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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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Zhan Z, Wang X. Ergodic criterion of a random diffusivity model. Phys Rev E 2024; 109:044115. [PMID: 38755829 DOI: 10.1103/physreve.109.044115] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2023] [Accepted: 03/06/2024] [Indexed: 05/18/2024]
Abstract
The random diffusivity, initially proposed to explain Brownian yet non-Gaussian diffusion, has garnered significant attention due to its capacity not only for elucidating the internal physical mechanism of non-Gaussian diffusion, but also for establishing an analytical framework to characterize particle motion in complex environments. In this paper, based on the correlation function C(t_{1},t_{2})=〈D(t_{1})D(t_{2})〉 of random diffusivity D(t), we quantitatively propose a general criterion of determining the ergodic property of the Langevin equation with the arbitrary random diffusivity D(t). Due to the critical role of correlation function C(t_{1},t_{2}), we derive the criterion for the two cases with stationary diffusivity or nonstationary diffusivity, respectively. By utilizing the quantitative criterion, we can directly judge the ergodic properties of the random diffusivity model based on the correlation function C(t_{1},t_{2}) of random diffusivity D(t). Several typical diffusivities, including the common square of the Brownian motion and of the (fractional) Ornstein-Uhlenbeck process, are found to contribute to different ergodic properties, which validates our proposed criterion built on the correlation function C(t_{1},t_{2}).
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Affiliation(s)
- Zhongshuai Zhan
- School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, People's Republic of China
| | - Xudong Wang
- School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, People's Republic of China
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Liao Q, Zhou L, Wang X, Liu Y. Cooling of mechanical resonator in a hybrid intracavity squeezing optomechanical system. OPTICS EXPRESS 2022; 30:38776-38788. [PMID: 36258435 DOI: 10.1364/oe.463802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/12/2022] [Accepted: 09/23/2022] [Indexed: 06/16/2023]
Abstract
A hybrid intracavity squeezing optomechanical cooling system, in which an auxiliary cavity couples to an optomechanical cavity with a nonlinear medium inside it, is proposed to realize the ground state cooling of the mechanical resonator in the highly unresolved sideband regime. We demonstrate that the quantum backaction heating can be suppressed perfectly by the intracavity squeezing, and the cooling process can be further promoted by adjusting the tunnel coupling between the coupled cavities. The scheme has good performance in resisting the environmental thermal noise and better tolerance for the auxiliary cavity quality factor and provides the possibility for the quantum manipulation of the mechanical resonator with large mass and low frequency.
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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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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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Rigo E, Dong Z, Park JH, Kennedy E, Hokmabadi M, Almonte-Garcia L, Ding L, Aluru N, Timp G. Measurements of the size and correlations between ions using an electrolytic point contact. Nat Commun 2019; 10:2382. [PMID: 31147537 PMCID: PMC6542849 DOI: 10.1038/s41467-019-10265-2] [Citation(s) in RCA: 30] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2018] [Accepted: 05/01/2019] [Indexed: 01/20/2023] Open
Abstract
The size of an ion affects everything from the structure of water to life itself. In this report, to gauge their size, ions dissolved in water are forced electrically through a sub-nanometer-diameter pore spanning a thin membrane and the current is measured. The measurements reveal an ion-selective conductance that vanishes in pores <0.24 nm in diameter-the size of a water molecule-indicating that permeating ions have a grossly distorted hydration shell. Analysis of the current noise power spectral density exposes a threshold, below which the noise is independent of current, and beyond which it increases quadratically. This dependence proves that the spectral density, which is uncorrelated below threshold, becomes correlated above it. The onset of correlations for Li+, Mg2+, Na+ and K+-ions extrapolates to pore diameters of 0.13 ± 0.11 nm, 0.16 ± 0.11 nm, 0.22 ± 0.11 nm and 0.25 ± 0.11 nm, respectively-consonant with diameters at which the conductance vanishes and consistent with ions moving through the sub-nanopore with distorted hydration shells in a correlated way.
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Affiliation(s)
- Eveline Rigo
- Electrical Engineering and Biological Science, University of Notre Dame, Notre Dame, IN, 46556, USA
| | - Zhuxin Dong
- Electrical Engineering and Biological Science, University of Notre Dame, Notre Dame, IN, 46556, USA
| | - Jae Hyun Park
- Department of Aerospace and Software Engineering and Research Center for Aircraft Parts Technology, Gyeongsang National University, Jinju, Gyeongnam, 52828, Republic of Korea
| | - Eamonn Kennedy
- Electrical Engineering and Biological Science, University of Notre Dame, Notre Dame, IN, 46556, USA
| | - Mohammad Hokmabadi
- Electrical Engineering and Biological Science, University of Notre Dame, Notre Dame, IN, 46556, USA
| | - Lisa Almonte-Garcia
- Electrical Engineering and Biological Science, University of Notre Dame, Notre Dame, IN, 46556, USA
| | - Li Ding
- Electrical Engineering and Biological Science, University of Notre Dame, Notre Dame, IN, 46556, USA
| | - Narayana Aluru
- Mechanical Engineering, University of Illinois, Urbana, IL, 61801, USA
| | - Gregory Timp
- Electrical Engineering and Biological Science, University of Notre Dame, Notre Dame, IN, 46556, USA.
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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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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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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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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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Leibovich N, Barkai E. Aging Wiener-Khinchin Theorem. PHYSICAL REVIEW LETTERS 2015; 115:080602. [PMID: 26340172 DOI: 10.1103/physrevlett.115.080602] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2015] [Indexed: 06/05/2023]
Abstract
The Wiener-Khinchin theorem shows how the power spectrum of a stationary random signal I(t) is related to its correlation function ⟨I(t)I(t+τ)⟩. We consider nonstationary processes with the widely observed aging correlation function ⟨I(t)I(t+τ)⟩∼t(γ)ϕ(EA)(τ/t) and relate it to the sample spectrum. We formulate two aging Wiener-Khinchin theorems relating the power spectrum to the time- and ensemble-averaged correlation functions, discussing briefly the advantages of each. When the scaling function ϕ(EA)(x) exhibits a nonanalytical behavior in the vicinity of its small argument we obtain the aging 1/f-type of spectrum. We demonstrate our results with three examples: blinking quantum dots, single-file diffusion, and Brownian motion in a logarithmic potential, showing that our approach is valid for a wide range of physical mechanisms.
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Affiliation(s)
- N Leibovich
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel
| | - E Barkai
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel
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