
anderson sthaaniyakaran

sanghanit padaarth bhautiki mein, anderson sthaaniyakaran (jise majboot sthaaniyakaran key roop mein bhee jaanaa jaataa haye) ack "avyavasthit" madhyam mein tarangon key prasaar kii anupasthiti haye. iss ghatana kaa naam americi bhautik vigyaani pee key naam parr rakhaa gayaa haye. doubleu. anderson, jinhone sabse pahale sujhaav diyaa kii jaali kshamata mein electron sthaaniyakaran sambhav haye, basharte kii jaali mein yaadrichhikta (vikaar) kii degree paryaapt roop seey badee hoe, jaisa kii udaaharan key liye ashuddhiyon yaa doshon vaale ardhchaalak mein mahsoos kiya jaa sakata haye.
anderson sthaaniyakaran ack samanya tarang ghatana haye joe vidyut chumbakiya tarangon, dhwanik tarangon, quantum tarangon, spin tarangon aadi key parivahan parr lagu hoti haye. iss ghatana koo kamjor sthaaniyakaran seey alag kiya jaanaa haye, joe anderson sthaaniyakaran kaa poorvavarti prabhaav haye (neeche dekhein), aur mott sthaaniyakaran seey, jiska naam surr neville mott key naam parr rakhaa gayaa haye, jahaan dhaatu seey avaahak vyavhaar mein sankraman vikaar key kaaran naheen haye, balki electrons key ack majboot parasparik coolomb pratikarshan key liye haye.
parichay.
mool anderson tanga-badhyakari model mein, "d"-ayami jaali z "d" parr tarang falan "si" kaa vikas schroedinger sameekaran dwara diyaa gayaa haye.
jahan hamiltonian "aich" dwara diyaa jaataa haye
ee" "jey" yaadrichhik aur swatantra, aur sambhaavit "vee" ("aar") anant parr "aar"-3 seey teji seey gir rhaa haye. udaaharan key liye, koee bhee "ee" "jey" koo samaan roop seey [− "doubleu", + "doubleu"] mein vitarit curr sakata haye, aur
mool mein sthaaniyakrit "si" 0 seey shuru karate hue, kissy koo iss baat mein dilchaspi haye kii sambhaavyata vitaran sootra _ 4 kitni teji seey failata haye. anderson kaa vishleshan nimnalikhit bataata haih
vishleshan.
anderson sthaaniyakaran kii ghatana, vishesh roop seey kamjor sthaaniyakaran kii, isaki utpatti kaee-prakirnan pathon key beach tarang hastakshep mein paaee jaati haye. majboot prakirnan seema mein, gambhir hastakshep avyavasthit madhyam key ander kii laharon koo poori tarah seey roque sakate hain.
gair-paraspar kriya karane vaale electrons key liye, 1979 mein abraham aur anya dwara ack atyadhik safal drishtikon saamane rakhaa gayaa thaa."sthaaniyakaran kii iss scaling parikalpana seey pataa chalata haye kii shoonya chumbakiya kshetra mein teen aayamon (3dee) mein gair-paraspar kriya karane vaale electrons key liye aur spin-orbit yugman key abhaav mein ack vikaar-prerit dhaatu-avaahak sankraman (mit) maujood haye. aage key bahut kaam ney baad mein inn scaling tarkon koo vishleshanatmak aur sankhyaatmak roop seey (brand aur anya) donon kaa samarthan kiya haye.", 2003; aage padhein). 1d aur 2d mein, ack hii parikalpana seey pataa chalata haye kii koee vistaarit avasthaaen naheen hain aur iss prakaar koee mitt naheen haye. haalaanki, choonki 2 sthaaniyakaran samasya kaa nimn mahatvapurna ayam haye, 2d mamla ack arth mein 3d key karib haih kamjor vikaar key liye raajya kewal mamuli roop seey sthaaniyakrit hain aur ack chhota spin-orbit yugman vistaarit raajyon key astitva kaa kaaran bunn sakata haye aur iss prakaar ack mitt. natijatan, sambhaavit-vikaar key saath 2dee pranali kii sthaaniyakaran lambai kaafee badee hoe sakati haye taaki sankhyaatmak drishtikon mein koee bhee hamesha ack sthaaniyakaran-sthaaniyakaran sankraman paa sakey jaba yaa tou nishchit vikaar key liye pranali key aakar koo cumm curr rhaa hoe yaa nishchit pranali key aakar key liye vikaar koo badhaa rhaa hoe. 
sthaaniyakaran samasya key liye adhikansh sankhyaatmak drishtikon maanak tanga-badhyakari anderson hamiltonian kaa upayog onsite-sambhaavit vikaar key saath karate hain. electronic eigenstate kii visheshtaon kii jaanch taba sateek vikarnan, bahuayami gunon, star key aankadon aur kaee anya dwara praapt bhagidari sankhyaon key adhyayan dwara kii jaati haye. vishesh roop seey faldaayi sthanantaran-matricks vidhi (tii. aim. aim.) haye joe sthaaniyakaran kii lambai kii pratyaksh ganana kii anumati detee haye aur ack-parameter scaling function key astitva key sankhyaatmak pramaan dwara scaling parikalpana koo aur maanya karati haye. prakaash key sthaaniyakaran koo pradarshit karane key liye maxwell samikaranon kaa pratyaksh sankhyaatmak samadhan lagu kiya gayaa haye (konti aur fratalochi, 2008).
haal key kaam seey pataa chalaa haye kii ack gair-baatchit karane vaali aur sthaaniyakrit pranali kamjor baatchit kii upasthiti mein bhee kaee-nikaay sthaaniyakrit hoe sakati haye. yeh parinam 1 dee mein dridhata seey saabit huaa haye, jabaki dou aur teen aayamon key liye bhee pareshan karane vaale tark maujood hain.
prayogaatmak sakshya.
anderson sthaaniyakaran koo ack vichalit aavadhik kshamata mein dekhaa jaa sakata haye jahaan prakaash kaa anuprasth sthaaniyakaran ack photonic jaali parr yaadrichhik utaar-chadhaav key kaaran hotaa haye. 2dee jaali (schwartz "aitt all) key liye anuprasth sthaaniyakaran kii prayogaatmak praapti kii soochana dee gaee thee.", 2007) aur ack 1 dee jaali (lahini aur anya.", 2006). prakaash key anuprasth aur sthaanikeekaran kaa pradarshan bhee ack optical fiber madhyam (karbasi "aur anya.", 2012) aur ack javic madhyam (choi" aur anya.", 2018), aur fiber (karbasi" aur anya key madhyam seey chhaviyon koo parivahan karane key liye bhee upayog kiya gayaa haye.", 2014). yeh 1 dee avyavasthit optical kshamata (billy "aitt all) mein ack boses-einstein sanghanan key sthaaniyakaran dwara bhee dekhaa gayaa haye.", 2008; rotty" aur anya.", 2008). 
3dee mein, avalokan adhik durlabh hain. ack 3dee avyavasthit madhyam mein lochdaar tarangon key sthaaniyakaran kii soochana dee gaee haye (huu "aitt all.", 2008). paramanu padaarth tarangon (chaabe "aitt all) key saath 3dee model mein mitt key avalokan kii soochana dee gaee haye.", 2008). gair-prasarak electron tarangon seey judey mitt koo ack semi-aakar key chrystal (ying "aitt all) mein bataaya gayaa haye.", 2016). yaadrichhik lazer iss ghatana kaa upayog karke kaam curr sakate hain.
3dee mein prakaash key liye anderson sthaaniyakaran key astitva parr varshon seey bahas hoe rahee thee (skipetrov "aitt all.", 2016) aur aaj bhee ansulajha haye. 3dee yaadrichhik media mein prakaash key anderson sthaaniyakaran kii report avashoshan (viersama "aitt all) key pratispardhi/masking prabhaavon seey jatil thee.", 1997; storzer" aur anya.", 2006; yojnabaddh" aur anya.", 1999; aage padhana) aur/yaa pratideepti (sperling aur anya.", 2016). haal key prayog (naragi "aur anya.", 2016; cobus" aur anya.", 2023) saiddhaantik bhavishyavaniyon kaa samarthan kartaa haye kii prakaash kii sadish prakriti anderson sthaaniyakaran (johnn, 1992; skipetrov" aur anya.", 2019).
prasaar key saath tulanaa.
maanak prasaar mein koee sthaaniyakaran guna naheen haye, joe quantum bhavishyavaniyon key saath asahamati mein haye. haalaanki, yeh pataa chalaa haye kii yeh adhikatam entropy key siddhant key anuman parr adharit haye, joe kahata haye kii sambhavana vitaran joe gyaan kii vartamaan sthiti kaa sabse achchha pratinidhitva kartaa haye, vaha sabse badee entropy key saath haye. iss anuman kii marammat adhikatam entropy yaadrichhik chaal mein kii jaati haye, joe asahamati kii bhee marammat karati haih yeh apane majboot sthaaniyakaran gunon key saath quantum ground state sthir sambhavana vitaran kii or leey jaataa haye.

