Bianchi I effective dynamics in quantum reduced loop gravity

AbstractThis paper is devoted to the analysis of Lindblad operators of Quantum Reset Models, describing the effective dynamics of tri-partite quantum systems subject to stochastic resets. We consider a chain of three independent subsystems, coupled by a Hamiltonian term. The two subsystems at each end of the chain are driven, independently from each other, by a reset Lindbladian, while the center system is driven by a Hamiltonian. Under generic assumptions on the coupling term, we prove the existence of a unique steady state for the perturbed reset Lindbladian, analytic in the coupling constant. We further analyze the large times dynamics of the corresponding CPTP Markov semigroup that describes the approach to the steady state. We illustrate these results with concrete examples corresponding to realistic open quantum systems.

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Formfactors of Relativistic Composite Particle Interactions in Unified Nonlinear Spinorfield Models

Zeitschrift für Naturforschung A ◽

10.1515/zna-1985-0717 ◽

1985 ◽

Vol 40 (7) ◽

pp. 752-773

Author(s):

H. Stumpf

Keyword(s):

Composite Particle ◽

Particle Interaction ◽

High Energy ◽

Field Theories ◽

Quantum Field Theories ◽

Statistical Interpretation ◽

Quantum Field ◽

Mapping Procedure ◽

Effective Dynamics ◽

Rough Approximation

Unified nonlinear spinorfield models are self-regularizing quantum field theories in which all observable (elementary and non-elementary) particles are assumed to be bound states of fermionic preon fields. Due to their large masses the preons themselves are confined and below the threshold of preon production the effective dynamics of the model is only concerned with bound state reactions. In preceding papers a functional energy representation, the statistical interpretation and the dynamical equations were derived and the effective dynamics for preon-antipreon boson states and three preon-fermion states (with corresponding anti-fermions) was studied in the low energy limit. The transformation of the functional energy representation of the spinorfield into composite particle functional operators produced a hierarchy of effective interactions at the composite particle level, the leading terms of which are identical with the functional energy representation of a phenomenological boson-fermion coupling theory. In this paper these calculations are extended into the high energy range. This leads to formfactors for the composite particle interaction terms which are calculated in a rough approximation and which in principle are observable. In addition, the mathematical and physical interpretation of nonlocal quantum field theories and the meaning of the mapping procedure, its relativistic invariance etc. are discussed.

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BIANCHI I SOLUTIONS OF EFFECTIVE QUADRATIC GRAVITY

International Journal of Modern Physics D ◽

10.1142/s021827181250037x ◽

2012 ◽

Vol 21 (04) ◽

pp. 1250037 ◽

Cited By ~ 4

Author(s):

DANIEL MÜLLER ◽

JULIANO A. DE DEUS

Keyword(s):

Numerical Solutions ◽

Relativity Theory ◽

De Sitter ◽

General Relativity Theory ◽

Spatial Metrics ◽

Effective Gravity ◽

Bianchi I ◽

Quadratic Theory ◽

Quadratic Gravity ◽

Planck Time

It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. Numerical solutions for the anisotropic generalization of the Friedmann "flat" model E3 for this effective gravity are given. It must be emphasized that although numeric, these solutions are exact in the sense that they depend only on the precision of the machine. The solutions are identified asymptotically in a certain sense. It is found solutions which asymptote de Sitter space, Minkowski space and a singularity. This work is a generalization for nondiagonal spatial metrics of a previous result obtained by one of us and a collaborator for Bianchi I spaces.

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Dimensionality Reduction of Complex Metastable Systems via Kernel Embeddings of Transition Manifolds

Journal of Nonlinear Science ◽

10.1007/s00332-020-09668-z ◽

2020 ◽

Vol 31 (1) ◽

Author(s):

Andreas Bittracher ◽

Stefan Klus ◽

Boumediene Hamzi ◽

Péter Koltai ◽

Christof Schütte

Keyword(s):

Stochastic Systems ◽

Reproducing Kernel ◽

Learning Algorithm ◽

Reproducing Kernel Hilbert Space ◽

Mathematical Framework ◽

Reaction Coordinates ◽

Effective Dynamics ◽

Distortion Bounds ◽

Low Dimensional ◽

Metastable Systems

AbstractWe present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework for the computation of optimal reaction coordinates of such systems that is based on learning a parameterization of a low-dimensional transition manifold in a certain function space. In this article, we enhance this approach by embedding and learning this transition manifold in a reproducing kernel Hilbert space, exploiting the favorable properties of kernel embeddings. Under mild assumptions on the kernel, the manifold structure is shown to be preserved under the embedding, and distortion bounds can be derived. This leads to a more robust and more efficient algorithm compared to the previous parameterization approaches.

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