Effective Dynamics for the Maxwell–Lorentz System

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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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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Effective dynamics of magnetic vortices

Advances in Mathematics ◽

10.1016/j.aim.2005.05.017 ◽

2006 ◽

Vol 199 (2) ◽

pp. 448-498 ◽

Cited By ~ 21

Author(s):

S. Gustafson ◽

I.M. Sigal

Keyword(s):

Magnetic Vortices ◽

Effective Dynamics

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Effective Dynamics of Disordered Quantum Systems

Physical Review X ◽

10.1103/physrevx.6.031023 ◽

2016 ◽

Vol 6 (3) ◽

Cited By ~ 20

Author(s):

Chahan M. Kropf ◽

Clemens Gneiting ◽

Andreas Buchleitner

Keyword(s):

Quantum Systems ◽

Effective Dynamics

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THE CONFINEMENT MECHANISM IN YANG–MILLS THEORY?

Modern Physics Letters A ◽

10.1142/s021773239900050x ◽

1999 ◽

Vol 14 (06) ◽

pp. 447-457 ◽

Cited By ~ 1

Author(s):

JOSE A. MAGPANTAY

Keyword(s):

Gluon Propagator ◽

Statistical Treatment ◽

Gauge Condition ◽

Classical Solutions ◽

Spherically Symmetric ◽

Yang Mills ◽

Effective Dynamics ◽

Gauge Fixing ◽

Parallel Surfaces ◽

Nonlinear Gauge

Using the recently proposed nonlinear gauge condition [Formula: see text] we show the area law behavior of the Wilson loop and the linear dependence of the instantaneous gluon propagator. The field configurations responsible for confinement are those in the nonlinear sector of the gauge-fixing condition (the linear sector being the Coulomb gauge). The nonlinear sector is actually composed of "Gribov horizons" on the parallel surfaces ∂ · Aa=fa≠0. In this sector, the gauge field [Formula: see text] can be expressed in terms of fa and a new vector field [Formula: see text]. The effective dynamics of fa suggests nonperturbative effects. This was confirmed by showing that all spherically symmetric (in 4-D Euclidean) fa(x) are classical solutions and averaging these solutions using a Gaussian distribution (thereby treating these fields as random) lead to confinement. In essence the confinement mechanism is not quantum mechanical in nature but simply a statistical treatment of classical spherically symmetric fields on the "horizons" of ∂ · Aa=fa(x) surfaces.

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Phenomenological Implications of Modified Loop Cosmologies: An Overview

Frontiers in Astronomy and Space Sciences ◽

10.3389/fspas.2021.701417 ◽

2021 ◽

Vol 8 ◽

Author(s):

Bao-Fei Li ◽

Parampreet Singh ◽

Anzhong Wang

Keyword(s):

Initial Conditions ◽

Scale Effects ◽

Hybrid Approach ◽

Planck Scale ◽

Power Spectra ◽

Big Bang ◽

Hamiltonian Constraint ◽

Hybrid Approaches ◽

Effective Dynamics ◽

The Big Bang

In this paper, we first provide a brief review of the effective dynamics of two recently well-studied models of modified loop quantum cosmologies (mLQCs), which arise from different regularizations of the Hamiltonian constraint and show the robustness of a generic resolution of the big bang singularity, replaced by a quantum bounce due to non-perturbative Planck scale effects. As in loop quantum cosmology (LQC), in these modified models the slow-roll inflation happens generically. We consider the cosmological perturbations following the dressed and hybrid approaches and clarify some subtle issues regarding the ambiguity of the extension of the effective potential of the scalar perturbations across the quantum bounce, and the choice of initial conditions. Both of the modified regularizations yield primordial power spectra that are consistent with current observations for the Starobinsky potential within the framework of either the dressed or the hybrid approach. But differences in primordial power spectra are identified among the mLQCs and LQC. In addition, for mLQC-I, striking differences arise between the dressed and hybrid approaches in the infrared and oscillatory regimes. While the differences between the two modified models can be attributed to differences in the Planck scale physics, the permissible choices of the initial conditions and the differences between the two perturbation approaches have been reported for the first time. All these differences, due to either the different regularizations or the different perturbation approaches in principle can be observed in terms of non-Gaussianities.

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Implementation on Electronic Circuits and RTR Pragmatical Adaptive Synchronization: Time-Reversed Uncertain Dynamical Systems' Analysis and Applications

Abstract and Applied Analysis ◽

10.1155/2013/909721 ◽

2013 ◽

Vol 2013 ◽

pp. 1-10 ◽

Cited By ~ 3

Author(s):

Shih-Yu Li ◽

Cheng-Hsiung Yang ◽

Li-Wei Ko ◽

Chin-Teng Lin ◽

Zheng-Ming Ge

Keyword(s):

Adaptive Control ◽

Stability Theory ◽

Initial Conditions ◽

Stability Theorem ◽

Phase Portraits ◽

Adaptive Synchronization ◽

Complex Signal ◽

Uncertain Parameters ◽

Chaotic Motions ◽

Lorentz System

We expose the chaotic attractors of time-reversed nonlinear system, further implement its behavior on electronic circuit, and apply the pragmatical asymptotically stability theory to strictly prove that the adaptive synchronization of given master and slave systems with uncertain parameters can be achieved. In this paper, the variety chaotic motions of time-reversed Lorentz system are investigated through Lyapunov exponents, phase portraits, and bifurcation diagrams. For further applying the complex signal in secure communication and file encryption, we construct the circuit to show the similar chaotic signal of time-reversed Lorentz system. In addition, pragmatical asymptotically stability theorem and an assumption of equal probability for ergodic initial conditions (Ge et al., 1999, Ge and Yu, 2000, and Matsushima, 1972) are proposed to strictly prove that adaptive control can be accomplished successfully. The current scheme of adaptive control—by traditional Lyapunov stability theorem and Barbalat lemma, which are used to prove the error vector—approaches zero, as time approaches infinity. However, the core question—why the estimated or given parameters also approach to the uncertain parameters—remains without answer. By the new stability theory, those estimated parameters can be proved approaching the uncertain values strictly, and the simulation results are shown in this paper.

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Inferring effective dynamics in large-scale networks of cortical neurons

BMC Neuroscience ◽

10.1186/1471-2202-14-s1-p266 ◽

2013 ◽

Vol 14 (Suppl 1) ◽

pp. P266

Author(s):

Netta Haroush ◽

Shimon Marom ◽

Paolo Giudice ◽

Maurizio Mattia

Keyword(s):

Cortical Neurons ◽

Large Scale ◽

Effective Dynamics ◽

Large Scale Networks

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