Abstract:
The Boltzmann echo (BE) is a measure of irreversibility and sensitivity to perturbations for non-isolated systems. Recently, different regimes of this quantity were described for chaotic systems. There is a perturbative regime where the BE decays with a rate given by the sum of a term depending on the accuracy with which the system is time reversed and a term depending on the coupling between the system and the environment. In addition, a parameter-independent regime, characterized by the classical Lyapunov exponent, is expected. In this paper, we study the behaviour of the BE in hyperbolic maps that are in contact with different environments. We analyse the emergence of the different regimes and show that the behaviour of the decay rate of the BE is strongly dependent on the type of environment. © 2011 The Royal Society.
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Artículo
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Título: | Irreversibility in quantum maps with decoherence |
Autor: | García-Mata, I.; Casabone, B.; Wisniacki, D.A. |
Filiación: | Departamento de Física, Laboratorio TANDAR, Comisión Nacional de Energía Atómica, Av. del Libertador 8250, C1429BNP Buenos Aires, Argentina Departamento de Física, FCEyN, Pabellón 1 Ciudad Universitaria, C1428EGA Buenos Aires, Argentina
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Palabras clave: | Decoherence; Quantum echoes; Quantum maps; Behavioral research; Decay (organic); Lyapunov methods; Quantum theory; Boltzmann; Decay rate; Decoherence; Isolated systems; Lyapunov exponent; Quantum echoes; Quantum maps; Time-reversed; Chaotic systems |
Año: | 2011
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Volumen: | 369
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Número: | 1935
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Página de inicio: | 278
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Página de fin: | 290
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DOI: |
http://dx.doi.org/10.1098/rsta.2010.0254 |
Título revista: | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
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Título revista abreviado: | Philos. Trans. R. Soc. A Math. Phys. Eng. Sci.
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ISSN: | 1364503X
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1364503X_v369_n1935_p278_GarciaMata |
Referencias:
- Peres, A., Stability of quantum motion in chaotic and regular systems (1984) Phys. Rev. A, 30, pp. 1610-1615. , doi:10.1103/PhysRevA.30.1610
- Jalabert, R.A., Pastawski, H.M., Environment-independent decoherence rate in classically chaotic systems (2001) Physical Review Letters, 86 (12), pp. 2490-2493. , DOI 10.1103/PhysRevLett.86.2490
- Jacquod, P., Silvestrov, P.G., Beenakker, C.W.J., Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo (2001) Phys. Rev. E, 64, p. 055203. , doi:10.1103/ PhysRevE.64.055203
- Gorin, T., Prosen, T., Seligman, T.H., Znidaric, M., Dynamics of Loschmidt echoes and fidelity decay (2006) Physics Reports, 435 (2-5), pp. 33-156. , DOI 10.1016/j.physrep.2006.09.003, PII S0370157306003310
- Petitjean, C., Jacquod, P., Decoherence, entanglement and irreversibility in quantum dynamical systems with few degrees of freedom (2009) Adv. Phys., 58, pp. 67-196. , doi:10.1080/00018730902831009
- Hahn, E.L., Spin echoes (1950) Phys. Rev., 80, pp. 580-594. , doi:10.1103/PhysRev.80.580
- Rhim, W.-K., Pines, A., Waugh, J.S., Violation of the spin-temperature hypothesis (1970) Phys. Rev. Lett., 25, pp. 218-220. , doi:10.1103/PhysRevLett.25.218
- Zhang, S., Meier, B.H., Ernst, R.R., Polarization echoes in NMR (1992) Phys. Rev. Lett., 69, pp. 2149-2151. , doi:10.1103/PhysRevLett.69.2149
- Pastawski, H.M., Levstein, P.R., Usaj, G., Raya, J., Hirschinger, J., A nuclear magnetic resonance answer to the Boltzmann Loschmidt controversy? (2000) Physica A, 283, pp. 166-170. , doi:10.1016/S0378-4371(00)00146-1
- Emerson, J., Weinstein, Y.S., Lloyd, S., Cory, D.G., Fidelity decay as an efficient indicator of quantum chaos (2002) Phys. Rev. Lett., 89, p. 284102. , doi:10.1103/PhysRevLett.89.284102
- Petitjean, C., Jacquod, Ph., Quantum reversibility and echoes in interacting systems (2006) Physical Review Letters, 97 (12), p. 124103. , http://oai.aps.org/oai?verb=GetRecord&Identifier=oai:aps.org: PhysRevLett.97.124103&metadataPrefix=oai_apsmeta_2, DOI 10.1103/PhysRevLett.97.124103
- Zurek, W.H., Decoherence, einselection, and the quantum origins of the classical (2003) Reviews of Modern Physics, 75 (3), pp. 715-775. , DOI 10.1103/RevModPhys.75.715
- Wang, W.-G., Casati, G., Li, B., Stability of quantum motion: Beyond Fermi-golden-rule and Lyapunov decay (2004) Phys. Rev. E, 69, p. 025201. , doi:10.1103/PhysRevE.69.025201
- Andersen, M.F., Kaplan, A., Grunzweig, T., Davidson, N., Decay of quantum correlations in atom optics billiards with chaotic and mixed dynamics (2006) Physical Review Letters, 97 (10), p. 104102. , http://oai.aps.org/oai?verb=GetRecord&Identifier=oai:aps.org: PhysRevLett.97.104102&metadataPrefix=oai_apsmeta_2, DOI 10.1103/PhysRevLett.97.104102
- Ares, N., Wisniacki, D.A., Loschmidt echo and the local density of states (2009) Phys. Rev. E, 80, p. 046216. , doi:10.1103/PhysRevE.80.046216
- Georgeot, B., Shepelyansky, D.L., Stable quantum computation of unstable classical chaos (2001) Physical Review Letters, 86 (23), pp. 5393-5396. , DOI 10.1103/PhysRevLett.86.5393
- Lévy, B., Georgeot, B., Shepelyansky, D.L., Quantum computing of quantum chaos in the kicked rotator model (2003) Phys. Rev. E, 67, p. 046220. , doi:10.1103/PhysRevE.67.046220
- Schack, R., Simulation on a quantum computer (2006) Informatik-Forschung und Entwicklung, 21, pp. 21-27. , doi:10.1007/s00450-006-0010-0
- Chirikov, B., Izrailev, F., Shepelyansky, D.L., Quantum chaos: Localization vs. ergodicity (1988) Physica D, 33, pp. 77-88. , doi:10.1016/S0167-2789(98)90011-2
- Leboeuf, P., Kurchan, J., Feingold, M., Arovas, D., Phase-space localization: Topological aspects of quantum chaos (1990) Phys. Rev. Lett., (65), pp. 3076-3079. , doi:10.1103/PhysRevLett.65.3076
- Kraus, K., (1983) States, Effects and Operations, , Berlin, Germany: Springer
- Lindblad, G., On the generators of quantum dynamical semigroups (1976) Commun. Math. Phys., 48, pp. 119-130. , doi:10.1007/BF01608499
- Schwinger, J., Unitary operator bases (1960) Proc. Natl Acad. Sci. USA, 46, pp. 570-579. , doi:10.1073/ pnas.46.4.570
- Bianucci, P., Miquel, C., Paz, J.P., Marcos Saraceno, M., (2002) Phys. Lett. A, 297, pp. 353-358. , doi:10.1016/S0375-9601(02)00391-2
- García-Mata, I., Saraceno, M., Spectral properties and classical decays in quantum open systems (2004) Phys. Rev. E, 69, p. 056211. , doi:10.1103/PhysRevE.69.056211
- Nonnenmacher, S., Spectral properties of noisy classical and quantum propagators (2003) Nonlinearity, 16 (5), pp. 1685-1713. , DOI 10.1088/0951-7715/16/5/309, PII S0951771503584225
- Basilio De Matos, M., Ozorio De Almeida, A.M., Quantization of Anosov maps (1995) Ann. Phys., (237), pp. 46-65. , doi:10.1006/aphy.1995.1003
- Keating, J.P., Mezzadri, F., Pseudo-symmetries of Anosov maps and spectral statistics (2000) Nonlinearity, 13, pp. 747-775. , doi:10.1088/0951-7715/13/3/313
- García-Mata, I., Saraceno, M., Spina, M.E., Classical decays in decoherent quantum maps (2003) Phys. Rev. Lett., 91, p. 064101. , doi:10.1103/PhysRevLett.91.064101
- Zurek, W.H., Paz, J.P., Decoherence, chaos and the second law (1994) Phys. Rev. Lett., 72, pp. 2508-2511. , doi:10.1103/PhysRevLett.72.2508
- Strunz, W.T., Percival, I.C., Classical mechanics from quantum state diffusion - a phase-space approach (1998) Journal of Physics A: Mathematical and General, 31 (7), pp. 1801-1814. , DOI 10.1088/0305-4470/31/7/014
- Carvalho, A.R.R., De Matos Filho, R.L., Davidovich, L., Environmental effects in the quantum-classical (2004) Phys. Rev. E, 70, p. 026211. , doi:10.1103/PhysRevE.70.026211
- Wisniacki, D.A., Toscano, F., Scaling laws in the quantum-to-classical transition in chaotic systems (2009) Phys. Rev. E, 79, p. 025203. , doi:10.1103/PhysRevE.79.025203
- Casabone, B., García-Mata, I., Wisniacki, D.A., Discrepancies between decoherence and the Loschmidt echo (2010) Europhys. Lett., (89), p. 50009. , doi:10.1209/0295-5075/89/50009
- Nielsen, A., Chuang, I.L., (2000) Quantum Computation and Quantum Information, , Cambridge, UK: Cambridge University Press
- Aolita, M.L., Garcia-Mata, I., Saraceno, M., Noise models for superoperators in the chord representation (2004) Physical Review A - Atomic, Molecular, and Optical Physics, 70 (6), pp. 0623011-0623019. , DOI 10.1103/PhysRevA.70.062301, 062301
- Schomerus, H., Lutz, E., Nonexponential decoherence and momentum subdiffusion in a quantum Lévy kicked rotator (2007) Physical Review Letters, 98 (26), p. 260401. , http://oai.aps.org/oai?verb=GetRecord&Identifier=oai:aps.org: PhysRevLett.98.260401&metadataPrefix=oai_apsmeta_2, DOI 10.1103/PhysRevLett.98.260401
Citas:
---------- APA ----------
García-Mata, I., Casabone, B. & Wisniacki, D.A.
(2011)
. Irreversibility in quantum maps with decoherence. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 369(1935), 278-290.
http://dx.doi.org/10.1098/rsta.2010.0254---------- CHICAGO ----------
García-Mata, I., Casabone, B., Wisniacki, D.A.
"Irreversibility in quantum maps with decoherence"
. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1935
(2011) : 278-290.
http://dx.doi.org/10.1098/rsta.2010.0254---------- MLA ----------
García-Mata, I., Casabone, B., Wisniacki, D.A.
"Irreversibility in quantum maps with decoherence"
. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 369, no. 1935, 2011, pp. 278-290.
http://dx.doi.org/10.1098/rsta.2010.0254---------- VANCOUVER ----------
García-Mata, I., Casabone, B., Wisniacki, D.A. Irreversibility in quantum maps with decoherence. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 2011;369(1935):278-290.
http://dx.doi.org/10.1098/rsta.2010.0254