Navegar

Colección

Datos Estadísticas

Parte de libro

Estamos trabajando para incorporar este artículo al repositorio

Abstract:

In textbooks on quantum mechanics, the laws of the theory are presented as applied to closed quantum systems. Although there is no universally accepted and definitive interpretation of the formalism, certain ideas allow us to think about the concept of quantum system. The state of a closed quantum system U is represented by a density operator ρ, and its unitary time evolution is governed by the Schrödinger equation. The study of phenomena such as relaxation and decoherence requires the introduction of the notion of open system, that is, a quantum system that interacts with other quantum systems. In general, the subsystems of a closed system U interact with each other. The state of each one of these subsystems is represented by a reduced operator ρ R , obtained from state ρ of the total system U by menas of the mathematical operation called partial trace. The reduced operator ρ R of a subsystem allows us to compute the mean value of all its observables. For this reason, the usual practice is to conceive open subsystems as legitimate quantum systems (for example, a particle), represented by their corresponding reduced states Rρ , whose evolution is not ruled by the Schrödinger equation. For this reason, an open quantum system can follow non-unitary evolutions, such as relaxation and decoherence [1]. Decoherence is a process originally proposed to explain the diagonalization of the reduced operator [2]. The orthodox version, environment-induced decoherence (EID), only applies to open systems because, as its name implies, considers the system under study embedded in an environment that induces decoherence. According to this approach, under certain conditions the reduced state of an open system becomes diagonal, and this fact makes possible its interpretation as a classical state [3]. Thus, decoherence allows us to study the quantum-to-classical transition of a quantum system, for instance, a quantum particle. In this paper we study the properties of open systems and we discuss their ontological status. First, we compare the mathematical properties of the quantum state with those of the reduced state. Following the road opened by Bernard d'Espagnat [4], we argue that although ρ and ρR have similar mathematical structure, they cannot be interpreted in the same fashion. In a second step, we study the phenomenon of decoherence in situations where the whole closed system can be split into an open system of interest and its environment in different ways [5 - 6]. We show that the lack of a criterion to define open system and environment is a manifestation of the relative nature of decoherence, and prevents us from conceiving the open system as a physical entity of the same ontological status as that of the closed system. Finally, based on [7], we propose a formalism designed to study the phenomena of relaxation and decoherence from a closed-system perspective. Since this formalism does not appeal to reduced states, it avoids the interpretive problems mentioned above. On the basis of this work we conclude that, given the problems of interpretation derived from the notion of reduced state, the use of the notion of open systems should be avoided. According to this viewpoint, the only legitimate quantum system is the whole closed system with its unitary evolution, and the study of its dynamical properties is sufficient to describe the phenomena of decoherence and relaxation. © 2014 by Nova Science Publishers, Inc. All rights reserved.

Registro:

Documento: Parte de libro
Título:The ontological status of open quantum systems sebastian fortin
Autor:Fortin, S.
Filiación:CONICET, Department of Physics, FCEN (UBA), Buenos Aires, Argentina
Palabras clave:Embedded systems; Mathematical operators; Ontology; Open systems; Closed quantum system; Dynamical properties; Environment-induced decoherence; Mathematical operations; Mathematical properties; Mathematical structure; Open quantum systems; Quantum to classical transition; Quantum optics
Año:2014
Página de inicio:387
Página de fin:410
Título revista:Advances in Quantum Systems Research
Título revista abreviado:Adv. in Quantum Syst. Res.
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97816294_v_n_p387_Fortin

Referencias:

  • Calzetta, E., Hu, B., (2008) Nonequilibrium Quantum Field Theory, , Cambridge University Press, Cambridge
  • Castagnino, M., Fortin, S., Laura, R., Lombardi, O., A general theoretical frameworkfor decoherence in open and closed systems (2008) Classical and Quantum Gravity, 25, p. 154002
  • Schlosshauer, M., (2007) Decoherence and the Quantum-to-Classical transition, , Springer, Berlin
  • d'Espagnat, B., (1976) Conceptual Foundations of Quantum Mechanics, , Benjamin, Reading MA
  • Castagnino, M., Fortin, S., Lombardi, O., Suppression of decoherence in a generalization of the spin-bath model (2010) Journal of Physics A: Mathematical and Theoretical, 43, p. 065304
  • Lombardi, O., Fortin, S., Castagnino, M., The problem of identifying the system and the environment in the phenomenon of decoherence (2012) Philosophical Issues in the Sciences, 3, pp. 161-174. , H. W. de Regt, S. Hartmann y S. Okasha (eds.), Springer Berlin
  • Castagnino, M., Fortin, S., Predicting decoherence in discrete models (2011) International Journal of Theoretical Physics, 50, pp. 2259-2267
  • Ballentine, L.E., (1990) Quantum Mechanics, , Prentice Hall, New York
  • Landau, L.D., Lifshitz, E.M., (1972) Mecánica Cuántica No-Relativista, , Reverté, Barcelona
  • Belot, G., Earman, J.J., Chaos out of order: Quantum mechanics, the correspondence principle and chaos (1997) Studies in History and Philosophy of Modern Physics, 28, pp. 147-182
  • Dito, G., Sternheimer, D., Deformation quantization: Genesis, developments and metamorphoses (2002) IRMA Lectures in Mathematics and Theoretical Physics, 1. , G. Halbout (ed.), W. de Gruyter & Co, Berlin
  • Kontsevich, M., Deformation quantization of poisson manifolds (2003) Letters in Mathematical Physics, 66, pp. 157-216
  • Zurek, W.H., Pointer basis of quantum apparatus: into what mixture does the wave packet collapse? (1981) Physical Review D, 24, pp. 1516-1524
  • Auletta, G., (2000) Foundations and Interpretation of Quantum Mechanics, , World Scientific, Singapore
  • Leggett, J., Reflections on the quantum measurement paradox (1987) Quantum Implications, pp. 85-104. , B. J. Hiley and F. D. Peat (eds.), Routledge and Kegan Paul, London
  • Bub, J., Quantum mechanics without the projecton postulate (1992) Foundations of Physics, 22, pp. 737-754
  • Anderson, P.W., Science: A 'dappled world' or a 'seamless web'? (2001) Studies in History and Philosophy of Modern Physics, 34, pp. 487-494
  • Healey, R., Dissipating the quantum measurement problem (1995) Topoi, 14, pp. 55-65
  • Bacciagaluppi, G., The role of decoherence in quantum mechanics The Stanford Encyclopedia of Philosophy, , http://plato.stanford.edu/archives/fall2008/entries/qm-decoherence/, E. N. Zalta (ed.), (Fall 2008 Edition)
  • Adler, S., Why decoherence has not solved the measurement problem: A response to P. W. Anderson (2003) Studies in History and Philosophy of Modern Physics, 34, pp. 135-142
  • Schrödinger, E., (2015) Mathematical Proceedings of the Cambridge Philosophical Society, 31, pp. 555-563
  • d'Espagnat, B., An elementary note about mixtures (2016) Preludes in Theoretical Physics, , A. De-Shalit, H. Feshbach and L. van Hove (eds.), North-Holland, Amsterdam
  • d'Espagnat, B., A note on measurement (2000) Physics Letters A, 282, pp. 133-137
  • Joos, E., Zeh, H.D., Kiefer, C., Giulini, D., Kupsch, J., Stamatescu, I.O., (2003) Decoherence and the Appearance of a Classical World in Quantum Theory, , Springer Verlag, Berlin
  • Zurek, W.H., Preferred sets of states, predictability, classicality and environment- induced decoherence (1994) Physical Origins of Time Asymmetry, , J. J. Halliwell, J. Pérez-Mercader and W. H. Zurek (eds.), Cambridge, Cambridge University Press
  • Zurek, W.H., Decoherence, einselection, and the existential interpretation (1998) Philosophical Transactions of the Royal Society, A356, pp. 1793-1821
  • Castagnino, M., Fortin, S., Non-Hermitian Hamiltonians in decoherence and equilibrium theory (2012) M. Castagnino and S. Fortin, Journal of Physics A: Mathematical and Theoretical, 45, p. 444009
  • Castagnino, M., Fortin, S., New bases for a general definition for the moving preferred basis (2011) Modern Physics Letters A, 26, pp. 2365-2373
  • Castagnino, M., Lombardi, O., Self-induced decoherence: A new approach (2004) Studies in History and Philosophy of Modern Physics, 35, pp. 73-107
  • Zurek, W.H., Environment-induced superselection rules (1982) Physical Review D, 26, pp. 1862-1880
  • Castagnino, M., Fortin, S., Lombardi, O., The effect of random coupling coefficientson decoherence (2010) Modern Physics Letters A, 25, pp. 611-617
  • Castagnino, M., Fortin, S., Lombardi, O., Is the decoherence of a system the result of its interaction with the environment? (2010) Modern Physics Letters A, 25, pp. 1431-1439
  • Omnés, R., Decoherence, irreversibility and the selection by decoherence of quantum states with definite probabilities (2002) Physical Review, A 65, p. 052120
  • Calzetta, E., Hu, B., (2008) Nonequilibrium Quantum Field Theory, , Cambridge U. Press, Cambridge
  • Castagnino, M., Fortin, S., Laura, R., Lombardi, O., A general theoretical framework for decoherence in open and closed systems (2008) Classical and Quantum Gravity, 25, p. 154002
  • Schlosshauer, M., (2007) Decoherence and the Quantum-to-Classical transition, , Springer, Berlin
  • d'Espagnat, B., (1976) Conceptual Foundations of Quantum Mechanics, , Benjamin, Reading MA
  • Castagnino, M., Fortin, S., Lombardi, O., Suppression of decoherence in a generalization of the spin-bath model (2010) Journal of Physics A: Mathematical and Theoretical, 43, p. 065304
  • Lombardi, O., Fortin, S., Castagnino, M., The problem of identifying the system and the environment in the phenomenon of decoherence (2012) Philosophical Issues in the Sciences, 3, pp. 161-174. , H. W. de Regt, S. Hartmann y S. Okasha (eds.), Springer, Berlin
  • Castagnino, M., Fortin, S., Predicting decoherence in discrete models (2011) International Journal of Theoretical Physics, 50, pp. 2259-2267

Citas:

---------- APA ----------
(2014) . The ontological status of open quantum systems sebastian fortin. Advances in Quantum Systems Research, 387-410.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97816294_v_n_p387_Fortin [ ]
---------- CHICAGO ----------
Fortin, S. "The ontological status of open quantum systems sebastian fortin" . Advances in Quantum Systems Research (2014) : 387-410.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97816294_v_n_p387_Fortin [ ]
---------- MLA ----------
Fortin, S. "The ontological status of open quantum systems sebastian fortin" . Advances in Quantum Systems Research, 2014, pp. 387-410.
Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97816294_v_n_p387_Fortin [ ]
---------- VANCOUVER ----------
Fortin, S. The ontological status of open quantum systems sebastian fortin. Adv. in Quantum Syst. Res. 2014:387-410.
Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97816294_v_n_p387_Fortin [ ]