Proizvodnja fermiona na meji širitvenega vesolja: gravitacijski analog hladnega atoma

Proizvodnja fermiona na meji širitvenega vesolja: gravitacijski analog hladnega atoma

Časovni žig: 21. junij 2023 12:31
Izvorno vozlišče: 2142460

Carlos Fulgado-Claudio, Jose M. Sánchez Velázquez in Alejandro Bermudez

Instituto de Física Teórica, UAM-CSIC, Universidad Autónoma de Madrid, Cantoblanco, 28049 Madrid, Španija.

Se vam zdi ta članek zanimiv ali želite razpravljati? Zaslišite ali pustite komentar na SciRate.

Minimalizem

Preučujemo pojav kozmološke produkcije delcev Diracovih fermionov v prostorskem času Friedmann-Robertson-Walker, pri čemer se osredotočamo na $(1+1)-$dimenzionalni primer, v katerem je razvoj faktorja lestvice določen z enačbami Jackiw-Teitelboima gravitacija. Kot prvi korak k kvantni simulaciji tega pojava obravnavamo dve možni ureditvi mreže, ki nam omogočata raziskovanje medsebojnega delovanja proizvodnje delcev in topoloških pojavov v prostor-času z mejo. Zlasti za Wilsonovo diskretizacijo Diracovega polja asimptotični vakuum Minkowskega, povezan z vmesno ekspanzijo, ustreza simetrično zaščitenim topološkim osnovnim stanjem in ima mejno manifestacijo v obliki ničelnih načinov, eksponentno lokaliziranih na prostorske meje. Pokažemo, da lahko proizvodnja delcev poseli tudi te ničelne načine, kar je v nasprotju s situacijo z diskretizacijo naivnih fermionov, v kateri konformna polja nične mase ne dovoljujejo proizvodnje delcev. Predstavljamo shemo za kvantno simulacijo tega gravitacijskega analoga s pomočjo ultrahladnih atomov v Ramanovih optičnih mrežah, ki zahtevajo realnočasovno kontrolo razklanosti Ramanovega žarka glede na faktor lestvice simuliranega prostor-časa, kot tudi pas - meritve kartiranja.

Predstavljena slika: Slikovni prikaz pojava proizvodnje delcev v vesolju, ki se širi. Dinamika metrike ozadja proizvaja vzbujanja polja v parih, ki se interpretirajo kot delci (predstavljeni z rdečo) in antidelci (predstavljeni z oranžno). Za določene mrežne diskretizacije polja lahko prostorske meje prostor-časa dejansko gostijo ničenergijske načine, ki so eksponentno lokalizirani na meje, in se tako širijo v nižji efektivni dimenziji. Raziskujemo pojav proizvodnje delcev za takšne ničelne načine, ki je mejnik medsebojnega delovanja topološkega vakuuma in ukrivljenega prostor-časa.

Priljubljen povzetek

Pri kvantnih poljih v ukrivljenem vesoljskem času, kot so hitro rastoče geometrije, se pojavlja osupljiv pojav, to je gravitacijska proizvodnja delcev. V zadnjem času je bilo na področju kvantnih simulacij predstavljenih več eksperimentalnih predlogov, ki lahko izvajajo dinamiko kozmoloških scenarijev in tako utirajo pot za vpogled v več vidikov tega pojava. Predlagamo novo eksperimentalno postavitev za preučevanje proizvodnje fermionov v gravitacijskem analogu s hladnim atomom.

Med možnostmi, ki jih omogoča to stališče, se osredotočamo na interakcije med proizvodnjo kozmoloških delcev in topološkimi fazami, ki so faze snovi, ki jih urejajo topološke invariante. Upoštevamo vesolje z zmanjšano dimenzionalnostjo, kjer se prisotnost teh faz kaže v pojavu ničelnih načinov, eksponentno lokaliziranih na prostorske meje vesolja. To nam omogoča, da preučimo, kako ti načini medsebojno delujejo z ozadjem, ki se širi, in da se spopademo z razlikami v zvezi z ustvarjanjem razmnoževalnih delcev.

Ta okvir omogoča preučevanje eksotičnih faz snovi znotraj kozmoloških kontekstov in odpira pot za raziskovanje bolj zapletenih modelov. Na primer, interakcije je mogoče enostavno implementirati, kar omogoča preučevanje neperturbativnih pojavov. Prav tako bi bilo zelo zanimivo posplošiti eksperimentalno postavitev na višjedimenzionalna vesolja, kjer bi se pojavile različne topološke faze. Te funkcije je mogoče enostavno implementirati v našo eksperimentalno shemo.

► BibTeX podatki

► Reference

[1] ME Peskin in DV Schroeder, Uvod v kvantno teorijo polja (Addison-Wesley, Reading, ZDA, 1995).
https: / / doi.org/ 10.1201 / 9780429503559

[2] E. Fradkin, Teorije polja fizike kondenzirane snovi, 2. izdaja. (Cambridge University Press, 2013).
https: / / doi.org/ 10.1017 / CBO9781139015509

[3] S. Sachdev, Kvantni fazni prehodi, 2. izd. (Cambridge University Press, 2011).
https: / / doi.org/ 10.1017 / CBO9780511973765

[4] AH Castro Neto, F. Guinea, NMR Peres, KS Novoselov in AK Geim, Rev. Mod. Phys. 81, 109 (2009).
https: / / doi.org/ 10.1103 / RevModPhys.81.109

[5] NP Armitage, EJ Mele in A. Vishwanath, Rev. Mod. Phys. 90, 015001 (2018).
https: / / doi.org/ 10.1103 / RevModPhys.90.015001

[6] X.-L. Qi in S.-C. Zhang, Rev. Mod. Fiz. 83, 1057 (2011).
https: / / doi.org/ 10.1103 / RevModPhys.83.1057

[7] PW Anderson, Science 177, 393 (1972).
https: / / doi.org/ 10.1126 / znanost.177.4047.393

[8] WG Unruh, Phys. Rev. Lett. 46, 1351 (1981).
https: / / doi.org/ 10.1103 / PhysRevLett.46.1351

[9] SM Carroll, Prostor-čas in geometrija: Uvod v splošno relativnost (Cambridge University Press, 2019).
https: / / doi.org/ 10.1017 / 9781108770385

[10] C. Barceló, S. Liberati in M. Visser, Living Reviews in Relativity 8, 12 (2005).
https: / / doi.org/ 10.12942 / lrr-2005-12

[11] MJ Jacquet, S. Weinfurtner in F. König, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, 20190239 (2020).
https: / / doi.org/ 10.1098 / rsta.2019.0239

[12] LE Parker in D. Toms, Quantum Field Theory in Curved Spacetime: Quantized Field and Gravity, Cambridge Monographs on Mathematical Physics (Cambridge University Press, 2009).
https: / / doi.org/ 10.1017 / CBO9780511813924

[13] SW Hawking, Nature 248, 30 (1974).
https: / / doi.org/ 10.1038 / 248030a0

[14] AH Guth, Phys. Rev. D 23, 347 (1981).
https: / / doi.org/ 10.1103 / PhysRevD.23.347

[15] F. Belgiorno, SL Cacciatori, G. Ortenzi, L. Rizzi, V. Gorini in D. Faccio, Phys. Rev. D 83, 024015 (2011).
https: / / doi.org/ 10.1103 / PhysRevD.83.024015

[16] TG Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. König in U. Leonhardt, Science 319, 1367 (2008).
https: / / doi.org/ 10.1126 / znanost.1153625

[17] F. Belgiorno, SL Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, VG Sala in D. Faccio, Phys. Rev. Lett. 105, 203901 (2010).
https: / / doi.org/ 10.1103 / PhysRevLett.105.203901

[18] J. Drori, Y. Rosenberg, D. Bermudez, Y. Silberberg in U. Leonhardt, Phys. Rev. Lett. 122, 010404 (2019).
https: / / doi.org/ 10.1103 / PhysRevLett.122.010404

[19] LJ Garay, JR Anglin, JI Cirac in P. Zoller, Phys. Rev. Lett. 85, 4643 (2000).
https: / / doi.org/ 10.1103 / PhysRevLett.85.4643

[20] O. Lahav, A. Itah, A. Blumkin, C. Gordon, S. Rinott, A. Zayats in J. Steinhauer, Phys. Rev. Lett. 105, 240401 (2010).
https: / / doi.org/ 10.1103 / PhysRevLett.105.240401

[21] J. Steinhauer, Nature Physics 12, 959 (2016).
https: / / doi.org/ 10.1038 / nphys3863

[22] VI Kolobov, K. Golubkov, JR Muñoz de Nova in J. Steinhauer, Nature Physics 17, 362 (2021).
https:/​/​doi.org/​10.1038/​s41567-020-01076-0

[23] WG Unruh, Phys. Rev. D 14, 870 (1976).
https: / / doi.org/ 10.1103 / PhysRevD.14.870

[24] J. Hu, L. Feng, Z. Zhang in C. Chin, Nature Physics 15, 785 (2019).
https:/​/​doi.org/​10.1038/​s41567-019-0537-1

[25] L. Parker, Phys. Rev. Lett. 21, 562 (1968).
https: / / doi.org/ 10.1103 / PhysRevLett.21.562

[26] L. Parker, Phys. Rev. 183, 1057 (1969).
https: / / doi.org/ 10.1103 / PhysRev.183.1057

[27] C. Barceló, S. Liberati in M. Visser, Phys. Rev. A 68, 053613 (2003).
https: / / doi.org/ 10.1103 / PhysRevA.68.053613

[28] PO Fedichev in UR Fischer, Phys. Rev. A 69, 033602 (2004).
https: / / doi.org/ 10.1103 / PhysRevA.69.033602

[29] C. Fey, T. Schaetz in R. Schützhold, Phys. Rev. A 98, 033407 (2018).
https: / / doi.org/ 10.1103 / PhysRevA.98.033407

[30] S. Eckel, A. Kumar, T. Jacobson, IB Spielman in GK Campbell, Phys. Rev. X 8, 021021 (2018).
https: / / doi.org/ 10.1103 / PhysRevX.8.021021

[31] M. Wittemer, F. Hakelberg, P. Kiefer, J.-P. Schröder, C. Fey, R. Schützhold, U. Warring in T. Schaetz, Phys. Rev. Lett. 123, 180502 (2019).
https: / / doi.org/ 10.1103 / PhysRevLett.123.180502

[32] C. Viermann, M. Sparn, N. Liebster, M. Hans, E. Kath, Á. Parra-López, M. Tolosa-Simeón, N. Sánchez-Kuntz, T. Haas, H. Strobel, S. Floerchinger in MK Oberthaler, Nature 611, 260 (2022).
https:/​/​doi.org/​10.1038/​s41586-022-05313-9

[33] M. Tolosa-Simeón, A. Parra-López, N. Sánchez-Kuntz, T. Haas, C. Viermann, M. Sparn, N. Liebster, M. Hans, E. Kath, H. Strobel, MK Oberthaler in S. Floerchinger, Phys. Rev. A 106, 033313 (2022).
https: / / doi.org/ 10.1103 / PhysRevA.106.033313

[34] N. Sanchez-Kuntz, A. Parra-López, M. Tolosa-Simeón, T. Haas in S. Floerchinger, Physical Review D 105 (2022), 10.1103/​physrevd.105.105020.
https: / / doi.org/ 10.1103 / physrevd.105.105020

[35] I. Bloch, J. Dalibard in W. Zwerger, Rev. Mod. Phys. 80, 885 (2008a).
https: / / doi.org/ 10.1103 / RevModPhys.80.885

[36] L. Parker, Phys. Rev. D 3, 346 (1971).
https: / / doi.org/ 10.1103 / PhysRevD.3.346

[37] T. Kaluza, International Journal of Modern Physics D 27, 1870001 (2018).
https: / / doi.org/ 10.1142 / S0218271818700017

[38] O. Klein, Zeitschrift für Physik 37, 895 (1926).
https: / / doi.org/ 10.1007 / BF01397481

[39] F. Khanna, A. Malbouisson, J. Malbouisson in A. Santana, Physics Reports 539, 135 (2014).
https: / / doi.org/ 10.1016 / j.physrep.2014.02.002

[40] RM Wald, Living Reviews in Relativity 4, 6 (2001).
https: / / doi.org/ 10.12942 / lrr-2001-6

[41] HBG Kazimir, Proc. Akad. Mokra. Amsterdam 51, 793 (1948).

[42] GT Moore, Journal of Mathematical Physics 11, 2679 (1970).
https: / / doi.org/ 10.1063 / 1.1665432

[43] E. Witten, Komunikacije v matematični fiziki 121, 351 (1989).

[44] S. Elitzur, G. Moore, A. Schwimmer in N. Seiberg, Nuclear Physics B 326, 108 (1989).
https:/​/​doi.org/​10.1016/​0550-3213(89)90436-7

[45] A. Balachandran, L. Chándal in E. Ercolessi, International Journal of Modern Physics A 10, 1969 (1995).
https: / / doi.org/ 10.1142 / S0217751X95000966

[46] MF Golterman, K. Jansen in DB Kaplan, Physics Letters B 301, 219 (1993).
https:/​/​doi.org/​10.1016/​0370-2693(93)90692-B

[47] C. Callan in J. Harvey, Nuclear Physics B 250, 427 (1985).
https:/​/​doi.org/​10.1016/​0550-3213(85)90489-4

[48] DB Kaplan, v Poletni šoli Les Houches: Seja 93: Sodobne perspektive v mrežni QCD: Kvantna teorija polja in visokozmogljivo računalništvo (2009) str. 223–272, arXiv:0912.2560 [hep-lat].
https: / / doi.org/ 10.1093 / acprof: oso / 9780199691609.001.0001
arXiv: 0912.2560

[49] DB Kaplan, Physics Letters B 288, 342 (1992).
https:/​/​doi.org/​10.1016/​0370-2693(92)91112-M

[50] RP Feynman, medn. J. Theor. Phys. 21, 467 (1982).
https: / / doi.org/ 10.1007 / bf02650179

[51] DJ Gross in A. Neveu, Phys. Rev. D 10, 3235 (1974).
https: / / doi.org/ 10.1103 / PhysRevD.10.3235

[52] JD Brown, Lower Dimensional Gravity (World Scientific, 1988).
https: / / doi.org/ 10.1142 / 0622

[53] LH Ford, Poročila o napredku v fiziki 84, 116901 (2021).
https:/​/​doi.org/​10.1088/​1361-6633/​ac1b23

[54] V. Mukhanov in S. Winitzki, Uvod v kvantne učinke v gravitaciji (Cambridge University Press, 2007).
https: / / doi.org/ 10.1017 / CBO9780511809149

[55] J. Preskill, “Kvantna teorija polja v ukrivljenem prostor-času,” (1990).
http://​/​theory.caltech.edu/​~preskill/​notes.html

[56] ND Birrell in PCW Davies, Quantum Fields in Curved Space, Cambridge Monographs on Mathematical Physics (Cambridge Univ. Press, Cambridge, UK, 1984).
https: / / doi.org/ 10.1017 / CBO9780511622632

[57] TS Bunch in PCW Davies, Proc. Roy. Soc. Lond. A 360, 117 (1978).
https: / / doi.org/ 10.1098 / rspa.1978.0060

[58] JF Barbero G., A. Ferreiro, J. Navarro-Salas in EJS Villaseñor, Phys. Rev. D 98, 025016 (2018).
https: / / doi.org/ 10.1103 / PhysRevD.98.025016

[59] JG Valatin, Il Nuovo Cimento 7, 843 (1958).
https: / / doi.org/ 10.1007 / BF02745589

[60] NN Bogolyubov, Il Nuovo Cimento 7, 794 (1958).
https: / / doi.org/ 10.1007 / BF02745585

[61] AE Sikkema in RB Mann, Klasična in kvantna gravitacija 8, 219 (1991).
https:/​/​doi.org/​10.1088/​0264-9381/​8/​1/​022

[62] PR Anderson, E. Mottola in DH Sanders, Phys. Rev. D 97, 065016 (2018), arXiv:1712.04522 [gr-qc].
https: / / doi.org/ 10.1103 / PhysRevD.97.065016
arXiv: 1712.04522

[63] A. Duncan, Phys. Rev. D 17, 964 (1978).
https: / / doi.org/ 10.1103 / PhysRevD.17.964

[64] I. Fuentes, RB Mann, E. Martín-Martínez in S. Moradi, Phys. Rev. D 82, 045030 (2010).
https: / / doi.org/ 10.1103 / PhysRevD.82.045030

[65] E. Martín-Martínez in NC Menicucci, Klasična in kvantna gravitacija 29, 224003 (2012).
https:/​/​doi.org/​10.1088/​0264-9381/​29/​22/​224003

[66] A. Grib, S. Mamajev, V. Mostepanenko in V. Mostepanenko, Vakuumski kvantni učinki v močnih poljih (Friedmann Laboratory Pub., 1994).
https://​/​books.google.es/​books?id=azBdcgAACAAJ

[67] J. Haro in E. Elizalde, Journal of Physics A: Mathematical and Theoretical 41, 372003 (2008).
https:/​/​doi.org/​10.1088/​1751-8113/​41/​37/​372003

[68] JJ Sakurai in J. Napolitano, Moderna kvantna mehanika, kvantna fizika, kvantne informacije in kvantno računanje (Cambridge University Press, 2020).
https: / / doi.org/ 10.1017 / 9781108587280

[69] DJH Chung, LL Everett, H. Yoo in P. Zhou, Phys. Lett. B 712, 147 (2012), arXiv:1109.2524 [astro-ph.CO].
https: / / doi.org/ 10.1016 / j.physletb.2012.04.066
arXiv: 1109.2524

[70] M. Abramowitz, IA Stegun in RH Romer, American Journal of Physics 56, 958 (1988).
https: / / doi.org/ 10.1119 / 1.15378

[71] Y. Ema, K. Nakayama in Y. Tang, Journal of High Energy Physics 2019, 60 (2019).
https: / / doi.org/ 10.1007 / JHEP07 (2019) 060

[72] DE Borrajo Gutiérrez, JAR Cembranos, LJ Garay in JM Sánchez Velázquez, Journal of High Energy Physics 2020, 69 (2020).
https: / / doi.org/ 10.1007 / JHEP09 (2020) 069

[73] VM Villalba, Phys. Rev. D 52, 3742 (1995), arXiv:hep-th/9507021.
https: / / doi.org/ 10.1103 / PhysRevD.52.3742
arXiv: hep-th / 9507021

[74] KG Wilson in J. Kogut, Physics Reports 12, 75 (1974).
https:/​/​doi.org/​10.1016/​0370-1573(74)90023-4

[75] KG Wilson, Phys. Rev. D 10, 2445 (1974a).
https: / / doi.org/ 10.1103 / PhysRevD.10.2445

[76] C. Gattringer in CB Lang, Kvantna kromodinamika na rešetki, letn. 788 (Springer, Berlin, 2010).
https:/​/​doi.org/​10.1007/​978-3-642-01850-3

[77] HJ Rothe, Lattice Gauge Theories: An Introduction (Fourth Edition), Vol. 43 (World Scientific Publishing Company, 2012).
https: / / doi.org/ 10.1142 / 8229

[78] KG Wilson, v New Phenomena in Subnuclear Physics (Springer US, 1977) str. 69–142.
https:/​/​doi.org/​10.1007/​978-1-4613-4208-3_6

[79] H. So, Napredek teoretične fizike 73, 528 (1985).
https: / / doi.org/ 10.1143 / PTP.73.528

[80] A. Bermudez, L. Mazza, M. Rizzi, N. Goldman, M. Lewenstein in MA Martin-Delgado, Phys. Rev. Lett. 105, 190404 (2010).
https: / / doi.org/ 10.1103 / PhysRevLett.105.190404

[81] DB Kaplan in S. Sun, Phys. Rev. Lett. 108, 181807 (2012).
https: / / doi.org/ 10.1103 / PhysRevLett.108.181807

[82] J. Jünemann, A. Piga, S.-J. Ran, M. Lewenstein, M. Rizzi in A. Bermudez, Phys. Rev. X 7, 031057 (2017).
https: / / doi.org/ 10.1103 / PhysRevX.7.031057

[83] A. Bermudez, E. Tirrito, M. Rizzi, M. Lewenstein in S. Hands, Annals of Physics 399, 149 (2018).
https: / / doi.org/ 10.1016 / j.aop.2018.10.007

[84] Y. Kuno, Phys. Rev. B 99, 064105 (2019).
https: / / doi.org/ 10.1103 / PhysRevB.99.064105

[85] E. Tirrito, M. Rizzi, G. Sierra, M. Lewenstein in A. Bermudez, Phys. Rev. B 99, 125106 (2019).
https: / / doi.org/ 10.1103 / PhysRevB.99.125106

[86] S. Sen, Phys. Rev. D 102, 094520 (2020).
https: / / doi.org/ 10.1103 / PhysRevD.102.094520

[87] DB Kaplan in S. Sen, »Indeksni izreki, posplošeni Hallovi tokovi in ​​topologija za defektne fermione brez vrzeli« (2021).
https://​/​doi.org/​10.48550/​ARXIV.2112.06954

[88] C.-X. Liu, S.-C. Zhang in X.-L. Qi, Letni pregled fizike kondenzirane snovi 7, 301 (2016).
https: / / doi.org/ 10.1146 / annurev-conmatphys-031115-011417

[89] FDM Haldane, Phys. Rev. Lett. 61, 2015 (1988).
https: / / doi.org/ 10.1103 / PhysRevLett.61.2015

[90] FDM Haldane, Rev. Mod. Phys. 89, 040502 (2017).
https: / / doi.org/ 10.1103 / RevModPhys.89.040502

[91] X.-L. Qi, TL Hughes in S.-C. Zhang, Phys. Rev. B 78, 195424 (2008).
https: / / doi.org/ 10.1103 / PhysRevB.78.195424

[92] LD Landau, Zh. Eksp. Teor. Fiz. 7, 19 (1937).
https:/​/​doi.org/​10.1016/​B978-0-08-010586-4.50034-1

[93] X.-G. Wen, Kvantna teorija polja sistemov več teles: od izvora zvoka do izvora svetlobe in elektronov (Oxford University Press, Oxford, 2007).
https: / / doi.org/ 10.1093 / acprof: oso / 9780199227259.001.0001

[94] DJ Thouless, M. Kohmoto, poslanec Nightingale in M. den Nijs, Phys. Rev. Lett. 49, 405 (1982).
https: / / doi.org/ 10.1103 / PhysRevLett.49.405

[95] M. Nakahara, Geometry, Topology and Physics (CRC Press, 2017).
https: / / doi.org/ 10.1201 / 9781315275826

[96] T. Senthil, Letni pregled fizike kondenzirane snovi 6, 299 (2015).
https: / / doi.org/ 10.1146 / annurev-conmatphys-031214-014740

[97] A. Kitaev, Zbornik konference AIP 1134, 22 (2009).
https: / / doi.org/ 10.1063 / 1.3149495

[98] C.-K. Chiu, JCY Teo, AP Schnyder in S. Ryu, Rev. Mod. Fiz. 88, 035005 (2016).
https: / / doi.org/ 10.1103 / RevModPhys.88.035005

[99] S. Ryu, AP Schnyder, A. Furusaki in AWW Ludwig, New Journal of Physics 12, 065010 (2010).
https:/​/​doi.org/​10.1088/​1367-2630/​12/​6/​065010

[100] WP Su, JR Schrieffer in AJ Heeger, Phys. Rev. Lett. 42, 1698 (1979).
https: / / doi.org/ 10.1103 / PhysRevLett.42.1698

[101] JK Asbóth, L. Oroszlány in A. Pályi, Kratek tečaj o topoloških izolatorjih, Vol. 919 (2016).
https:/​/​doi.org/​10.1007/​978-3-319-25607-8

[102] R. Shankar, “Topološki izolatorji – pregled,” (2018).
https://​/​doi.org/​10.48550/​ARXIV.1804.06471

[103] J. Zak, Phys. Rev. Lett. 62, 2747 (1989).
https: / / doi.org/ 10.1103 / PhysRevLett.62.2747

[104] MV Berry, Zbornik Kraljeve družbe v Londonu. A. Matematične in fizikalne znanosti 392, 45 (1984).
https: / / doi.org/ 10.1098 / rspa.1984.0023

[105] D. Xiao, M.-C. Chang in Q. Niu, Rev. Mod. Fiz. 82, 1959 (2010).
https: / / doi.org/ 10.1103 / RevModPhys.82.1959

[106] R. Jackiw in C. Rebbi, Phys. Rev. D 13, 3398 (1976).
https: / / doi.org/ 10.1103 / PhysRevD.13.3398

[107] G. Magnifico, D. Vodola, E. Ercolessi, SP Kumar, M. Müller in A. Bermudez, Phys. Rev. D 99, 014503 (2019a).
https: / / doi.org/ 10.1103 / PhysRevD.99.014503

[108] G. Magnifico, D. Vodola, E. Ercolessi, SP Kumar, M. Müller in A. Bermudez, Phys. Rev. B 100, 115152 (2019b).
https: / / doi.org/ 10.1103 / PhysRevB.100.115152

[109] J. Kogut in L. Susskind, Phys. Rev. D 11, 395 (1975).
https: / / doi.org/ 10.1103 / PhysRevD.11.395

[110] L. Susskind, Phys. Rev. D 16, 3031 (1977).
https: / / doi.org/ 10.1103 / PhysRevD.16.3031

[111] M. Creutz, Phys. Rev. Lett. 83, 2636 (1999a).
https: / / doi.org/ 10.1103 / PhysRevLett.83.2636

[112] M. Creutz, Rev. Mod. Phys. 73, 119 (2001).
https: / / doi.org/ 10.1103 / RevModPhys.73.119

[113] L. Mazza, A. Bermudez, N. Goldman, M. Rizzi, MA Martin-Delgado in M. Lewenstein, New Journal of Physics 14, 015007 (2012).
https:/​/​doi.org/​10.1088/​1367-2630/​14/​1/​015007

[114] CG Velasco in B. Paredes, (2019), arXiv:1907.11460 [cond-mat.quant-gas].
arXiv: 1907.11460

[115] J. Zurita, C. Creffield in G. Platero, Quantum 5, 591 (2021).
https:/​/​doi.org/​10.22331/​q-2021-11-25-591

[116] O. Viyuela, A. Rivas in MA Martin-Delgado, Phys. Rev. B 86, 155140 (2012).
https: / / doi.org/ 10.1103 / PhysRevB.86.155140

[117] O. Viyuela, A. Rivas in MA Martin-Delgado, Phys. Rev. Lett. 112, 130401 (2014).
https: / / doi.org/ 10.1103 / PhysRevLett.112.130401

[118] A. Bermudez, D. Patanè, L. Amico in MA Martin-Delgado, Phys. Rev. Lett. 102, 135702 (2009).
https: / / doi.org/ 10.1103 / PhysRevLett.102.135702

[119] R. Jafari, H. Johannesson, A. Langari in MA Martin-Delgado, Phys. Rev. B 99, 054302 (2019).
https: / / doi.org/ 10.1103 / PhysRevB.99.054302

[120] N. Sun in L.-K. Lim, Phys. Rev. B 96, 035139 (2017).
https: / / doi.org/ 10.1103 / PhysRevB.96.035139

[121] A. Haller, M. Rizzi in M. Filippone, Phys. Rev. Research 2, 023058 (2020).
https: / / doi.org/ 10.1103 / PhysRevResearch.2.023058

[122] SM Chan, B. Grémaud in GG Batrouni, Phys. Rev. B 105, 024502 ​​(2022).
https: / / doi.org/ 10.1103 / PhysRevB.105.024502

[123] T. Orito, Y. Kuno in I. Ichinose, Phys. Rev. B 105, 094201 (2022).
https: / / doi.org/ 10.1103 / PhysRevB.105.094201

[124] T. Orito, Y. Kuno in I. Ichinose, Phys. Rev. B 103, L060301 (2021a).
https://​/​doi.org/​10.1103/​PhysRevB.103.L060301

[125] T. Orito, Y. Kuno in I. Ichinose, Phys. Rev. B 104, 094202 (2021b).
https: / / doi.org/ 10.1103 / PhysRevB.104.094202

[126] G.-Q. Zhang, L.-Z. Tang, L.-F. Zhang, D.-W. Zhang in S.-L. Zhu, Phys. Rev. B 104, L161118 (2021).
https://​/​doi.org/​10.1103/​PhysRevB.104.L161118

[127] D. González-Cuadra, L. Tagliacozzo, M. Lewenstein in A. Bermudez, Phys. Rev. X 10, 041007 (2020).
https: / / doi.org/ 10.1103 / PhysRevX.10.041007

[128] E. Tirrito, M. Lewenstein in A. Bermudez, Phys. Rev. B 106, 045147 (2022).
https: / / doi.org/ 10.1103 / PhysRevB.106.045147

[129] KG Wilson, Phys. Rev. D 10, 2445 (1974b).
https: / / doi.org/ 10.1103 / PhysRevD.10.2445

[130] T. Kibble, Physics Reports 67, 183 (1980).
https:/​/​doi.org/​10.1016/​0370-1573(80)90091-5

[131] W. Zurek, Physics Reports 276, 177 (1996).
https:/​/​doi.org/​10.1016/​S0370-1573(96)00009-9

[132] WH Zurek, U. Dorner in P. Zoller, Phys. Rev. Lett. 95, 105701 (2005).
https: / / doi.org/ 10.1103 / PhysRevLett.95.105701

[133] M. Creutz, Phys. Rev. Lett. 83, 2636 (1999b).
https: / / doi.org/ 10.1103 / PhysRevLett.83.2636

[134] I. Bloch, J. Dalibard in S. Nascimbène, Nature Physics 8, 267 (2012).
https: / / doi.org/ 10.1038 / nphys2259

[135] N. Goldman, JC Budich in P. Zoller, Nature Physics 12, 639 (2016).
https: / / doi.org/ 10.1038 / nphys3803

[136] M. Lewenstein, A. Sanpera, V. Ahufinger, B. Damski, A. Sen(De) in U. Sen, Napredek v fiziki 56, 243 (2007).
https: / / doi.org/ 10.1080 / 00018730701223200

[137] O. Boada, A. Celi, JI Latorre in M. Lewenstein, New Journal of Physics 13, 035002 (2011).
https:/​/​doi.org/​10.1088/​1367-2630/​13/​3/​035002

[138] J. Minář in B. Grémaud, Journal of Physics A: Mathematical and Theoretical 48, 165001 (2015).
https:/​/​doi.org/​10.1088/​1751-8113/​48/​16/​165001

[139] J. Rodríguez-Laguna, L. Tarruell, M. Lewenstein in A. Celi, Phys. Rev. A 95, 013627 (2017).
https: / / doi.org/ 10.1103 / PhysRevA.95.013627

[140] A. Celi, The European Physical Journal Special Topics 226, 2729 (2017).
https://​/​doi.org/​10.1140/​epjst/​e2016-60390-y

[141] A. Kosior, M. Lewenstein in A. Celi, SciPost Phys. 5, 061 (2018).
https: / / doi.org/ 10.21468 / SciPostPhys.5.6.061

[142] U.-J. Wiese, Annalen der Physik 525, 777 (2013).
https: / / doi.org/ 10.1002 / andp.201300104

[143] E. Zohar, JI Cirac in B. Reznik, Poročila o napredku fizike 79, 014401 (2015).
https:/​/​doi.org/​10.1088/​0034-4885/​79/​1/​014401

[144] MC Bañuls, R. Blatt, J. Catani, A. Celi, JI Cirac, M. Dalmonte, L. Fallani, K. Jansen, M. Lewenstein, S. Montangero, CA Muschik, B. Reznik, E. Rico, L Tagliacozzo, K. Van Acoleyen, F. Verstraete, U.-J. Wiese, M. Wingate, J. Zakrzewski in P. Zoller, The European Physical Journal D 74, 165 (2020).
https: / / doi.org/ 10.1140 / epjd / e2020-100571-8

[145] MC Bañuls in K. Cichy, Poročila o napredku v fiziki 83, 024401 (2020).
https: / / doi.org/ 10.1088 / 1361-6633 / ab6311

[146] M. Aidelsburger, L. Barbiero, A. Bermudez, T. Chanda, A. Dauphin, D. González-Cuadra, PR Grzybowski, S. Hands, F. Jendrzejewski, J. Jünemann, G. Juzeliūnas, V. Kasper, A Piga, S.-J. Ran, M. Rizzi, G. Sierra, L. Tagliacozzo, E. Tirrito, TV Zache, J. Zakrzewski, E. Zohar in M. Lewenstein, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 380, 20210064 (2022).
https: / / doi.org/ 10.1098 / rsta.2021.0064

[147] N. Klco, A. Roggero in MJ Savage, Poročila o napredku v fiziki 85, 064301 (2022).
https:/​/​doi.org/​10.1088/​1361-6633/​ac58a4

[148] L. Ziegler, E. Tirrito, M. Lewenstein, S. Hands in A. Bermudez, Phys. Rev. Research 4, L042012 (2022).
https://​/​doi.org/​10.1103/​PhysRevResearch.4.L042012

[149] L. Ziegler, E. Tirrito, M. Lewenstein, S. Hands in A. Bermudez, Annals of Physics 439, 168763 (2022), arXiv:2111.04485.
https: / / doi.org/ 10.1016 / j.aop.2022.168763
arXiv: 2111.04485

[150] L. Zhang in X.-J. Liu, v Synthetic Spin-Orbit Coupling in Cold Atoms (WORLD SCIENTIFIC, 2018) str. 1–87.
https: / / doi.org/ 10.1142 / 9789813272538_0001

[151] X.-J. Liu, Z.-X. Liu in M. Cheng, Phys. Rev. Lett. 110, 076401 (2013).
https: / / doi.org/ 10.1103 / PhysRevLett.110.076401

[152] X.-J. Liu, KT Law in TK Ng, Phys. Rev. Lett. 112, 086401 (2014a).
https: / / doi.org/ 10.1103 / PhysRevLett.112.086401

[153] X.-J. Liu, KT Law in TK Ng, Phys. Rev. Lett. 113, 059901 (2014b).
https: / / doi.org/ 10.1103 / PhysRevLett.113.059901

[154] MA Cazalilla in AM Rey, Poročila o napredku v fiziki 77, 124401 (2014).
https:/​/​doi.org/​10.1088/​0034-4885/​77/​12/​124401

[155] M.-C. Liang, Y.-D. Wei, L. Zhang, X.-J. Wang, H. Zhang, W.-W. Wang, W. Qi, X.-J. Liu in X. Zhang, Phys. Rev. Res. 5, L012006 (2023).
https://​/​doi.org/​10.1103/​PhysRevResearch.5.L012006

[156] Z. Wu, L. Zhang, W. Sun, X.-T. Xu, B.-Z. Wang, S.-C. Ji, Y. Deng, S. Chen, X.-J. Liu in J.-W. Pan, Science 354, 83 (2016).
https: / / doi.org/ 10.1126 / science.aaf6689

[157] W. Sun, B.-Z. Wang, X.-T. Xu, C.-R. Yi, L. Zhang, Z. Wu, Y. Deng, X.-J. Liu, S. Chen in J.-W. Pan, Phys. Rev. Lett. 121, 150401 (2018).
https: / / doi.org/ 10.1103 / PhysRevLett.121.150401

[158] B. Song, L. Zhang, C. He, TFJ Poon, E. Hajiyev, S. Zhang, X.-J. Liu in G.-B. Jo, Science Advances 4, eaao4748 (2018).
https: / / doi.org/ 10.1126 / sciadv.aao4748

[159] D. Jaksch, C. Bruder, JI Cirac, CW Gardiner in P. Zoller, Phys. Rev. Lett. 81, 3108 (1998).
https: / / doi.org/ 10.1103 / PhysRevLett.81.3108

[160] W. Hofstetter, JI Cirac, P. Zoller, E. Demler in MD Lukin, Phys. Rev. Lett. 89, 220407 (2002).
https: / / doi.org/ 10.1103 / PhysRevLett.89.220407

[161] D. Jaksch in P. Zoller, New Journal of Physics 5, 56 (2003).
https:/​/​doi.org/​10.1088/​1367-2630/​5/​1/​356

[162] M. Ben Dahan, E. Peik, J. Reichel, Y. Castin in C. Salomon, Phys. Rev. Lett. 76, 4508 (1996).
https: / / doi.org/ 10.1103 / PhysRevLett.76.4508

[163] X. Huang in L. Parker, Phys. Rev. D 79, 024020 (2009).
https: / / doi.org/ 10.1103 / PhysRevD.79.024020

[164] I. Bloch, J. Dalibard in W. Zwerger, Rev. Mod. Phys. 80, 885 (2008b).
https: / / doi.org/ 10.1103 / revmodphys.80.885

[165] W. Ketterle in MW Zwierlein, La Rivista del Nuovo Cimento 31, 247–422 (2008).
https://​/​doi.org/​10.1393/​ncr/​i2008-10033-1

[166] M. Greiner, I. Bloch, O. Mandel, TW Hänsch in T. Esslinger, 87, 160405 (2001), arXiv:cond-mat/​0105105 [cond-mat.soft].
https: / / doi.org/ 10.1103 / PhysRevLett.87.160405
arXiv: cond-mat / 0105105

[167] M. Köhl, H. Moritz, T. Stöferle, K. Günter in T. Esslinger, Physical Review Letters 94 (2005), 10.1103/​physrevlett.94.080403.
https: / / doi.org/ 10.1103 / physrevlett.94.080403

[168] A. Kastberg, WD Phillips, SL Rolston, RJC Spreeuw in PS Jessen, 74, 1542 (1995).
https: / / doi.org/ 10.1103 / PhysRevLett.74.1542

[169] L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu in T. Esslinger, 483, 302 (2012), arXiv:1111.5020 [cond-mat.quant-gas].
https: / / doi.org/ 10.1038 / nature10871
arXiv: 1111.5020

[170] E. Alba, X. Fernandez-Gonzalvo, J. Mur-Petit, JK Pachos in JJ Garcia-Ripoll, Phys. Rev. Lett. 107, 235301 (2011).
https: / / doi.org/ 10.1103 / PhysRevLett.107.235301

[171] NR Cooper, J. Dalibard in IB Spielman, Reviews of Modern Physics 91, 015005 (2019), arXiv:1803.00249 [cond-mat.quant-gas].
https: / / doi.org/ 10.1103 / RevModPhys.91.015005
arXiv: 1803.00249

[172] S. Weinberg, Kvantna teorija polj, Vol. 1 (Cambridge University Press, 1995).
https: / / doi.org/ 10.1017 / CBO9781139644167

[173] DZ Freedman in A. Van Proeyen, Supergravitacija (Cambridge University Press, 2012).
https: / / doi.org/ 10.1017 / CBO9781139026833

[174] TWB Kibble, Journal of Mathematical Physics 2, 212 (1961).
https: / / doi.org/ 10.1063 / 1.1703702

[175] IL Shapiro, Vesolje 8 (2022), 10.3390/​universe8110586.
https: / / doi.org/ 10.3390 / university8110586

[176] C. Teitelboim, Phys. Lett. B 126, 41 (1983).
https:/​/​doi.org/​10.1016/​0370-2693(83)90012-6

[177] R. Jackiw, Nucl. Phys. B 252, 343 (1985).
https:/​/​doi.org/​10.1016/​0550-3213(85)90448-1

[178] RB Mann, A. Shiekh in L. Tarasov, Nucl. Phys. B 341, 134 (1990).
https:/​/​doi.org/​10.1016/​0550-3213(90)90265-F

[179] C. Sabín, New Journal of Physics 20, 053028 (2018).
https://​/​doi.org/​10.1088/​1367-2630/​aac0db

[180] JF García in C. Sabín, Phys. Rev. D 99, 025008 (2019).
https: / / doi.org/ 10.1103 / PhysRevD.99.025008

[181] IS Gradshteyn in IM Ryzhik, Tabela integralov, serij in produktov, sedma izdaja. (Elsevier/​Academic Press, Amsterdam, 2007) str. xlviii+1171, prevedeno iz ruščine, prevod uredil in s predgovorom Alan Jeffrey in Daniel Zwillinger, z enim CD-ROM-om (Windows, Macintosh in UNIX).

[182] AA Grib, SG Mamaev in VM Mostepanenko, Gen. Rel. Grav. 7, 535 (1976).
https: / / doi.org/ 10.1007 / BF00766413

[183] Y. Shtanov, JH Traschen in RH Brandenberger, Phys. Rev. D 51, 5438 (1995), arXiv:hep-ph/9407247.
https: / / doi.org/ 10.1103 / PhysRevD.51.5438
arXiv:hep-ph/9407247

[184] K. Svozil, Phys. Rev. Lett. 65, 3341 (1990).
https: / / doi.org/ 10.1103 / PhysRevLett.65.3341

[185] M. Ban, J. Opt. Soc. Am. B 10, 1347 (1993).
https: / / doi.org/ 10.1364 / JOSAB.10.001347

Navedel

Pridobitve ni bilo mogoče Crossref citirani podatki med zadnjim poskusom 2023-06-21 16:39:11: ni bilo mogoče pridobiti navajanih podatkov za 10.22331 / q-2023-06-21-1042 od podjetja Crossref. To je normalno, če je bil DOI registriran pred kratkim. Na SAO / NASA ADS ni bilo najdenih podatkov o navajanju del (zadnji poskus 2023-06-21 16:39:11).

Ta dokument je objavljen v Quantumu pod Priznanje avtorstva Creative Commons 4.0 International (CC BY 4.0) licenca. Avtorske pravice ostajajo pri izvirnih imetnikih avtorskih pravic, kot so avtorji ali njihove ustanove.

Časovni žig:

Več od Quantum Journal