Lévy flights over quantum paths

Communications in Nonlinear Science and Numerical Simulation

Volumn 12, Issue 1, 2007, Pages 2-18

  Laskin, Nick ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

L vy flights; Path integral; Quantum mechanical kernel

Indexed keywords

INTEGRAL EQUATIONS; INTEGRATION; SET THEORY;

L VY FLIGHTS; PATH INTEGRAL; QUANTUM MECHANICAL KERNEL; QUANTUM PATHS;

QUANTUM THEORY;

INTEGRAL EQUATIONS; INTEGRATION; QUANTUM THEORY; SET THEORY;

EID: 33745268883     PISSN: 10075704     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cnsns.2006.01.001     Document Type: Article

References (26)

1. Zaslavsky G.M. Phys Rep 371 (2002) 461-580
2. Metzler R., and Klafter J. Phys Rep 339 (2000) 1-77
3. Bardou F., Bouchaud J.-P., Aspect A., and Cohen-Tannoudji C. Lévy statistics and laser cooling (2002), Cambridge University Press, Cambridge
4. Schlipf S., Katori H., Perotti L., and Waiyher H. Opt Express 3 (1998) 97-103
5. Zimbardo G., Veltri P., Basile G., and Principato S. Phys Plasmas 2 7 (1995) 2653
6. Klappauf B.G., Oskay W.H., Steck D.A., and Raizen M.G. Phys Rev Lett 81 (1998) 4044
7. Feynman R.P., and Hibbs A.R. Quantum mechanics and path integrals (1965), McGraw-Hill, New York
8. Feynman R.P. Statistical mechanics (1972), Benjamin, Reading, MA
9. Laskin N. Phys Rev E 62 (2000) 3135
10. Laskin N. Chaos 10 (2000) 780
11. Laskin N. Phys Rev E 66 (2002) 056108
12. Kleinert H. Path integrals in quantum mechanics, statistics and polymer physics (1990), World Scientific, Singapore
13. Fox C. Trans Am Math Soc 98 (1961) 395
14. Mathai A.M., and Saxena R.K. The H-function with applications in statistics and other disciplines (1978), Wiley Eastern, New Delhi
15. Srivastava H.M., Gupta K.C., and Goyal S.P. The H-function of one and two variables with applications (1982), South Asian Publishers, New Delhi-Madras
16. West B.J., and Seshadri V. Physica 113A (1982) 203
17. Barnes E.W. Proc Lond Math Soc 6 (1908) 141
18. Mellin H.J. Math Ann 68 (1910) 395
19. Dixon A.L., and Ferrat W.L. Q J Math Oxford Ser 7 (1936) 81
20. Braaksma B.L.J. Compos Math 15 (1964) 239
21. Meijer CS. Proc Nedel Akad Wetensch 49: 227, 344, 457, 632, 765, 936, 1062, 1165 (1).
22. Oldham K.B., and Spanier J. The fractional calculus (1974), Academic Press, New York
23. Nishimoto K. Fractional calculus (1989), University of New Haven Press, New Haven, CT
24. Miller K.S., and Ross B. An introduction to the fractional calculus and fractional differential equations (1993), Wiley, New York
25. Samko S.G., Kilbas A.A., and Marichev O.I. Fractional integrals and derivatives, theory and applications (1993), Gordon and Breach, Amsterdam
26. Ingold G-L. Available from: quant-ph/020826.