Fractals, dissipation and coherent states

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 7620 LNCS, Issue , 2012, Pages 68-79

  Vitiello, Giuseppe ^a  

^a UNIVERSITY OF SALERNO   (Italy)

Author keywords

dissipation; fractals; logarithmic spiral; noncommutative geometry; squeezed coherent states

Indexed keywords

COHERENT STATE; DISSIPATIVE DYNAMICS; FRACTAL STRUCTURES; LOCAL DEFORMATIONS; LOGARITHMIC SPIRAL; NON-COMMUTATIVE GEOMETRY; SELF SIMILARITY PROPERTIES; SELF-SIMILAR FRACTALS; SQUEEZED COHERENT STATE; TIME EVOLUTIONS; TIME REVERSAL SYMMETRIES;

ARTIFICIAL INTELLIGENCE; ENERGY DISSIPATION;

FRACTALS;

EID: 84870837308     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-35659-9_7     Document Type: Conference Paper

References (34)

1. Vitiello, G.: Fractals and the Fock-Bargmann Representation of Coherent States. In: Bruza, P., Sofge, D., Lawless, W., van Rijsbergen, K., Klusch, M., et al. (eds.) QI 2009. LNCS, vol. 5494, pp. 6-16. Springer, Heidelberg (2009)
2. Vitiello, G.: Coherent states, fractals and brain waves. New Mathematics and Natural Computation 5, 245-264 (2009);
3. Vitiello, G.: Topological defects, fractals and the structure of quantum field theory. In: Licata, I., Sakaji, A.J. (eds.) Vision of Oneness, pp. 155-180. Aracne Edizioni, Roma (2011)
4. Perelomov, A.: Generalized Coherent States and Their Applications. Springer, Heidelberg (1986)
5. Peitgen, H.O., Jürgens, H., Saupe, D.: Chaos and Fractals. New Frontiers of Science. Springer, Heidelberg (1986)
6. Fodor, J., Piattelli-Palmarini, M.: What Darwin got wrong. Farrar Straus and Giroux, New York (2010)
7. Piattelli-Palmarini, M., Uriagereka, J.: Still a bridge too far? Biolinguistic questions for grounding language on brains. Physics of Life Reviews 5, 207-224 (2008)
8. Bunde, A., Havlin, S. (eds.): Fractals in Science. Springer, Heidelberg (1995)
9. Bak, P., Creutz, M.: Fractals and self-organized criticality. In: Bunde, A., Havlin, S. (eds.) Fractals in Science, pp. 1-25. Springer, Heidelberg (1995)
10. Vitiello, G.: Fractals, coherent states and self-similarity induced noncommutative geometry. Phys. Lett. A 376, 2527-2532 (2012)
11. Celeghini, E., Rasetti, M., Vitiello, G.: Quantum dissipation. Annals Phys. 215, 156-170 (1992)
12. Blasone, M., Srivastava, Y.N., Vitiello, G., Widom, A.: Phase coherence and quantum Brownian motion. Annals Phys. 267, 61-74 (1998);
13. Graziano, E., Pashaev, O.K., Vitiello, G.: Dissipation and topologically massive gauge theories in pseudoeuclidean plane. Annals Phys. 252, 115-132 (1996)
14. Srivastava, Y.N., Vitiello, G., Widom, A.: Quantum dissipation and quantum noise. Annals Phys. 238, 200-207 (1995)
15. Vitiello, G.: Links. Relating different physical systems through the common QFT algebraic structure. In: Unruh, W.G., Schuetzhold, R. (eds.) Quantum Analogues: From Phase Transitions to Black Holes and Cosmology. Lectures Notes in Physics, vol. 718, pp. 165-205. Springer, Heidelberg (2007); hep-th/0610094
16. Blasone, M., Jizba, P., Vitiello, G.: Quantum Field Theory and its macroscopic manifestations. Imperial College Press, London (2011)
17. Schwinger, J.: Brownian Motion of a Quantum Oscillator. J. Math. Phys. 2, 407-433 (1961)
18. 't Hooft, G.: Quantum Gravity as a Dissipative Deterministic System. Class. Quant. Grav. 16, 3263-3279 (1999);
19. 't Hooft, G.: In: Basics and Highlights of Fundamental Physics. Erice (1999) [arXiv:hep-th/0003005]
20. 't Hooft, G.: A mathematical theory for deterministic quantummechanics. J. Phys.: Conf. Series 67, 012015 (2007)
21. Blasone, M., Jizba, P., Vitiello, G.: Dissipation and quantization. Phys. Lett. A 287, 205-210 (2001);
22. Blasone, M., Celeghini, E., Jizba, P., Vitiello, G.: Quantization, group contraction and zero point energy. Phys. Lett. A 310, 393-399 (2003);
23. Blasone, M., Jizba, P., Scardigli, F., Vitiello, G.: Dissipation and quantization in composite systems. Phys. Lett. A 373, 4106-4112 (2009)
24. Umezawa, H.,Matsumoto, H., Tachiki, M.: Thermo Field Dynamics and Condensed States. North-Holland, Amsterdam (1982)
25. Celeghini, E., De Martino, S., De Siena, S., Rasetti, M., Vitiello, G.: Quantum groups, coherent states, squeezing and lattice quantum mechanics. Annals Phys. 241, 50-67 (1995);
26. Celeghini, E., Rasetti, M., Tarlini, M., Vitiello, G.: SU(1, 1) Squeezed States as Damped Oscillators. Mod. Phys. Lett. B 3, 1213-1220 (1989);
27. Celeghini, E., Rasetti, M., Vitiello, G.: On squeezing and quantum groups. Phys. Rev. Lett. 66, 2056-2059 (1991)
28. Sivasubramanian, S., Srivastava, Y.N., Vitiello, G., Widom, A.: Quantum dissipation induced noncommutative geometry. Phys. Lett. A 311, 97-105 (2003)
29. Freeman, W.J., Livi, R., Obinata, M., Vitiello, G.: Cortical phase transitions, nonequilibrium thermodynamics and the time-dependent Ginzburg-Landau equation. Int. J. Mod. Phys. B 26, 1250035 (2012) arXiv:1110.3677v1 [physics.bio-ph]
30. Celeghini, E., De Martino, S., De Siena, S., Iorio, A., Rasetti, M., Vitiello, G.: Thermo field dynamics and quantum algebras. Phys. Lett. A 244, 455-461 (1998)
31. Iorio, A., Vitiello, G.: Quantum groups and Von Neumann theorem. Mod. Phys. Lett. B 8, 269-276 (1994)
32. Banerjee, R.: Dissipation and noncommutativity in planar quantum mechanics. Mod. Phys. Lett. A 17, 631-645 (2002);
33. Banerjee, R., Mukherjee, P.: A Canonical approach to dissipation. J. Phys. A: Math. Gen. 35, 5591-5598 (2002)
34. Chen, Y.S., Choi, W., Papanikolaou, S., Sethna, J.P.: Bending Crystals: Emergence of fractal dislocation structures. Phys. Rev. Lett. 105, 105501 (2010)