This review is devoted to one of the most interesting and actively developing fields in condensed matter physics—theory of topological insulators.Apart from its importance for theoretical physics,this theory enjoys n...This review is devoted to one of the most interesting and actively developing fields in condensed matter physics—theory of topological insulators.Apart from its importance for theoretical physics,this theory enjoys numerous connections with modern mathematics,in particular,with topology and homotopy theory,Clifford algebras,K-theory and non-commutative geometry.From the physical point of view topological invariance is equivalent to adiabatic stability.Topological insulators are characterized by the broad energy gap,stable under small deformations,which motivates application of topological methods.A key role in the study of topological ob jects in the solid state physics is played by their symmetry groups.There are three main types of symmetries—time reversion symmetry,preservation of the number of particles(charge symmetry)and PH-symmetry(particle-hole symmetry).Based on the study of symmetry groups and representation theory of Clifford algebras Kitaev proposed a classification of topological ob jects in solid state physics.In this review we pay special attention to the topological insulators invariant under time reversion.展开更多
In this paper the energy diffusion controlled reaction rate in dissipative Hamiltonian systems is investigated by using the stochastic averaging method for quasi Hamiltonian systems. The boundary value problem of mean...In this paper the energy diffusion controlled reaction rate in dissipative Hamiltonian systems is investigated by using the stochastic averaging method for quasi Hamiltonian systems. The boundary value problem of mean first- passage time （MFPT） of averaged system is formulated and the energy diffusion controlled reaction rate is obtained as the inverse of MFPT. The energy diffusion controlled reaction rate in the classical Kramers bistable potential and in a two-dimensional bistable potential with a heat bath are obtained by using the proposed approach respectively. The obtained results are then compared with those from Monte Carlo simulation of original systems and from the classical Kraraers theory. It is shown that the reaction rate obtained by using the proposed approach agrees well with that from Monte Carlo simulation and is more accurate than the classical Kramers rate.展开更多
We investigate the escape behavior of systems governed by the one-dimensional nonlinear Kramers＇ equation δW/δt = -vδW/δx ＋ （f＇（x）/m）（δW/δv） ＋ γδ（vW）/δv ＋ （γκBT/m）（δ2W^μ/δv^2）, where f（...We investigate the escape behavior of systems governed by the one-dimensional nonlinear Kramers＇ equation δW/δt = -vδW/δx ＋ （f＇（x）/m）（δW/δv） ＋ γδ（vW）/δv ＋ （γκBT/m）（δ2W^μ/δv^2）, where f（x） is a metastable potential and μ an anomalous exponent. We obtain an expression for the transition state theory escape rate, whose predictions are in good agreement with numerical simulations. The results exhibit the anomalies due to the nonlinearity in W that the TST rate grows with T and drops as μbecomes large at a fixed T. Indeed, particles in the subdiffusive media （μ 〉 1） can escape over the barrier only when T is above a critical value, while there does not exist this confinement in the superdiffusive media （μ 〈 1）.展开更多
This paper presents a generalized framework of stochastic modeling for particle kinetics in wall-bounded flow.We modified a reflected Brownian motion process and straightforwardly obtained a Kramers equation for parti...This paper presents a generalized framework of stochastic modeling for particle kinetics in wall-bounded flow.We modified a reflected Brownian motion process and straightforwardly obtained a Kramers equation for particle probability density function(PDF).After the wall effects were accounted for as a drift from zero in the mean displacement and suppression in the diffusivity of a particle,an analytical solution was worked out for PDF.Three distinguishable mechanisms were identified to affect the profile of particle probability distribution:external forces,turbophoresis effect,and wall-drift effect.The proposed formulation covers the Huang et al.(2009)model of a wall that produces electrostatic repulsion force and van der Waals force,as well as Monte-Carlo solutions for the Peter and Barenbrug(2002)model under a variety of relaxation times.Moreover,it successfully reproduces the two patterns of particle concentration profiles observed in experiments of sediment-laden open-channel flows.The strength of the wall-drift effect was found to be connected with the interaction frequency between particle and wall.Further exploration of the relationship among flow turbulence,particle inertia,and particle concentration is worthwhile.展开更多
We propose and investigate the use of a Kramers–Kronig(KK) receiver in a single sideband orthogonal frequency division multiplexing radio over fiber(SSB-OFDM-RoF) link based on an optical remote heterodyne solution. ...We propose and investigate the use of a Kramers–Kronig(KK) receiver in a single sideband orthogonal frequency division multiplexing radio over fiber(SSB-OFDM-RoF) link based on an optical remote heterodyne solution. This scheme is effective in eliminating the signal-to-signal beating interference introduced by square-law detection of a photo-detector in an SSB-OFDM-RoF link. We extensively study the influences of different carrier-to-signal power ratios(CSPRs), laser linewidths, and transmission distances on our proposed scheme. It is proved that the KK-based receiver can reduce optimal CSPR by more than 5 dB and provide about 1.1 dB gain over the conventional mixer-based receiver scheme with CSPR of 11 dB after 75 km fiber transmission.展开更多
Based on a Hamfltonian identity, we study one-dimensional generalized hypervirial theorem, Blanchardlike （non-diagonal case） and Kramers＇ （diagonal case） recurrence relations for arbitrary x^k which is independen...Based on a Hamfltonian identity, we study one-dimensional generalized hypervirial theorem, Blanchardlike （non-diagonal case） and Kramers＇ （diagonal case） recurrence relations for arbitrary x^k which is independent of the central potential V（x）. Some significant results in diagonal case are obtained for special k in xk （k ≥2）. In particular, we find the orthogonal relation 〈n1｜n2〉 = δh1,n2 （k = 0）, 〈n1[V＇（x）｜n2〉 = （En1-En2）^2〈n1｜x｜n2〉 （k = 1）, En = （n｜V＇（x）x/2｜n〉 ＋ （n｜V（x）｜n〉 （k = 2） and -4En（n｜x｜n） ~ 〈n｜V＇（x）x^2｜n〉 ＋ 4〈n｜V（x）x｜n〉 =0 （k=3）. The latter two formulas can be used directly to calculate the energy levels. We present useYul explicit relations for some well known physical potentials without requiring the energy spectra of quantum system.展开更多
We show that the breakdown of dipole approximation can be adopted to explain the asymmetry structure in the photoelectron momentum distributions along the beam propagation direction, which is defined as the photoelect...We show that the breakdown of dipole approximation can be adopted to explain the asymmetry structure in the photoelectron momentum distributions along the beam propagation direction, which is defined as the photoelectron longitudinal momentum distributions（PLMD）, in tunneling regime（K ？ 1）, based on the strong field approximation theory. The nondipole Hamiltonian for photoelectrons interacting with laser fields from a hydrogen-like atom is transformed into the Kramers–Henneberger frame in our model. To introduce the correction of dipole approximation, the spatial variable is kept in a vector potential （r, t）, demonstrating that the breakdown of dipole approximation is the major reason for the shift of the peak in PLMD. The nondipole effects are apparent when circularly polarized lasers are adopted to ionize the atoms, and clear tendency to increase offsets is found for increasing laser intensities.展开更多
基金Supported by RFBR(Grant Nos.19-01-00474,20-51-05006)。
文摘This review is devoted to one of the most interesting and actively developing fields in condensed matter physics—theory of topological insulators.Apart from its importance for theoretical physics,this theory enjoys numerous connections with modern mathematics,in particular,with topology and homotopy theory,Clifford algebras,K-theory and non-commutative geometry.From the physical point of view topological invariance is equivalent to adiabatic stability.Topological insulators are characterized by the broad energy gap,stable under small deformations,which motivates application of topological methods.A key role in the study of topological ob jects in the solid state physics is played by their symmetry groups.There are three main types of symmetries—time reversion symmetry,preservation of the number of particles(charge symmetry)and PH-symmetry(particle-hole symmetry).Based on the study of symmetry groups and representation theory of Clifford algebras Kitaev proposed a classification of topological ob jects in solid state physics.In this review we pay special attention to the topological insulators invariant under time reversion.
基金Project supported by the National Natural Science Foundation of China （Key Grant No 10332030）, the Specialized Research Fund for the Doctoral Program of Higher Education of China （Grant No 20060335125） and the National Science Foundation for Post-doctoral Scientists of China （Grant No 20060390338）.
文摘In this paper the energy diffusion controlled reaction rate in dissipative Hamiltonian systems is investigated by using the stochastic averaging method for quasi Hamiltonian systems. The boundary value problem of mean first- passage time （MFPT） of averaged system is formulated and the energy diffusion controlled reaction rate is obtained as the inverse of MFPT. The energy diffusion controlled reaction rate in the classical Kramers bistable potential and in a two-dimensional bistable potential with a heat bath are obtained by using the proposed approach respectively. The obtained results are then compared with those from Monte Carlo simulation of original systems and from the classical Kraraers theory. It is shown that the reaction rate obtained by using the proposed approach agrees well with that from Monte Carlo simulation and is more accurate than the classical Kramers rate.
文摘We investigate the escape behavior of systems governed by the one-dimensional nonlinear Kramers＇ equation δW/δt = -vδW/δx ＋ （f＇（x）/m）（δW/δv） ＋ γδ（vW）/δv ＋ （γκBT/m）（δ2W^μ/δv^2）, where f（x） is a metastable potential and μ an anomalous exponent. We obtain an expression for the transition state theory escape rate, whose predictions are in good agreement with numerical simulations. The results exhibit the anomalies due to the nonlinearity in W that the TST rate grows with T and drops as μbecomes large at a fixed T. Indeed, particles in the subdiffusive media （μ 〉 1） can escape over the barrier only when T is above a critical value, while there does not exist this confinement in the superdiffusive media （μ 〈 1）.
基金supported by the National Natural Science Foundation of China(Grant Nos.51379100 and 51039003)
文摘This paper presents a generalized framework of stochastic modeling for particle kinetics in wall-bounded flow.We modified a reflected Brownian motion process and straightforwardly obtained a Kramers equation for particle probability density function(PDF).After the wall effects were accounted for as a drift from zero in the mean displacement and suppression in the diffusivity of a particle,an analytical solution was worked out for PDF.Three distinguishable mechanisms were identified to affect the profile of particle probability distribution:external forces,turbophoresis effect,and wall-drift effect.The proposed formulation covers the Huang et al.(2009)model of a wall that produces electrostatic repulsion force and van der Waals force,as well as Monte-Carlo solutions for the Peter and Barenbrug(2002)model under a variety of relaxation times.Moreover,it successfully reproduces the two patterns of particle concentration profiles observed in experiments of sediment-laden open-channel flows.The strength of the wall-drift effect was found to be connected with the interaction frequency between particle and wall.Further exploration of the relationship among flow turbulence,particle inertia,and particle concentration is worthwhile.
基金supported by the National Natural Science Foundation of China(Nos.61420106011 and 61471088)the Fundamental Research Funds for the Central Universities(No.ZYGX2016J014)
文摘We propose and investigate the use of a Kramers–Kronig(KK) receiver in a single sideband orthogonal frequency division multiplexing radio over fiber(SSB-OFDM-RoF) link based on an optical remote heterodyne solution. This scheme is effective in eliminating the signal-to-signal beating interference introduced by square-law detection of a photo-detector in an SSB-OFDM-RoF link. We extensively study the influences of different carrier-to-signal power ratios(CSPRs), laser linewidths, and transmission distances on our proposed scheme. It is proved that the KK-based receiver can reduce optimal CSPR by more than 5 dB and provide about 1.1 dB gain over the conventional mixer-based receiver scheme with CSPR of 11 dB after 75 km fiber transmission.
基金Supported in part by Project 20150964-SIP-IPN,COFAA-IPN,Mexico
文摘Based on a Hamfltonian identity, we study one-dimensional generalized hypervirial theorem, Blanchardlike （non-diagonal case） and Kramers＇ （diagonal case） recurrence relations for arbitrary x^k which is independent of the central potential V（x）. Some significant results in diagonal case are obtained for special k in xk （k ≥2）. In particular, we find the orthogonal relation 〈n1｜n2〉 = δh1,n2 （k = 0）, 〈n1[V＇（x）｜n2〉 = （En1-En2）^2〈n1｜x｜n2〉 （k = 1）, En = （n｜V＇（x）x/2｜n〉 ＋ （n｜V（x）｜n〉 （k = 2） and -4En（n｜x｜n） ~ 〈n｜V＇（x）x^2｜n〉 ＋ 4〈n｜V（x）x｜n〉 =0 （k=3）. The latter two formulas can be used directly to calculate the energy levels. We present useYul explicit relations for some well known physical potentials without requiring the energy spectra of quantum system.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11274149 and 11304185the Program of Shenyang Key Laboratory of Optoelectronic Materials and Technology under Grant No F12-254-1-00
文摘We show that the breakdown of dipole approximation can be adopted to explain the asymmetry structure in the photoelectron momentum distributions along the beam propagation direction, which is defined as the photoelectron longitudinal momentum distributions（PLMD）, in tunneling regime（K ？ 1）, based on the strong field approximation theory. The nondipole Hamiltonian for photoelectrons interacting with laser fields from a hydrogen-like atom is transformed into the Kramers–Henneberger frame in our model. To introduce the correction of dipole approximation, the spatial variable is kept in a vector potential （r, t）, demonstrating that the breakdown of dipole approximation is the major reason for the shift of the peak in PLMD. The nondipole effects are apparent when circularly polarized lasers are adopted to ionize the atoms, and clear tendency to increase offsets is found for increasing laser intensities.
