1
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Cai X, Feng Y, Ren J, Peng Y, Zheng Y. Quantum decoherence dynamics in stochastically fluctuating environments. J Chem Phys 2024; 161:044106. [PMID: 39041876 DOI: 10.1063/5.0217863] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2024] [Accepted: 07/08/2024] [Indexed: 07/24/2024] Open
Abstract
We theoretically study the decoherence of a two-level quantum system coupled to noisy environments exhibiting linear and quadratic fluctuations within the framework of a stochastic Liouville equation. It is shown that the intrinsic energy levels of the quantum system renormalize under either the linear or quadratic influence of the environmental noise. In the case of quadratic dependence, the renormalization of the energy levels of the system emerges even if the environmental noise exhibits stationary statistical properties. This is in contrast to the case under linear influence, where the intrinsic energy levels of the system renormalize only if the environmental noise displays nonstationary statistics. We derive the analytical expressions of the decoherence function in the cases where the fluctuation of the frequency difference depends linearly and quadratically on the nonstationary Ornstein-Uhlenbeck noise (OUN) and random telegraph noise (RTN) processes, respectively. In the case of the linear dependence of the OUN, the environmental nonstationary statistical property can enhance the dynamical decoherence. However, the nonstationary statistics of the environmental noise can suppress the quantum decoherence in this case under the quadratic influence of the OUN. In the presence of the RTN, the quadratic influence of the environmental noise does not give rise to decoherence but only causes a determinate frequency renormalization in dynamical evolution. The environmental nonstationary statistical property can suppress the quantum decoherence of the case under the linear influence of the RTN.
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Affiliation(s)
- Xiangji Cai
- School of Science, Shandong Jianzhu University, Jinan 250101, China
| | - Yanyan Feng
- School of Science, Shandong Jianzhu University, Jinan 250101, China
| | - Jing Ren
- School of Science, Shandong Jianzhu University, Jinan 250101, China
| | - Yonggang Peng
- School of Physics, Shandong University, Jinan 250100, China
| | - Yujun Zheng
- School of Physics, Shandong University, Jinan 250100, China
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2
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Analysis of Train Car-Body Comfort Zonal Distribution by Random Vibration Method. APPLIED SCIENCES-BASEL 2022. [DOI: 10.3390/app12157442] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
With the increase in train speeds on high-speed railways, the excitation frequency of track irregularities increases, which has a negative impact on train comfort and opposes the passengers’ desire for high ride comfort. In addition, the uncertainty of train comfort results from the stationary randomness of track irregularities and the different zonal distribution in the car body. Therefore, the application of the stationary random vibration method to analyze the zonal distribution of train comfort and the relevant influencing factors is important to guarantee the passengers’ comfortable experience in each ride and to provide a theoretical basis for comfort optimization. First, the train was modeled using eight independent vehicle elements. Second, the pseudo-excitation method was applied to obtain the theoretical zonal distribution of the Sperling index, an indicator of comfort, via the linearity of the power spectrum density of train acceleration. Third, considering various factors affecting train comfort, the results were compared with those calculated using the Monte Carlo method. It was found that the most comfortable area was located slightly in the front of the center of the car body. Improving track irregularities and reasonably controlling the speed of a train will increase the train’s comfort, while it will deteriorate with a loss in car-body mass and damage to the secondary suspension system.
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3
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Fox ZR, Barkai E, Krapf D. Aging power spectrum of membrane protein transport and other subordinated random walks. Nat Commun 2021; 12:6162. [PMID: 34697310 PMCID: PMC8546023 DOI: 10.1038/s41467-021-26465-8] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2021] [Accepted: 10/04/2021] [Indexed: 11/09/2022] Open
Abstract
Single-particle tracking offers detailed information about the motion of molecules in complex environments such as those encountered in live cells, but the interpretation of experimental data is challenging. One of the most powerful tools in the characterization of random processes is the power spectral density. However, because anomalous diffusion processes in complex systems are usually not stationary, the traditional Wiener-Khinchin theorem for the analysis of power spectral densities is invalid. Here, we employ a recently developed tool named aging Wiener-Khinchin theorem to derive the power spectral density of fractional Brownian motion coexisting with a scale-free continuous time random walk, the two most typical anomalous diffusion processes. Using this analysis, we characterize the motion of voltage-gated sodium channels on the surface of hippocampal neurons. Our results show aging where the power spectral density can either increase or decrease with observation time depending on the specific parameters of both underlying processes.
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Affiliation(s)
- Zachary R Fox
- School of Biomedical Engineering, Colorado State University, Fort Collins, CO, USA
- The Center for Nonlinear Studies and Computational and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, NM, USA
| | - Eli Barkai
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan, Israel
| | - Diego Krapf
- School of Biomedical Engineering, Colorado State University, Fort Collins, CO, USA.
- Electrical and Computer Engineering, Colorado State University, Fort Collins, CO, USA.
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4
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Yamamoto E, Akimoto T, Mitsutake A, Metzler R. Universal Relation between Instantaneous Diffusivity and Radius of Gyration of Proteins in Aqueous Solution. PHYSICAL REVIEW LETTERS 2021; 126:128101. [PMID: 33834804 DOI: 10.1103/physrevlett.126.128101] [Citation(s) in RCA: 48] [Impact Index Per Article: 16.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/05/2020] [Accepted: 02/09/2021] [Indexed: 06/12/2023]
Abstract
Protein conformational fluctuations are highly complex and exhibit long-term correlations. Here, molecular dynamics simulations of small proteins demonstrate that these conformational fluctuations directly affect the protein's instantaneous diffusivity D_{I}. We find that the radius of gyration R_{g} of the proteins exhibits 1/f fluctuations that are synchronous with the fluctuations of D_{I}. Our analysis demonstrates the validity of the local Stokes-Einstein-type relation D_{I}∝1/(R_{g}+R_{0}), where R_{0}∼0.3 nm is assumed to be a hydration layer around the protein. From the analysis of different protein types with both strong and weak conformational fluctuations, the validity of the Stokes-Einstein-type relation appears to be a general property.
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Affiliation(s)
- Eiji Yamamoto
- Department of System Design Engineering, Keio University, Yokohama, Kanagawa 223-8522, Japan
| | - Takuma Akimoto
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
| | - Ayori Mitsutake
- Department of Physics, Meiji University, Kawasaki, Kanagawa 214-8571, Japan
| | - Ralf Metzler
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
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5
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Ray S, Reuveni S. Diffusion with resetting in a logarithmic potential. J Chem Phys 2020; 152:234110. [DOI: 10.1063/5.0010549] [Citation(s) in RCA: 41] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023] Open
Affiliation(s)
- Somrita Ray
- School of Chemistry, The Center for Physics and Chemistry of Living Systems, The Raymond and Beverly Sackler Center for Computational Molecular and Materials Science, and The Ratner Center for Single Molecule Science, Tel Aviv University, Tel Aviv 69978, Israel
| | - Shlomi Reuveni
- School of Chemistry, The Center for Physics and Chemistry of Living Systems, The Raymond and Beverly Sackler Center for Computational Molecular and Materials Science, and The Ratner Center for Single Molecule Science, Tel Aviv University, Tel Aviv 69978, Israel
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6
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Wang X, Chen Y, Deng W. Theory of relaxation dynamics for anomalous diffusion processes in harmonic potential. Phys Rev E 2020; 101:042105. [PMID: 32422812 DOI: 10.1103/physreve.101.042105] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2019] [Accepted: 03/10/2020] [Indexed: 11/07/2022]
Abstract
An important physical property for a stochastic process is how it responds to an external force or spatial confinement. This paper aims to study the relaxation dynamics of a generic process confined in a harmonic potential. We find the dependence of ensemble- and time-averaged mean squared displacements of the confined process on the velocity correlation function C(t,t+τ) of the original process without any external force. Combining two kinds of scaling forms of C(t,t+τ) for small τ and large τ, the stationary value and the relaxation behaviors can be immediately obtained. Our results are valid for a large amount of anomalous diffusion processes, including the ones with single-scaled velocity correlation function (such as fractional Brownian motion and scaled Brownian motion) and the multiscaled ones (like Lévy walk with a broad range of power law exponents of flight time distribution). Note that the latter includes a special case with telegraphic active noise, which could take up athermal energy from the environment.
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Affiliation(s)
- Xudong Wang
- School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, People's Republic of China
| | - Yao Chen
- School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, People's Republic of China
| | - Weihua Deng
- School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, Lanzhou 730000, People's Republic of China
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7
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Li YY, Lee YW, Ho TS, Wang JH, Wu IC, Hsu TW, Chen YT, Huang SL. Spectroscopic characterization of Si/Mo thin-film stack at extreme ultraviolet range. OPTICS LETTERS 2018; 43:4029-4032. [PMID: 30106944 DOI: 10.1364/ol.43.004029] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2018] [Accepted: 07/21/2018] [Indexed: 06/08/2023]
Abstract
A noninvasive method for characterizing Si/Mo thin-film stack thickness and its complex transfer function using common-path optical coherence tomography is proposed, analyzed, and experimentally demonstrated. A laser-produced plasma (LPP)-based extreme ultraviolet (EUV) source was excited by a four-stage nanosecond Yb:fiber laser amplifier with a pulse energy of 1.01 mJ. The tabletop LPP EUV source was compact and stable for generating the EUV interference fringes. The measured complex transfer function of the Si/Mo stack was verified near the pristine 13.5-nm wavelength range.
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Rodríguez MA, Coarer FDL, Valle Á. 1/f noise in the intensity fluctuations of vertical-cavity surface-emitting lasers subject to parallel optical injection. Phys Rev E 2018; 97:042105. [PMID: 29758632 DOI: 10.1103/physreve.97.042105] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2017] [Indexed: 11/07/2022]
Abstract
A first analysis of fluctuations of the light intensity of vertical-cavity surface-emitting lasers operating in a bistable regime reveals the presence of 1/f noise. In this regime the intensity fluctuates between two recently characterized states with residence times {τ_{1}} and {τ_{2}}. We identify three distinct processes. One of them presents a coherence enhancement phenomenon, and in the other two the distribution of residence times in one of the states follows either a power law P(τ_{1})∼τ_{1}^{-2} or P(τ_{2})∼τ_{2}^{-2}, and this is the cause of the 1/f shape in the spectral density of the intensity. The process at the coherence enhancement zone shows 1/f fluctuations in the light intensity and also in the time residence process. It is shown that the origin of these fluctuations is due to a power-law distribution in the time separation between pulses observed in the time residence series.
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Affiliation(s)
- Miguel A Rodríguez
- Instituto de Física de Cantabria (IFCA), CSIC-UNICAN, E-39005 Santander, Spain
| | - Florian Denis-le Coarer
- OPTEL Research Group, LMOPS Laboratory, CentraleSupélec, Université de Paris-Saclay and Université de Lorraine, 57070 Metz, France
| | - Ángel Valle
- Instituto de Física de Cantabria (IFCA), CSIC-UNICAN, E-39005 Santander, Spain
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9
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Yadav AC, Ramaswamy R, Dhar D. General mechanism for the 1/f noise. Phys Rev E 2017; 96:022215. [PMID: 28950591 DOI: 10.1103/physreve.96.022215] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2016] [Indexed: 11/07/2022]
Abstract
We consider the response of a memoryless nonlinear device that acts instantaneously, converting an input signal ξ(t) into an output η(t) at the same time t. For input Gaussian noise with power-spectrum 1/f^{α}, the nonlinearity can modify the spectral index of the output to give a spectrum that varies as 1/f^{α^{'}} with α^{'}≠α. We show that the value of α^{'} depends on the nonlinear transformation and can be tuned continuously. This provides a general mechanism for the ubiquitous 1/f noise found in nature.
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Affiliation(s)
- Avinash Chand Yadav
- Department of Physics and Astronomical Sciences, Central University of Jammu, Samba 181 143, India
| | | | - Deepak Dhar
- Department of Physics, Indian Institute of Science, Education and Research, Dr. Homi Bhabha Road, Pashan, Pune 411 008, India
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10
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Leibovich N, Barkai E. Conditional 1/f^{α} noise: From single molecules to macroscopic measurement. Phys Rev E 2017; 96:032132. [PMID: 29346920 DOI: 10.1103/physreve.96.032132] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/23/2017] [Indexed: 06/07/2023]
Abstract
We demonstrate that the measurement of 1/f^{α} noise at the single molecule or nano-object limit is remarkably distinct from the macroscopic measurement over a large sample. The single-particle measurements yield a conditional time-dependent spectrum. However, the number of units fluctuating on the time scale of the experiment is increasing in such a way that the macroscopic measurements appear perfectly stationary. The single-particle power spectrum is a conditional spectrum, in the sense that we must make a distinction between idler and nonidler units on the time scale of the experiment. We demonstrate our results based on stochastic and deterministic models, in particular the well-known approach of superimposed Lorentzians, the blinking quantum dot model, and deterministic dynamics generated by a nonlinear mapping. Our results show that the 1/f^{α} spectrum is inherently nonstationary even if the macroscopic measurement completely obscures the underlying time dependence of the phenomena.
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Affiliation(s)
- N Leibovich
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 5290002, Israel
| | - E Barkai
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 5290002, Israel
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11
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Rodríguez MA. Relating the large-scale structure of time series and visibility networks. Phys Rev E 2017; 95:062309. [PMID: 28709363 DOI: 10.1103/physreve.95.062309] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2017] [Indexed: 11/07/2022]
Abstract
The structure of time series is usually characterized by means of correlations. A new proposal based on visibility networks has been considered recently. Visibility networks are complex networks mapped from surfaces or time series using visibility properties. The structures of time series and visibility networks are closely related, as shown by means of fractional time series in recent works. In these works, a simple relationship between the Hurst exponent H of fractional time series and the exponent of the distribution of edges γ of the corresponding visibility network, which exhibits a power law, is shown. To check and generalize these results, in this paper we delve into this idea of connected structures by defining both structures more properly. In addition to the exponents used before, H and γ, which take into account local properties, we consider two more exponents that, as we will show, characterize global properties. These are the exponent α for time series, which gives the scaling of the variance with the size as var∼T^{2α}, and the exponent κ of their corresponding network, which gives the scaling of the averaged maximum of the number of edges, 〈k_{M}〉∼N^{κ}. With this representation, a more precise connection between the structures of general time series and their associated visibility network is achieved. Similarities and differences are more clearly established, and new scaling forms of complex networks appear in agreement with their respective classes of time series.
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Affiliation(s)
- Miguel A Rodríguez
- Instituto de Física de Cantabria (IFCA), CSIC-UNICAN, E-39005 Santander, Spain
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12
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Chen K, He D, Zhao H. Violation of the virial theorem and generalized equipartition theorem for logarithmic oscillators serving as a thermostat. Sci Rep 2017; 7:3460. [PMID: 28615728 PMCID: PMC5471288 DOI: 10.1038/s41598-017-03694-w] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2016] [Accepted: 05/10/2017] [Indexed: 11/09/2022] Open
Abstract
A logarithmic oscillator has been proposed to serve as a thermostat recently since it has a peculiar property of infinite heat capacity according to the virial theorem. In order to examine its feasibility in numerical simulations, a modified logarithmic potential has been applied in previous studies to eliminate the singularity at the origin. The role played by the modification has been elucidated in the present study. We argue that the virial theorem is practically violated in finite-time simulations of the modified log-oscillator illustrated by a linear dependence of kinetic temperature on energy. Furthermore, as far as a thermalized log-oscillator is concerned, our calculation based on the canonical ensemble average shows that the generalized equipartition theorem is broken if the temperature is higher than a critical temperature. Finally, we show that log-oscillators fail to serve as thermostats for their incapability of maintaining a nonequilibrium steady state even though their energy is appropriately assigned.
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Affiliation(s)
- Kai Chen
- Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen, 361005, China
| | - Dahai He
- Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen, 361005, China.
| | - Hong Zhao
- Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen, 361005, China.,Collaborative Innovation Center of Chemistry for Energy Materials, Xiamen University, Xiamen, 361005, China
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13
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Leibovich N, Dechant A, Lutz E, Barkai E. Aging Wiener-Khinchin theorem and critical exponents of 1/f^{β} noise. Phys Rev E 2016; 94:052130. [PMID: 27967149 DOI: 10.1103/physreve.94.052130] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2016] [Indexed: 06/06/2023]
Abstract
The power spectrum of a stationary process may be calculated in terms of the autocorrelation function using the Wiener-Khinchin theorem. We here generalize the Wiener-Khinchin theorem for nonstationary processes and introduce a time-dependent power spectrum 〈S_{t_{m}}(ω)〉 where t_{m} is the measurement time. For processes with an aging autocorrelation function of the form 〈I(t)I(t+τ)〉=t^{Υ}ϕ_{EA}(τ/t), where ϕ_{EA}(x) is a nonanalytic function when x is small, we find aging 1/f^{β} noise. Aging 1/f^{β} noise is characterized by five critical exponents. We derive the relations between the scaled autocorrelation function and these exponents. We show that our definition of the time-dependent spectrum retains its interpretation as a density of Fourier modes and discuss the relation to the apparent infrared divergence of 1/f^{β} noise. We illustrate our results for blinking-quantum-dot models, single-file diffusion, and Brownian motion in a logarithmic potential.
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Affiliation(s)
- N Leibovich
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel
| | - A Dechant
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel
- Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
| | - E Lutz
- Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
| | - E Barkai
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel
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14
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Dean DS, Iorio A, Marinari E, Oshanin G. Sample-to-sample fluctuations of power spectrum of a random motion in a periodic Sinai model. Phys Rev E 2016; 94:032131. [PMID: 27739768 DOI: 10.1103/physreve.94.032131] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2016] [Indexed: 06/06/2023]
Abstract
The Sinai model of a tracer diffusing in a quenched Brownian potential is a much-studied problem exhibiting a logarithmically slow anomalous diffusion due to the growth of energy barriers with the system size. However, if the potential is random but periodic, the regime of anomalous diffusion crosses over to one of normal diffusion once a tracer has diffused over a few periods of the system. Here we consider a system in which the potential is given by a Brownian bridge on a finite interval (0,L) and then periodically repeated over the whole real line and study the power spectrum S(f) of the diffusive process x(t) in such a potential. We show that for most of realizations of x(t) in a given realization of the potential, the low-frequency behavior is S(f)∼A/f^{2}, i.e., the same as for standard Brownian motion, and the amplitude A is a disorder-dependent random variable with a finite support. Focusing on the statistical properties of this random variable, we determine the moments of A of arbitrary, negative, or positive order k and demonstrate that they exhibit a multifractal dependence on k and a rather unusual dependence on the temperature and on the periodicity L, which are supported by atypical realizations of the periodic disorder. We finally show that the distribution of A has a log-normal left tail and exhibits an essential singularity close to the right edge of the support, which is related to the Lifshitz singularity. Our findings are based both on analytic results and on extensive numerical simulations of the process x(t).
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Affiliation(s)
- David S Dean
- Université Bordeaux and CNRS, Laboratoire Ondes et Matière d'Aquitaine (LOMA), UMR 5798, F-33400 Talence, France
| | - Antonio Iorio
- Dipartimento di Fisica, Sapienza Università di Roma, P.le A. Moro 2, I-00185 Roma, Italy
- Dipartimento di Matematica e Fisica, Università Roma Tre, Via della Vasca Navale 84, I-00146 Roma, Italy
| | - Enzo Marinari
- Dipartimento di Fisica, Sapienza Università di Roma, P.le A. Moro 2, I-00185 Roma, Italy
- INFN, Sezione di Roma 1 and Nanotech-CNR, UOS di Roma, P.le A. Moro 2, I-00185 Roma, Italy
| | - Gleb Oshanin
- Sorbonne Universités, UPMC Univ Paris 06, UMR 7600, LPTMC, F-75005, Paris, France
- CNRS, UMR 7600, Laboratoire de Physique Théorique de la Matière Condensée, F-75005, Paris, France
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15
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Ryabov A, Berestneva E, Holubec V. Brownian motion in time-dependent logarithmic potential: Exact results for dynamics and first-passage properties. J Chem Phys 2015; 143:114117. [PMID: 26395697 DOI: 10.1063/1.4931474] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Artem Ryabov
- Charles University in Prague, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, 180 00 Praha 8, Czech Republic
| | - Ekaterina Berestneva
- Charles University in Prague, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, 180 00 Praha 8, Czech Republic
| | - Viktor Holubec
- Charles University in Prague, Faculty of Mathematics and Physics, Department of Macromolecular Physics, V Holešovičkách 2, 180 00 Praha 8, Czech Republic
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16
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Dechant A, Lutz E. Wiener-Khinchin Theorem for Nonstationary Scale-Invariant Processes. PHYSICAL REVIEW LETTERS 2015; 115:080603. [PMID: 26340173 DOI: 10.1103/physrevlett.115.080603] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2015] [Indexed: 06/05/2023]
Abstract
We derive a generalization of the Wiener-Khinchin theorem for nonstationary processes by introducing a time-dependent spectral density that is related to the time-averaged power. We use the nonstationary theorem to investigate aging processes with asymptotically scale-invariant correlation functions. As an application, we analyze the power spectrum of three paradigmatic models of anomalous diffusion: scaled Brownian motion, fractional Brownian motion, and diffusion in a logarithmic potential. We moreover elucidate how the nonstationarity of generic subdiffusive processes is related to the infrared catastrophe of 1/f noise.
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Affiliation(s)
- Andreas Dechant
- Department of Physics, Friedrich-Alexander Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany
| | - Eric Lutz
- Department of Physics, Friedrich-Alexander Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany
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