References analysis of the Wikipedia article "Supersymmetric theory of stochastic dynamics" in the English version

arxiv.org

Niemi, A. J.; Pasanen, P. (1996-10-03). "Topological σ-model, Hamiltonian dynamics and loop space Lefschetz number". Physics Letters B. 386 (1): 123–130. arXiv:hep-th/9508067. Bibcode:1996PhLB..386..123N. doi:10.1016/0370-2693(96)00941-0. S2CID 119102809.

Tailleur, J.; Tănase-Nicola, S.; Kurchan, J. (2006-02-01). "Kramers Equation and Supersymmetry". Journal of Statistical Physics. 122 (4): 557–595. arXiv:cond-mat/0503545. Bibcode:2006JSP...122..557T. doi:10.1007/s10955-005-8059-x. ISSN 0022-4715. S2CID 119716999.

Kleinert, H.; Shabanov, S. V. (1997-10-27). "Supersymmetry in stochastic processes with higher-order time derivatives". Physics Letters A. 235 (2): 105–112. arXiv:quant-ph/9705042. Bibcode:1997PhLA..235..105K. doi:10.1016/s0375-9601(97)00660-9. S2CID 119459346.

Ovchinnikov, I. V. (2016-03-28). "Introduction to Supersymmetric Theory of Stochastics". Entropy. 18 (4): 108. arXiv:1511.03393. Bibcode:2016Entrp..18..108O. doi:10.3390/e18040108. S2CID 2388285.

Dijkgraaf, R.; Orlando, D.; Reffert, S. (2010-01-11). "Relating field theories via stochastic quantization". Nuclear Physics B. 824 (3): 365–386. arXiv:0903.0732. Bibcode:2010NuPhB.824..365D. doi:10.1016/j.nuclphysb.2009.07.018. S2CID 2033425.

Mallick, K.; Moshe, M.; Orland, H. (2007-11-13). "Supersymmetry and Nonequilibrium Work Relations". arXiv:0711.2059 [cond-mat.stat-mech].

Mostafazadeh, A. (2002-07-19). "Pseudo-Hermiticity versus PT-symmetry III: Equivalence of pseudo-Hermiticity and the presence of antilinear symmetries". Journal of Mathematical Physics. 43 (8): 3944–3951. arXiv:math-ph/0203005. Bibcode:2002JMP....43.3944M. doi:10.1063/1.1489072. ISSN 0022-2488. S2CID 7096321.

Ovchinnikov, I.V. (2013-01-15). "Topological field theory of dynamical systems. II". Chaos: An Interdisciplinary Journal of Nonlinear Science. 23 (1): 013108. arXiv:1212.1989. Bibcode:2013Chaos..23a3108O. doi:10.1063/1.4775755. ISSN 1054-1500. PMID 23556945. S2CID 34229910.

Ovchinnikov, I.V.; Ensslin, T. A. (2016). "Kinematic dynamo, supersymmetry breaking, and chaos". Physical Review D. 93 (8): 085023. arXiv:1512.01651. Bibcode:2016PhRvD..93h5023O. doi:10.1103/PhysRevD.93.085023. S2CID 59367815.

Ovchinnikov, I. V.; Di Ventra, M. (2019). "Chaos as a symmetry-breaking phenomenon". Modern Physics Letters B. 33 (24): 1950287–1950474. arXiv:1702.06561. Bibcode:2019MPLB...3350287O. doi:10.1142/S0217984919502877. S2CID 203039897.

Chung, D. J. H.; Everett, L. L.; Kane, G. L.; King, S. F.; Lykken, J.; Wang, Lian-Tao (2005-02-01). "The soft supersymmetry-breaking Lagrangian: theory and applications". Physics Reports. 407 (1–3): 1–203. arXiv:hep-ph/0312378. Bibcode:2005PhR...407....1C. doi:10.1016/j.physrep.2004.08.032. S2CID 119344585.

Watkins, N. W.; Pruessner, G.; Chapman, S. C.; Crosby, N. B.; Jensen, H. J. (2016-01-01). "25 Years of Self-organized Criticality: Concepts and Controversies". Space Science Reviews. 198 (1–4): 3–44. arXiv:1504.04991. Bibcode:2016SSRv..198....3W. doi:10.1007/s11214-015-0155-x. ISSN 0038-6308. S2CID 34782655.

Bouya, I.; Dormy, E. (2013-03-01). "Revisiting the ABC flow dynamo". Physics of Fluids. 25 (3): 037103–037103–10. arXiv:1206.5186. Bibcode:2013PhFl...25c7103B. doi:10.1063/1.4795546. ISSN 1070-6631. S2CID 118722952.

Frenkel, E.; Losev, A.; Nekrasov, N. (2007). "Notes on instantons in topological field theory and beyond". Nuclear Physics B: Proceedings Supplements. 171: 215–230. arXiv:hep-th/0702137. Bibcode:2007NuPhS.171..215F. doi:10.1016/j.nuclphysbps.2007.06.013. S2CID 14914819.

Di Ventra, M.; Traversa, F. L.; Ovchinnikov, I. V. (2017). "Topological Field Theory and Computing with Instantons". Annalen der Physik. 2017 (12): 1700123. arXiv:1609.03230. Bibcode:2017AnP...52900123D. doi:10.1002/andp.201700123. ISSN 1521-3889. S2CID 9437990.

doi.org

Parisi, G.; Sourlas, N. (1979). "Random Magnetic Fields, Supersymmetry, and Negative Dimensions". Physical Review Letters. 43 (11): 744–745. Bibcode:1979PhRvL..43..744P. doi:10.1103/PhysRevLett.43.744.

Parisi, G. (1982). "Supersymmetric field theories and stochastic differential equations". Nuclear Physics B. 206 (2): 321–332. Bibcode:1982NuPhB.206..321P. doi:10.1016/0550-3213(82)90538-7.

Gozzi, E.; Reuter, M. (1990). "Classical mechanics as a topological field theory". Physics Letters B. 240 (1–2): 137–144. Bibcode:1990PhLB..240..137G. doi:10.1016/0370-2693(90)90422-3.

Niemi, A. J. (1995). "A lower bound for the number of periodic classical trajectories". Physics Letters B. 355 (3–4): 501–506. Bibcode:1995PhLB..355..501N. doi:10.1016/0370-2693(95)00780-o.

Gozzi, E.; Reuter, M. (1989-12-28). "Algebraic characterization of ergodicity". Physics Letters B. 233 (3): 383–392. Bibcode:1989PhLB..233..383G. doi:10.1016/0370-2693(89)91327-0.

Ovchinnikov, I. V. (2016-03-28). "Introduction to Supersymmetric Theory of Stochastics". Entropy. 18 (4): 108. arXiv:1511.03393. Bibcode:2016Entrp..18..108O. doi:10.3390/e18040108. S2CID 2388285.

Aharony, A.; Imry, Y.; Ma, S.K. (1976). "Lowering of dimensionality in phase transitions with random fields". Physical Review Letters. 37 (20): 1364–1367. Bibcode:1976PhRvL..37.1364A. doi:10.1103/PhysRevLett.37.1364.

Cecotti, S; Girardello, L (1983-01-01). "Stochastic and parastochastic aspects of supersymmetric functional measures: A new non-perturbative approach to supersymmetry". Annals of Physics. 145 (1): 81–99. Bibcode:1983AnPhy.145...81C. doi:10.1016/0003-4916(83)90172-0.

Zinn-Justin, J. (1986-09-29). "Renormalization and stochastic quantization". Nuclear Physics B. 275 (1): 135–159. Bibcode:1986NuPhB.275..135Z. doi:10.1016/0550-3213(86)90592-4.

Kurchan, J. (1992-07-01). "Supersymmetry in spin glass dynamics". Journal de Physique I. 2 (7): 1333–1352. Bibcode:1992JPhy1...2.1333K. doi:10.1051/jp1:1992214. ISSN 1155-4304. S2CID 124073976.

Gozzi, E. (1984). "Onsager principle of microscopic reversibility and supersymmetry". Physical Review D. 30 (6): 1218–1227. Bibcode:1984PhRvD..30.1218G. doi:10.1103/physrevd.30.1218.

Bernstein, M. (1984). "Supersymmetry and the Bistable Fokker-Planck Equation". Physical Review Letters. 52 (22): 1933–1935. Bibcode:1984PhRvL..52.1933B. doi:10.1103/physrevlett.52.1933.

Olemskoi, A. I; Khomenko, A. V; Olemskoi, D. A (2004-02-01). "Field theory of self-organization". Physica A: Statistical Mechanics and Its Applications. 332: 185–206. Bibcode:2004PhyA..332..185O. doi:10.1016/j.physa.2003.10.035.

Ruelle, D. (1990-12-01). "An extension of the theory of Fredholm determinants". Publications Mathématiques de l'Institut des Hautes Études Scientifiques. 72 (1): 175–193. doi:10.1007/bf02699133. ISSN 0073-8301. S2CID 121869096.

Birmingham, D; Blau, M.; Rakowski, M.; Thompson, G. (1991). "Topological field theory". Physics Reports. 209 (4–5): 129–340. Bibcode:1991PhR...209..129B. doi:10.1016/0370-1573(91)90117-5.

Witten, E. (1988-09-01). "Topological sigma models". Communications in Mathematical Physics. 118 (3): 411–449. Bibcode:1988CMaPh.118..411W. doi:10.1007/BF01466725. ISSN 0010-3616. S2CID 34042140.

Baulieu, L.; Singer, I.M. (1988). "The topological sigma model". Communications in Mathematical Physics. 125 (2): 227–237. doi:10.1007/BF01217907. S2CID 120150962.

Witten, E. (1988-09-01). "Topological quantum field theory". Communications in Mathematical Physics. 117 (3): 353–386. Bibcode:1988CMaPh.117..353W. doi:10.1007/BF01223371. ISSN 0010-3616. S2CID 43230714.

Witten, E. (1982). "Supersymmetry and Morse theory". Journal of Differential Geometry. 17 (4): 661–692. doi:10.4310/jdg/1214437492. ISSN 0022-040X.

Labastida, J. M. F. (1989-12-01). "Morse theory interpretation of topological quantum field theories". Communications in Mathematical Physics. 123 (4): 641–658. Bibcode:1989CMaPh.123..641L. CiteSeerX 10.1.1.509.3123. doi:10.1007/BF01218589. ISSN 0010-3616. S2CID 53555484.

Nicolai, H. (1980-12-22). "Supersymmetry and functional integration measures". Nuclear Physics B. 176 (2): 419–428. Bibcode:1980NuPhB.176..419N. doi:10.1016/0550-3213(80)90460-5. hdl:11858/00-001M-0000-0013-5E89-E.

Nicolai, H. (1980-01-28). "On a new characterization of scalar supersymmetric theories" (PDF). Physics Letters B. 89 (3): 341–346. Bibcode:1980PhLB...89..341N. doi:10.1016/0370-2693(80)90138-0.

Klein, A.; Landau, L.J.; Perez, J.F. (1984). "Supersymmetry and the Parisi-Sourlas dimensional reduction: a rigorous proof". Communications in Mathematical Physics. 94 (4): 459–482. Bibcode:1984CMaPh..94..459K. doi:10.1007/BF01403882. S2CID 120640917.

Baulieu, L.; Grossman, B. (1988). "A topological interpretation of stochastic quantization". Physics Letters B. 212 (3): 351–356. Bibcode:1988PhLB..212..351B. doi:10.1016/0370-2693(88)91328-7.

Graham, R. (1988). "Lyapunov Exponents and Supersymmetry of Stochastic Dynamical Systems". EPL. 5 (2): 101–106. Bibcode:1988EL......5..101G. doi:10.1209/0295-5075/5/2/002. ISSN 0295-5075. S2CID 250788554.

Slavík, A. (2013). "Generalized differential equations: Differentiability of solutions with respect to initial conditions and parameters". Journal of Mathematical Analysis and Applications. 402 (1): 261–274. doi:10.1016/j.jmaa.2013.01.027.

Ovchinnikov, I. V. (2016-06-01). "Supersymmetric Theory of Stochastics: Demystification of Self-Organized Criticality". In Skiadas C.H. and Skiadas C. (ed.). Handbook of Applications of Chaos Theory. Chapman and Hall/CRC. pp. 271–305. doi:10.1201/b20232. ISBN 9781466590441.

Bak, P.; Tang, C.; Wiesenfeld, K. (1987). "Self-organized criticality: An explanation of the 1/f noise". Physical Review Letters. 59 (4): 381–384. Bibcode:1987PhRvL..59..381B. doi:10.1103/PhysRevLett.59.381. PMID 10035754. S2CID 7674321.

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Parisi, G. (1982). "Supersymmetric field theories and stochastic differential equations". Nuclear Physics B. 206 (2): 321–332. Bibcode:1982NuPhB.206..321P. doi:10.1016/0550-3213(82)90538-7.

Gozzi, E.; Reuter, M. (1990). "Classical mechanics as a topological field theory". Physics Letters B. 240 (1–2): 137–144. Bibcode:1990PhLB..240..137G. doi:10.1016/0370-2693(90)90422-3.

Niemi, A. J. (1995). "A lower bound for the number of periodic classical trajectories". Physics Letters B. 355 (3–4): 501–506. Bibcode:1995PhLB..355..501N. doi:10.1016/0370-2693(95)00780-o.

Gozzi, E.; Reuter, M. (1989-12-28). "Algebraic characterization of ergodicity". Physics Letters B. 233 (3): 383–392. Bibcode:1989PhLB..233..383G. doi:10.1016/0370-2693(89)91327-0.

Ovchinnikov, I. V. (2016-03-28). "Introduction to Supersymmetric Theory of Stochastics". Entropy. 18 (4): 108. arXiv:1511.03393. Bibcode:2016Entrp..18..108O. doi:10.3390/e18040108. S2CID 2388285.

Zinn-Justin, J. (1986-09-29). "Renormalization and stochastic quantization". Nuclear Physics B. 275 (1): 135–159. Bibcode:1986NuPhB.275..135Z. doi:10.1016/0550-3213(86)90592-4.

Kurchan, J. (1992-07-01). "Supersymmetry in spin glass dynamics". Journal de Physique I. 2 (7): 1333–1352. Bibcode:1992JPhy1...2.1333K. doi:10.1051/jp1:1992214. ISSN 1155-4304. S2CID 124073976.

Gozzi, E. (1984). "Onsager principle of microscopic reversibility and supersymmetry". Physical Review D. 30 (6): 1218–1227. Bibcode:1984PhRvD..30.1218G. doi:10.1103/physrevd.30.1218.

Bernstein, M. (1984). "Supersymmetry and the Bistable Fokker-Planck Equation". Physical Review Letters. 52 (22): 1933–1935. Bibcode:1984PhRvL..52.1933B. doi:10.1103/physrevlett.52.1933.

Birmingham, D; Blau, M.; Rakowski, M.; Thompson, G. (1991). "Topological field theory". Physics Reports. 209 (4–5): 129–340. Bibcode:1991PhR...209..129B. doi:10.1016/0370-1573(91)90117-5.

Nicolai, H. (1980-01-28). "On a new characterization of scalar supersymmetric theories" (PDF). Physics Letters B. 89 (3): 341–346. Bibcode:1980PhLB...89..341N. doi:10.1016/0370-2693(80)90138-0.

nih.gov

pubmed.ncbi.nlm.nih.gov

semanticscholar.org

api.semanticscholar.org

Ovchinnikov, I. V. (2016-03-28). "Introduction to Supersymmetric Theory of Stochastics". Entropy. 18 (4): 108. arXiv:1511.03393. Bibcode:2016Entrp..18..108O. doi:10.3390/e18040108. S2CID 2388285.

Kurchan, J. (1992-07-01). "Supersymmetry in spin glass dynamics". Journal de Physique I. 2 (7): 1333–1352. Bibcode:1992JPhy1...2.1333K. doi:10.1051/jp1:1992214. ISSN 1155-4304. S2CID 124073976.

Baulieu, L.; Singer, I.M. (1988). "The topological sigma model". Communications in Mathematical Physics. 125 (2): 227–237. doi:10.1007/BF01217907. S2CID 120150962.

worldcat.org

search.worldcat.org

Kurchan, J. (1992-07-01). "Supersymmetry in spin glass dynamics". Journal de Physique I. 2 (7): 1333–1352. Bibcode:1992JPhy1...2.1333K. doi:10.1051/jp1:1992214. ISSN 1155-4304. S2CID 124073976.

Witten, E. (1982). "Supersymmetry and Morse theory". Journal of Differential Geometry. 17 (4): 661–692. doi:10.4310/jdg/1214437492. ISSN 0022-040X.

Ancona, A.; Elworthy, K. D.; Emery, M.; Kunita, H. (2013). Stochastic differential geometry at Saint-Flour. Springer. ISBN 9783642341700. OCLC 811000422.

Kunita, H. (1997). Stochastic flows and stochastic differential equations. Cambridge University Press. ISBN 978-0521599252. OCLC 36864963.

Gilmore, R.; Lefranc, M. (2011). The topology of chaos : Alice in stretch and squeezeland. Wiley-VCH. ISBN 9783527410675. OCLC 967841676.

Supersymmetric theory of stochastic dynamics (English Wikipedia)

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