Solving Generalized Non-degenerate Two-Mode Two-Photon Jaynes-Cummings Model by Supersymmetric Unitary Transformation

Based on supersymmetric quantum mechanics theory, we introduced a supersymmetric unitary transfor mation to diagonalize the Hamiltonian of non-degenerate two-mode two-photon Jaynes-Cummings models which include any forms of intensity-dependent coupling, field-dependent detuning, and field nonlinearity. Its eigenvalue, eigenstates,and time evolution of state vector are obtained.     

Solving Generalized Non-degenerate Two-Mode Two-Photon Jaynes-Cummings Model by Supersymmetric Unitary Transformation

Based on supersymmetric quantum mechanics theory, we introduced a supersymmetric unitary transformation to diagonalize the Hamiltonian of non-degenerate two-mode two-photon Jaynes-Cummings models which include any forms of intensity-dependent coupling, field-dependent detuning, and field nonlinearity. Its eigenvalue, eigenstates, and time evolution of state vector are obtained.     

EXACT SOLUTION FOR SUPER-JAYNES-CUMMINGS MODEL

Based on the linear quantum transformation theory, we further propose a supersymmetric unitary transformation, whose operator can be constructed by the supersymmetric generators of Lie superalgebra. Therefore, by making use of the supersymmetric unitary transformation, we can obtain the eigenspectrum, the eigenstates and the super-partition function for the Super-Jaynes-Cummings model when the coupling constants are Grrassmann valued.     

Solving Multiphoton Jaynes–Cummings Model with Field Nonlinearity by Supersymmetric Unitary Transformation

We introduce a supersymmetric unitary transformation, to diagonalize the multiphoton Jaynes–Cummings model Hamiltonian based on supersymmetric quantum mechanics theory, that includes any forms of intensity-dependent coupling and field nonlinearity. On doing so, we obtain its eigenvalue and eigenstates, and the time evolution of state vector.     

Exact Solution for a Multiphoton Generalized Jaynes-Cummings Model with Inverse Operators

A new exactly solvable multiphoton generalized Jaynes-Cummings model is presented, whose Hamiltonian is related to the inverse of field mode creation and annihilation operators. Then we use supersymmetric unitary operators to diagonalize the Hamiltonian above and obtain their energy spectra and eigenstates. In addition, its pseudo-invariant eigen-operator is found as well, directly leading to the corresponding energy-level gap.     

SUSY formalism for the symmetric double well potential

Using first- and second-order supersymmetric Darboüx formalism and starting with symmetric double well potential barrier we have obtained a class of exactly solvable potentials subject to moving boundary condition. The eigenstates are also obtained by the same technique.     

Entanglement,superselection rules and supersymmetric quantum mechanics

In this paper we show that the energy eigenstates of supersymmetric quantum mechanics (SUSYQM) with non-definite “fermion” number are entangled states. They are “physical states” of the model provided that observables with odd number of spin variables are allowed in the theory like it happens in the Jaynes–Cummings model. Those states generalize the so-called “spin-spring” states of the Jaynes–Cummings model which have played an important role in the study of entanglement.     

Higgs bosons in the two-doublet model involving <Emphasis Type="Italic">CP</Emphasis> violation

An effective two-doublet Higgs potential that involves complex-valued parameters and whose CP invariance is violated both explicitly and spontaneously is considered. The problem of diagonalizing the mass term of this potential at a local minimum is solved. The eigenstates of Higgs bosons and their mass spectrum are obtained for the special case of the two-doublet Higgs sector of the minimal supersymmetric model, where the CP invariance of the effective potential is violated owing to the interactions of the Higgs fields with the third-generation scalar quarks.     

A quantum Hamilton–Jacobi proof of the nodal structure of the wave functions of supersymmetric partner potentials

Quantum Hamilton–Jacobi formalism is used to give a proof for Gozzi’s criterion, which states that for eigenstates of the supersymmetric partners, corresponding to the same energy, the difference in the number of nodes is equal to one when supersymmetry (SUSY) is unbroken and is zero when SUSY is broken. We also show that this proof is also applicable to the case, where isospectral deformation is involved.     

用超对称幺正变换解双光子过程的Jaynes-Cummings模型

本文发现了描写双光子过程的Jaynes-Cummings哈密顿量的超对称结构.根据超对称量子力学理论,引入了超对称幺正变换使其哈密顿量对角化.从而,得到了它的本征值、本征态,同时也计算了态的演化和跃迁几率.     

用不变量方法解具有非线性场和原子与场非线性耦合的Jaynes-Cummings模型

采用Lewis-Riesenfeld不变量方法研究了具有非线性场和任意形式原子与场相互作用的Jaynes-Cummings模型.该模型由于具有超对称代数结构,因此其Hamiltonian量可用超对称算符的线性组合表示.在算符N′的本征值子空间,用生成元算符构造出系统的不变量后,利用不变量方法求得了系统的一般波函数和时间演化算符,同时也计算了原子布居数和光子数的时间演化表达式.     

Investigation of phase-equivalent potentials by a halo transfer reaction

Using the supersymmetric quantum mechanics, we investigate the wave function-sensitive properties of the supersymmetric potentials which have received a lot of attention in the literature recently. We show that a superdeep potential and its phase-equivalent shallow-partner potential give very similar rms radius values for the weakly bound systems such as the deuteron and ¹¹Be nuclei. Although the corresponding eigenstates differ in the node-number, our investigation on the ¹¹Be(p, d )¹⁰Be single nucleon halo transfer reaction at 35 MeV show that also other physical quantities such as the cross-section angular distributions calculated using these wave functions reflect the nodal structure rather weakly. This lends support to two nearly equivalent treatments of the Pauli principle. Received: 15 May 2000 / Accepted: 14 September 2000     

15顶角模型反射方程的常数解

得到了15顶角模型A2(1)模型和超对称t–J模型反射方程的非对角解,结果发现,A2(1)模型具有三种形式的非对角解,超对称t–J模型具有一种形式的非对角解,每种形式的非对角解均含有两个解,每个非对角解中均含有三个任意参数.关于对角解也得到了一些新的形式的解.     

Invariant theory and exact solutions of the time-dependent supersymmetric two-level multiphoton Jaynes－Cummings model

On the basis of the fact that the two-level multiphoton Jaynes－Cummings (TLMJC) model possesses a supersymmetric structure, an invariant is constructed in terms of the supersymmetric generators by working in the sub-Hilbert-space corresponding to a particular eigenvalue of the conserved supersymmetric generators (the time-independent invariant). In this paper, we investigate the invariant-related unitary transformation approach to exact solutions of the time-dependent TLMJC model.     

Full spectrum of the Rabi model

It is shown that in the Rabi model, for an integer value of the spectral parameter x, in addition to the finite number of the classical Judd states there exist infinitely many possible eigenstates. These eigenstates exist if the parameters of the problem are zeros of a certain transcendental function; in other words, there are infinitely many possible choices of parameters for which integer x belongs to the spectrum. Moreover, it is shown that the classical Judd eigenstates appear as degenerate cases of the confluent Heun function.     

MULTIPHOTON JAYNES-CUMMINGS MODEL SOLVED VIA SUPERSYMMETRIC UNITARY TRANSFORMATION

For multiphoton Jaynes-Cummings(JC) model Hamiltonian, we find its supersymmetric structure. Based on this, we introduce a supersymmetric unitary transformation to diagonalize the JC Hamiltonian, in so doing, its eigenvalues and eigenfunctions are obtained. The transition process is also calculated.     

Supersymmetric Electroweak Corrections to Top Quark Production at LHC

The am_t²/m²w order supersymmetric electroweak corrections arising from loops of chargino, neu tralino and squark to top quark pair production by gg fusion at LHC are calculated in the minimal supersymmetric model. We found that the corrections amount about a few percent.     

Resonant invisibility with finite range interacting fermions

We study the eigenstates of two opposite spin fermions on a one-dimensional lattice with finite range interaction. The eigenstates are projected onto the set of Fock eigenstates of the noninteracting case. We find antiresonances for symmetric eigenstates, which eliminate the interaction between two symmetric Fock states when satisfying a corresponding selection rule.     

Supersymmetric structures of Dirac oscillators in commutative and noncommutative spaces

The supersymmetric properties of a charged planar Dirac oscillator coupling to a uniform perpendicular magnetic field are studied. We find that there is an N=2 supersymmetric structure in both commutative and noncommutative cases. We construct the generators of the supersymmetric algebras explicitly and show that the generators of the supersymmetric algebras can be mapped onto ones which only contain the left or right-handed chiral phonons by unitary transformations.