Concurrence of Quantum States: Algebraic Dynamical Method Study XXX Models in a Time-Depending Random External Field

Based on algebraic dynamics and the concept of the concurrence of the entanglement, we investigate the evolutive properties of the two-qubit entanglement that formed by Heisenberg XXX models under a time-depending external field. For this system, the property of the concurrence that is only dependent on the coupling constant J and total values of the external field is proved. Furthermore, we found that the thermal concurrence of the system under a static random external field is a function of the coupling constant J, temperature T, and the magnitude of external field.

Entanglement dynamics of a moving multi-photon Jaynes-Cummings model in mixed states

Using the algebraic dynamical method, the entanglement dynamics of an atom-field bipartite system in a mixed state is investigated. The atomic center-of-mass motion and the field-mode structure are also included in this system. We find that the values of the detuning and the average photon number are larger, the amplitude of the entanglement is smaller, but its period does not increase accordingly. Moreover, with the increase of the field-mode structure parameter and the transition photon number, the amplitude of the entanglement varies slightly while the oscillation becomes more and more fast. Interestingly, a damping evolution of the entanglement appears when both the detuning and the atomic motion are considered simultaneously.

Microscopic shell-model description of irrotational-flow dynamics in^(102)Pd

The structure of the low-lying collective excitations in 102Pd is examined within the recently proposed microscopic shell-model version of the Bohr-Mottelson(BM)collective model.A good description of the excitation energies of the lowest ground,γ,andβbands,as well as the staggering function between the collective states of theγband and some other energy-dependent quantities,is obtained.The low-energy intraband and interband quadrupole dynamics is reasonably well described within the present proton-neutron sympletic based shell-model approach without the use of an effective charge and compared with the predictions of nuclear structure models.The obtained results of the present study shed light on the question of the existence of irrotational-flow type quadrupole dynamics,which lies on the ground of the original BM model of quantized vibrations and surface-wave rotations in atomic nuclei.

Entanglement Evolution of Two-Coupled Spins in a Time-Dependent Rotating Magnetic Field

We study the dynamics evolution of a two-qubit Heisenberg XXX spin chain under a time-dependent rotating magnetic field. Based on the algebraic structure of the non-autonomous system, the exact solution of the Schrodinger equation is obtained by using the method of algebraic dynamics. Based on the time-dependent analytical solution, we further study the entanglement evolution between the two coupled spins for different initial states, and find that the entanglement is determined by the coefficients of the initial state and the coupling constant J of the system.

Anisotropic Spin Cluster as a Qubit

We study an anisotropic spin cluster of 3 spin S=1/2 particles with antiferromagnetic exchange interactionwith non-uniform coupling constants.A time-dependent magnetic field is applied to control the time evolution of thecluster.It is well known that for an odd number of sites a spin cluster qubit can be defined in terms of the ground statedoublet.The universal one-qubit logic gate can be constructed from the time evolution operator of the non-autonomousmany-body system,and the six basic one-qubit gates can be realized by adjusting the applied time-dependent magneticfield.

Dynamical Properties of Two Coupled Dissipative QED Cavities Driven by Coherent Fields

When two identical QED cavities driven by the coherent fields are located in a uniform environment, in addition to dissipation, there appears an indirect coupling between the two cavities induced by the background fields. We investigate the effects of the coherent fields, the dissipation as well as the incoherent coupling on the following dynamical properties of the system： photon transfer, reversible decoherence, and quantum state transfer, etc. We find that the photons in the cavities do not leak completely into the environment due to the collective coupling between the cavities and the enviroment, and the photons are transferred irreversibly from the cavity with more photons to the cavity with less ones due to the incoherent coupling so that they are equally distributed among the two cavities. The coherent field pumping on the two cavities increases the mean photons, complements the revived magnitude of the reversible decoherence, but hinders the quantum state transfer between the two cavities. The above phenomena may find applications in quantum communication and other basic fields.

Exact results on cavity cooling in a system of a two-level atom and a cavity field

Using the algebraic dynamical method, this paper investigates the laser cooling of a moving two-level atom coupled to a cavity field. Analytical solutions of optical forces and the cooling temperatures are obtained. Considering Rb atoms as an example, it finds that the numerical results are relevant to the recent experimental laser cooling investigations.

Partial entropy change and entanglement in the mixed state for a Jaynes-Cummings model with Kerr medium

By using the algebraic dynamical approach, an atom--field bipartite system in mixed state is employed to investigate the partial entropy change and the entanglement in a cavity filled with Kerr medium. The effects of different nonlinear intensities are studied. One can find that the Kerr nonlinearity can reduce the fluctuation amplitudes of the partial entropy changes and the entanglement of the two subsystems, and also influence their periodic evolution. Meanwhile, increasing the Kerr nonlinear strength can convert the anti-correlated behaviour of the partial entropy change to the positively correlated behaviour. Furthermore, the entanglement greatly depends on the temperature. When the temperature or the nonlinear intensity increases to a certain value, the entanglement can be suppressed greatly.

Shell-model representations of the microscopic version of the Bohr-Mottelson collective model

The structure of the irreducible collective spaces of the group Sp(12,R),which many-particle nuclear states are classified according to the chain Sp(12,R)⊃U(6)⊃SO(6)⊃SU_(pn)(3)⊗SO(2)⊃SO(3)of the proton-neutron symplectic model(PNSM),is considered in detail.This chain of the PNSM was recently shown to correspond to a microscopic shell-model version of the Bohr-Mottelson collective model.The construction of the relevant shell-model representations of the Sp(12,R)group along this chain is considered for three nuclei with varying collective properties and from different mass regions.It is shown that the SU_(pn)(3)basis states of the Sp(12,R)representations belonging to the SO(6)irreps with seniorityυ≥υ0,withυ0 denoting the maximal seniority SO(6)irrep contained in the Sp(12,R)bandhead,are always Pauli allowed,but organized in a different way into different SO(6)shells.This is in contrast to the case of filling the levels of the standard three-dimensional harmonic oscillator and using the plethysm operation.Although the SU_(pn)(3)multiplets withinυ<υ0 are not all Pauli forbidden,it is safe to discard them.The results obtained in the present work are important for the practical application of the microscopic version of the Bohr-Mottelson collective model.

Proton-neutron symplectic model description of ^(106)Cd

In this study,a microscopic shell-model description of the low-lying collective states in the weakly deformed nucleus ^(106)Cd within the recently proposed microscopic version of the Bohr-Mottelson model is provided.A good description of the excitation energies of the lowest ground,γ,andβquasibands is obtained without the adjustable kinetic energy term.Furthermore,γdegrees of freedom are shown to play a crucial role in the description of spectroscopy of this nucleus.A modified SU(3)SU(3)preserving high-order interaction is used to produce aγ-unstable type of odd-even staggering,observed experimentally between the states of the quasi-γband.The current approach enables the characterization of observed intraband and interband quadrupole collectivity.The findings of this study propose an alternative interpretation of the fundamental question regarding the nature of low-energy vibrations,as well as the emergence of deformation and collectivity in weakly deformed atomic nuclei.

Hybrid extended Fourier series for optimal control of nonlinear algebraic dynamical systems

The paper introduces a new method for finding optimal control of algebraic dynamic systems. The structure of algebraic dynamical systems is nonlinear with quadratic and bilinear terms. A new hybrid extended Fourier series is introduced, and state and control variables of the system are expanded by this series. Moreover, properties of new series are presented, and integration and product operational matrices are obtained. Using operational matrices, optimal control of the systems is converted to a set of simultaneous nonlinear algebraic relations. An illustrative example is included to compare our results with those in the literature.

On the microscopic shell-model version of the Bohr-Mottelson collective model

The recently proposed microscopic shell-model version of the Bohr-Mottelson(BM) collective model is considered in more detail in the coordinate representation.The latter possesses a clear and transparent physical meaning,which reveals several features of the new version of the collective model missed in the previous formulation.The relationship to the original BM model is considered,along with the relationships between the different limiting submodels of the microscopic version of the BM model,which closely resemble the relationships of the original Wilets-Jean and rotor models.The kinematically correct many-particle wave functions of the microscopic version of the BM model,conserving the experimentally observed integrals of motion,are shown to consist of collective irrotational-flow and intrinsic components-in accordance with the original BM unified model.The general BM Hamiltonian is obtained as a contraction limit of the microscopic many-particle nuclear Hamiltonian,or,alternatively,by restricting the latter to the scalar O(m) irreducible collective space.

Banach Algebra Dynamical Systems

Abstract This paper generalizes the C＊-dynamical system to the Banach algebra dynam- ical system （A, G, α） and define the crossed product A αG of a given Banach algebra dynamical system （A, G,α）. Then the representation of A α G is described when A ad- mits a bounded left approximate identity. In a natural way, the authors define the reduced crossed product A αG and discuss the question when A α G coincides with A αG.

Matrix elements in the SU(1,1)⊗SO(6)limit of the proton-neutron symplectic model

The matrix elements along the reduction chain Sp(12,R)⊃SU(1,1)⊗SO(6)⊃U(1)⊗SUpn(3)⊗SO(2)⊃SO(3)of the proton-neutron symplectic model(PNSM)are considered.Closed analytical expressions are obtained for the matrix elements of the basic building blocks of the PNSM and the Sp(12,R)symplectic generators,allowing the computation of matrix elements of other physical operators as well.The computational technique developed in the present study generally provides us with the required algebraic tool for performing realistic symplectic-based shell-model calculations of nuclear collective excitations.Utilizing two simple examples,we illustrate the application of the theory.

Reduced Crossed Products of Pro-Banach Algebras

This paper gives the concept of the reduced pro-Banach algebra crossed product associated with inversely pro-Banach algebra dynamical system,and shows that the reduced crossed product is an inverse limit of an inverse system of Banach algebra crossed products.Also,the authors show that if the locally compact group is amenable,then the crossed product and the reduced crossed product are isometrically isomorphic.