Dynamic Structure Factor for a Harmonic Oscillator and the Harmonic Oscillator Chain

The recurrance relation method is employed to determine the dynamic structure factor for the single harmonic oscillator and a linear chain of harmonic oscillators. Approximative schemes based on this approach are proposed. Comparison is made with exactly known results (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermal Conductivity for a Noisy Disordered Harmonic Chain

We consider a d-dimensional disordered harmonic chain (DHC) perturbed by an energy conservative noise. We obtain uniform in the volume upper and lower bounds for the thermal conductivity defined through the Green-Kubo formula. These bounds indicate a positive finite conductivity. We prove also that the infinite volume homogenized Green-Kubo formula converges.     

A Compact Exponential Operator for Generating Rotating and Squeezing Transformations

We point out that the compact exponential operator V≡exp[-i(λ₁Q²-λ₂P²)/2] (where λ₁, λ₂ are real;P and Q are momentum and coordinate operators, respectively;the units of h=m=ω=l is taken, m and ω are harmonic oscillator's mass and'frequency, respectively) is a generalized single-mode squeeze operator which can generate mixed squeezing and rotating transformations. The decomposition of V as a product of a squeeze operator and a rotating operator is derived through the technique of integration within an ordered product.The fluctuation in quadrature phases for the squeezed vacuum state generated by V is analyzed.     

Quantum Heat Transfer in a Harmonic Chain with a Dephasing Reservoir

The quantum heat transfer in a harmonic chain with a dephasing reservoir is investigated based on the master equation method. The incoming phonons from the thermal reservoir will be scattered back partially into the reservoir at the contact site, leading to the contact resistance. Dephasing in the harmonic chain suppresses the transmitting of scattered phonons into the harmonic chain. Then the heat flux in the chain is reduced by dephasing. However, the heat t~ux is symmetric to interchanging the reservoirs temperatures even with the dephasing. Therefore, the thermal rectification csnnot be realized with pure depha~ing only.     

Behavior for Large Time of a Two-Component Chain of Harmonic Oscillators

We consider a model consisting of two semi-infinite chains of harmonic oscillators with a special particle subject to a harmonic external potential.We study the Cauchy problem for this model. The main goal is to derive the dispersive bounds for the solutions in the energy weighted norms.     

Error Analysis of the Density-Matrix Renormalization Group Algorithm for a Chain of Harmonic Oscillators

We investigate the application of the density-matrix renormalization group （DMRG） algorithm to a one-dimensional harmonic oscillator chain and compare the results with exact solutions, aiming at improving the algorithm＇s ef- ficiency. It is demonstrated that the algorithm can show quite accurate results if the procedure is properly organized; for example, by using the optimized bases. The errors of calculated ground state energy and the energy gap between the ground state and the first excited state are analyzed, and they are found to be critically dependent upon the size of the system or the energy level structure of the studied system and the number of states targeted during the DMRG procedure.     

Rigorous Scaling Law for the Heat Current in Disordered Harmonic Chain

We study the energy current in a model of heat conduction, first considered in detail by Casher and Lebowitz. The model consists of a one-dimensional disordered harmonic chain of n i.i.d. random masses, connected to their nearest neighbors via identical springs, and coupled at the boundaries to Langevin heat baths, with respective temperatures T ₁ and T _n . Let E J _n be the steady-state energy current across the chain, averaged over the masses. We prove that E J _n ~ (T ₁ − T _n )n ^−3/2 in the limit n → ∞, as has been conjectured by various authors over the time. The proof relies on a new explicit representation for the elements of the product of associated transfer matrices.     

Anomalous Fluctuations for a Perturbed Hamiltonian System with Exponential Interactions

A one-dimensional Hamiltonian system with exponential interactions perturbed by a conservative noise is considered. It is proved that energy superdiffuses and upper and lower bounds describing this anomalous diffusion are obtained.     

Analytical Solutions for the Two-Dimensional Gross-Pitaevskii Equation with a Harmonic Trap

Both the homotopy analysis method and Galerkin spectral method are applied to find the analytical solutions of the two-dimensional and time-independent Gross-Pitaevskii equation,a nonlinear Schrdinger equation used in describing the system of Bose-Einstein condensates trapped in a harmonic potential.The approximate analytical solutions are obtained successfully.Comparisons between the analytical solutions and the numerical solutions have been made.The results indicate that they are agreement very well with each other when the atomic interaction is not too strong.     

Calculation of the Probabilities of Molecular Transitions in Modeling Interisomeric Structural Transformations

The problems of a computational procedure in modeling structural isomer–isomer transitions in multiatomic molecules are considered. A number of approximations that allow one to considerably simplify calculation of the probabilities of these transformations are suggested. In comparison with traditional calculations of potential surfaces and determination of their saddle points, in the proposed approach the relationship between the electronic and vibrational components of a general problem is virtually changed. A particular emphasis is put on the vibrational part, which seems to be more physical. It is shown that the problem of structural isomer–isomer conversions can be solved without resorting at all to explicit calculation of the contribution of an electronic matrix element to the probability of transition. There is no need to study in detail the shapes of potential surfaces; it suffices only to know the positions of their minima. The calculation of multidimensional vibrational integrals is replaced by calculation of one-dimensional integrals. The results obtained form a basis for constructing methods for modeling the dynamic spectra of complex molecules considering their structural transformations.     

Fourier's Law for a Harmonic Crystal with Self-Consistent Stochastic Reservoirs

Journal of Statistical Physics - We consider a d-dimensional harmonic crystal in contact with a stochastic Langevin type heat bath at each site. The temperatures of the “exterior” left...     

光子晶体缺陷模的带宽与品质因子研究

利用光学传输矩阵法研究了结构参量对缺陷态光子晶体的缺陷模带宽和品质因子的影响.研究发现,当缺陷介质层厚度h₀的值较小时,缺陷模的带宽很小且基本保持不变;当h₀较大时,缺陷模的带宽随h₀的增加而快速增加.另外发现,缺陷模的品质因子在某个h₀处取最大值.但是总体上看,h₀较小时的品质因子要远大于h₀较大时的品质因子.此外,缺陷模的品质因子随光子晶体的周期数增加而急剧增加约4.788倍,而带宽则随周期数的增加而急剧减少约4.788倍.当周期数为13时就可以获得10⁹以上的品质因子值和小于10^-9的相对带宽值.     

Form-Preserving Transformations for Hamiltonians with Linear Terms in the Momentum

No Heading We consider Hamiltonians in (1+1) dimensions that contain linear terms in the momentum, resembling systems under the influence of a vector potential. For the time-dependent Schr?dinger equation (TDSE) associated with such Hamiltonians, we obtain the most general form-preserving transformation. This transformation is a valuable tool for tracking down solvable potentials and exact wave-functions of the TDSE.     

Integral-Type Darboux Transformations for the mKdV Hierarchy with Self-Consistent Sources

We present integral-type Darboux transformation for the mKdV hierarchy and for the mKdV hierarchy withself-consistent sources. In contrast with the normal Darboux transformation, the integral-type Darboux transformationscan offer non-auto-Backlund transformation between two (2n 1)-th mKdV equations with self-consistent sources withdifferent degrees. This kind of Darboux transformation enables us to construct the N-soliton solution for the mKdVhierarchy with self-consistent sources. We also propose the formulas for the m times repeated integral-type Darbouxtransformations for both mKdV hierarchy and mKdV hierarchy with self-consistent sources.     

Theoretical Exploration of the Isotopic Effect on Molecular High-Order Harmonic Generation

The isotopic effect on the generation of the molecular high-order harmonics is studied by numerically solving the one-dimensional time-dependent Schrödinger equation when the model hydrogen molecule ions/hydrogen deuterium molecule ions are exposed to an intense laser pulse. To explain the effect more clearly, not only the ionization probabilities but also the electron–nuclear probability density distributions and time-frequency profiles are calculated. The results show that more intense harmonics are generated in the asymmetric diatomic molecule ions/hydrogen deuterium molecule ions than those of hydrogen molecule ions. Moreover, the interference minimum in the harmonic spectra is investigated by adjusting the laser intensity and the initial vibrational state. It is shown that the interference minimum is sensitive to the laser intensity and the initial vibrational level for hydrogen molecule ions; in contrast, it is only dependent on the initial vibrational level for hydrogen deuterium molecule ions.