By employing Husimi quasiprobability distributions, we show that a bounded portion of an unbounded phase space induces a finite effective dimension in an infinite-dimensional Hilbert space. We compare our general expressions with numerical results for the spin-boson Dicke model in the chaotic energy regime, restricting its unbounded four-dimensional phase space to a classically chaotic energy shell. This effective dimension can be employed to characterize quantum phenomena in infinite-dimensional systems, such as localization and scarring.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1103/PhysRevE.105.064209 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Infinite-Dimensional Quantum Entropy: The Unified Entropy Case.
Entropy (Basel)
December 2024
Institute of Control & Computation Engineering, University of Zielona Góra, Licealna 9, 65-417 Zielona Góra, Poland.
Infinite-dimensional systems play an important role in the continuous-variable quantum computation model, which can compete with a more standard approach based on qubit and quantum circuit computation models. But, in many cases, the value of entropy unfortunately cannot be easily computed for states originating from an infinite-dimensional Hilbert space. Therefore, in this article, the unified quantum entropy (which extends the standard von Neumann entropy) notion is extended to the case of infinite-dimensional systems by using the Fredholm determinant theory.
View Article and Find Full Text PDFLearning-based optimal boundary control for parabolic distributed parameter system with actuator dynamics.
ISA Trans
January 2025
School of Automation, Central South University, Changsha 410083, China. Electronic address:
Article Synopsis
- * The challenge lies in managing boundary conditions in the ODE-style actuator dynamics, and this work is a pioneering effort in addressing optimal control under Neumann boundary conditions for this type of system.
- * A novel control algorithm is developed using neural networks, which promotes flexibility in control policies and ensures the stability of the system throughout the learning process, with successful results shown in simulations related to diffusion-reaction processes.
Kernel-Based Decentralized Policy Evaluation for Reinforcement Learning.
IEEE Trans Neural Netw Learn Syst
September 2024
Article Synopsis
- The research explores how multiple agents can work together in reinforcement learning to evaluate state-value functions while keeping their rewards private and using sampled state transitions.
- The study employs a regression-based iteration technique with gradient descent in a mathematical framework called reproducing kernel Hilbert space, and uses Nyström approximation to simplify calculations.
- The paper establishes new statistical error bounds for estimating value functions in decentralized settings and compares their method to previous approaches, specifically kernel temporal difference methods.
Quantum and Classical Spin-Network Algorithms for q-Deformed Kogut-Susskind Gauge Theories.
Phys Rev Lett
October 2023
Institute for Theoretical Physics, University of Innsbruck, 6020 Innsbruck, Austria and Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, 6020 Innsbruck, Austria.
Treating the infinite-dimensional Hilbert space of non-Abelian gauge theories is an outstanding challenge for classical and quantum simulations. Here, we employ q-deformed Kogut-Susskind lattice gauge theories, obtained by deforming the defining symmetry algebra to a quantum group. In contrast to other formulations, this approach simultaneously provides a controlled regularization of the infinite-dimensional local Hilbert space while preserving essential symmetry-related properties.
View Article and Find Full Text PDFSimultaneous Measurements of Noncommuting Observables: Positive Transformations and Instrumental Lie Groups.
Entropy (Basel)
August 2023
Center for Quantum Information and Control, University of New Mexico, Albuquerque, NM 87131, USA.
We formulate a general program for describing and analyzing continuous, differential weak, simultaneous measurements of noncommuting observables, which focuses on describing the measuring instrument , without states. The Kraus operators of such measuring processes are time-ordered products of fundamental , which generate nonunitary transformation groups that we call . The temporal evolution of the instrument is equivalent to the diffusion of a , defined relative to the invariant measure of the instrumental Lie group.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!