Hyperbolic ring based formulation for thermo field dynamics, quantum dissipation, entanglement, and holography
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Regular Article - Theoretical Physics
Hyperbolic ring based formulation for thermo field dynamics, quantum dissipation, entanglement, and holography R. Cartas-Fuentevilla1, J. Berra-Montiel2,a , O. Meza-Aldama3 1
Instituto de Física, Universidad Autónoma de Puebla, Apartado postal J-48, 72570 Puebla Pue, Mexico Facultad de Ciencias, Universidad Autónoma de San Luis Potosí Campus Pedregal, Av. Parque Chapultepec 1610, Col. Privadas del Pedregal, 78217 San Luis Potosí, SLP, Mexico 3 Lux Systems, C.P. 27010, Blvrd Independencia 2002, Colonia Estrella, Torreón, Coah, Mexico
2
Received: 7 April 2020 / Accepted: 16 June 2020 © The Author(s) 2020
Abstract The classical and quantum formulations for open systems related to dissipative dynamics are constructed on a complex hyperbolic ring, following universal symmetry principles, and considering the double thermal fields approach for modeling the system of interest, and the environment. The hyperbolic rotations are revealed as an underlying internal symmetry for the dissipative dynamics, and a chemical potential is identified as conjugate variable to the charge operator, and thus a grand partition function is constructed. As opposed to the standard scheme, there are not patologies associated with the existence of many unitarity inequivalent representations on the hyperbolic ring, since the whole of the dissipative quantum dynamics is realized by choosing only one representation of the field commutation relations. Entanglement entropy operators for the subsystem of interest and the environment, are constructed as a tool for study the entanglement generated from the dissipation. The holographic perspectives of our results are discussed.
1 Antecedents, motivations, and results At microscopic level, the existence of quantum entanglement has been demonstrated in systems involving photons, electrons, ions, etc; however, although at macroscopic level the entanglement is sensitive to environmental perturbations, such a phenomenon has been inferred by several experiments involving macroscopic-scale objects; for example in [1], two massive micromechanical oscillators are coupled to an electromagnetic cavity, and the existence of entanglement is inflicted from the measurements of mechanical fluctuations, and analysis of the microwaves coming from the cavity. Furthermore, it has been shown experimentally that dissipation a e-mail:
generates entanglement between two macroscopic objects [2]; dissipative dynamics is intrinsically stable under perturbations, stabilizing the entanglement, in contrast to other schemes based on coherent evolution, which is always susceptible to undergo decoherence. The entanglement generated in this experiment corresponds to an EPR type one, and thus relevant in areas such as quantum information, cryptography, and others. Dissipative quantum field theories are of interest in high energy physics; for example, finite temperature techniques are necessary for estimating the transport coefficients of the quark-gluon plasma, and the holographic techniques hav
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