In this paper, we consider the continuous parabolic Anderson model with a logcorrelated Gaussian field, and obtain the precise quenched long-time asymptotics and spatial asymptotics. To overcome the difficulties arisi...In this paper, we consider the continuous parabolic Anderson model with a logcorrelated Gaussian field, and obtain the precise quenched long-time asymptotics and spatial asymptotics. To overcome the difficulties arising from the log-correlated Gaussian field in the proof of the lower bound of the spatial asymptotics, we first establish the relation between quenched long-time asymptotics and spatial asymptotics, and then get the lower bound of the spatial asymptotics through the lower bound of the quenched long-time asymptotics.展开更多
Based on the algebraic equation of motion(AEOM)approach,we have studied the single-impurity Anderson model by analytically solving the AEOM of the f-electron one-particle Green function in the Kondo limit.The related ...Based on the algebraic equation of motion(AEOM)approach,we have studied the single-impurity Anderson model by analytically solving the AEOM of the f-electron one-particle Green function in the Kondo limit.The related spectral function satisfies the sum rule and shows that there is a well-known three-peak structure at zero temperature.In the low energy limit,we obtain the analytical formula of the Kondo temperature that is the same as the exact solution in form except for a prefactor.We also show that the shape of the Kondo resonance is the Lorentzian form and the corresponding weight is proportional to the spin-flip correlation function.展开更多
We obtain the Holder continuity and joint Holder continuity in space and time for the random field solution to the parabolic Anderson equation(■t-1/2△)u=u◇Win d-dimensional space, where W is a mean zero Gaussian no...We obtain the Holder continuity and joint Holder continuity in space and time for the random field solution to the parabolic Anderson equation(■t-1/2△)u=u◇Win d-dimensional space, where W is a mean zero Gaussian noise with temporal covariance γo and spatial covariance given by a spectral density μ(ζ).We assume that γo(t)≤c|t|^-α0 and |μ(ζ)|≤c ∏di=1|ζi|^-αi or|μ(ζ)|≤c|ζ|^-α, where α,α1,…,αd can take both positive and negative values.展开更多
We investigate the electronic transport properties of the single-impurity Anderson model. By employing the cluster expansions, the equations of motion of Green＇s functions are transformed into the corresponding equat...We investigate the electronic transport properties of the single-impurity Anderson model. By employing the cluster expansions, the equations of motion of Green＇s functions are transformed into the corresponding equation of motion of connected Green＇s functions, which contains the correlation of two conduction electrons beyond the Lacroix approximation. With the method we show that the asymmetric line shape of zero bias conductance manifests itself as the Fano effect, and the Kondo effect is observed in the narrow peak of differential conductance curve of the system. The Fano and the Kondo effects can coexist in the single-impurity Anderson model when the impurity level is adjusted to an appropriate position.展开更多
Periodic Anderson model is one of the most important models in the field of strongly correlated electrons. With the recent developed numerical method density matriX embedding theory, we study the ground state properti...Periodic Anderson model is one of the most important models in the field of strongly correlated electrons. With the recent developed numerical method density matriX embedding theory, we study the ground state properties of the periodic Anderson model on a two-dimensional square lattice. We systematically investigate the phase diagram away from half filling. We find three different phases in this region, which are distinguished by the local moment and the spin-spin correlation functions. The phase transition between the two antiferromagnetic phases is of first order. It is the so-called Lifshitz transition accompanied by a reconstruction of the Fermi surface. As the filling is close to half filling, there is no difference between the two antiferromagnetic phases. From the results of the spin-spin correlation, we find that the Kondo singlet is formed even in the antiferromagnetic phase.展开更多
In this paper, we study some ergodic theorems of a class of linear systems of interacting diffusions, which is a parabolic Anderson model. First, under the assumption that the transition kernel a = （a（i,j））i,j∈s ...In this paper, we study some ergodic theorems of a class of linear systems of interacting diffusions, which is a parabolic Anderson model. First, under the assumption that the transition kernel a = （a（i,j））i,j∈s is doubly stochastic, we obtain the long-time convergence to an invariant probability measure Vh starting from a bounded a-harmonic function h based on self-duality property, and then we show the convergence to the invariant probability measure Uh holds for a broad class of initial distributions. Second, if （a（i, j））i,j∈s is transient and symmetric, and the diffusion parameter c remains below a threshold, we are able to determine the set of extremal invariant probability measures with finite second moment. Finally, in the case that the transition kernel （a（i,j））i,j∈s is doubly stochastic and satisfies Case I （see Case I in [Shiga, T.： An interacting system in population genetics. J. Math. Kyoto Univ., 20, 213-242 （1980）]）, we show that this parabolic Anderson model locally dies out independent of the diffusion parameter c.展开更多
We investigate a modified Anderson model at the large-N limit,where the Coulomb interaction is replaced by the Sachdev-Ye-Kitaev random interaction.The resistivity of conduction electron ρ_(c) has a minimum value aro...We investigate a modified Anderson model at the large-N limit,where the Coulomb interaction is replaced by the Sachdev-Ye-Kitaev random interaction.The resistivity of conduction electron ρ_(c) has a minimum value around temperature T^(*),which is similar to the Kondo system,but the impurity electron’s density of state A_(d)(ω) demonstrates no sharp-peak like the Kondo resonance around the Fermi surface.This provides a counterintuitive example where resistivity minimum exists without Kondo resonance.The impurity electron’s entropy S_(d) and specific heat capacity C_(v) show a crossover from Fermi liquid to a non-Fermi liquid behavior dependent on temperature.The system is a Fermi liquid at T T^(*),and then becomes a Fermi gas at sufficiently high temperatures T>>T^(*).The non-Fermi liquid at the intermediate-T regime does not occur in the standard Anderson model.We also make a renormalization group analysis,which confirms the crossover from Fermi liquid to the non-Fermi behavior.It is emphasized that the resistivity minimum emerges in our model when the system behaves as a non-Fermi liquid rather than Fermi liquid,which provides an alternative example showing resistivity minimum in condensed matter physics.展开更多
The authors are concerned with a class of one-dimensional stochastic Anderson models with double-parameter fractional noises,whose differential operators are fractional.A unique solution for the model in some appropri...The authors are concerned with a class of one-dimensional stochastic Anderson models with double-parameter fractional noises,whose differential operators are fractional.A unique solution for the model in some appropriate Hilbert space is constructed.Moreover,the Lyapunov exponent of the solution is estimated,and its Hlder continuity is studied.On the other hand,the absolute continuity of the solution is also discussed.展开更多
We investigate the behavior for the Lyapunov exponent around the band center in one-dimensional Anderson model with weak disorder. Using a parametrization method we derive the corresponding differential equation and s...We investigate the behavior for the Lyapunov exponent around the band center in one-dimensional Anderson model with weak disorder. Using a parametrization method we derive the corresponding differential equation and solve the associated invariant distribution. We obtain the coe?cient for the leading correction term for small energy in band center anomaly. A high precision Pade′ approximation formula is applied to fully amend the anomalous behavior of Lyapunov exponent near band center.展开更多
基金supported by the National Natural Science Foundation of China (12201282)the Institute of Meteorological Big Data-Digital Fujian and the Fujian Key Laboratory of Data Science and Statistics (2020L0705)the Education Department of Fujian Province (JAT200325)。
文摘In this paper, we consider the continuous parabolic Anderson model with a logcorrelated Gaussian field, and obtain the precise quenched long-time asymptotics and spatial asymptotics. To overcome the difficulties arising from the log-correlated Gaussian field in the proof of the lower bound of the spatial asymptotics, we first establish the relation between quenched long-time asymptotics and spatial asymptotics, and then get the lower bound of the spatial asymptotics through the lower bound of the quenched long-time asymptotics.
基金Project supported by the National Natural Science Foundation of China(Grant No.11974420)。
文摘Based on the algebraic equation of motion(AEOM)approach,we have studied the single-impurity Anderson model by analytically solving the AEOM of the f-electron one-particle Green function in the Kondo limit.The related spectral function satisfies the sum rule and shows that there is a well-known three-peak structure at zero temperature.In the low energy limit,we obtain the analytical formula of the Kondo temperature that is the same as the exact solution in form except for a prefactor.We also show that the shape of the Kondo resonance is the Lorentzian form and the corresponding weight is proportional to the spin-flip correlation function.
基金supported by an NSERC granta startup fund of University of Albertasupported by Martin Hairer’s Leverhulme Trust leadership award
文摘We obtain the Holder continuity and joint Holder continuity in space and time for the random field solution to the parabolic Anderson equation(■t-1/2△)u=u◇Win d-dimensional space, where W is a mean zero Gaussian noise with temporal covariance γo and spatial covariance given by a spectral density μ(ζ).We assume that γo(t)≤c|t|^-α0 and |μ(ζ)|≤c ∏di=1|ζi|^-αi or|μ(ζ)|≤c|ζ|^-α, where α,α1,…,αd can take both positive and negative values.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10375039 and 90503008）, the Doctoral Fund of Ministry of Education of China, and the Center of Theoretical Nuclear Physics of Heavy Ion Facilities of Lanzhou of China.
文摘We investigate the electronic transport properties of the single-impurity Anderson model. By employing the cluster expansions, the equations of motion of Green＇s functions are transformed into the corresponding equation of motion of connected Green＇s functions, which contains the correlation of two conduction electrons beyond the Lacroix approximation. With the method we show that the asymmetric line shape of zero bias conductance manifests itself as the Fano effect, and the Kondo effect is observed in the narrow peak of differential conductance curve of the system. The Fano and the Kondo effects can coexist in the single-impurity Anderson model when the impurity level is adjusted to an appropriate position.
基金Project supported by the National Natural Science Foundation of China(Grant No.11504023)
文摘Periodic Anderson model is one of the most important models in the field of strongly correlated electrons. With the recent developed numerical method density matriX embedding theory, we study the ground state properties of the periodic Anderson model on a two-dimensional square lattice. We systematically investigate the phase diagram away from half filling. We find three different phases in this region, which are distinguished by the local moment and the spin-spin correlation functions. The phase transition between the two antiferromagnetic phases is of first order. It is the so-called Lifshitz transition accompanied by a reconstruction of the Fermi surface. As the filling is close to half filling, there is no difference between the two antiferromagnetic phases. From the results of the spin-spin correlation, we find that the Kondo singlet is formed even in the antiferromagnetic phase.
基金The first author is supported by National Natural Science Foundation of China (Grant Nos. 10531070,11071008)SRF for ROCS,Science and Technology Ministry 973 project (2006CB805900)the Doctoral Program Foundation of the Ministry of Education,China
文摘In this paper, we study some ergodic theorems of a class of linear systems of interacting diffusions, which is a parabolic Anderson model. First, under the assumption that the transition kernel a = （a（i,j））i,j∈s is doubly stochastic, we obtain the long-time convergence to an invariant probability measure Vh starting from a bounded a-harmonic function h based on self-duality property, and then we show the convergence to the invariant probability measure Uh holds for a broad class of initial distributions. Second, if （a（i, j））i,j∈s is transient and symmetric, and the diffusion parameter c remains below a threshold, we are able to determine the set of extremal invariant probability measures with finite second moment. Finally, in the case that the transition kernel （a（i,j））i,j∈s is doubly stochastic and satisfies Case I （see Case I in [Shiga, T.： An interacting system in population genetics. J. Math. Kyoto Univ., 20, 213-242 （1980）]）, we show that this parabolic Anderson model locally dies out independent of the diffusion parameter c.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11674139,11704166,and 11834005)the Fundamental Research Funds for the Central Universities,China,and PCSIRT(Grant No.IRT-16R35)。
文摘We investigate a modified Anderson model at the large-N limit,where the Coulomb interaction is replaced by the Sachdev-Ye-Kitaev random interaction.The resistivity of conduction electron ρ_(c) has a minimum value around temperature T^(*),which is similar to the Kondo system,but the impurity electron’s density of state A_(d)(ω) demonstrates no sharp-peak like the Kondo resonance around the Fermi surface.This provides a counterintuitive example where resistivity minimum exists without Kondo resonance.The impurity electron’s entropy S_(d) and specific heat capacity C_(v) show a crossover from Fermi liquid to a non-Fermi liquid behavior dependent on temperature.The system is a Fermi liquid at T T^(*),and then becomes a Fermi gas at sufficiently high temperatures T>>T^(*).The non-Fermi liquid at the intermediate-T regime does not occur in the standard Anderson model.We also make a renormalization group analysis,which confirms the crossover from Fermi liquid to the non-Fermi behavior.It is emphasized that the resistivity minimum emerges in our model when the system behaves as a non-Fermi liquid rather than Fermi liquid,which provides an alternative example showing resistivity minimum in condensed matter physics.
基金supported by the National Natural Science Foundation of China (No. 10871103)
文摘The authors are concerned with a class of one-dimensional stochastic Anderson models with double-parameter fractional noises,whose differential operators are fractional.A unique solution for the model in some appropriate Hilbert space is constructed.Moreover,the Lyapunov exponent of the solution is estimated,and its Hlder continuity is studied.On the other hand,the absolute continuity of the solution is also discussed.
基金Supported by National Natural Science Foundation of China under Grant Nos.1121403 and 11745006
文摘We investigate the behavior for the Lyapunov exponent around the band center in one-dimensional Anderson model with weak disorder. Using a parametrization method we derive the corresponding differential equation and solve the associated invariant distribution. We obtain the coe?cient for the leading correction term for small energy in band center anomaly. A high precision Pade′ approximation formula is applied to fully amend the anomalous behavior of Lyapunov exponent near band center.
