无限势阱中负δ势的低能态

给出了无限势阱中负的δ势存在能量等于或小于零低能态的必要条件,并给出相应能态波函数的表示式和能级公式.     

Numerical study on formation of electronic quantum states due to self-coherency in a non-periodic system

In order to investigate formation process of electronic quantum states in a confined system, we simulate motion of a wavepacket state and show how an eigenstate is formed due to coherence of electronic wave from the viewpoint that an eigenstate arises as a result of self-interference of a moving electron. Numerical results for a Hénon–Heiles potential in which chaotic motion can occur in the classical mechanics indicate that electronic eigenstates can arise even when motion of an electron is non-periodic. The results show that, in the quantum mechanics, periodicity is unnecessary for the formation of eigenstates.     

No Approximate Complex Fermion Coherent States

Whereas boson coherent states with complex parametrization provide an elegant, and intuitive representation, there is no counterpart for fermions using complex parametrization. However, a complex parametrization provides a valuable way to describe amplitude and phase of a coherent beam. Thus we pose the question of whether a fermionic beam can be described, even approximately, by a complex-parametrized coherent state and define, in a natural way, approximate complex-parametrized fermion coherent states. Then we identify four appealing properties of boson coherent states (eigenstate of annihilation operator, displaced vacuum state, preservation of product states under linear coupling, and factorization of correlators) and show that these approximate complex fermion coherent states fail all four criteria. The inapplicability of complex parametrization supports the use of Grassman algebras as an appropriate alternative.      

Coordinate Eigenstate Representation in Noncommutative Space as a New Entangled State in Quantum Mechanics

For the first time we construct the eigenstate ｜τ〉 of noncommutatlve coordinate. It turns out that｜τ〉 is an entangled state in the ordinary space. Remarkably, its Schmidt decomposition has definite expression in the coordinate representation and the momentum representation. The 〈τ｜ representation can simplify some calculations for obtaining energy level of two-dimensional oscillator in noncommutative space.     

N掺杂SnO2材料光电性质的第一性原理研究

采用全电势线性缀加平面波(full potential linearized augmented plane wave method,简记为FP-LAPW)方法,基于密度泛函理论第一性原理计算分析N掺杂SnO₂材料,研究了在N替代O原子和N替代Sn原子情况下的电子态密度、电荷密度分布以及光学性质.研究表明N掺杂替代Sn较之N掺杂替代O原子的带隙要宽,都宽于SnO₂的本征带隙,且两种情况下N分别处于负氧化态和正氧化态,其介电函数谱也与带隙对应发生蓝移,从理论上指出     

Uncertainty relations for a q-deformed coherent spin state

A Coherent Spin State (CSS) is defined as an eigenstate of the spin component in the direction specified by angles (θ₀,?₀). This state satisfies minimum uncertainty relation, with uncertainties equally distributed on any two orthogonal components normal to the direction of the total spin vector 〈S〉. Starting from this concept, we apply the notion of CSS to quantum groups and discuss the properties of q-deformed CSS and the associated uncertainty relations. We show that these states behave as Intelligent Spin States (ISS) on two orthogonal components normal to the direction of the mean value of the spin operator.     

无限方势阱本征态的稳定性

我们用存活率(SP)的概念研究了无限方势阱本征态的稳定性,做了理论上的推导,并进行了数值计算,发现基态在外界的扰动下非常稳定,而激发态则非常不稳定,能级越高,越不稳定.     

Analytical method for yrast line states in the interacting two—component Bose—Einstein condensate

The yrast spectrum for the harmonically trapped two-component Bose-Einstein condensate (BEC),omitting the difference between the two components,has been studied using an analytical method.The energy eigenstates and eigenvalues for L=0,1,2,3 are given,We illustrate that there are different eigenstate behaviours between the even L and odd L cases for the two-component BEC in two dimensions.Except for symmetric states,there are antisymmetric states for the permutation of the two components,which cannot reduce to those in a single condensate case when the value of L is odd.     

QCD Factorization of Semi-Inclusive DIS Process at Operator Level

The operator level proof of factorization theorem exhibited in [ar Xiv:hep-ph/1307.4194] is extended to the semi-inclusive deep inelastic scattering process(SIDIS). Factorization theorem can be proved at operator level if there are not detected soft hadrons. The key point is that the initial one-nucleon state is the eigenstate of QCD.     

SU(1,1) Coherent States for the Generalized Two-Mode Time-Dependent Quadratic Hamiltonian System

The SU(1,1) coherent states, so-called Barut-Girardello coherent state and Perelomov coherent state, for the generalized two-mode time-dependent quadratic Hamiltonian system are investigated through SU(1,1) Lie algebraic formulation. Two-mode Schrödinger cat states defined as an eigenstate of $\hat{K}_{-}^{2}The SU(1,1) coherent states, so-called Barut-Girardello coherent state and Perelomov coherent state, for the generalized two-mode time-dependent quadratic Hamiltonian system are investigated through SU(1,1) Lie algebraic formulation. Two-mode Schr?dinger cat states defined as an eigenstate of are also studied. We applied our development to two-mode Caldirola-Kanai oscillator which is a typical example of the time-dependent quadratic Hamiltonian system. The time evolution of the quadrature distribution for the probability density in the coherent states are analyzed for the two-mode Caldirola-Kanai oscillator by plotting relevant figures.     

The convergence of the one-dimensional ground states to an infinite lattice

For one-dimensional systems interacting via a two-body potential, the sequence of ground states is proved to converge to an infinite lattice, for a large open class of interactions, containing in particular the Lennard-Jones potential.     

Note on the convergence of normal and antinormal ordering expansions of the boson exponential operator exp(-μâ+â)

For the boson exponential operator f(â⁺â) = exp(-μâ⁺â) it is shown by an elementary direct calculation using occupation number eigenstates that for a certain domain of the complex μ-plane the formally defined antinormally ordered expansion of f yields states of infinite norm when applied to an occupation number eigenstate. The normally ordered expansion, however, is well defined for all μ.     

Quenching Evolution in a Quantum-Classical Hybrid System

The adiabatic theorem, an important theory in quantum mechanics, tells that a quantum system subjected to gradually changing external conditions remains to the same instantaneous eigenstate of its Hamiltonian as it initially in. In this paper, we study the quench evolution that is another extreme circumstance where the external conditions vary rapidly such that the quantum system can not follow the change and remains in its initial state (or wavefunction). We examine the matter-wave pressure and derive the requirement for such an evolution. The study is conducted by considering a quantum particle in an infinitely deep potential, the potential width Q is assumed to be change rapidly. We show that the total energy of the quantum subsystem decreases as Q increases, and this rapidly change exerts a force on the wall which plays the role of boundary of the potential. For Q < Q₀ (Q₀ is the initial width of the potential), the force is repulsive, and for Q > Q₀, the force is positive. The condition for the quenching evolution evolution is given via a spin-\( \frac{1}{2} \) in a rotating magnetic field.

     

时间相关外场中量子系统的辛算法

引入辅助变量将时间相关外场中量子系统的显含时间哈密顿系统转换成不显含时间的可分哈密顿系统,给出了任意阶精度的显式辛格式,计算了一维有限宽无限深势阱中的电子与模拟激光场的相互作用,结果与理论分析一致,且很好地保持了波函数模方归一,表明该方法适于计算激光场与原子的相互作用.     

Atomic-dipole squeezing for arbitrarily prepared atom and field in multi-photon interaction

Summary The atomic-dipole squeezing condition for arbitrarily prepared atomic and field states in multi-photon Jaynes-Cummings model was derived. Three special cases were discussed. For the field initially in a vacuum state and a certain eigenstate of the Susskind-Glogower phase operator, the analytical dipole squeezing conditions were obtained and the maximum squeezing values were calculated. For a squeezed vacuum input field, the dipole squeezing behaviours under the influence of the field squeezing parameterr and the phased atom were numerically treated.     

Examples of Bosonic de Finetti States over Finite Dimensional Hilbert Spaces

According to the Quantum de Finetti Theorem, locally normal infinite particle states with Bose–Einstein symmetry can be represented as mixtures of infinite tensor powers of vector states. This note presents examples of infinite-particle states with Bose–Einstein symmetry that arise as limits of Gibbs ensembles on finite dimensional spaces, and displays their de Finetti representations. We consider Gibbs ensembles for systems of bosons in a finite dimensional setting and discover limits as the number of particles tends to infinity, provided the temperature is scaled in proportion to particle number     

The Canopy Graph and Level Statistics for Random Operators on Trees

For operators with homogeneous disorder, it is generally expected that there is a relation between the spectral characteristics of a random operator in the infinite setup and the distribution of the energy gaps in its finite volume versions, in corresponding energy ranges. Whereas pure point spectrum of the infinite operator goes along with Poisson level statistics, it is expected that purely absolutely continuous spectrum would be associated with gap distributions resembling the corresponding random matrix ensemble. We prove that on regular rooted trees, which exhibit both spectral types, the eigenstate point process has always Poissonian limit. However, we also find that this does not contradict the picture described above if that is carefully interpreted, as the relevant limit of finite trees is not the infinite homogenous tree graph but rather a single-ended ‘canopy graph.’ For this tree graph, the random Schrödinger operator is proven here to have only pure-point spectrum at any strength of the disorder. For more general single-ended trees it is shown that the spectrum is always singular – pure point possibly with singular continuous component which is proven to occur in some cases.     

Inconsistency in the application of the adiabatic theorem

The adiabatic theorem states that an initial eigenstate of a slowly varying Hamiltonian remains close to an instantaneous eigenstate of the Hamiltonian at a later time. We show that a perfunctory application of this statement is problematic if the change in eigenstate is significant, regardless of how closely the evolution satisfies the requirements of the adiabatic theorem. We also introduce an example of a two-level system with an exactly solvable evolution to demonstrate the inapplicability of the adiabatic approximation for a particular slowly varying Hamiltonian.     

Continuously infinite commensurate-incommensurate phase transition of a two-dimensional competing Ising model

We consider the critical behavior of a two-dimensional competing axial Ising model including interactions up to third nearest neighbors in one direction. On the basis of a low-temperature analysis relating the transfer matrix of this model with the Hamiltonian of theS = 1/2XXZ chain, it is shown that the usual square root singularity dominating commensurate-incommensurate phase transitions of two-dimensional systems merges into a continuously infinite transition for certain relations among the coupling parameters. The conjectured equivalence between the maximum eigenstate of the transfer matrix associated with this model and the ground state of theXXZ chain is tested numerically for lattice widths up to 18 sites.     

On the possibility of designing interacting semiconductor quantum wells with zero perturbation coupling

The paper describes the possibility of designing matched interacting semiconductor quantum wells. It is shown that for a given eigenstate of a quantum well (QW), it is always possible to find another QW in such a way that the coupling leaves the original eigenstate of the host QW unperturbed irrespective of the strength of interaction. For rectangular QWs, the condition is met with whenever the second QW has appropriate width and depth so that phase travelled by an electron wave through it is an integral multiple of π.