A perturbation theory model that describes splitting of the spectra in highly symmetrical molecular species in electrostatic field is proposed. An anahrmonie model of a two-dimensional oscillator having Kratzer potent...A perturbation theory model that describes splitting of the spectra in highly symmetrical molecular species in electrostatic field is proposed. An anahrmonie model of a two-dimensional oscillator having Kratzer potential energy function is used to model the molecular species and to represent the unperturbed system. A selection rule for the radial quantum number of the oscillator is derived. The eigenfunctions of a two-dimensional anharmonic oscillator in cylindrical coordinates are used for the matrix elements representing the probability for energy transitions in dipole approximation to be calculated. Several forms of perturbation operators are proposed to model the interaction between the polyatomic molecular species and an electrostatic field. It is found that the degeneracy is removed in the presence of the electric field and spectral splitting occurs. Anharmonic approximation for the unperturbed system is more accurate and reliable representation of a reaJ polyatomic molecular species.展开更多
This paper discusses the properties of amplitude-squared squeezing of the generalized odd-even coherent states of anharmonic oscillator in finite-dimensional Hilbert space. It demonstrates that the generalized odd coh...This paper discusses the properties of amplitude-squared squeezing of the generalized odd-even coherent states of anharmonic oscillator in finite-dimensional Hilbert space. It demonstrates that the generalized odd coherent states do exhibit strong amplitude-squared squeezing effects in comparison with the generalized even coherent states.展开更多
Using thermal entangled state representation,we solve the master equation of a diffusive anharmonic oscillator（AHO） to obtain the exact time evolution formula for the density operator in the infinitive operator-sum ...Using thermal entangled state representation,we solve the master equation of a diffusive anharmonic oscillator（AHO） to obtain the exact time evolution formula for the density operator in the infinitive operator-sum representation.We present a new evolution formula of the Wigner function（WF） for any initial state of the diffusive AHO by converting the WF calculation into an overlap between two pure states in an enlarged Fock space.It is found that this formula is very convenient in investigating the WF＇s evolution of any known initial state.As applications,this formula is used to obtain the evolution of the WF for a coherent state and the evolution of the photon-number distribution of diffusive AHOs.展开更多
The two-dimensional hydrogen with a linear potential in a magnetic field is solved by two different methods.Furthermore the connection between the model and an anharmonic oscillator is investigated by methods of KStra...The two-dimensional hydrogen with a linear potential in a magnetic field is solved by two different methods.Furthermore the connection between the model and an anharmonic oscillator is investigated by methods of KStransformation.展开更多
In order to investigate a complicated physical system, it is convenient to consider a simple, easy to solve model, which is chosen to reflect as much physics as possible of the original system, as an ideal approximati...In order to investigate a complicated physical system, it is convenient to consider a simple, easy to solve model, which is chosen to reflect as much physics as possible of the original system, as an ideal approximation. Motivated by this fundamental idea, we propose a novel asymptotic method, the nonsensitive homotopy-Pade approach. In this method, homotopy relations are constructed to link the original system with an ideal, solvable model. An artificial homotopy parameter is introduced to the homotopy relations as the normal perturbation parameter to generate the perturbation series, and is used to implement the Padd approximation. Meanwhile, some other auxiliary nonperturbative parameters, which are used to control the convergence of the perturbation series, are inserted to the approximants, and are fixed via the principle of minimal sensitivity. The method is used to study the eigenvalue problem of the quantum anharmonic oscillators. Highly accurate numerical results show its validity. Possible further studies on this method are also briefly discussed.展开更多
A method to describe the generation channels of high-order harmonics is proposed. According to this method, the mechanism of generation-channel interference of high-order harmonics is revealed clearly. We take the anh...A method to describe the generation channels of high-order harmonics is proposed. According to this method, the mechanism of generation-channel interference of high-order harmonics is revealed clearly. We take the anharmonic oscillator driven by bi-chrome fields as an example to illustrate that this method can be used to understand the effect of generation-channel interference.展开更多
Using a model anharmonic oscillator with asymptotically decreasing effective mass to study the effect of compositional grading on the quantum mechanical properties of a semiconductor heterostructure, we determine the ...Using a model anharmonic oscillator with asymptotically decreasing effective mass to study the effect of compositional grading on the quantum mechanical properties of a semiconductor heterostructure, we determine the exact bound states and spectral values of the system. Furthermore, we show that ordering ambiguity only brings about a spectral shift on the quantum anharmonic oscillator with spatially varying effective mass. A study of thermodynamic properties of the system reveals a resonance condition dependent on the magnitude of the anharmonicity parameter. This resonance condition is seen to set a critical value on the said parameter beyond which a complex valued entropy which is discussed, emerges.展开更多
In this work thermal conduction in one-dimensional （1D） chains of anharmonic oscillators are studied using computer simulation. The temperature profile, heat flux and thermal conductivity are investigated for chain ...In this work thermal conduction in one-dimensional （1D） chains of anharmonic oscillators are studied using computer simulation. The temperature profile, heat flux and thermal conductivity are investigated for chain length N = 100, 200, 400, 800 and 1600. In the computer simulation anharmonicity is introduced due to Fermi-Pasta- U1am-β （FPU-β） model For substrate interaction, an onsite potential due to Frenkel-Kontorova （FK） model has been used. Numerical simulations demonstrate that temperature gradient scales behave as N-1 linearly with the relation J = 0.1765/N. For the thermal conductivity K, KN to N obey the linear relation of the type KN = 0.8805N. It is shown that thermal transport is dependent on phonon-phonon interaction as web as phonon-lattice interaction. The thermal conductivity increases linearly with increase inanharmonicity and predicts relation κ =0.133 ＋ 0.804β. It is also concluded that for higher value of the strength of the onsite potential system tends to a thermal insulator.展开更多
The bond stretching vibrations of XF_5 molecules with D_(3h)symmetry are treated computa- tionally on the Morse oscillator model in which the bond oscillators are coupled harmonically.Each calculation involves four pa...The bond stretching vibrations of XF_5 molecules with D_(3h)symmetry are treated computa- tionally on the Morse oscillator model in which the bond oscillators are coupled harmonically.Each calculation involves four parameters for two types of Morse potential and three parameters for the kinetic-energy,potontial coupling terms.The eigenvalue formula for overtone and combination states up to three are presented and can be used to predict all the vibrational energylevels from local mode molecules through normal mode molecules.For PF_5,AsF_5 and VF_5,the coupled Morse oscillator model gives a prediction in good agreement with the experimental data.展开更多
In atomic dynamics, oscillation Mong different axes can be studied separately in the harmonic trap. When the trap is not harmonic, motion in different directions may couple together. In this work, we observe a two- di...In atomic dynamics, oscillation Mong different axes can be studied separately in the harmonic trap. When the trap is not harmonic, motion in different directions may couple together. In this work, we observe a two- dimensional oscillation by exciting atoms in one direction, where the atoms are transferred to an anharmonic region. Theoretical calculations are coincident to the experimental results. These oscillations in two dimensions not only can be used to measure trap parameters but also have potential applications in atomic interferometry and precise measurements.展开更多
Irradiated by infrared laser, the surface reducibility and adsorbability of Cu-Cr complex could be improved, owing to the interaction of photo-fragmentation and laser texturing. Analyzed by the binding energy spectra ...Irradiated by infrared laser, the surface reducibility and adsorbability of Cu-Cr complex could be improved, owing to the interaction of photo-fragmentation and laser texturing. Analyzed by the binding energy spectra and the auger spectra, the valence states of chromium ion and copper ion were+3 and+1 after radiation respectively, which still had the reducibility to release electrons. In contrast with the near-infrared(NIR)1 064 nm and mid-infrared(MIR) 10 600 nm laser at the same average output power of 15 W, the reduced metal percentage in the Cu-Cr complex was obviously distinguished at the depth from nanometer to micron. After chemical plating, the average coating thickness and mean-square deviation of the NIR sample were 11.61 μm and 0.30 for copper layer, and 2.69 μm and 0.08 for nickel layer. The results were much better than those of the MIR sample.展开更多
An approximate formula is proposed for the decay rate of energy eigenfunctions in classically energetically inaccessible regions in more than one-dimensional configuration spaces. This is achieved by generalizing an a...An approximate formula is proposed for the decay rate of energy eigenfunctions in classically energetically inaccessible regions in more than one-dimensional configuration spaces. This is achieved by generalizing an approach proposed recently for energy eigenfunctions in the one-dimensional configuration space. The formula is tested numerically in the Pullen-Edmonds model.展开更多
We present a semiclassical （SC） approach for quantum dissipative dynamics, constructed on basis of the hierarchical-equation-of-motion （HEOM） formalism. The dynamical components considered in the developed SC-HEOM...We present a semiclassical （SC） approach for quantum dissipative dynamics, constructed on basis of the hierarchical-equation-of-motion （HEOM） formalism. The dynamical components considered in the developed SC-HEOM are wavepackets＇ phase-space moments of not only the primary reduced system density operator but also the auxiliary density operators （ADOs） of HEOM. It is a highly numerically efficient method, meanwhile taking into account the high-order effcts of system-bath couplings. The SC-HEOM methodology is exemplified in this work on the hierarchical quantum master equation [J. Chem. Phys. 131, 214111 （2009）] and numerically demonstrated on linear spectra of anharmonic oscillators.展开更多
文摘A perturbation theory model that describes splitting of the spectra in highly symmetrical molecular species in electrostatic field is proposed. An anahrmonie model of a two-dimensional oscillator having Kratzer potential energy function is used to model the molecular species and to represent the unperturbed system. A selection rule for the radial quantum number of the oscillator is derived. The eigenfunctions of a two-dimensional anharmonic oscillator in cylindrical coordinates are used for the matrix elements representing the probability for energy transitions in dipole approximation to be calculated. Several forms of perturbation operators are proposed to model the interaction between the polyatomic molecular species and an electrostatic field. It is found that the degeneracy is removed in the presence of the electric field and spectral splitting occurs. Anharmonic approximation for the unperturbed system is more accurate and reliable representation of a reaJ polyatomic molecular species.
文摘This paper discusses the properties of amplitude-squared squeezing of the generalized odd-even coherent states of anharmonic oscillator in finite-dimensional Hilbert space. It demonstrates that the generalized odd coherent states do exhibit strong amplitude-squared squeezing effects in comparison with the generalized even coherent states.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11147009 and 11244005)the Natural Science Foundation of Shandong Province,China (Grant No. ZR2012AM004)
文摘Using thermal entangled state representation,we solve the master equation of a diffusive anharmonic oscillator（AHO） to obtain the exact time evolution formula for the density operator in the infinitive operator-sum representation.We present a new evolution formula of the Wigner function（WF） for any initial state of the diffusive AHO by converting the WF calculation into an overlap between two pure states in an enlarged Fock space.It is found that this formula is very convenient in investigating the WF＇s evolution of any known initial state.As applications,this formula is used to obtain the evolution of the WF for a coherent state and the evolution of the photon-number distribution of diffusive AHOs.
基金Supported in part by National Natural Science Foundation of China under Grant Nos.10605013 and 10975075 the Fundamental Research Funds for the Central Universities
文摘The two-dimensional hydrogen with a linear potential in a magnetic field is solved by two different methods.Furthermore the connection between the model and an anharmonic oscillator is investigated by methods of KStransformation.
基金Supported by the National Natural Science Foundations of China under Grant Nos.10735030,10475055,10675065 and 90503006National Basic Research Program of China (973 Program) under Grant No.2007CB814800+2 种基金Program for Changjiang Scholars and Innovative Research Team (IRT0734)the Research Fund of Postdoctoral of China under Grant No.20070410727Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20070248120
文摘In order to investigate a complicated physical system, it is convenient to consider a simple, easy to solve model, which is chosen to reflect as much physics as possible of the original system, as an ideal approximation. Motivated by this fundamental idea, we propose a novel asymptotic method, the nonsensitive homotopy-Pade approach. In this method, homotopy relations are constructed to link the original system with an ideal, solvable model. An artificial homotopy parameter is introduced to the homotopy relations as the normal perturbation parameter to generate the perturbation series, and is used to implement the Padd approximation. Meanwhile, some other auxiliary nonperturbative parameters, which are used to control the convergence of the perturbation series, are inserted to the approximants, and are fixed via the principle of minimal sensitivity. The method is used to study the eigenvalue problem of the quantum anharmonic oscillators. Highly accurate numerical results show its validity. Possible further studies on this method are also briefly discussed.
基金Project supported by the National Natural Science Foundation of China (Grant No.10874133)
文摘A method to describe the generation channels of high-order harmonics is proposed. According to this method, the mechanism of generation-channel interference of high-order harmonics is revealed clearly. We take the anharmonic oscillator driven by bi-chrome fields as an example to illustrate that this method can be used to understand the effect of generation-channel interference.
文摘Using a model anharmonic oscillator with asymptotically decreasing effective mass to study the effect of compositional grading on the quantum mechanical properties of a semiconductor heterostructure, we determine the exact bound states and spectral values of the system. Furthermore, we show that ordering ambiguity only brings about a spectral shift on the quantum anharmonic oscillator with spatially varying effective mass. A study of thermodynamic properties of the system reveals a resonance condition dependent on the magnitude of the anharmonicity parameter. This resonance condition is seen to set a critical value on the said parameter beyond which a complex valued entropy which is discussed, emerges.
文摘In this work thermal conduction in one-dimensional （1D） chains of anharmonic oscillators are studied using computer simulation. The temperature profile, heat flux and thermal conductivity are investigated for chain length N = 100, 200, 400, 800 and 1600. In the computer simulation anharmonicity is introduced due to Fermi-Pasta- U1am-β （FPU-β） model For substrate interaction, an onsite potential due to Frenkel-Kontorova （FK） model has been used. Numerical simulations demonstrate that temperature gradient scales behave as N-1 linearly with the relation J = 0.1765/N. For the thermal conductivity K, KN to N obey the linear relation of the type KN = 0.8805N. It is shown that thermal transport is dependent on phonon-phonon interaction as web as phonon-lattice interaction. The thermal conductivity increases linearly with increase inanharmonicity and predicts relation κ =0.133 ＋ 0.804β. It is also concluded that for higher value of the strength of the onsite potential system tends to a thermal insulator.
基金Supported by the National Natural Science Fundation of China as Item of Major Project.
文摘The bond stretching vibrations of XF_5 molecules with D_(3h)symmetry are treated computa- tionally on the Morse oscillator model in which the bond oscillators are coupled harmonically.Each calculation involves four parameters for two types of Morse potential and three parameters for the kinetic-energy,potontial coupling terms.The eigenvalue formula for overtone and combination states up to three are presented and can be used to predict all the vibrational energylevels from local mode molecules through normal mode molecules.For PF_5,AsF_5 and VF_5,the coupled Morse oscillator model gives a prediction in good agreement with the experimental data.
基金Supported by the State Key Development Program for Basic Research of China under Grant No 2016YFA0301501the National Natural Science Foundation of China under Grant Nos 61475007,11334001 and 91336103
文摘In atomic dynamics, oscillation Mong different axes can be studied separately in the harmonic trap. When the trap is not harmonic, motion in different directions may couple together. In this work, we observe a two- dimensional oscillation by exciting atoms in one direction, where the atoms are transferred to an anharmonic region. Theoretical calculations are coincident to the experimental results. These oscillations in two dimensions not only can be used to measure trap parameters but also have potential applications in atomic interferometry and precise measurements.
基金Supported by the National Basic Research Program of China("973"Program,No.2010CB327800)National Natural Science Foundation of China(No.11004150)Postdoctoral Science Foundation of China(No.20090460690)
文摘Irradiated by infrared laser, the surface reducibility and adsorbability of Cu-Cr complex could be improved, owing to the interaction of photo-fragmentation and laser texturing. Analyzed by the binding energy spectra and the auger spectra, the valence states of chromium ion and copper ion were+3 and+1 after radiation respectively, which still had the reducibility to release electrons. In contrast with the near-infrared(NIR)1 064 nm and mid-infrared(MIR) 10 600 nm laser at the same average output power of 15 W, the reduced metal percentage in the Cu-Cr complex was obviously distinguished at the depth from nanometer to micron. After chemical plating, the average coating thickness and mean-square deviation of the NIR sample were 11.61 μm and 0.30 for copper layer, and 2.69 μm and 0.08 for nickel layer. The results were much better than those of the MIR sample.
基金Supported by the National Natural Science Foundation of China under Grant No 10275011.
文摘An approximate formula is proposed for the decay rate of energy eigenfunctions in classically energetically inaccessible regions in more than one-dimensional configuration spaces. This is achieved by generalizing an approach proposed recently for energy eigenfunctions in the one-dimensional configuration space. The formula is tested numerically in the Pullen-Edmonds model.
基金supported by the National Natural Science Foundation of China(No.21373191,No.21573202,No.21633006,and No.21703225)the Fundamental Research Funds for the Central Universities(No.2030020028,No.2060030025,and No.2340000074)
文摘We present a semiclassical （SC） approach for quantum dissipative dynamics, constructed on basis of the hierarchical-equation-of-motion （HEOM） formalism. The dynamical components considered in the developed SC-HEOM are wavepackets＇ phase-space moments of not only the primary reduced system density operator but also the auxiliary density operators （ADOs） of HEOM. It is a highly numerically efficient method, meanwhile taking into account the high-order effcts of system-bath couplings. The SC-HEOM methodology is exemplified in this work on the hierarchical quantum master equation [J. Chem. Phys. 131, 214111 （2009）] and numerically demonstrated on linear spectra of anharmonic oscillators.
