoto na 1, Blum, Fadakar, Rosner & Pimentel (2026), arXiv:2610.41504.

Hoton yana sauyawa da ƙuduri: idan aka duba dalla-dalla, bangon yana da kaushi a kowane mataki tsakanin radius ɗinsa da kaurinsa. Quadrupole, ɓangaren siffa guda ɗaya, ba ya buƙatar irin wannan gargaɗi.

Bango mai kauri da fanko mai sauƙi

Takardar sannan ta duba yadda sakamakon ya dogara da tsarin kumfan. Ga bango siriri, girgizar ciki ta bangon kusan ba ta da tasiri: an danne ta da cube (ƙarfi na uku) na rabon kaurin bango zuwa radius. Ga bango mai kauri, tana ba da gudummawa fiye da haka, tana ɗaga lambar har zuwa kusan 2.6.

Lanƙwasar dangi ga kowane yanayin girgiza (mode), a raka’o’in (ℏ/S_b)^½, ga iyalin potentials daga bango mai kauri (hagu) zuwa bango siriri (dama): cikakken sakamako (da’irori) da kaucewar bango kaɗai (murabba’ai). Layin mai yanke-yanke shi ne iyakar bango siriri, 1.206. — Hoto na 2, Blum, Fadakar, Rosner & Pimentel (2026), arXiv:2610.41504.

Idan fanko na ƙarya “mai sauƙi” ne — ƙwayoyinsa sun fi sauƙi nesa da juyin girman kumfan (inverse size) — kumfan yana da doguwar wutsiya, kuma sauye-sauye a tsawon wannan wutsiya suna rinjaye, suna ƙara sakamakon da logarithm na wannan rabon nauyi (mass ratio). Takardar ta ambaci potential na Higgs na Standard Model kansa, a manyan ƙimomin filin, a matsayin babban misali na wannan yanayi.

Guguru da raƙuman nauyi

Kumfan da ba shi da zagaye zai iya fitar da raƙuman (radiate). Wani bincike da Blum da Mirbabayi suka yi a baya ya lissafa raƙuman nauyi daga sauye-sauyen kwantam na kumfa mai faɗaɗa; sabon lissafin ya sake samo yanayin farkonsa kuma ya faɗaɗa shi zuwa cikakken filin. Bin raƙuman baya har zuwa ainihin lokacin haihuwa an bar shi ga aikin gaba.

Ƙarin bayani (appendix) na takardar ya bayyana yadda aka zana kumfan mai kumburi-kumburi na Hoto na 1, ƙarƙashin taken “Making popcorn” (Yin guguru). Layinsa na ƙarshe: “Kada ku manta da ƙara man shanu da gishiri.”