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.     

Pseudo Invariant Eigenoperator Method for Some Generalized Jaynes-Cummings Models

Based on the method of pseudo invariant eigenoperator (PIEO), we investigate three kinds of the generalized Jaynes-Cummings (JC) models such as the super JC model, the Kerr nonlinear JC model, and the two-atomic two-photon JC model. Our main task lies in finding the so-called pseudo invariant eigenoperators and deriving the energy-level gap for the above Hamiltonians, respectively. Compared with the usual Schrodinger equation approach or the directly diagonalizing Hamiltonian, the PIEO method could be quite concise and effective to obtain energy-level gap of the given system.     

Unitary transformation method for solving generalized Jaynes-Cummings models

Two fully quantized generalized Jaynes-Cummings models for the interaction of a two-level atom with radiation field are treated, one involving intensity dependent coupling and the other involving multiphoton interaction between the field and the atom. The unitary transformation method presented here not only solves the time dependent problem but also allows a determination of the eigensolutions of the interacting Hamiltonian at the same time.     

Generalized Supersymmetric Perturbation Theory

Using the basic ingredient of supersymmetry, a simple alternative approach is developed to perturbation theory in one-dimensional non-relativistic quantum mechanics. The formulae for the energy shifts and wavefunctions do not involve tedious calculations which appear in the available perturbation theories. The model applicable in the same form to both the ground state and excited bound states, unlike the recently introduced supersymmetric perturbation technique which, together with other approaches based on logarithmic perturbation theory, are involved within the more general framework of the present formalism.     

Dynamical Localization for Unitary Anderson Models

This paper establishes dynamical localization properties of certain families of unitary random operators on the d-dimensional lattice in various regimes. These operators are generalizations of one-dimensional physical models of quantum transport and draw their name from the analogy with the discrete Anderson model of solid state physics. They consist in a product of a deterministic unitary operator and a random unitary operator. The deterministic operator has a band structure, is absolutely continuous and plays the role of the discrete Laplacian. The random operator is diagonal with elements given by i.i.d. random phases distributed according to some absolutely continuous measure and plays the role of the random potential. In dimension one, these operators belong to the family of CMV-matrices in the theory of orthogonal polynomials on the unit circle. We implement the method of Aizenman-Molchanov to prove exponential decay of the fractional moments of the Green function for the unitary Anderson model in the following three regimes: In any dimension, throughout the spectrum at large disorder and near the band edges at arbitrary disorder and, in dimension one, throughout the spectrum at arbitrary disorder. We also prove that exponential decay of fractional moments of the Green function implies dynamical localization, which in turn implies spectral localization. These results complete the analogy with the self-adjoint case where dynamical localization is known to be true in the same three regimes.     

Generalized Jaynes-Cummings model with atomic motion

Following the recent experiments in the elementary Bose-Fermi interaction, we extend the Jaynes-Cummings model, to include the atomic motion and the mode structure. Using the above extended model, we study the quantum noise distribution in the two quadrature components of the radiation mode.     

多光子集体辐射原子的J-C模型超对称求解

根据已有的双光子情形具有两个集体辐射原子的Jaynes-Cumm ings(J-C)模型,将之推广到多光子情形。找出了该模型的超对称生成元,然后用超对称变换的方法十分简洁地求解出了它的能量本征值和能量本征态。     

A Generalized Jaynes-Cummings Model for Two Collectively Radiating Atoms

The Jaynes-Cummings model in theoretically generalized to the simplest case of collectively radiating atoms. The comsponding Hamiltonian is diagonalked and some transition process in calculated.     

Simulating Entangling Unitary Operator Using Non-maximally Entangled States

We use non-maximally entangled states （NMESs） to simulate an entangling unitary operator （EUO） with a certain probability. Given entanglement resources, the probability of the success we achieve is a decreasing function of the parameters of the EUO. Given an EUO, for certain entanglement resources the result is optimal, i.e., the probability obtains a maximal vaiue, and for optimal result higher parameters of the EUO match more amount of entanglement resources. The probability of the success we achieve is higher than the known results under some condition.     

Some Generalized Scalar Field Models with Abundant Soliton-Like configurations

Some generahed scalar field models are presented. It is shown that there exist generally three types of soliton solutions for the extended models. The form of the first type of the soliton solutions is model-independent. An arbitrary constant can be included in the second type of the soliton excitations which is model-dependent. The third type of the soliton solutions is also modeldependent but with no arbitrary constant. The extended φ⁴ model and sine-Gordon model are studied in detail.     

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.     

Geometric Phase in a Generalized Time-Dependent Jaynes-Cummings Model

By using the Lewis–Riesenfeld invariant theory, we have studied the dynamical and the geometric phases in a generalized time-dependent Jaynes-Cummings model. It is found that the geometric phases in a cycle case have nothing to do with the frequency of the electromagnetic wave, the energy difference between two levels of the atom, and the coupling strength between the atom and the light field.     

Integrable Lattice Spin Models from Supersymmetric Dualities

Recently, there has been observed an interesting correspondence between supersymmetric quiver gauge theories with four supercharges and integrable lattice models of statistical mechanics such that the two-dimensional spin lattice is the quiver diagram, the partition function of the lattice model is the partition function of the gauge theory and the Yang–Baxter equation expresses the identity of partition functions for dual pairs. This correspondence is a powerful tool which enables us to generate new integrable models. The aim of the present paper is to give a short account on a progress in integrable lattice models which has been made due to the relationship with supersymmetric gauge theories and make clear notes on the special functions used by several authors.     

Generalized Self-Duality for the Supersymmetric Yang-Mills Theory with a Scalar Multiplet

Abstract

Generalized Self-Duality Equations for the Supersymmetric Yang-Mills Theory with a Scalar Multiplet are Presented in Terms of Component Fields and Superfields as Well.     

Unitary Operator and Density Matrix for a Ring of Coupled Oscillator Model

A unitary operator U which can directly diagonalize the Hamiltonian of a ring of N coupled oscillators is found. With use of the technique of integration within an ordered product of operators we see that U includes a squeezing transformation. For large N it turns out that, except a zero-mode, the ring Hamiltonian has the same spectrum as the one-dimensional monatomic lattice model plus the Born-Von-Karmen boundary condition. The density matrix of this model is calculated by the U transformation, which further leads us to derive the heat capacity of the coupled oscillators in the large N limit.     

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.     

Scattering in Supersymmetric M(atrix) Models

We review several tests of the M(atrix)‐Model conjecture that asserts that the dynamics of M‐Theory, the eleven‐dimensional Ur‐theory containing all known string theories and also eleven‐dimensional supergravity in specific limits, is given by a quantum mechanical matrix model. In particular, scattering processes are analyzed both from the M(atrix)‐Model and from the supergravity perspective and the corresponding S‐matrix elements are compared. We find impressive agreement between these two theories as long as only classical supergravity is considered. If one includes also quantum effects on the supergravity side, the agreement does not persist. In addition to these calculations, the question of the existence of classical solutions to the M(atrix)‐Model equations of motion with momentum transfer is addressed and answered negatively.     

Supersymmetric WZ-Poisson Sigma Model and Twisted Generalized Complex Geometry

It has been shown recently that extended supersymmetry in twisted first-order sigma models is related to twisted generalized complex geometry in the target. In the general case there are additional algebraic and differential conditions relating the twisted generalized complex structure and the geometrical data defining the model. We study in the Hamiltonian formalism the case of vanishing metric, which is the supersymmetric version of the WZ-Poisson sigma model. We prove that the compatibility conditions reduce to an algebraic equation, which represents a considerable simplification with respect to the general case. We also show that this algebraic condition has a very natural geometrical interpretation. In the derivation of these results the notion of contravariant connections on twisted Poisson manifolds turns out to be very useful.