Exact Eigenfunctions of N-body System with Quadratic Pair Potential

We obtain the energy spectrum and all the corresponding eigenfunctions of N-body Bose and Fermi systems with Quadratic Pair Potentials in one dimension. The original first excited state or energy level is disappeared in one dimension, which results from the operation of symmetry or antisymmetry of identical particles. In two and higher dimensions, we give the energy spectrum and the analytical ground state wave functions and the degree of degeneracy. By comparison, we refine Avinash Khare's results by making some items in his article precisely.     

Energy spectrum of fermionized bosonic atoms in optical lattices

We investigate the energy spectrum of fermionized bosonic atoms, which behave very much like spinless noninteracting fermions, in optical lattices by means of the perturbation expansion and the retarded Green's function method. The results show that the energy spectrum splits into two energy bands with single-occupation; the fermionized bosonic atom occupies nonvanishing energy state and left hole has a vanishing energy at any given momentum, and the system is in Mott-insulating state with a energy gap.Using the characteristic of energy spectra we obtained a criterion with which one can judge whether the Tonks-Girardeau (TG) gas is achieved or not.     

Tunneling and reflection of an exciton incident upon a quantum heterostructure barrier

We investigate, in one spatial dimension, the quantum mechanical tunneling of an exciton incident upon a heterostructure barrier. We model the relative motion eigenstates of the exciton using a form of the one-dimensional hydrogen atom which avoids difficulties previously associated with 1D hydrogenic states. We obtain probabilities of reflection and transmission using the method of variable transmission and reflection amplitudes. Our calculations may be broadly divided into two sets. In the first set, we consider general qualitative aspects of exciton tunneling, such as the effect of different effective masses for electrons and holes and a relative difference in electron and hole barrier strengths. The second set models the tunneling of an exciton in a GaAs/Al(x)Ga(1-x)As heterostructure. In these calculations we find that, for energies such that the two lowest exciton states are coupled, the probability spectrum for transition from the ground state to the first excited state is identical to that for transition from the first excited state to the ground state. In addition, narrow peaks in the probability spectrum for transition are observed across this energy range for low dopant concentration x. Other interesting phenomena correlated with these peaks in the transition probability are reported.     

The fractal energy measurement and the singularity energy spectrum analysis

The singularity exponent (SE) is the characteristic parameter of fractal and multifractal signals. Based on SE, the fractal dimension reflecting the global self-similar character, the instantaneous SE reflecting the local self-similar character, the multifractal spectrum (MFS) reflecting the distribution of SE, and the time-varying MFS reflecting pointwise multifractal spectrum were proposed. However, all the studies were based on the depiction of spatial or differentiability characters of fractal signals. Taking the SE as the independent dimension, this paper investigates the fractal energy measurement (FEM) and the singularity energy spectrum (SES) theory. Firstly, we study the energy measurement and the energy spectrum of a fractal signal in the singularity domain, propose the conception of FEM and SES of multifractal signals, and investigate the Hausdorff measure and the local direction angle of the fractal energy element. Then, we prove the compatibility between FEM and traditional energy, and point out that SES can be measured in the fractal space. Finally, we study the algorithm of SES under the condition of a continuous signal and a discrete signal, and give the approximation algorithm of the latter, and the estimations of FEM and SES of the Gaussian white noise, Fractal Brownian motion and the multifractal Brownian motion show the theoretical significance and application value of FEM and SES.     

Antiferromagnetism in the Hubbard model

The energy spectrum of the two-sublattice Hubbard model is obtained in the static-fluctuation approximation. It is shown how the structure of the energy spectrum is modified as the parameters of the Hubbard model are varied. The ground state of the simple Hubbard model of dimension d=2 is the dielectric antiferromagnetic state. The author derives a consistency equation for the magnetization, which has an antiferromagnetic solution. Fiz. Tverd. Tela (St. Petersburg) 39, 1594–1599 (September 1997)     

Noiseless quantum circuits for the Peres separability criterion

In this Letter we give a method for constructing sets of simple circuits that can determine the spectrum of a partially transposed density matrix, without requiring either a tomographically complete positive-operator-valued measurement or the addition of noise to make the spectrum non-negative. These circuits depend only on the dimension of the Hilbert space and are otherwise independent of the state.     

Harmonic Interaction Model and Its Applications in Bose–Einstein Condensation

We exactly solve the model of N harmonic interacting Bosons in a harmonic trap in any dimension. The exact ground state wavefunction, free energy, spectrum, and low excitation states are calculated. The finite particle number effect is addressed when the exact solution is compared with a mean field solution. Then we compare the harmonic interaction system with a pseudo-potential interaction system. In spite of the seemingly quite different nature of interaction, several similarities are found between the two systems.     

Flat Information Geometries in Black Hole Thermodynamics

The Hessian of either the entropy or the energy function can be regarded as a metric on a Gibbs surface. For two parameter families of asymptotically flat black holes in arbitrary dimension one or the other of these metrics are flat, and the state space is a flat wedge. The mathematical reason for this is traced back to the scale invariance of the Einstein–Maxwell equations. The picture of state space that we obtain makes some properties such as the occurence of divergent specific heats transparent.Supported by VR.     

Relativistic Cloud-In-Cell Simulation of Free Electron Laser

We have developed one-and a half-dimensional (one space dimension and two velocity components) relativistic electromagnetic cloud-in-cell simulation (CIC-R) code which is suitable for simulating the free-electron laser process. Using CIC-R we have simulated the temporal evolution of the free-electron laser, and obtained the results on the linear growth rates of the unstable spectrum and the dispersion relation of the coupling between the electromagnetic waves and electrostatic waves which agree with the theory. Other results such as the time development of the electron distribution function, nonlinear saturation and the efficiency of energy conversion are also presented in detail.     

A renormalization group study of the Anderson Hamiltonian for arbitrary band-filling

The Anderson hamiltonian has been studied for arbitrarily filled bands using the real space renormalization group (RSRG) method. The ground state energy is determined in one dimension for the scale factors n_s = 3 and n_s = 5. Direct application of RSRG gives, for a certain n_s, the results for only n_s number of discrete cases of band-filling. We then devise an interpolation scheme which spans the entire region of the band and gives the ground state energy for any general filling. The results, as provided by our scheme, satisfy the desired particle-hole symmetry exactly and are always an upper bound to the exact one. The non-linear dependence of the band energy on its filling is represented correctly, even for small n_s. Finally, we discuss how the results improve for large n_s.     

Cooling nonlinear lattices toward energy localization

We describe the energy relaxation process produced by surface damping on lattices of classical anharmonic oscillators. Spontaneous emergence of localized vibrations dramatically slows down dissipation and gives rise to quasistationary states where energy is trapped in the form of a gas of weakly interacting discrete breathers. In one dimension, strong enough on-site coupling may yield stretched-exponential relaxation which is reminiscent of glassy dynamics. We illustrate the mechanism generating localized structures and discuss the crucial role of the boundary conditions. For two-dimensional lattices, the existence of a gap in the breather spectrum causes the localization process to become activated. A statistical analysis of the resulting quasistationary state through the distribution of breathers' energies yield information on their effective interactions.     

Mixtures of maximally entangled pure states

We study the conditions when mixtures of maximally entangled pure states remain entangled. We found that the resulting mixed state remains entangled when the number of entangled pure states to be mixed is less than or equal to the dimension of the pure states. For the latter case of mixing a number of pure states equal to their dimension, we found that the mixed state is entangled provided that the entangled pure states to be mixed are not equally weighted. We also found that one can restrict the set of pure states that one can mix from in order to ensure that the resulting mixed state is genuinely entangled. Also, we demonstrate how these results could be applied as a way to detect entanglement in mixtures of the entangled pure states with noise.     

Excitation Spectra of λ(φφ+)2 Relativistic Bose condensate

Using the Bogolu bov transformation method, we calculate excitation energy spectra for a charged relativistic Bose-Einstein condensate with λ(φφ⁺)² interactions. There are two distinct spectra. In the long-wavelength limit one of the spectra approaches to the phonon spectrum for an uncharged nonrelativistic boson condensate, and the other to the nonrelativistic particle energy spectrum. Theground state is explicitly constructed as a coherent state which contains zero-momentum bosons and pairs of quanta with nonzero opposite momenta.     

Integrability of N-Component Bariev Model Under Open Boundary Conditions

N-component Bariev model for correlated hopping under open boundary conditions in one dimension is studied in the framework of Bethe ansatz method. The energy spectrum and the related Bethe ansatz equations are obtained.     

On the negative point spectrum of quantum mechanical three-body systems

We consider quantum mechanical three-body systems interacting with two-body potentials that are sufficiently regular locally, decrease faster than r^?(2+?) at infinity, and are such that either one two-body subsystem (at least) has a negative energy bound state, or no two-body subsystem has a zero energy bound state or resonance. (This assumption excludes the possibility of the Efimov effect.) We then prove that (1) the discrete spectrum is finite, (2) the point spectrum has no negative accumulation points. (These results have been proved earlier by Sigal and Yafaev, respectively, by different methods and with slightly different assumptions.)     

开边界条件下一类新Hubbard模型的精确解

用坐标Bethe ansatz方法详细研究了开边界条件下一类新Hubbard模型的可积性问题. 得到了系统的能谱、可积边界条件和Bethe ansatz方程.     

BeAl2O4:Cr3+紫外光谱的研究

在强场理论的基础上,本文考虑了组态相互作用,拟合了各能级位置,并对其紫外光谱进行了讨论.     

Constructive proof of localization in the Anderson tight binding model

We prove that, for large disorder or near the band tails, the spectrum of the Anderson tight binding Hamiltonian with diagonal disorder consists exclusively of discrete eigenvalues. The corresponding eigenfunctions are exponentially well localized. These results hold in arbitrary dimension and with probability one. In one dimension, we recover the result that all states are localized for arbitrary energies and arbitrarily small disorder. Our techniques extend to other physical systems which exhibit localization phenomena, such as infinite systems of coupled harmonic oscillators, or random Schrödinger operators in the continuum.Work supported in part by National Science Foundations grant MCS-8108814 (A03).Work supported in part by National Science Foundation grant DMR 81-00417.     

Exact Solutions of One-Dimensional N-Component Bariev Model with General Boundary Conditions

The N-component Bariev model for correlated hopping with open boundary conditions in one dimension is studied in the framework of coordinate Bethe ansatz method. The energy spectrum, integrable boundary conditions and the corresponding Bethe ansatz equations are derived.