Time's Arrow and Irreversibility in Time‐Asymmetric Quantum Mechanics

References

• Albert , D. 2000 . Time and chance , Cambridge : Harvard University Press .
   Google Scholar
• Antoniou , I. , Gadella , M. and Pronko , G. 1998 . Gamow vectors for degenerate scattering resonances . Journal of Mathematical Physics , 39 : 2459 – 75 .
   Web of Science ®Google Scholar
• Antoniou , I. and Prigogine , I. 1993 . Intrinsic irreversibility and integrability of dynamics . Physica A , 192 : 443 – 64 .
   Web of Science ®Google Scholar
• Arntzenius , F. 2004 . Time reversal operations, representations of the Lorentz group, and the direction of time . Studies in History and Philosophy of Modern Physics , 35 : 31 – 44 .
   Web of Science ®Google Scholar
• Bishop , R. 1999 . Chaotic Dynamics, Indeterminacy and Free Will Presented to the Faculty of the Graduate School of The University of Texas at Austin
   Google Scholar
• Bishop , R. 2003 . A tale of two arrows . International Journal of Theoretical Physics , 42 : 2371 – 77 .
   Web of Science ®Google Scholar
• Bishop , R. 2004a . Arrow of time in rigged Hilbert space quantum mechanics . International Journal of Theoretical Physics , 43 : 1675 – 87 .
   Web of Science ®Google Scholar
• Bishop , R. 2004b . Nonequilibrium statistical mechanics Brussels–Austin style . Studies in History and Philosophy of Modern Physics , 35 : 1 – 30 .
   Web of Science ®Google Scholar
• Bohm , A. 1981 . Resonance poles and Gamow vectors in the rigged Hilbert space formulation of quantum mechanics . Journal of Mathematical Physics , 22 : 2813 – 23 .
   Web of Science ®Google Scholar
• Bohm , A. , Antoniou , I. and Kielanowski , P. 1995 . A quantum mechanical arrow of time and the semigroup time evolution of Gamow vectors . Journal of Mathematical Physics , 36 : 2593 – 604 .
   Web of Science ®Google Scholar
• Bohm , A. and Gadella , M. 1989 . Dirac Kets, Gamow vectors and Gel’fand triplets, Springer Lecture Notes in Physics , Vol. 348 , New York : Springer .
   Google Scholar
• Bohm , A. , Gadella , M. and Mithaiwala , M. 2003 . “ Time asymmetric quantum theory: foundations and applications ” . In The physics of communication, Proceedings of the XXII Solvay Conference on Physics , Singapore : World Scientific .
   Google Scholar
• Bohm , A. and Harshamn , N. L. 1998 . “ Quantum theory in the rigged Hilbert space. Irreversibility from causality ” . In Lectures Notes in Physics 504 , Edited by: Bohm , A. , Doebner , H. D. and Kielanowski , P. Berlin : Springer .
   Google Scholar
• Bohm , A. , Loewe , M. and van de Ven , B. 2003 . Time asymmetic quantum theory. Modifying and axiom of quantum physics . Fortschritte der Physik , 51 : 551 – 68 .
   Web of Science ®Google Scholar
• Bohm , A. , Maxson , S. , Loewe , M. and Gadella , M. 1997 . Quantum mechanical irreversibility . Physica A , 236 : 485 – 549 .
   Web of Science ®Google Scholar
• Bohm , A. and Scurek , R. 2000 . “ The phenomenological preparation‐registration arrow of time and its semigroup representation in the RHS quantum theory ” . In Trends in quantum mechanics , Edited by: Doebner , H. D. , Ali , S. T. , Keyl , M. and Werner , R. F. Singapore : World Scientific .
   Google Scholar
• Bohm , A. and Wickramasekara , S. 2002 . “ A new topology for an axiom of quantum mechanics ” . In Irreversible Quantum Dynamics, Lecture Notes in Physics , Vol. 622 , Berlin : Springer .
   Google Scholar
• Castagnino , M. , Gadella , M. , Id Betan , R. and Laura , R. 2001 . Gamow functionals on operator algebras . Journal of Physics A , 34 : 10067 – 84 .
   Google Scholar
• Castagnino , M. , Id Betan , R. , Laura , R. and Liotta , R. 2002 . Quantum decay processes and Gamov states . Journal of Physics A , 35 : 6055 – 74 .
   Google Scholar
• Castagnino , M. , Lara , L. and Lombardi , O. 2003a . The cosmological origin of time‐asymmetry . Classical and Quantum Gravity , 20 : 369 – 91 .
   Web of Science ®Google Scholar
• Castagnino , M. , Lara , L. and Lombardi , O. 2003b . The direction of time: from the global arrow to the local arrow . International Journal of Theoretical Physics , 42 : 2487 – 504 .
   Web of Science ®Google Scholar
• Castagnino , M. and Laura , R. 1997 . Minimal irreversible quantum mechanics: Pure‐state formalism . Physical Review A , 56 : 108 – 19 .
   Web of Science ®Google Scholar
• Castagnino , M. and Lombardi , O. 2004 . The generic nature of the global and non‐entropic arrow of time and the double role of the energy‐momentum tensor . Journal of Physics A , 37 : 4445 – 63 .
   Google Scholar
• Castagnino , M. and Lombardi , O. 2005a . “ A global and non‐entropic approach to the problem of the arrow of time ” . In Spacetime physics research trends. Horizons in world physics , Edited by: Reimer , A. Vol. 248 , Hauppauge, NY : Nova .
   Google Scholar
• Castagnino , M. and Lombardi , O. 2005b . “ The global non‐entropic arrow of time: from global geometrical asymmetry to local energy flow ” . In Synthese forthcoming
   Google Scholar
• Castagnino , M. , Lombardi , O. and Lara , L. 2003 . The global arrow of time as a geometrical property of the universe . Foundations of Physics , 33 : 877 – 912 .
   Web of Science ®Google Scholar
• Civitarese , O. and Gadella , M. 2004 . Physical and mathematical aspects of Gamow states . Physics Reports , 396 : 41 – 113 .
   Google Scholar
• Earman , J. 2002 . What time reversal invariance is and why it matters . International Studies in the Philosophy of Science , 16 : 245 – 64 .
   Google Scholar
• Ehrenfest , P. and Ehrenfest , T. 1959 . The conceptual foundations of the statistical approach in mechanics , Ithaca, NY : Cornell University Press . (original 1912)
   Google Scholar
• Gadella , M. 1983 . A description of virtual scattering states in the rigged Hilbert space formulation of quantum mechanics . Journal of Mathematical Physics , 24 : 2142 – 45 .
   Web of Science ®Google Scholar
• Gadella , M. 1984 . On the RHS description of resonances and virtual states . Journal of Mathematical Physics , 25 : 2481 – 85 .
   Web of Science ®Google Scholar
• Gadella , M. 1997 . Derivation of Gamow vectors for resonances in cut‐off potentials . Letters in Mathematical Physics , 41 : 279 – 90 .
   Web of Science ®Google Scholar
• Gadella , M. and de la Madrid , R. 1999 . Resonances and time reversal operator in rigged Hilbert spaces . International Journal of Theoretical Physics , 38 : 93 – 113 .
   Web of Science ®Google Scholar
• Gamow , G. 1928 . Zur Quantentheorie des Atomkernes . Zeitschrift für Physik , 51 : 204 – 212 .
   Google Scholar
• Gel’fand , I. and Vilenkin , N. 1964 . Generalized functions, vol. 3: Theory of differential equations , New York : Academic Press .
   Google Scholar
• Grossmann , A. 1964 . Nested Hilbert spaces in quantum mechanics I . Journal of Mathematical Physics , 5 : 1025 – 37 .
   Web of Science ®Google Scholar
• Lax , P. and Phillips , R. 1979 . Scattering theory , New York : Academic Press .
   Google Scholar
• Lindblad , G. and Nagel , B. 1970 . Continuous bases for unitary irreducible representation of SU (1,1) . Annales de l’Institut Henri Poincaré A , 13 : 27 – 56 .
   Web of Science ®Google Scholar
• Ludwig , G. 1983–1985 . Foundations of quantum mechanics , vol. I and vol. II , Berlin : Springer .
   Google Scholar
• Misra , B. and Prigogine , I. 1983 . Irreversibility and nonlocality . Letters in Mathematical Physics , 7 : 421 – 29 .
   Web of Science ®Google Scholar
• Paley , R. and Wiener , N. 1934 . Fourier transforms in the complex domain , New York : American Mathematical Society .
   Google Scholar
• Penrose , R. 1979 . “ Singularities and time asymmetry ” . In General relativity, an Einstein centenary survey , Edited by: Hawking , S. and Israel , W. Cambridge : Cambridge University Press .
   Google Scholar
• Petrosky , T. and Prigogine , I. 1997 . The extension of classical dynamics for unstable Hamiltonian systems . Computers and Mathematics with Applications , 34 : 1 – 44 .
   Web of Science ®Google Scholar
• Price , H. 1996 . Time’s arrow and the Archimedes’ point , Oxford : Oxford University Press .
   Google Scholar
• Prigogine , I. 1980 . From being to becoming. Time and complexity in the physical sciences , New York : W. H. Freeman .
   Google Scholar
• Prigogine , I. and George , C. 1983 . The second law as a selection principle: The microscopic theory of dissipative processes in quantum systems . Proceedings of the National Academy of the Sciences of the United States of America , 80 : 4590 – 94 .
   PubMed Web of Science ®Google Scholar
• Sachs , R. G. 1987 . The physics of time‐reversal , Chicago : University of Chicago Press .
   Google Scholar
• Schäffer , H. H. 1970 . Topological vector spaces , New York : Heidelberg .
   Google Scholar
• Titchmarsh , E. C. 1937 . Introduction to the theory of Fourier integrals , Oxford : Clarendon Press .
   Google Scholar
• van Winter , C. 1974 . Complex dynamical variables for multiparticle systems with analytic interactions. I . Journal of Mathematical Analysis and Applications , 47 : 633 – 70 .
   Web of Science ®Google Scholar