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Grimaudo R, Valenti D, Spagnolo B, Troisi A, Filatrella G, Guarcello C. Axion Field Influence on Josephson Junction Quasipotential. MATERIALS (BASEL, SWITZERLAND) 2023; 16:5972. [PMID: 37687664 PMCID: PMC10488603 DOI: 10.3390/ma16175972] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2023] [Revised: 08/23/2023] [Accepted: 08/29/2023] [Indexed: 09/10/2023]
Abstract
The direct effect of an axion field on Josephson junctions is analyzed through the consequences on the effective potential barrier that prevents the junction from switching from the superconducting to the finite-voltage state. We describe a method to reliably compute the quasipotential with stochastic simulations, which allows for the spanning of the coupling parameter from weakly interacting axion to tight interactions. As a result, we obtain an axion field that induces a change in the potential barrier, therefore determining a significant detectable effect for such a kind of elusive particle.
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Affiliation(s)
- Roberto Grimaudo
- Dipartimento di Fisica e Chimica “E. Segrè”, Group of Theoretical Interdisciplinary Physics, Università degli Studi di Palermo, Viale delle Scienze, Ed. 18, 90128 Palermo, Italy; (R.G.); (D.V.); (B.S.)
| | - Davide Valenti
- Dipartimento di Fisica e Chimica “E. Segrè”, Group of Theoretical Interdisciplinary Physics, Università degli Studi di Palermo, Viale delle Scienze, Ed. 18, 90128 Palermo, Italy; (R.G.); (D.V.); (B.S.)
| | - Bernardo Spagnolo
- Dipartimento di Fisica e Chimica “E. Segrè”, Group of Theoretical Interdisciplinary Physics, Università degli Studi di Palermo, Viale delle Scienze, Ed. 18, 90128 Palermo, Italy; (R.G.); (D.V.); (B.S.)
- Radiophysics Department, Lobachevskii State University of Nizhnii Novgorod, 23 Gagarin Ave., Nizhnii Novgorod 603950, Russia
| | - Antonio Troisi
- Department of Sciences and Technologies, University of Sannio, Via De Sanctis, 82100 Benevento, Italy;
| | - Giovanni Filatrella
- Department of Sciences and Technologies, University of Sannio, Via De Sanctis, 82100 Benevento, Italy;
- Istituto Nazionale di Fisica Nucleare, Sezione di Napoli Gruppo Collegato di Salerno, Complesso Universitario di Monte S. Angelo, 80126 Napoli, Italy
| | - Claudio Guarcello
- Istituto Nazionale di Fisica Nucleare, Sezione di Napoli Gruppo Collegato di Salerno, Complesso Universitario di Monte S. Angelo, 80126 Napoli, Italy
- Dipartimento di Fisica “E.R. Caianiello”, Università di Salerno, Via Giovanni Paolo II, 132, 84084 Fisciano, Italy
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Ashwin P, Creaser J, Tsaneva-Atanasova K. Quasipotentials for coupled escape problems and the gate-height bifurcation. Phys Rev E 2023; 107:014213. [PMID: 36797857 DOI: 10.1103/physreve.107.014213] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2022] [Accepted: 12/21/2022] [Indexed: 06/18/2023]
Abstract
The escape statistics of a gradient dynamical system perturbed by noise can be estimated using properties of the associated potential landscape. More generally, the Freidlin and Wentzell quasipotential (QP) can be used for similar purposes, but computing this is nontrivial and it is only defined relative to some starting point. In this paper we focus on computing quasipotentials for coupled bistable units, numerically solving a Hamilton- Jacobi-Bellman type problem. We analyze noise induced transitions using the QP in cases where there is no potential for the coupled system. Gates (points on the boundary of basin of attraction that have minimal QP relative to that attractor) are used to understand the escape rates from the basin, but these gates can undergo a global change as coupling strength is changed. Such a global gate-height bifurcation is a generic qualitative transition in the escape properties of parametrized nongradient dynamical systems for small noise.
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Affiliation(s)
- Peter Ashwin
- Department of Mathematics and Statistics, University of Exeter, Exeter EX4 4QF, United Kingdom
| | - Jennifer Creaser
- Department of Mathematics and Statistics, University of Exeter, Exeter EX4 4QF, United Kingdom
| | - Krasimira Tsaneva-Atanasova
- Department of Mathematics and Statistics, and EPSRC Hub for Quantitative Modelling in Healthcare, University of Exeter, Exeter EX4 4QJ, United Kingdom and Institute for Advanced Study, Technical University of Munich, Lichtenbergstrasse 2 a, D-85748 Garching, Germany
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Li Y, Duan J, Liu X. Machine learning framework for computing the most probable paths of stochastic dynamical systems. Phys Rev E 2021; 103:012124. [PMID: 33601611 DOI: 10.1103/physreve.103.012124] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2020] [Accepted: 01/08/2021] [Indexed: 11/07/2022]
Abstract
The emergence of transition phenomena between metastable states induced by noise plays a fundamental role in a broad range of nonlinear systems. The computation of the most probable paths is a key issue to understanding the mechanism of transition behaviors. The shooting method is a common technique for this purpose to solve the Euler-Lagrange equation for the associated action functional, while losing its efficacy in high-dimensional systems. In the present work, we develop a machine learning framework to compute the most probable paths in the sense of Onsager-Machlup action functional theory. Specifically, we reformulate the boundary value problem of a Hamiltonian system and design a neural network to remedy the shortcomings of the shooting method. The successful applications of our algorithms to several prototypical examples demonstrate its efficacy and accuracy for stochastic systems with both (Gaussian) Brownian noise and (non-Gaussian) Lévy noise. This approach is effective in exploring the internal mechanisms of rare events triggered by random fluctuations in various scientific fields.
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Affiliation(s)
- Yang Li
- State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, 29 Yudao Street, Nanjing 210016, China.,Department of Applied Mathematics, College of Computing, Illinois Institute of Technology, Chicago, Illinois 60616, USA
| | - Jinqiao Duan
- Department of Applied Mathematics, College of Computing, Illinois Institute of Technology, Chicago, Illinois 60616, USA
| | - Xianbin Liu
- State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, 29 Yudao Street, Nanjing 210016, China
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Li Y, Duan J, Liu X, Zhang Y. Most probable dynamics of stochastic dynamical systems with exponentially light jump fluctuations. CHAOS (WOODBURY, N.Y.) 2020; 30:063142. [PMID: 32611085 DOI: 10.1063/5.0006292] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2020] [Accepted: 06/01/2020] [Indexed: 06/11/2023]
Abstract
The emergence of the exit events from a bounded domain containing a stable fixed point induced by non-Gaussian Lévy fluctuations plays a pivotal role in practical physical systems. In the limit of weak noise, we develop a Hamiltonian formalism under the Lévy fluctuations with exponentially light jumps for one- and two-dimensional stochastic dynamical systems. This formalism is based on a recently proved large deviation principle for dynamical systems under non-Gaussian Lévy perturbations. We demonstrate how to compute the most probable exit path and the quasi-potential by several examples. Meanwhile, we explore the impacts of the jump measure on the quasi-potential quantitatively and on the most probable exit path qualitatively. Results show that the quasi-potential can be well estimated by an approximate analytical expression. Moreover, we discover that although the most probable exit paths are analogous to the Gaussian case for the isotropic noise, the anisotropic noise leads to significant changes in the structure of the exit paths. These findings shed light on the underlying qualitative mechanism and quantitative feature of the exit phenomenon induced by non-Gaussian noise.
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Affiliation(s)
- Yang Li
- State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, 29 Yudao Street, Nanjing 210016, China
| | - Jinqiao Duan
- Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois 60616, USA
| | - Xianbin Liu
- State Key Laboratory of Mechanics and Control of Mechanical Structures, College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, 29 Yudao Street, Nanjing 210016, China
| | - Yanxia Zhang
- Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois 60616, USA
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