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Barbosa ALR, Lima JRF, Pereira LFC. Wave transmission and its universal fluctuations in one-dimensional systems with Lévy-like disorder: Schrödinger, Klein-Gordon, and Dirac equations. Phys Rev E 2022; 106:054127. [PMID: 36559490 DOI: 10.1103/physreve.106.054127] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2022] [Accepted: 10/11/2022] [Indexed: 06/17/2023]
Abstract
We investigate the propagation of waves in one-dimensional systems with Lévy-type disorder. We perform a complete analysis of nonrelativistic and relativistic wave transmission submitted to potential barriers whose width, separation, or both follow Lévy distributions characterized by an exponent 0<α<1. For the first two cases, where one of the parameters is fixed, nonrelativistic and relativistic waves present anomalous localization, 〈T〉∝L^{-α}. However, for the latter case, in which both parameters follow a Lévy distribution, nonrelativistic and relativistic waves present a transition between anomalous and standard localization as the incidence energy increases relative to the barrier height. Moreover, we obtain the localization diagram delimiting anomalous and standard localization regimes, in terms of incidence angle and energy. Finally, we verify that transmission fluctuations, characterized by its standard deviation, are universal, independent of barrier architecture, wave equation type, incidence energy, and angle, further extending earlier studies on electronic localization.
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Affiliation(s)
- Anderson L R Barbosa
- Departamento de Física, Universidade Federal Rural de Pernambuco, 52171-900, Recife, PE, Brazil
| | - Jonas R F Lima
- Departamento de Física, Universidade Federal Rural de Pernambuco, 52171-900, Recife, PE, Brazil
| | - Luiz Felipe C Pereira
- Departamento de Física, Universidade Federal de Pernambuco, 50670-901, Recife, PE, Brazil
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2
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Stationary Probability Density Analysis for the Randomly Forced Phytoplankton–Zooplankton Model with Correlated Colored Noises. MATHEMATICS 2022. [DOI: 10.3390/math10142383] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Abstract
In this paper, we propose a stochastic phytoplankton–zooplankton model driven by correlated colored noises, which contains both anthropogenic and natural toxins. Using Khasminskii transformation and the stochastic averaging method, we first transform the original system into an Itô diffusion system. Afterwards, we derive the stationary probability density of the averaging amplitude equation by utilizing the corresponding Fokker–Planck–Kolmogorov equation. Then, the stability of the averaging amplitude is studied and the joint probability density of the original two-dimensional system is given. Finally, the theoretical results are verified by numerical simulations, and the effects of noise characteristics and toxins on system dynamics are further illustrated.
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Sabbar Y, Kiouach D, Rajasekar SP, El-Idrissi SEA. The influence of quadratic Lévy noise on the dynamic of an SIC contagious illness model: New framework, critical comparison and an application to COVID-19 (SARS-CoV-2) case. CHAOS, SOLITONS, AND FRACTALS 2022; 159:112110. [PMID: 35502416 PMCID: PMC9035369 DOI: 10.1016/j.chaos.2022.112110] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/05/2022] [Revised: 04/08/2022] [Accepted: 04/10/2022] [Indexed: 06/14/2023]
Abstract
This study concentrates on the analysis of a stochastic SIC epidemic system with an enhanced and general perturbation. Given the intricacy of some impulses caused by external disturbances, we integrate the quadratic Lévy noise into our model. We assort the long-run behavior of a perturbed SIC epidemic model presented in the form of a system of stochastic differential equations driven by second-order jumps. By ameliorating the hypotheses and using some new analytical techniques, we find the exact threshold value between extinction and ergodicity (persistence) of our system. The idea and analysis used in this paper generalize the work of N. T. Dieu et al. (2020), and offer an innovative approach to dealing with other random population models. Comparing our results with those of previous studies reveals that quadratic jump-diffusion has no impact on the threshold value, but it remarkably influences the dynamics of the infection and may worsen the pandemic situation. In order to illustrate this comparison and confirm our analysis, we perform numerical simulations with some real data of COVID-19 in Morocco. Furthermore, we arrive at the following results: (i) the time average of the different classes depends on the intensity of the noise (ii) the quadratic noise has a negative effect on disease duration (iii) the stationary density function of the population abruptly changes its shape at some values of the noise intensity. Mathematics Subject Classification 2020: 34A26; 34A12; 92D30; 37C10; 60H30; 60H10.
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Affiliation(s)
- Yassine Sabbar
- LPAIS Laboratory, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, Fez, Morocco
| | - Driss Kiouach
- LPAIS Laboratory, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, Fez, Morocco
| | - S P Rajasekar
- Department of Mathematics, Government Arts College for Women, Nilakottai 624202, Tamilnadu, India
| | - Salim El Azami El-Idrissi
- LPAIS Laboratory, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, Fez, Morocco
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van Kan A, Alexakis A, Brachet ME. Lévy on-off intermittency. Phys Rev E 2021; 103:052115. [PMID: 34134220 DOI: 10.1103/physreve.103.052115] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/12/2021] [Accepted: 04/27/2021] [Indexed: 11/07/2022]
Abstract
We present an alternative form of intermittency, Lévy on-off intermittency, which arises from multiplicative α-stable white noise close to an instability threshold. We study this problem in the linear and nonlinear regimes, both theoretically and numerically, for the case of a pitchfork bifurcation with fluctuating growth rate. We compute the stationary distribution analytically and numerically from the associated fractional Fokker-Planck equation in the Stratonovich interpretation. We characterize the system in the parameter space (α,β) of the noise, with stability parameter α∈(0,2) and skewness parameter β∈[-1,1]. Five regimes are identified in this parameter space, in addition to the well-studied Gaussian case α=2. Three regimes are located at 1<α<2, where the noise has finite mean but infinite variance. They are differentiated by β and all display a critical transition at the deterministic instability threshold, with on-off intermittency close to onset. Critical exponents are computed from the stationary distribution. Each regime is characterized by a specific form of the density and specific critical exponents, which differ starkly from the Gaussian case. A finite or infinite number of integer-order moments may converge, depending on parameters. Two more regimes are found at 0<α≤1. There, the mean of the noise diverges, and no critical transition occurs. In one case, the origin is always unstable, independently of the distance μ from the deterministic threshold. In the other case, the origin is conversely always stable, independently of μ. We thus demonstrate that an instability subject to nonequilibrium, power-law-distributed fluctuations can display substantially different properties than for Gaussian thermal fluctuations, in terms of statistics and critical behavior.
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Affiliation(s)
- Adrian van Kan
- Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Alexandros Alexakis
- Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Marc-Etienne Brachet
- Laboratoire de Physique de l'Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
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Dubkov AA, Dybiec B, Spagnolo B, Kharcheva A, Guarcello C, Valenti D. Statistics of residence time for Lévy flights in unstable parabolic potentials. Phys Rev E 2020; 102:042142. [PMID: 33212570 DOI: 10.1103/physreve.102.042142] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2020] [Accepted: 09/22/2020] [Indexed: 11/07/2022]
Abstract
We analyze the residence time problem for an arbitrary Markovian process describing nonlinear systems without a steady state. We obtain exact analytical results for the statistical characteristics of the residence time. For diffusion in a fully unstable potential profile in the presence of Lévy noise we get the conditional probability density of the particle position and the average residence time. The noise-enhanced stability phenomenon is observed in the system investigated. Results from numerical simulations are in very good agreement with analytical ones.
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Affiliation(s)
- Alexander A Dubkov
- Radiophysics Department, Lobachevsky State University of Nizhni Novgorod, Gagarin Avenue 23, 603950 Nizhni Novgorod, Russia
| | - Bartłomiej Dybiec
- Institute of Theoretical Physics and Mark Kac Center for Complex Systems Research, Jagiellonian University, ul. St. Łojasiewicza 11, 30-348 Kraków, Poland
| | - Bernardo Spagnolo
- Radiophysics Department, Lobachevsky State University of Nizhni Novgorod, Gagarin Avenue 23, 603950 Nizhni Novgorod, Russia.,Dipartimento di Fisica e Chimica "Emilio Segrè," Group of Interdisciplinary Theoretical Physics, Università di Palermo and CNISM, Unità di Palermo, Viale delle Scienze, Edificio 18, I-90128 Palermo, Italy.,Istituto Nazionale di Fisica Nucleare, Sezione di Catania, Via S. Sofia 64, I-90123 Catania, Italy
| | - Anna Kharcheva
- Radiophysics Department, Lobachevsky State University of Nizhni Novgorod, Gagarin Avenue 23, 603950 Nizhni Novgorod, Russia.,Dipartimento di Fisica e Chimica "Emilio Segrè," Group of Interdisciplinary Theoretical Physics, Università di Palermo and CNISM, Unità di Palermo, Viale delle Scienze, Edificio 18, I-90128 Palermo, Italy
| | - Claudio Guarcello
- Dipartimento di Fisica "E. R. Caianiello," Università di Salerno, Via Giovanni Paolo II 132, I-84084 Fisciano (SA), Italy.,INFN, Sezione di Napoli Gruppo Collegato di Salerno, Complesso Universitario di Monte S. Angelo, I-80126 Napoli, Italy
| | - Davide Valenti
- Dipartimento di Fisica e Chimica "Emilio Segrè," Group of Interdisciplinary Theoretical Physics, Università di Palermo and CNISM, Unità di Palermo, Viale delle Scienze, Edificio 18, I-90128 Palermo, Italy.,CNR-IRIB, Consiglio Nazionale delle Ricerche-Istituto per la Ricerca e l'Innovazione Biomedica, Via Ugo La Malfa 153, 90146 Palermo, Italy
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Pountougnigni OV, Yamapi R, Tchawoua C, Pierro V, Filatrella G. Detection of signals in presence of noise through Josephson junction switching currents. Phys Rev E 2020; 101:052205. [PMID: 32575208 DOI: 10.1103/physreve.101.052205] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2020] [Accepted: 04/13/2020] [Indexed: 11/07/2022]
Abstract
Josephson junctions can be employed to reveal a sinusoidal signal in presence of Gaussian noise. To mimic realistic setups, the detection is performed linearly ramping the bias current until a switch to the finite voltage occurs; the analysis of the resulting switching currents can be exploited to decide about the presence of the harmonic drive. The signal is applied in two conditions: with an unknown initial phase (incoherent strategy) and with a known initial phase (coherent strategy). In both conditions, the analysis of the efficiency of the detection, performed through the signal-to-noise ratio, as estimated by the Kumar-Carrol index, shows that the dependence upon the Josephson junction ramp rate is beneficial, especially for relatively fast speed. One can conclude that the collection of the switching currents is a robust technique, and thus it is possible to exploit the advantages of a predetermined finite time to collect the data.
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Affiliation(s)
- O V Pountougnigni
- Laboratory of Mechanics and Materials, Department of Physics, Faculty of Science, University of Yaoundé I, Box 812, Yaoundé, Cameroon
| | - R Yamapi
- Fundamental Physics Laboratory, Physics of Complex System Group, Department of Physics, Faculty of Science, University of Douala, Box 24 157 Douala, Cameroon
| | - C Tchawoua
- Laboratory of Mechanics and Materials, Department of Physics, Faculty of Science, University of Yaoundé I, Box 812, Yaoundé, Cameroon
| | - V Pierro
- Department of Engineering, and Gruppo Collegato Salerno INFN, Corso Garibaldi, I-82100 Benevento, Italy
| | - G Filatrella
- Department of Sciences and Technologies, and INFN, Gruppo Collegato Salerno, University of Sannio, Via F. De Sanctis, I-82100 Benevento, Italy
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Revin LS, Pankratov AL, Gordeeva AV, Yablokov AA, Rakut IV, Zbrozhek VO, Kuzmin LS. Microwave photon detection by an Al Josephson junction. BEILSTEIN JOURNAL OF NANOTECHNOLOGY 2020; 11:960-965. [PMID: 32647595 PMCID: PMC7323616 DOI: 10.3762/bjnano.11.80] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/08/2020] [Accepted: 06/10/2020] [Indexed: 05/14/2023]
Abstract
An aluminium Josephson junction (JJ), with a critical current suppressed by a factor of three compared with the maximal value calculated from the gap, is experimentally investigated for application as a threshold detector for microwave photons. We present the preliminary results of measurements of the lifetime of the superconducting state and the probability of switching by a 9 GHz external signal. We found an anomalously large lifetime, not described by the Kramers' theory for the escape time over a barrier under the influence of fluctuations. We explain it by the phase diffusion regime, which is evident from the temperature dependence of the switching current histograms. Therefore, phase diffusion allows for a significant improvement of the noise immunity of a device, radically decreasing the dark count rate, but it will also decrease the single-photon sensitivity of the considered threshold detector. Quantization of the switching probability tilt as a function of the signal attenuation for various bias currents through the JJ is observed, which resembles the differentiation between N and N + 1 photon absorption.
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Affiliation(s)
- Leonid S Revin
- Institute for Physics of Microstructures of RAS, GSP-105, Nizhny Novgorod, 603950, Russia
- Center of Cryogenic Nanoelectronics, Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia
| | - Andrey L Pankratov
- Institute for Physics of Microstructures of RAS, GSP-105, Nizhny Novgorod, 603950, Russia
- Center of Cryogenic Nanoelectronics, Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia
- Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
| | - Anna V Gordeeva
- Center of Cryogenic Nanoelectronics, Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia
| | - Anton A Yablokov
- Institute for Physics of Microstructures of RAS, GSP-105, Nizhny Novgorod, 603950, Russia
- Center of Cryogenic Nanoelectronics, Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia
| | - Igor V Rakut
- Center of Cryogenic Nanoelectronics, Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia
- Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, Russia
| | - Victor O Zbrozhek
- Center of Cryogenic Nanoelectronics, Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia
| | - Leonid S Kuzmin
- Center of Cryogenic Nanoelectronics, Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia
- Chalmers University of Technology, SE-41296 Gothenburg, Sweden
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Lima JRF, Pereira LFC, Barbosa ALR. Dirac wave transmission in Lévy-disordered systems. Phys Rev E 2019; 99:032118. [PMID: 30999483 DOI: 10.1103/physreve.99.032118] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2018] [Indexed: 11/07/2022]
Abstract
We investigate the propagation of electronic waves described by the Dirac equation subject to a Lévy-type disorder distribution. Our numerical calculations, based on the transfer matrix method, in a system with a distribution of potential barriers show that it presents a phase transition from anomalous to standard to anomalous localization as the incidence energy increases. In contrast, electronic waves described by the Schrödinger equation do not present such transitions. Moreover, we obtain the phase diagram delimiting anomalous and standard localization regimes, in the form of an incidence angle versus incidence energy diagram, and argue that transitions can also be characterized by the behavior of the dispersion of the transmission. We attribute this transition to an abrupt reduction in the transmittance of the system when the incidence angle is higher than a critical value which induces a decrease in the transmission fluctuations.
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Affiliation(s)
- Jonas R F Lima
- Departamento de Física, Universidade Federal Rural de Pernambuco, 52171-900, Recife, PE, Brazil
| | - Luiz Felipe C Pereira
- Departamento de Física, Universidade Federal do Rio Grande do Norte, 59078-970, Natal, RN, Brazil
| | - Anderson L R Barbosa
- Departamento de Física, Universidade Federal Rural de Pernambuco, 52171-900, Recife, PE, Brazil
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Giubileo F, Martucciello N, Di Bartolomeo A. Focus on graphene and related materials. NANOTECHNOLOGY 2017; 28:410201. [PMID: 28901299 DOI: 10.1088/1361-6528/aa848d] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
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