We present our investigation on the spin relaxation of cobalt phthalocyanine (CoPc) films on Au(111) (CoPc/Au(111)) surface using scanning tunneling microscopy and spectroscopy. The spin relaxation time derive...We present our investigation on the spin relaxation of cobalt phthalocyanine (CoPc) films on Au(111) (CoPc/Au(111)) surface using scanning tunneling microscopy and spectroscopy. The spin relaxation time derived from the linewidth of spin-flip inelastic electron tunneling spectroscopy is quantitatively analyzed according to the Korringa-like formula. We find that although this regime of the spin relaxation time calculation by just considering the exchange interaction between itinerant conduction electrons and localized d-shells (s-d exchange interaction) can successfully reproduce the experimental value of the adsorbed magnetic atom, it fails in our case of CoPc/Au(111). Instead, we can obtain the relaxation time that is in good agreement with the experimental result by considering the fact that the 7c electrons in CoPc molecules are spin polarized, where the spin polarized 7c electrons extended at the Pc macrocycle may also scatter the conduction electrons in addition to the localized d spins. Our analyses indicate that the scattering by the π electrons provides an efficient spin relaxation channel in addition to the s-d interaction and thus leads to much short relaxation time in such a kind of molecular system on a metal substrate.展开更多
Atomic spin relaxation in a vapor cell, which can be characterized by the magnetic resonance linewidth(MRL),is an important parameter that eventually determines the sensitivity of an atomic magnetometer. In this paper...Atomic spin relaxation in a vapor cell, which can be characterized by the magnetic resonance linewidth(MRL),is an important parameter that eventually determines the sensitivity of an atomic magnetometer. In this paper, we have extensively studied how the pump intensity affects the spin relaxation. The experiment is performed with a cesium vapor cell, and the influence of the pump intensity on MRL is measured at room temperature at zero-field resonance. A simple model with five atomic levels of a Λ-like configuration is discussed theoretically, which can be used to represent the experimental process approximately, and the experimental results can be explained to some extent. Both the experimental and the theoretical results show a nonlinear broadening of the MRL when the pump intensity is increasing. The work helps to understand the mechanism of pump induced atomic spin relaxation in the atomic magnetometers.展开更多
A miniature quad-channel optically pumped atomic magnetometer(OPM) has been developed based on the spinexchange relaxation-free(SERF) mechanism. With a vapor cell of size 8 mm×8 mm×8 mm, we have incorporated...A miniature quad-channel optically pumped atomic magnetometer(OPM) has been developed based on the spinexchange relaxation-free(SERF) mechanism. With a vapor cell of size 8 mm×8 mm×8 mm, we have incorporated four SERF magnetometer channels, which provides sufficient spatial resolution for magnetoencephalography(MEG). The four channels share the same laser beam for the best cancellation of common mode noise due to laser fluctuations. With gradient measurement, the sensitivities of the four sensors are better than 6 fT/Hz^(1/2), which is also good enough for MEG measurement. The vapor cell is heated to 160℃ by a novel nonmagnetic current-heating structure. Our sensor with high spatial resolution and compact size is particularly suitable for MEG systems.展开更多
A transverse relaxation determination of spin-exchange relaxation free (SERF) magnetometer based on polarization modulation technique is proposed. Compared with the radio-frequency (RF) excitation and light intens...A transverse relaxation determination of spin-exchange relaxation free (SERF) magnetometer based on polarization modulation technique is proposed. Compared with the radio-frequency (RF) excitation and light intensity excitation meth- ods used in SERF magnetometer, the light polarization modulation method has a high stability in low-frequency range, which indicates a more accurate transverse relaxation measurement.展开更多
The laser-pumped potassium spin-exchange relaxation free (SERF) magnetometer is the most sensitive detector of magnetic field and has many important applications. We present the experimental results of our potassium...The laser-pumped potassium spin-exchange relaxation free (SERF) magnetometer is the most sensitive detector of magnetic field and has many important applications. We present the experimental results of our potassium SERF magne- tometer. A pump-probe approach is used to identify the unique spin dynamics of the atomic ensemble in the SERF regime. A single channel sensitivity of 8 f.THz-1/2 is achieved with our SERF magnetometer.展开更多
Within the frame of the Pavlov–Firsov spin–phonon coupling model, we study the spin-flip assisted by the acoustical phonon scattering between the first-excited state and the ground state in quantum dots. We analyze ...Within the frame of the Pavlov–Firsov spin–phonon coupling model, we study the spin-flip assisted by the acoustical phonon scattering between the first-excited state and the ground state in quantum dots. We analyze the behaviors of the spin relaxation rates as a function of an external magnetic field and lateral radius of quantum dot. The different trends of the relaxation rates depending on the magnetic field and lateral radius are obtained, which may serve as a channel to distinguish the relaxation processes and thus control the spin state effectively.展开更多
The nuclear spin relaxation rate (l/T1) is measured for GaAs two-dimensional (2D) electron systems in the quantum Hall regime with an all-electrical technique for agitating and probing the nuclear spins. A "tilte...The nuclear spin relaxation rate (l/T1) is measured for GaAs two-dimensional (2D) electron systems in the quantum Hall regime with an all-electrical technique for agitating and probing the nuclear spins. A "tilted plateau" feature is observed near the Landau level filling factor v = 1 in 1/T1 versus v. Both the width and magnitude of the plateau increase with decreasing electron density. At low temperatures, lIT1 exhibits an Arrhenius temperature dependence within the tilted plateau regime. The extracted energy gaps are up to two orders of magnitude smaller than the corresponding charge transport gaps. These results point to a nontrivial mechanism for the disorder-enhanced nuclear spin relaxation, in which microscopic inhomogeneities play a key role for the low energy spin excitations related to skyrmions.展开更多
The total effective spin-exchange relaxation of naturally abundant Rb in a K–Rb–21Ne comagnetometer is analyzed,and the results show that the coexistence of 87Rb and 85Rb isotopes in the same volume can lead to a la...The total effective spin-exchange relaxation of naturally abundant Rb in a K–Rb–21Ne comagnetometer is analyzed,and the results show that the coexistence of 87Rb and 85Rb isotopes in the same volume can lead to a large extra spinexchange broadening compared to pure 87Rb.This broadening mainly comes from the contribution of the equivalent reduction in the Rb spin-exchange rate.On this basis,an approximate relaxation model is proposed and experimentally demonstrated to be more accurate than that from a previous work.This study also provides a method for determining the properties of alkali-metal vapor cells.展开更多
We report the first detection of the effect of Na-Na spin exchange collisions on spin relaxation of optically pumped Na in Xe gas by studying the relaxation in the'dark"of the variable<SZ>in a mixture o...We report the first detection of the effect of Na-Na spin exchange collisions on spin relaxation of optically pumped Na in Xe gas by studying the relaxation in the'dark"of the variable<SZ>in a mixture of dense sodium vapor(number density[Na]~10^(13 )cm^(-3)),and buffer gas helium,xenon and nitrogen as a function of[Na]and xenon pressure.展开更多
A multilayered spin valve film with a structure of Ta(5 nm)/Co_(75)Fe_(25)(5 nm)/Cu(2.5 nm)/Co_(75)Fe_(25)(5 nm)/Ir_(20)Mn_(80)(12 nm)/Ta(8 nm)is prepared by the high-vacuum direct current(DC)magnetron sputtering.The ...A multilayered spin valve film with a structure of Ta(5 nm)/Co_(75)Fe_(25)(5 nm)/Cu(2.5 nm)/Co_(75)Fe_(25)(5 nm)/Ir_(20)Mn_(80)(12 nm)/Ta(8 nm)is prepared by the high-vacuum direct current(DC)magnetron sputtering.The effect of temperature on the spin valve structure and the magnetic properties are studied by x-ray diffraction(XRD),atomic force microscopy(AFM),and vibrating sample magnetometry.The effect of temperature on the exchange bias field thermomagnetic properties of multilayered spin valve is studied by the residence time of samples in a reverse saturation field.The results show that as the temperature increases,the IrMn(111)texture weakens,surface/interface roughness increases,and the exchange bias field decreases.Below 200℃,the exchange bias field decreases with the residence time increasing,and at the beginning of the negative saturation field,the exchange bias field Hex decreases first quickly and then slowly gradually.When the temperature is greater than 200℃,the exchange bias field is unchanged with the residence time increasing.展开更多
Spin noise spectroscopy (SNS) of electrons in n-doped bulk GaAs is studied as functions of temperature and the probe-laser energy. Experimental results show that the SNS signal comes from localized electrons in the ...Spin noise spectroscopy (SNS) of electrons in n-doped bulk GaAs is studied as functions of temperature and the probe-laser energy. Experimental results show that the SNS signal comes from localized electrons in the donor band. The spin relaxation time of electrons~ which is retrieved from the SNS measurement, depends on the probe light energy and temperature, and it can be ascribed to the variation of electron localization degree.展开更多
The carrier-density-dependent spin relaxation dynamics for modulation-doped GaAs/Al0.3 Gao,TAs quantum wells is studied using the time-resolved magneto-Kerr rotation measurements. The electron spin relaxation time and...The carrier-density-dependent spin relaxation dynamics for modulation-doped GaAs/Al0.3 Gao,TAs quantum wells is studied using the time-resolved magneto-Kerr rotation measurements. The electron spin relaxation time and its in-plane anisotropy are studied as a function of the optically injected electron density, Moreover, the relative strength of the Rashba and the Dresselhaus spin-rbit coupling fields, and thus the observed spin relaxation time anisotropy, is further tuned by the additional excitation of a 532nm continuous wave laser, demonstrating an effective spin relaxation manipulation via an optical gating method.展开更多
The dissipative part of the linear magnetic dynamic susceptibility of dipolar spin glasses is considered. Due to the transition of the system (at enough high concentration of the magnetic dipoles) from a paramagnetic ...The dissipative part of the linear magnetic dynamic susceptibility of dipolar spin glasses is considered. Due to the transition of the system (at enough high concentration of the magnetic dipoles) from a paramagnetic phase to magnetic dipolar one, an anomalous temperature dependence of the dissipative part of the magnetic susceptibility is found. Our results are in qualitative agreement with experiments performed on the dipolar-coupled Ising magnet LiHoxY1-xF4.展开更多
C spin-lattice relaxtion times for polystyrene nanolatex particles have been investigated. It was found that the dramatic increase at 80℃ annealing temperature is well below the Tg temperature of bulk polystyrene, t...C spin-lattice relaxtion times for polystyrene nanolatex particles have been investigated. It was found that the dramatic increase at 80℃ annealing temperature is well below the Tg temperature of bulk polystyrene, the increase of relaxation time of aromatic carbons is larger than that of for aliphatic carbons at transition annealing temperature.展开更多
A method of measuring in-situ magnetic field gradient is proposed in this paper. The magnetic shield is widely used in the atomic magnetometer. However, there is magnetic field gradient in the magnetic shield, which w...A method of measuring in-situ magnetic field gradient is proposed in this paper. The magnetic shield is widely used in the atomic magnetometer. However, there is magnetic field gradient in the magnetic shield, which would lead to additional gradient broadening. It is impossible to use an ex-situ magnetometer to measure magnetic field gradient in the region of a cell, whose length of side is several centimeters. The method demonstrated in this paper can realize the in-situ measurement of the magnetic field gradient inside the cell, which is significant for the spin relaxation study. The magnetic field gradients along the longitudinal axis of the magnetic shield are measured by a spin-exchange relaxation-free (SERF) magnetometer by adding a magnetic field modulation in the probe beam's direction. The transmissivity of the cell for the probe beam is always inhomogeneous along the pump beam direction, and the method proposed in this paper is independent of the intensity of the probe beam, which means that the method is independent of the cell's transmissivity. This feature makes the method more practical experimentally. Moreover, the AC-Stark shift can seriously degrade and affect the precision of the magnetic field gradient measurement. The AC-Stark shift is suppressed by locking the pump beam to the resonance of potassium's D1 line. Furthermore, the residual magnetic fields are measured with σ+- and σ--polarized pump beams, which can further suppress the effect of the AC-Stark shift. The method of measuring in-situ magnetic field gradient has achieved a magnetic field gradient precision of better than 30 pT/mm.展开更多
The carbon-13 spin-spin relaxation times of fluorine-containing ionomers are measured and motional correlation times τ;and τ;are calculated by using VJGM model . The results show that the motions of polymer main cha...The carbon-13 spin-spin relaxation times of fluorine-containing ionomers are measured and motional correlation times τ;and τ;are calculated by using VJGM model . The results show that the motions of polymer main chain in ionomers become more difficult with increasing of ionization degree and contents of functional group, and depend on the fine structures and stability of ionic microdomains.展开更多
We have analytically derived the relaxation function for one-dimensional disordered complex systems in terms of autocorrelation function of fractal time random walk by using operator formalism. We have shown that the ...We have analytically derived the relaxation function for one-dimensional disordered complex systems in terms of autocorrelation function of fractal time random walk by using operator formalism. We have shown that the relaxation function has stretched exponential, i.e. the Kohlrausch-Williams-Watts character for a fractal time random walk process.展开更多
基金This work was supported by the National Natural Science Foundation of China (No.91321309, No.91421313, No.21421063, and No.21273210), the "Strategic Priority Research Program" of the Chinese Academy of Sciences (No.XDB01020100), and the Fundamental Research Funds for the Central Universities (No.2340000050 and No.2340000074).
文摘We present our investigation on the spin relaxation of cobalt phthalocyanine (CoPc) films on Au(111) (CoPc/Au(111)) surface using scanning tunneling microscopy and spectroscopy. The spin relaxation time derived from the linewidth of spin-flip inelastic electron tunneling spectroscopy is quantitatively analyzed according to the Korringa-like formula. We find that although this regime of the spin relaxation time calculation by just considering the exchange interaction between itinerant conduction electrons and localized d-shells (s-d exchange interaction) can successfully reproduce the experimental value of the adsorbed magnetic atom, it fails in our case of CoPc/Au(111). Instead, we can obtain the relaxation time that is in good agreement with the experimental result by considering the fact that the 7c electrons in CoPc molecules are spin polarized, where the spin polarized 7c electrons extended at the Pc macrocycle may also scatter the conduction electrons in addition to the localized d spins. Our analyses indicate that the scattering by the π electrons provides an efficient spin relaxation channel in addition to the s-d interaction and thus leads to much short relaxation time in such a kind of molecular system on a metal substrate.
基金supported by the National Key R&D Program of China(Grant No.2017YFA0304502)the National Natural Science Foundation of China(Grant Nos.11634008,11674203,11574187,and 61227902)
文摘Atomic spin relaxation in a vapor cell, which can be characterized by the magnetic resonance linewidth(MRL),is an important parameter that eventually determines the sensitivity of an atomic magnetometer. In this paper, we have extensively studied how the pump intensity affects the spin relaxation. The experiment is performed with a cesium vapor cell, and the influence of the pump intensity on MRL is measured at room temperature at zero-field resonance. A simple model with five atomic levels of a Λ-like configuration is discussed theoretically, which can be used to represent the experimental process approximately, and the experimental results can be explained to some extent. Both the experimental and the theoretical results show a nonlinear broadening of the MRL when the pump intensity is increasing. The work helps to understand the mechanism of pump induced atomic spin relaxation in the atomic magnetometers.
基金Project supported by the National Key Research and Development Program of China(Grant Nos.2016YFA0300600 and 2016YFA0301500)the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB07030000)the National Natural Science Foundation of China(Grant No.11474347)
文摘A miniature quad-channel optically pumped atomic magnetometer(OPM) has been developed based on the spinexchange relaxation-free(SERF) mechanism. With a vapor cell of size 8 mm×8 mm×8 mm, we have incorporated four SERF magnetometer channels, which provides sufficient spatial resolution for magnetoencephalography(MEG). The four channels share the same laser beam for the best cancellation of common mode noise due to laser fluctuations. With gradient measurement, the sensitivities of the four sensors are better than 6 fT/Hz^(1/2), which is also good enough for MEG measurement. The vapor cell is heated to 160℃ by a novel nonmagnetic current-heating structure. Our sensor with high spatial resolution and compact size is particularly suitable for MEG systems.
基金Project supported by the National Natural Science Foundation of China(Grant No.61227902)the National Key R&D Program of China(Grant No.2017YFB0503100)the Natural Science Foundation of Beijing Municipality,China(Grant No.4162038)
文摘A transverse relaxation determination of spin-exchange relaxation free (SERF) magnetometer based on polarization modulation technique is proposed. Compared with the radio-frequency (RF) excitation and light intensity excitation meth- ods used in SERF magnetometer, the light polarization modulation method has a high stability in low-frequency range, which indicates a more accurate transverse relaxation measurement.
基金supported by the National Natural Science Foundation of China(Grant No.61227902)
文摘The laser-pumped potassium spin-exchange relaxation free (SERF) magnetometer is the most sensitive detector of magnetic field and has many important applications. We present the experimental results of our potassium SERF magne- tometer. A pump-probe approach is used to identify the unique spin dynamics of the atomic ensemble in the SERF regime. A single channel sensitivity of 8 f.THz-1/2 is achieved with our SERF magnetometer.
基金supported by the National Natural Science Foundation of China(Grant No.11264001)the Natural Science Foundation of Inner Mongolia,China(Grant No.2012MS0116)
文摘Within the frame of the Pavlov–Firsov spin–phonon coupling model, we study the spin-flip assisted by the acoustical phonon scattering between the first-excited state and the ground state in quantum dots. We analyze the behaviors of the spin relaxation rates as a function of an external magnetic field and lateral radius of quantum dot. The different trends of the relaxation rates depending on the magnetic field and lateral radius are obtained, which may serve as a channel to distinguish the relaxation processes and thus control the spin state effectively.
基金Project supported by the National Basic Research Program of China(Grant Nos.2012CB921703 and 2015CB921102)the National Natural Science Foundation of China(Grant Nos.91121003,11374337,and 61425015)the Chinese Academy of Sciences,the BMBF,and the German–Israel Foundation
文摘The nuclear spin relaxation rate (l/T1) is measured for GaAs two-dimensional (2D) electron systems in the quantum Hall regime with an all-electrical technique for agitating and probing the nuclear spins. A "tilted plateau" feature is observed near the Landau level filling factor v = 1 in 1/T1 versus v. Both the width and magnitude of the plateau increase with decreasing electron density. At low temperatures, lIT1 exhibits an Arrhenius temperature dependence within the tilted plateau regime. The extracted energy gaps are up to two orders of magnitude smaller than the corresponding charge transport gaps. These results point to a nontrivial mechanism for the disorder-enhanced nuclear spin relaxation, in which microscopic inhomogeneities play a key role for the low energy spin excitations related to skyrmions.
基金Project supported by the National Key R&D Program of China(Grant Nos.2016YFB0501600 and 2017YFB0503100)the National Natural Science Foundation of China(Grant Nos.61773043,61673041,61721091,and 61703025)the National Science Fund for Distinguished Young Scholars of China(Grant No.61925301)。
文摘The total effective spin-exchange relaxation of naturally abundant Rb in a K–Rb–21Ne comagnetometer is analyzed,and the results show that the coexistence of 87Rb and 85Rb isotopes in the same volume can lead to a large extra spinexchange broadening compared to pure 87Rb.This broadening mainly comes from the contribution of the equivalent reduction in the Rb spin-exchange rate.On this basis,an approximate relaxation model is proposed and experimentally demonstrated to be more accurate than that from a previous work.This study also provides a method for determining the properties of alkali-metal vapor cells.
文摘We report the first detection of the effect of Na-Na spin exchange collisions on spin relaxation of optically pumped Na in Xe gas by studying the relaxation in the'dark"of the variable<SZ>in a mixture of dense sodium vapor(number density[Na]~10^(13 )cm^(-3)),and buffer gas helium,xenon and nitrogen as a function of[Na]and xenon pressure.
基金supported by the Yunnan Provincial Ten Thousand Talents Plan Young Talents Training Fund,China(Grant No.KKRD201952029)the Applied Basic Research Program of Yunnan Province,China(Grant No.2011FB037)the School Talent Cultivation Foundation,China(Grant No.KKSY201252017)。
文摘A multilayered spin valve film with a structure of Ta(5 nm)/Co_(75)Fe_(25)(5 nm)/Cu(2.5 nm)/Co_(75)Fe_(25)(5 nm)/Ir_(20)Mn_(80)(12 nm)/Ta(8 nm)is prepared by the high-vacuum direct current(DC)magnetron sputtering.The effect of temperature on the spin valve structure and the magnetic properties are studied by x-ray diffraction(XRD),atomic force microscopy(AFM),and vibrating sample magnetometry.The effect of temperature on the exchange bias field thermomagnetic properties of multilayered spin valve is studied by the residence time of samples in a reverse saturation field.The results show that as the temperature increases,the IrMn(111)texture weakens,surface/interface roughness increases,and the exchange bias field decreases.Below 200℃,the exchange bias field decreases with the residence time increasing,and at the beginning of the negative saturation field,the exchange bias field Hex decreases first quickly and then slowly gradually.When the temperature is greater than 200℃,the exchange bias field is unchanged with the residence time increasing.
基金Supported by the National Key Research and Development Program of China under Grant No 2016YFA0301202the National Basic Research Program of China under Grant No 2013CB922304+1 种基金the National Natural Science Foundation of China under Grant Nos 91321310 and 11674311the K.C.Wong Education Foundation
文摘Spin noise spectroscopy (SNS) of electrons in n-doped bulk GaAs is studied as functions of temperature and the probe-laser energy. Experimental results show that the SNS signal comes from localized electrons in the donor band. The spin relaxation time of electrons~ which is retrieved from the SNS measurement, depends on the probe light energy and temperature, and it can be ascribed to the variation of electron localization degree.
基金Supported by the National Natural Science Foundation Program of China under Grant Nos 11274302,11474276 and 61290303
文摘The carrier-density-dependent spin relaxation dynamics for modulation-doped GaAs/Al0.3 Gao,TAs quantum wells is studied using the time-resolved magneto-Kerr rotation measurements. The electron spin relaxation time and its in-plane anisotropy are studied as a function of the optically injected electron density, Moreover, the relative strength of the Rashba and the Dresselhaus spin-rbit coupling fields, and thus the observed spin relaxation time anisotropy, is further tuned by the additional excitation of a 532nm continuous wave laser, demonstrating an effective spin relaxation manipulation via an optical gating method.
文摘The dissipative part of the linear magnetic dynamic susceptibility of dipolar spin glasses is considered. Due to the transition of the system (at enough high concentration of the magnetic dipoles) from a paramagnetic phase to magnetic dipolar one, an anomalous temperature dependence of the dissipative part of the magnetic susceptibility is found. Our results are in qualitative agreement with experiments performed on the dipolar-coupled Ising magnet LiHoxY1-xF4.
基金This work was supported by National Key Project for Fundamental Research (N.95-11) and National Natural Science Foundation of Ch
文摘C spin-lattice relaxtion times for polystyrene nanolatex particles have been investigated. It was found that the dramatic increase at 80℃ annealing temperature is well below the Tg temperature of bulk polystyrene, the increase of relaxation time of aromatic carbons is larger than that of for aliphatic carbons at transition annealing temperature.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61227902,61374210,and 61121003)
文摘A method of measuring in-situ magnetic field gradient is proposed in this paper. The magnetic shield is widely used in the atomic magnetometer. However, there is magnetic field gradient in the magnetic shield, which would lead to additional gradient broadening. It is impossible to use an ex-situ magnetometer to measure magnetic field gradient in the region of a cell, whose length of side is several centimeters. The method demonstrated in this paper can realize the in-situ measurement of the magnetic field gradient inside the cell, which is significant for the spin relaxation study. The magnetic field gradients along the longitudinal axis of the magnetic shield are measured by a spin-exchange relaxation-free (SERF) magnetometer by adding a magnetic field modulation in the probe beam's direction. The transmissivity of the cell for the probe beam is always inhomogeneous along the pump beam direction, and the method proposed in this paper is independent of the intensity of the probe beam, which means that the method is independent of the cell's transmissivity. This feature makes the method more practical experimentally. Moreover, the AC-Stark shift can seriously degrade and affect the precision of the magnetic field gradient measurement. The AC-Stark shift is suppressed by locking the pump beam to the resonance of potassium's D1 line. Furthermore, the residual magnetic fields are measured with σ+- and σ--polarized pump beams, which can further suppress the effect of the AC-Stark shift. The method of measuring in-situ magnetic field gradient has achieved a magnetic field gradient precision of better than 30 pT/mm.
基金The work was supported by National Natural Science Foundation of China
文摘The carbon-13 spin-spin relaxation times of fluorine-containing ionomers are measured and motional correlation times τ;and τ;are calculated by using VJGM model . The results show that the motions of polymer main chain in ionomers become more difficult with increasing of ionization degree and contents of functional group, and depend on the fine structures and stability of ionic microdomains.
文摘We have analytically derived the relaxation function for one-dimensional disordered complex systems in terms of autocorrelation function of fractal time random walk by using operator formalism. We have shown that the relaxation function has stretched exponential, i.e. the Kohlrausch-Williams-Watts character for a fractal time random walk process.