Tunneling catastrophes of the partition function

Brazilian Journal of Physics

Volumn 27, Issue 3, 1997, Pages 373-378

  De Carvalho, C A A ^a   Cavalcanti, R M ^b  

^a FEDERAL UNIVERSITY OF RIO DE JANEIRO   (Brazil)

^b PONTIFICAL CATHOLIC UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031325426     PISSN: 01039733     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965).
2. R. P. Feynman, Statistical Mechanics (Benjamin, Reading, MA, 1972).
3. M. Creutz and B. Freedman, Ann. Phys. (NY) 132, 427 (1981).
4. See, for example, R. Rajaraman, Solitons and Instantons (North-Holland, Amsterdam, 1987), Sec. 6.3.
5. To arrive at this result we adapted techniques described in: J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Oxford University Press, Oxford, 1993). A full derivation, together with explicit calculations for a number of potentials, will appear elsewhere.
6. I. S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series and Products (Academic Press, New York, 1965).
7. A partial examination of such a structure is found in: J. Ankerhold and H. Grabert, Physica A 188, 568 (1992); Phys. Rev. E 52, 4704 (1995); F. J. Weiper, J. Ankerhold and H. Grabert, Physica A 223, 193 (1996).
8. A partial examination of such a structure is found in: J. Ankerhold and H. Grabert, Physica A 188, 568 (1992); Phys. Rev. E 52, 4704 (1995); F. J. Weiper, J. Ankerhold and H. Grabert, Physica A 223, 193 (1996).
9. A partial examination of such a structure is found in: J. Ankerhold and H. Grabert, Physica A 188, 568 (1992); Phys. Rev. E 52, 4704 (1995); F. J. Weiper, J. Ankerhold and H. Grabert, Physica A 223, 193 (1996).
10. M. Berry, in Physics of Defects, Les Houches Session XXXV (1980), eds. R. Balian et al. (North-Holland, Amsterdam, 1981); M. V. Berry and C. Upstill, in Progress in Optics XVIII, ed. by E. Wolf (North-Holland, Amsterdam, 1980).
11. M. Berry, in Physics of Defects, Les Houches Session XXXV (1980), eds. R. Balian et al. (North-Holland, Amsterdam, 1981); M. V. Berry and C. Upstill, in Progress in Optics XVIII, ed. by E. Wolf (North-Holland, Amsterdam, 1980).
12. P. T. Saunders, An Introduction to Catastrophe Theory (Cambridge University Press, Cambridge, 1980).
13. R. Thom, Structural Stability and Morphogenesis (Benjamin, Reading, MA, 1975); T. Poston and I. N. Stewart, Catastrophe Theory and its Applications (Pitman, London, 1978); E. C. Zeeman, Catastrophe Theory: Selected Papers 1972-1977 (Addison-Wesley, Reading, MA, 1977).
14. R. Thom, Structural Stability and Morphogenesis (Benjamin, Reading, MA, 1975); T. Poston and I. N. Stewart, Catastrophe Theory and its Applications (Pitman, London, 1978); E. C. Zeeman, Catastrophe Theory: Selected Papers 1972-1977 (Addison-Wesley, Reading, MA, 1977).
15. R. Thom, Structural Stability and Morphogenesis (Benjamin, Reading, MA, 1975); T. Poston and I. N. Stewart, Catastrophe Theory and its Applications (Pitman, London, 1978); E. C. Zeeman, Catastrophe Theory: Selected Papers 1972-1977 (Addison-Wesley, Reading, MA, 1977).
16. This is an example of a sigma-decomposition. See, for example, M. Peixoto and R. Thom, C. R. Acad. Sc. Paris I, 303, 629 and 693 (1986); 307, 197 (1988) (Erratum); M. M. Peixoto and A. R. Silva, An. Acad. Bras. Ci. 62 (4), 321 (1990); M. M. Peixoto and A. R. Silva, preprint (1995).
17. This is an example of a sigma-decomposition. See, for example, M. Peixoto and R. Thom, C. R. Acad. Sc. Paris I, 303, 629 and 693 (1986); 307, 197 (1988) (Erratum); M. M. Peixoto and A. R. Silva, An. Acad. Bras. Ci. 62 (4), 321 (1990); M. M. Peixoto and A. R. Silva, preprint (1995).
18. This is an example of a sigma-decomposition. See, for example, M. Peixoto and R. Thom, C. R. Acad. Sc. Paris I, 303, 629 and 693 (1986); 307, 197 (1988) (Erratum); M. M. Peixoto and A. R. Silva, An. Acad. Bras. Ci. 62 (4), 321 (1990); M. M. Peixoto and A. R. Silva, preprint (1995).
19. This is an example of a sigma-decomposition. See, for example, M. Peixoto and R. Thom, C. R. Acad. Sc. Paris I, 303, 629 and 693 (1986); 307, 197 (1988) (Erratum); M. M. Peixoto and A. R. Silva, An. Acad. Bras. Ci. 62 (4), 321 (1990); M. M. Peixoto and A. R. Silva, preprint (1995).
20. G. Dangelmayr and W. Veit, Ann. Phys. (NY) 118, 108 (1979).
21. L. S. Schulman, Techniques and Applications of Path Integration (Wiley, New York, 1981).
22. U. Weiss, Quantum Dissipative Systems (World Scientific, Singapore, 1993).