Landau–Zener formula (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Landau–Zener formula" in English language version.

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32doi.org

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30harvard.edu

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26semanticscholar.org

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archive.org

Abramowitz, M.; I. A. Stegun (1976). Handbook of Mathematical Functions (9 ed.). Dover Publications. pp. 498. ISBN 978-0-486-61272-0.

arxiv.org

N. A. Sinitsyn; J. Lin; V. Y. Chernyak (2017). "Constraints on scattering amplitudes in multistate Landau-Zener theory". Physical Review A. 95 (1): 0112140. arXiv:1609.06285. Bibcode:2017PhRvA..95a2140S. doi:10.1103/PhysRevA.95.012140. S2CID 73696036.
B. Dobrescu; N. A. Sinitsyn (2006). "Comment on 'Exact results for survival probability in the multistate Landau–Zener model'". Journal of Physics B. 39 (5): 1253. arXiv:cond-mat/0505571. Bibcode:2006JPhB...39.1253D. doi:10.1088/0953-4075/39/5/N01. S2CID 118943836.
N. A. Sinitsyn (2004). "Counterintuitive transitions in the multistate Landau–Zener problem with linear level crossings". Journal of Physics A. 37 (44): 10691–10697. arXiv:quant-ph/0403113. Bibcode:2004JPhA...3710691S. doi:10.1088/0305-4470/37/44/016. S2CID 8268705.
N. A. Sinitsyn (2015). "Exact results for models of multichannel quantum nonadiabatic transitions". Physical Review A. 90 (7): 062509. arXiv:1411.4307. Bibcode:2014PhRvA..90f2509S. doi:10.1103/PhysRevA.90.062509. S2CID 119211541.
F. Li; N. A. Sinitsyn (2016). "Dynamic Symmetries and Quantum Nonadiabatic Transitions". Chemical Physics. 481: 28–33. arXiv:1604.00106. Bibcode:2016CP....481...28L. doi:10.1016/j.chemphys.2016.05.029. S2CID 119167653.
N. A. Sinitsyn; F. Li (2016). "Solvable multistate model of Landau-Zener transitions in cavity QED". Physical Review A. 93 (6): 063859. arXiv:1602.03136. Bibcode:2016PhRvA..93f3859S. doi:10.1103/PhysRevA.93.063859. S2CID 119331736.
C. Sun; N. A. Sinitsyn (2016). "Landau-Zener extension of the Tavis-Cummings model: Structure of the solution". Physical Review A. 94 (3): 033808. arXiv:1606.08430. Bibcode:2016PhRvA..94c3808S. doi:10.1103/PhysRevA.94.033808. S2CID 119317114.
R. Malla; V. Y. Chernyak; C. Sun; N. A. Sinitsyn (2022). "Coherent Reaction between Molecular and Atomic Bose-Einstein Condensates: Integrable Model". Physical Review Letters. 128 (3): 033201. arXiv:2112.12302. Bibcode:2022PhRvL.129c3201M. doi:10.1103/PhysRevLett.129.033201. PMID 35905368. S2CID 245425087.
V. Y. Chernyak; N. A. Sinitsyn; C. Sun (2019). "Dynamic spin localization and gamma-magnets". Physical Review B. 10 (22): 224304. arXiv:1905.05287. Bibcode:2019PhRvB.100v4304C. doi:10.1103/PhysRevB.100.224304. S2CID 153312716.
N. A. Sinitsyn (2002). "Multiparticle Landau–Zener problem: Application to quantum dots". Physical Review B. 66 (20): 205303. arXiv:cond-mat/0212017. Bibcode:2002PhRvB..66t5303S. doi:10.1103/PhysRevB.66.205303. S2CID 119101393.
A. Patra; E. A. Yuzbashyan (2015). "Quantum integrability in the multistate Landau–Zener problem". Journal of Physics A. 48 (24): 245303. arXiv:1412.4926. Bibcode:2015JPhA...48x5303P. doi:10.1088/1751-8113/48/24/245303. S2CID 117049526.
G. S. Vasilev; S. S. Ivanov; N. V. Vitanov (2007). "Degenerate Landau-Zener model: Analytical solution". Physical Review A. 75 (1): 013417. arXiv:0909.5396. Bibcode:2007PhRvA..75a3417V. doi:10.1103/PhysRevA.75.013417. S2CID 52213633.
R. W. Cherng; L. S. Levitov (2006). "Entropy and correlation functions of a driven quantum spin chain". Physical Review A. 73 (4): 043614. arXiv:cond-mat/0512689. Bibcode:2006PhRvA..73d3614C. doi:10.1103/PhysRevA.73.043614. S2CID 115915571.
J. Dziarmaga (2005). "Dynamics of a Quantum Phase Transition: Exact Solution of the Quantum Ising Model". Physical Review Letters. 95 (24): 245701. arXiv:cond-mat/0509490. Bibcode:2005PhRvL..95x5701D. doi:10.1103/PhysRevLett.95.245701. PMID 16384394. S2CID 20437466.
N. A. Sinitsyn (2013). "Landau-Zener Transitions in Chains". Physical Review A. 87 (3): 032701. arXiv:1212.2907. Bibcode:2013PhRvA..87c2701S. doi:10.1103/PhysRevA.87.032701. S2CID 119321544.
V. L. Pokrovsky; N. A. Sinitsyn (2002). "Landau–Zener transitions in a linear chain". Physical Review B. 65 (15): 153105. arXiv:cond-mat/0112419. Bibcode:2002PhRvB..65o3105P. doi:10.1103/PhysRevB.65.153105. hdl:1969.1/146790. S2CID 29899890.
Eq. 42 in V. L. Pokrovsky; N. A. Sinitsyn (2004). "Fast noise in the Landau–Zener theory". Physical Review B. 67 (14): 045603. arXiv:cond-mat/0212016. Bibcode:2003PhRvB..67n4303P. doi:10.1103/PhysRevB.67.144303. hdl:1969.1/127315. S2CID 15014229.
V. L. Pokrovsky; D. Sun (2007). "Fast quantum noise in the Landau–Zener transition". Physical Review B. 76 (2): 024310. arXiv:cond-mat/0702476. Bibcode:2007PhRvB..76b4310P. doi:10.1103/PhysRevB.76.024310. hdl:1969.1/127339. S2CID 28133130.
D. Sun; A. Abanov; V. L. Pokrovsky (2008). "Molecular production at a broad Feshbach resonance in a Fermi gas of cooled atoms". EPL. 83 (1): 16003. arXiv:0707.3630. Bibcode:2008EL.....8316003S. doi:10.1209/0295-5075/83/16003. S2CID 54044811.
D. Sun; A. Abanov; V. L. Pokrovsky (2009). "Static and Dynamic properties of a Fermi-gas of cooled atoms near a wide Feshbach resonance". arXiv:0902.2178 [cond-mat.other].
M. Wubs; K. Saito; S. Kohler; P. Hanggi; Y. Kayanuma (2006). "Gauging a quantum heat bath with dissipative Landau-Zener transitions". Physical Review Letters. 97 (20): 200404. arXiv:cond-mat/0608333. Bibcode:2006PhRvL..97t0404W. doi:10.1103/PhysRevLett.97.200404. PMID 17155667. S2CID 13008030.
K. Saito; M. Wubs; S. Kohler; Y. Kayanuma; P. Hanggi (2007). "Dissipative Landau-Zener transitions of a qubit: Bath-specific and universal behavior". Physical Review B. 75 (21): 214308. arXiv:cond-mat/0703596. Bibcode:2007PhRvB..75u4308S. doi:10.1103/PhysRevB.75.214308. S2CID 16905765.

doi.org

C. Zener (1932). "Non-Adiabatic Crossing of Energy Levels". Proceedings of the Royal Society of London A. 137 (6): 696–702. Bibcode:1932RSPSA.137..696Z. doi:10.1098/rspa.1932.0165. JSTOR 96038. S2CID 120348552.
E. C. G. Stueckelberg (1932). "Theorie der unelastischen Stösse zwischen Atomen". Helvetica Physica Acta. 5: 369. doi:10.5169/seals-110177.
E. Majorana (1932). "Atomi orientati in campo magnetico variabile". Il Nuovo Cimento. 9 (2): 43–50. Bibcode:1932NCim....9...43M. doi:10.1007/BF02960953. S2CID 122738040.
C. Wittig (2005). "The Landau–Zener Formula". Journal of Physical Chemistry B. 109 (17): 8428–8430. doi:10.1021/jp040627u. PMID 16851989.
N. A. Sinitsyn; J. Lin; V. Y. Chernyak (2017). "Constraints on scattering amplitudes in multistate Landau-Zener theory". Physical Review A. 95 (1): 0112140. arXiv:1609.06285. Bibcode:2017PhRvA..95a2140S. doi:10.1103/PhysRevA.95.012140. S2CID 73696036.
S. Brundobler; V. Elser (1993). "S-matrix for generalized Landau–Zener problem". Journal of Physics A. 26 (5): 1211. Bibcode:1993JPhA...26.1211B. doi:10.1088/0305-4470/26/5/037.
B. Dobrescu; N. A. Sinitsyn (2006). "Comment on 'Exact results for survival probability in the multistate Landau–Zener model'". Journal of Physics B. 39 (5): 1253. arXiv:cond-mat/0505571. Bibcode:2006JPhB...39.1253D. doi:10.1088/0953-4075/39/5/N01. S2CID 118943836.
M. V. Volkov; V. N. Ostrovsky (2004). "Exact results for survival probability in the multistate Landau–Zener model". Journal of Physics B. 37 (20): 4069. doi:10.1088/0953-4075/37/20/003. S2CID 250804220.
N. A. Sinitsyn (2004). "Counterintuitive transitions in the multistate Landau–Zener problem with linear level crossings". Journal of Physics A. 37 (44): 10691–10697. arXiv:quant-ph/0403113. Bibcode:2004JPhA...3710691S. doi:10.1088/0305-4470/37/44/016. S2CID 8268705.
M. V. Volkov; V. N. Ostrovsky (2005). "No-go theorem for bands of potential curves in multistate Landau–Zener model". Journal of Physics B. 38 (7): 907. Bibcode:2005JPhB...38..907V. doi:10.1088/0953-4075/38/7/011. S2CID 122560197.
N. A. Sinitsyn (2015). "Exact results for models of multichannel quantum nonadiabatic transitions". Physical Review A. 90 (7): 062509. arXiv:1411.4307. Bibcode:2014PhRvA..90f2509S. doi:10.1103/PhysRevA.90.062509. S2CID 119211541.
F. Li; N. A. Sinitsyn (2016). "Dynamic Symmetries and Quantum Nonadiabatic Transitions". Chemical Physics. 481: 28–33. arXiv:1604.00106. Bibcode:2016CP....481...28L. doi:10.1016/j.chemphys.2016.05.029. S2CID 119167653.
Yu. N. Demkov; V. N. Ostrovsky (2001). "The exact solution of the multistate Landau–Zener type model: the generalized bow-tie model". Journal of Physics B. 34 (12): 2419. Bibcode:2001JPhB...34.2419D. doi:10.1088/0953-4075/34/12/309. S2CID 250846731.
N. A. Sinitsyn; F. Li (2016). "Solvable multistate model of Landau-Zener transitions in cavity QED". Physical Review A. 93 (6): 063859. arXiv:1602.03136. Bibcode:2016PhRvA..93f3859S. doi:10.1103/PhysRevA.93.063859. S2CID 119331736.
C. Sun; N. A. Sinitsyn (2016). "Landau-Zener extension of the Tavis-Cummings model: Structure of the solution". Physical Review A. 94 (3): 033808. arXiv:1606.08430. Bibcode:2016PhRvA..94c3808S. doi:10.1103/PhysRevA.94.033808. S2CID 119317114.
R. Malla; V. Y. Chernyak; C. Sun; N. A. Sinitsyn (2022). "Coherent Reaction between Molecular and Atomic Bose-Einstein Condensates: Integrable Model". Physical Review Letters. 128 (3): 033201. arXiv:2112.12302. Bibcode:2022PhRvL.129c3201M. doi:10.1103/PhysRevLett.129.033201. PMID 35905368. S2CID 245425087.
V. Y. Chernyak; N. A. Sinitsyn; C. Sun (2019). "Dynamic spin localization and gamma-magnets". Physical Review B. 10 (22): 224304. arXiv:1905.05287. Bibcode:2019PhRvB.100v4304C. doi:10.1103/PhysRevB.100.224304. S2CID 153312716.
N. A. Sinitsyn (2002). "Multiparticle Landau–Zener problem: Application to quantum dots". Physical Review B. 66 (20): 205303. arXiv:cond-mat/0212017. Bibcode:2002PhRvB..66t5303S. doi:10.1103/PhysRevB.66.205303. S2CID 119101393.
A. Patra; E. A. Yuzbashyan (2015). "Quantum integrability in the multistate Landau–Zener problem". Journal of Physics A. 48 (24): 245303. arXiv:1412.4926. Bibcode:2015JPhA...48x5303P. doi:10.1088/1751-8113/48/24/245303. S2CID 117049526.
G. S. Vasilev; S. S. Ivanov; N. V. Vitanov (2007). "Degenerate Landau-Zener model: Analytical solution". Physical Review A. 75 (1): 013417. arXiv:0909.5396. Bibcode:2007PhRvA..75a3417V. doi:10.1103/PhysRevA.75.013417. S2CID 52213633.
R. W. Cherng; L. S. Levitov (2006). "Entropy and correlation functions of a driven quantum spin chain". Physical Review A. 73 (4): 043614. arXiv:cond-mat/0512689. Bibcode:2006PhRvA..73d3614C. doi:10.1103/PhysRevA.73.043614. S2CID 115915571.
J. Dziarmaga (2005). "Dynamics of a Quantum Phase Transition: Exact Solution of the Quantum Ising Model". Physical Review Letters. 95 (24): 245701. arXiv:cond-mat/0509490. Bibcode:2005PhRvL..95x5701D. doi:10.1103/PhysRevLett.95.245701. PMID 16384394. S2CID 20437466.
N. A. Sinitsyn (2013). "Landau-Zener Transitions in Chains". Physical Review A. 87 (3): 032701. arXiv:1212.2907. Bibcode:2013PhRvA..87c2701S. doi:10.1103/PhysRevA.87.032701. S2CID 119321544.
V. L. Pokrovsky; N. A. Sinitsyn (2002). "Landau–Zener transitions in a linear chain". Physical Review B. 65 (15): 153105. arXiv:cond-mat/0112419. Bibcode:2002PhRvB..65o3105P. doi:10.1103/PhysRevB.65.153105. hdl:1969.1/146790. S2CID 29899890.
Y. Kayanuma (1984). "Nonadiabatic Transitions in Level Crossing with Energy Fluctuation. I. Analytical Investigations". Journal of the Physical Society of Japan. 53 (1): 108–117. Bibcode:1984JPSJ...53..108K. doi:10.1143/JPSJ.53.108.
Eq. 42 in V. L. Pokrovsky; N. A. Sinitsyn (2004). "Fast noise in the Landau–Zener theory". Physical Review B. 67 (14): 045603. arXiv:cond-mat/0212016. Bibcode:2003PhRvB..67n4303P. doi:10.1103/PhysRevB.67.144303. hdl:1969.1/127315. S2CID 15014229.
Table I in P. Ao; J. Rammer (1991). "Quantum Dynamics of a Two-State System in a Dissipative Environment". Physical Review B. 43 (7): 5497–5518. Bibcode:1991PhRvB..43.5397A. doi:10.1103/PhysRevB.43.5397. PMID 9997936.
N. A. Sinitsyn; N. Prokof'ev (2003). "Nuclear spin bath effects on Landau–Zener transitions in nanomagnets". Physical Review B. 67 (13): 134403. Bibcode:2003PhRvB..67m4403S. doi:10.1103/PhysRevB.67.134403.
V. L. Pokrovsky; D. Sun (2007). "Fast quantum noise in the Landau–Zener transition". Physical Review B. 76 (2): 024310. arXiv:cond-mat/0702476. Bibcode:2007PhRvB..76b4310P. doi:10.1103/PhysRevB.76.024310. hdl:1969.1/127339. S2CID 28133130.
D. Sun; A. Abanov; V. L. Pokrovsky (2008). "Molecular production at a broad Feshbach resonance in a Fermi gas of cooled atoms". EPL. 83 (1): 16003. arXiv:0707.3630. Bibcode:2008EL.....8316003S. doi:10.1209/0295-5075/83/16003. S2CID 54044811.
M. Wubs; K. Saito; S. Kohler; P. Hanggi; Y. Kayanuma (2006). "Gauging a quantum heat bath with dissipative Landau-Zener transitions". Physical Review Letters. 97 (20): 200404. arXiv:cond-mat/0608333. Bibcode:2006PhRvL..97t0404W. doi:10.1103/PhysRevLett.97.200404. PMID 17155667. S2CID 13008030.
K. Saito; M. Wubs; S. Kohler; Y. Kayanuma; P. Hanggi (2007). "Dissipative Landau-Zener transitions of a qubit: Bath-specific and universal behavior". Physical Review B. 75 (21): 214308. arXiv:cond-mat/0703596. Bibcode:2007PhRvB..75u4308S. doi:10.1103/PhysRevB.75.214308. S2CID 16905765.

handle.net

hdl.handle.net

V. L. Pokrovsky; N. A. Sinitsyn (2002). "Landau–Zener transitions in a linear chain". Physical Review B. 65 (15): 153105. arXiv:cond-mat/0112419. Bibcode:2002PhRvB..65o3105P. doi:10.1103/PhysRevB.65.153105. hdl:1969.1/146790. S2CID 29899890.
Eq. 42 in V. L. Pokrovsky; N. A. Sinitsyn (2004). "Fast noise in the Landau–Zener theory". Physical Review B. 67 (14): 045603. arXiv:cond-mat/0212016. Bibcode:2003PhRvB..67n4303P. doi:10.1103/PhysRevB.67.144303. hdl:1969.1/127315. S2CID 15014229.
V. L. Pokrovsky; D. Sun (2007). "Fast quantum noise in the Landau–Zener transition". Physical Review B. 76 (2): 024310. arXiv:cond-mat/0702476. Bibcode:2007PhRvB..76b4310P. doi:10.1103/PhysRevB.76.024310. hdl:1969.1/127339. S2CID 28133130.

harvard.edu

ui.adsabs.harvard.edu

C. Zener (1932). "Non-Adiabatic Crossing of Energy Levels". Proceedings of the Royal Society of London A. 137 (6): 696–702. Bibcode:1932RSPSA.137..696Z. doi:10.1098/rspa.1932.0165. JSTOR 96038. S2CID 120348552.
E. Majorana (1932). "Atomi orientati in campo magnetico variabile". Il Nuovo Cimento. 9 (2): 43–50. Bibcode:1932NCim....9...43M. doi:10.1007/BF02960953. S2CID 122738040.
N. A. Sinitsyn; J. Lin; V. Y. Chernyak (2017). "Constraints on scattering amplitudes in multistate Landau-Zener theory". Physical Review A. 95 (1): 0112140. arXiv:1609.06285. Bibcode:2017PhRvA..95a2140S. doi:10.1103/PhysRevA.95.012140. S2CID 73696036.
S. Brundobler; V. Elser (1993). "S-matrix for generalized Landau–Zener problem". Journal of Physics A. 26 (5): 1211. Bibcode:1993JPhA...26.1211B. doi:10.1088/0305-4470/26/5/037.
B. Dobrescu; N. A. Sinitsyn (2006). "Comment on 'Exact results for survival probability in the multistate Landau–Zener model'". Journal of Physics B. 39 (5): 1253. arXiv:cond-mat/0505571. Bibcode:2006JPhB...39.1253D. doi:10.1088/0953-4075/39/5/N01. S2CID 118943836.
N. A. Sinitsyn (2004). "Counterintuitive transitions in the multistate Landau–Zener problem with linear level crossings". Journal of Physics A. 37 (44): 10691–10697. arXiv:quant-ph/0403113. Bibcode:2004JPhA...3710691S. doi:10.1088/0305-4470/37/44/016. S2CID 8268705.
M. V. Volkov; V. N. Ostrovsky (2005). "No-go theorem for bands of potential curves in multistate Landau–Zener model". Journal of Physics B. 38 (7): 907. Bibcode:2005JPhB...38..907V. doi:10.1088/0953-4075/38/7/011. S2CID 122560197.
N. A. Sinitsyn (2015). "Exact results for models of multichannel quantum nonadiabatic transitions". Physical Review A. 90 (7): 062509. arXiv:1411.4307. Bibcode:2014PhRvA..90f2509S. doi:10.1103/PhysRevA.90.062509. S2CID 119211541.
F. Li; N. A. Sinitsyn (2016). "Dynamic Symmetries and Quantum Nonadiabatic Transitions". Chemical Physics. 481: 28–33. arXiv:1604.00106. Bibcode:2016CP....481...28L. doi:10.1016/j.chemphys.2016.05.029. S2CID 119167653.
Yu. N. Demkov; V. I. Osherov (1968). "Stationary and nonstationary problems in quantum mechanics that can be solved by means of contour integration". Soviet Physics JETP. 24: 916. Bibcode:1968JETP...26..916D.
Yu. N. Demkov; V. N. Ostrovsky (2001). "The exact solution of the multistate Landau–Zener type model: the generalized bow-tie model". Journal of Physics B. 34 (12): 2419. Bibcode:2001JPhB...34.2419D. doi:10.1088/0953-4075/34/12/309. S2CID 250846731.
N. A. Sinitsyn; F. Li (2016). "Solvable multistate model of Landau-Zener transitions in cavity QED". Physical Review A. 93 (6): 063859. arXiv:1602.03136. Bibcode:2016PhRvA..93f3859S. doi:10.1103/PhysRevA.93.063859. S2CID 119331736.
C. Sun; N. A. Sinitsyn (2016). "Landau-Zener extension of the Tavis-Cummings model: Structure of the solution". Physical Review A. 94 (3): 033808. arXiv:1606.08430. Bibcode:2016PhRvA..94c3808S. doi:10.1103/PhysRevA.94.033808. S2CID 119317114.
R. Malla; V. Y. Chernyak; C. Sun; N. A. Sinitsyn (2022). "Coherent Reaction between Molecular and Atomic Bose-Einstein Condensates: Integrable Model". Physical Review Letters. 128 (3): 033201. arXiv:2112.12302. Bibcode:2022PhRvL.129c3201M. doi:10.1103/PhysRevLett.129.033201. PMID 35905368. S2CID 245425087.
V. Y. Chernyak; N. A. Sinitsyn; C. Sun (2019). "Dynamic spin localization and gamma-magnets". Physical Review B. 10 (22): 224304. arXiv:1905.05287. Bibcode:2019PhRvB.100v4304C. doi:10.1103/PhysRevB.100.224304. S2CID 153312716.
N. A. Sinitsyn (2002). "Multiparticle Landau–Zener problem: Application to quantum dots". Physical Review B. 66 (20): 205303. arXiv:cond-mat/0212017. Bibcode:2002PhRvB..66t5303S. doi:10.1103/PhysRevB.66.205303. S2CID 119101393.
A. Patra; E. A. Yuzbashyan (2015). "Quantum integrability in the multistate Landau–Zener problem". Journal of Physics A. 48 (24): 245303. arXiv:1412.4926. Bibcode:2015JPhA...48x5303P. doi:10.1088/1751-8113/48/24/245303. S2CID 117049526.
G. S. Vasilev; S. S. Ivanov; N. V. Vitanov (2007). "Degenerate Landau-Zener model: Analytical solution". Physical Review A. 75 (1): 013417. arXiv:0909.5396. Bibcode:2007PhRvA..75a3417V. doi:10.1103/PhysRevA.75.013417. S2CID 52213633.
R. W. Cherng; L. S. Levitov (2006). "Entropy and correlation functions of a driven quantum spin chain". Physical Review A. 73 (4): 043614. arXiv:cond-mat/0512689. Bibcode:2006PhRvA..73d3614C. doi:10.1103/PhysRevA.73.043614. S2CID 115915571.
J. Dziarmaga (2005). "Dynamics of a Quantum Phase Transition: Exact Solution of the Quantum Ising Model". Physical Review Letters. 95 (24): 245701. arXiv:cond-mat/0509490. Bibcode:2005PhRvL..95x5701D. doi:10.1103/PhysRevLett.95.245701. PMID 16384394. S2CID 20437466.
N. A. Sinitsyn (2013). "Landau-Zener Transitions in Chains". Physical Review A. 87 (3): 032701. arXiv:1212.2907. Bibcode:2013PhRvA..87c2701S. doi:10.1103/PhysRevA.87.032701. S2CID 119321544.
V. L. Pokrovsky; N. A. Sinitsyn (2002). "Landau–Zener transitions in a linear chain". Physical Review B. 65 (15): 153105. arXiv:cond-mat/0112419. Bibcode:2002PhRvB..65o3105P. doi:10.1103/PhysRevB.65.153105. hdl:1969.1/146790. S2CID 29899890.
Y. Kayanuma (1984). "Nonadiabatic Transitions in Level Crossing with Energy Fluctuation. I. Analytical Investigations". Journal of the Physical Society of Japan. 53 (1): 108–117. Bibcode:1984JPSJ...53..108K. doi:10.1143/JPSJ.53.108.
Eq. 42 in V. L. Pokrovsky; N. A. Sinitsyn (2004). "Fast noise in the Landau–Zener theory". Physical Review B. 67 (14): 045603. arXiv:cond-mat/0212016. Bibcode:2003PhRvB..67n4303P. doi:10.1103/PhysRevB.67.144303. hdl:1969.1/127315. S2CID 15014229.
Table I in P. Ao; J. Rammer (1991). "Quantum Dynamics of a Two-State System in a Dissipative Environment". Physical Review B. 43 (7): 5497–5518. Bibcode:1991PhRvB..43.5397A. doi:10.1103/PhysRevB.43.5397. PMID 9997936.
N. A. Sinitsyn; N. Prokof'ev (2003). "Nuclear spin bath effects on Landau–Zener transitions in nanomagnets". Physical Review B. 67 (13): 134403. Bibcode:2003PhRvB..67m4403S. doi:10.1103/PhysRevB.67.134403.
V. L. Pokrovsky; D. Sun (2007). "Fast quantum noise in the Landau–Zener transition". Physical Review B. 76 (2): 024310. arXiv:cond-mat/0702476. Bibcode:2007PhRvB..76b4310P. doi:10.1103/PhysRevB.76.024310. hdl:1969.1/127339. S2CID 28133130.
D. Sun; A. Abanov; V. L. Pokrovsky (2008). "Molecular production at a broad Feshbach resonance in a Fermi gas of cooled atoms". EPL. 83 (1): 16003. arXiv:0707.3630. Bibcode:2008EL.....8316003S. doi:10.1209/0295-5075/83/16003. S2CID 54044811.
M. Wubs; K. Saito; S. Kohler; P. Hanggi; Y. Kayanuma (2006). "Gauging a quantum heat bath with dissipative Landau-Zener transitions". Physical Review Letters. 97 (20): 200404. arXiv:cond-mat/0608333. Bibcode:2006PhRvL..97t0404W. doi:10.1103/PhysRevLett.97.200404. PMID 17155667. S2CID 13008030.
K. Saito; M. Wubs; S. Kohler; Y. Kayanuma; P. Hanggi (2007). "Dissipative Landau-Zener transitions of a qubit: Bath-specific and universal behavior". Physical Review B. 75 (21): 214308. arXiv:cond-mat/0703596. Bibcode:2007PhRvB..75u4308S. doi:10.1103/PhysRevB.75.214308. S2CID 16905765.

jstor.org

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pubmed.ncbi.nlm.nih.gov

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semanticscholar.org

api.semanticscholar.org

C. Zener (1932). "Non-Adiabatic Crossing of Energy Levels". Proceedings of the Royal Society of London A. 137 (6): 696–702. Bibcode:1932RSPSA.137..696Z. doi:10.1098/rspa.1932.0165. JSTOR 96038. S2CID 120348552.
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N. A. Sinitsyn (2004). "Counterintuitive transitions in the multistate Landau–Zener problem with linear level crossings". Journal of Physics A. 37 (44): 10691–10697. arXiv:quant-ph/0403113. Bibcode:2004JPhA...3710691S. doi:10.1088/0305-4470/37/44/016. S2CID 8268705.
M. V. Volkov; V. N. Ostrovsky (2005). "No-go theorem for bands of potential curves in multistate Landau–Zener model". Journal of Physics B. 38 (7): 907. Bibcode:2005JPhB...38..907V. doi:10.1088/0953-4075/38/7/011. S2CID 122560197.
N. A. Sinitsyn (2015). "Exact results for models of multichannel quantum nonadiabatic transitions". Physical Review A. 90 (7): 062509. arXiv:1411.4307. Bibcode:2014PhRvA..90f2509S. doi:10.1103/PhysRevA.90.062509. S2CID 119211541.
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N. A. Sinitsyn; F. Li (2016). "Solvable multistate model of Landau-Zener transitions in cavity QED". Physical Review A. 93 (6): 063859. arXiv:1602.03136. Bibcode:2016PhRvA..93f3859S. doi:10.1103/PhysRevA.93.063859. S2CID 119331736.
C. Sun; N. A. Sinitsyn (2016). "Landau-Zener extension of the Tavis-Cummings model: Structure of the solution". Physical Review A. 94 (3): 033808. arXiv:1606.08430. Bibcode:2016PhRvA..94c3808S. doi:10.1103/PhysRevA.94.033808. S2CID 119317114.
R. Malla; V. Y. Chernyak; C. Sun; N. A. Sinitsyn (2022). "Coherent Reaction between Molecular and Atomic Bose-Einstein Condensates: Integrable Model". Physical Review Letters. 128 (3): 033201. arXiv:2112.12302. Bibcode:2022PhRvL.129c3201M. doi:10.1103/PhysRevLett.129.033201. PMID 35905368. S2CID 245425087.
V. Y. Chernyak; N. A. Sinitsyn; C. Sun (2019). "Dynamic spin localization and gamma-magnets". Physical Review B. 10 (22): 224304. arXiv:1905.05287. Bibcode:2019PhRvB.100v4304C. doi:10.1103/PhysRevB.100.224304. S2CID 153312716.
N. A. Sinitsyn (2002). "Multiparticle Landau–Zener problem: Application to quantum dots". Physical Review B. 66 (20): 205303. arXiv:cond-mat/0212017. Bibcode:2002PhRvB..66t5303S. doi:10.1103/PhysRevB.66.205303. S2CID 119101393.
A. Patra; E. A. Yuzbashyan (2015). "Quantum integrability in the multistate Landau–Zener problem". Journal of Physics A. 48 (24): 245303. arXiv:1412.4926. Bibcode:2015JPhA...48x5303P. doi:10.1088/1751-8113/48/24/245303. S2CID 117049526.
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J. Dziarmaga (2005). "Dynamics of a Quantum Phase Transition: Exact Solution of the Quantum Ising Model". Physical Review Letters. 95 (24): 245701. arXiv:cond-mat/0509490. Bibcode:2005PhRvL..95x5701D. doi:10.1103/PhysRevLett.95.245701. PMID 16384394. S2CID 20437466.
N. A. Sinitsyn (2013). "Landau-Zener Transitions in Chains". Physical Review A. 87 (3): 032701. arXiv:1212.2907. Bibcode:2013PhRvA..87c2701S. doi:10.1103/PhysRevA.87.032701. S2CID 119321544.
V. L. Pokrovsky; N. A. Sinitsyn (2002). "Landau–Zener transitions in a linear chain". Physical Review B. 65 (15): 153105. arXiv:cond-mat/0112419. Bibcode:2002PhRvB..65o3105P. doi:10.1103/PhysRevB.65.153105. hdl:1969.1/146790. S2CID 29899890.
Eq. 42 in V. L. Pokrovsky; N. A. Sinitsyn (2004). "Fast noise in the Landau–Zener theory". Physical Review B. 67 (14): 045603. arXiv:cond-mat/0212016. Bibcode:2003PhRvB..67n4303P. doi:10.1103/PhysRevB.67.144303. hdl:1969.1/127315. S2CID 15014229.
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D. Sun; A. Abanov; V. L. Pokrovsky (2008). "Molecular production at a broad Feshbach resonance in a Fermi gas of cooled atoms". EPL. 83 (1): 16003. arXiv:0707.3630. Bibcode:2008EL.....8316003S. doi:10.1209/0295-5075/83/16003. S2CID 54044811.
M. Wubs; K. Saito; S. Kohler; P. Hanggi; Y. Kayanuma (2006). "Gauging a quantum heat bath with dissipative Landau-Zener transitions". Physical Review Letters. 97 (20): 200404. arXiv:cond-mat/0608333. Bibcode:2006PhRvL..97t0404W. doi:10.1103/PhysRevLett.97.200404. PMID 17155667. S2CID 13008030.
K. Saito; M. Wubs; S. Kohler; Y. Kayanuma; P. Hanggi (2007). "Dissipative Landau-Zener transitions of a qubit: Bath-specific and universal behavior". Physical Review B. 75 (21): 214308. arXiv:cond-mat/0703596. Bibcode:2007PhRvB..75u4308S. doi:10.1103/PhysRevB.75.214308. S2CID 16905765.