Monte Carlo calculations of angular momentum projected many-body matrix elements in the Pairing Plus Quadrupole Model

We extend the recently presented formalism for Monte Carlo calculations of the partition function, for both even and odd particle number systems (Phys. Rev. C 59, 2500 (1999)), to the calculation of many-body matrix elements of the type <ψ| e ^{- βℋ}|ψ> where |ψ> is a many-body state with a definite angular momentum, parity, neutron and proton numbers. For large β such matrix elements are dominated by the lowest eigenstate of the many-body Hamiltonian ℋ, corresponding with a given angular momentum parity and particle number. Emphasis is placed on odd-mass nuclei. Negligible sign fluctuations in the Monte Carlo calculation are found provided the neutron and proton chemical potentials are properly adjusted. The formalism is applied to the J ^π = 0⁺ state in ¹⁶⁶ Er and to the J ^π = 9/2^-, 13/2⁺, 5/2^- states in ¹⁶⁵ Er using the pairing-plus-quadrupole model. Received: 28 April 2000 / Accepted: 20 September 2000     

Generalized Hellmann-Feynman Theorem for Ensemble Average Expressed in the Formalism of Pure State Expectation

We show that the generalized Hellmann-Feynman theorem (GHFT) for ensemble average can be expressed in the formalism of pure state expectation. We employ the thermo field dynamics proposed by Umezawa and Takahash to realize this goal, the pure state |0(β)〉 is defined in doubled eigenvector space of the Hamiltonian. Relation between the GHFT and entropy-variation in the context of |0(β)〉 is also derived.     

Complex Wavelet Transform of the Bell States

By employing the technique of an integral within an ordered product (IWOP) of operators we recast the complex wavelet transform to a matrix element of the two-mode squeezing-displacing operator U ₂(μ,σ) between the mother wavelet vector 〈ψ| and the two-mode quantum state vector |f〉 to be transformed, i.e., we propose that 〈ψ|U ₂(μ,σ)|f〉 can be considered as a new kind of spectra for analyzing |f〉, this may have some potential applications in quantum information and calculation. As an example, we numerically calculate wavelet-transform spectrum for the Bell states, which may play a role of distinguishing them one from another.     

The Controlled Teleportation of an Arbitrary Two-Atom Entangled State in Driven Cavity QED

In this paper, we propose a scheme for the controlled teleportation of an arbitrary two-atom entangled state |φ〉₁₂=a|gg〉₁₂+b|ge〉₁₂+c|eg〉₁₂+d|ee〉₁₂ in driven cavity QED. An arbitrary two-atom entangled state can be teleported perfectly with the help of the cooperation of the third side by constructing a three-atom GHZ entangled state as the controlled channel. This scheme does not involve apparent (or direct) Bell-state measurement and is insensitive to the cavity decay and the thermal field. The probability of the success in our scheme is 1.0.     

Entangled Husimi Distribution and Complex Wavelet Transformation

Similar in spirit to the preceding work (Int. J. Theor. Phys. 48:1539, 2009) where the relationship between wavelet transformation and Husimi distribution function is revealed, we study this kind of relationship to the entangled case. We find that the optical complex wavelet transformation can be used to study the entangled Husimi distribution function in phase space theory of quantum optics. We prove that, up to a Gaussian function, the entangled Husimi distribution function of a two-mode quantum state |ψ〉 is just the modulus square of the complex wavelet transform of e^-|h|2/2e^{-\vert \eta \vert ^{2}/2} with ψ(η) being the mother wavelet.     

Cuspons and Smooth Solitons of the Degasperis–Procesi Equation Under Inhomogeneous Boundary Condition

This paper is contributed to explore all possible single peakon solutions for the Degasperis–Procesi (DP) equation m _t  + m _x u + 3mu _x  = 0, m = u − u _xx . Our procedure shows that the DP equation either has cusp soliton and smooth soliton solutions only under the inhomogeneous boundary condition lim_|x|→ ∞ u =A ≠0, or possesses the regular peakon solutions ce ^{− |x − ct|} ∈ H ¹ (c is the wave speed) only when lim_|x|→ ∞ u = 0 (see Theorem 4.1). In particular, we first time obtain the stationary cuspon solution of the DP equation. Moreover we present new cusp solitons (in the space of ) and smooth soliton solutions in an explicit form. Asymptotic analysis and numerical simulations are provided for smooth solitons and cusp solitons of the DP equation.      

Wavelet Transform of Even- and Odd-Coherent States

By employing the technique of integral within an ordered product (IWOP) of operators we recast classical wavelet transform to a matrix element of the squeezing-displacing operator U(μ,s) between the mother wavelet vector 〈ψ| and the state vector |f〉 to be transformed, i.e., we propose that 〈ψ|U(μ,s)|f〉 can be considered as a new kind of spectrum for analyzing the quantum state |f〉. In this way we do numerical calculation of wavelet-transform spectrum for the even- and odd-coherent states and then plot their figures, respectively. Thus this kind of spectrum can be used to recognize a variety of quantum optical states.     

A Dynamical Uncertainty Principle in von Neumann Algebras by Operator Monotone Functions

Suppose that A ₁,…,A _N are observables (selfadjoint matrices) and ρ is a state (density matrix). In this case the standard uncertainty principle, proved by Robertson, gives a bound for the quantum generalized variance, namely for det {Cov  _ρ (A _j ,A _k )}, using the commutators [A _j ,A _k ]; this bound is trivial when N is odd. Recently a different inequality of Robertson-type has been proved by the authors with the help of the theory of operator monotone functions. In this case the bound makes use of the commutators [ρ,A _j ] and is non-trivial for any N. In the present paper we generalize this new result to the von Neumann algebra case. Nevertheless the proof appears to simplify all the existing ones.     

Entanglement and Mixedness of Locally Cloned Non-Maximal W-State

In this work we describe a protocol by which two of three parties generate two bipartite entangled state among themselves without involving third party, from a non maximal W-state or W-type state |X〉=α|001〉₁₂₃+β|010〉₁₂₃+γ|100〉₁₂₃,α ²+β ²+γ ²=1 shared by three distant partners. Also we have considered the case β=γ, to obtain a range for α ², for which the local output states are separable and non local output states are inseparable. We also find out the dependence of the mixedness of inseparable states with their amount of inseparability, for that range of α ².     

Constructing Bell Inequality of Four-Qubit Entangled States

In this paper, a Bell inequality is given to study the nonlocality of four-qubit states. It is shown that the inequality is maximally violated by the four-qubit state |ψ〉. Some other states, such as the state |χ〉, the cluster state, violate this inequality, too, but not maximally. And it is not violated by the four-qubit GHZ state. In addition, the state |ψ〉 also violates other bell inequalities, but not so optimally. Therefore the inequality can detect the entanglement of |ψ〉 well, experimentally.     

Kraus Operator-Sum Representation and Time Evolution of Distribution Functions in Phase-Sensitive Reservoirs

Using the thermal entangled state representation 〈η|, we examine the master equation (ME) describing phase-sensitive reservoirs. We present the analytical expression of solution to the ME, i.e., the Kraus operator-sum representation of density operator ρ is given, and its normalization is also proved by using the IWOP technique. Further, by converting the characteristic function χ(λ) into an overlap between two “pure states” in enlarged Fock space, i.e., χ(λ)=〈η _=−λ |ρ|η ₌₀〉, we consider time evolution of distribution functions, such as Wigner, Q- and P-function. As applications, the photon-count distribution and the evolution of Wigner function of photon-added coherent state are examined in phase-sensitive reservoirs. It is shown that the Wigner function has a negative value when kt\leqslant\frac 12ln( 1+m_￥) \kappa t\leqslant\frac {1}{2}\ln ( 1+\mu_{\infty}) is satisfied, where μ _∞ depends on the squeezing parameter |M|² of environment, and increases as the increase of |M|.     

On certain correspondences among various coupled-cluster theories for closed-shell systems

In this paper certain correspondences have been shown among various formulations of coupled-cluster theories for many electron closed-shell systems. Specifically it is shown that (i) the energy functional using unitary ansatz of the form exp (T−T ⁺) is exactly sameorder by order inT with the size-consistent energy functional 〈ψ|H|ψ〉/〈ψ|ψ〉 recently obtained by us in coupled-cluster framework; (ii) in the framework of unitary ansatz of the form exp (T−T ⁺), both non-variational and variational approaches lead to identical equations upto any given order inT andT ⁺ inT∼T ₂ approximation; (iii) variational procedure using our size-consistent energy functional or using the functional obtained in the framework of unitary ansatz (as envisaged by Kutzelnigg) leads to energy in both cases, inT∼T ₂ approximation, for a total of quadratic powers inT andT ⁺, same as Cizek’s linearised coupled pair many electron theory energy; (iv) in case of practical calculation of the energy through the variational procedures using our size-consistent energy functional and the functional in unitary ansatz framework, there is a loss of upper bound.     

A Volume Inequality for Quantum Fisher Information and the Uncertainty Principle

Let A ₁,…,A _N be complex self-adjoint matrices and let ρ be a density matrix. The Robertson uncertainty principle

Obtaining Multimode Entangled State Representation by Generalized Radon Transformation of the Wigner Operator

In a preceding paper (Fan and Lv in J. Math. Phys. 50:102108, 2009), the phase-space integration corresponding to the straight line characteristic of two different real parameters λ,τ over the Wigner operator (i.e. the Radon transformation) leads to pure-state density operator |u〉 _{λ,τ  λ,τ} 〈u|, where |u〉 _λ,τ is just the coordinate-momentum intermediate representation. In this work we show that generalized Radon transformation of the Wigner operator yields multimode density operator of continuum variables. This provides us with a new approach for obtaining multimode entangled state representation. The Weyl ordering of the Wigner operator is used in our discussions.     

Stationary Properties and Stochastic Resonance for a Saturation Laser Model with Cross-correlation Between Quantum Noise Terms

The stationary properties of a saturation laser model with cross-correlation between the real and imaginary parts of the quantum noise are investigated theoretically. Using the Novikov theorem and the Sargent technique, we obtain the analytic expressions of the stationary probability density distribution, the mean, the variance and the skewness of the saturation laser model. The cross-correlation coefficient λ and other parameters can make the stationary probability density distribution P _st (I) generate interesting two-extrema structure, one-extremum structure, or no-extremum structure. It is clearly found that a first- order-like-transition is induced by the coupling strength |λ| of the complex quantum noise terms in the saturation laser model. When the laser system is operated above the threshold, the mean 〈I〉 becomes larger and the output of the laser intensity increases; however the coupling strength |λ| attenuates the output of the laser intensity. When the laser is operated near and below the threshold, the mean 〈I〉 becomes smaller, the output of the laser intensity decreases, and |λ| still attenuates the output of the laser intensity. When a periodic signal is added to a saturation laser model with cross-correlation between quantum noise terms, the interesting stochastic resonance phenomena occur at λ=0. The noise intensity Q decreases the values of the resonance peak, however, the amplitude of the periodic signal B enhances the values of the resonance peak.     

Quantum states transfer between coupled fields

We study the exchange of states in coupled fields along their time evolution. The coupling is described by a quadratic form in terms of annihilation and creation operator in the field Hamiltonian. An analytical approach is employed to describe the time evolution of the field state in Fock's space and the conditions for an arbitrary initial states to be transferred with 100% fidelity is determined. We show that only for initial states C₀|0>+C_N|N>, this situation can occurs. The important |1〉↔|0〉 qubits transfer is a particular case of this transference of number state. The relation between the coupling constant and characteristic field frequencies for complete state transference is also determined.     

Emissions from high-density potassium atoms excited by either nanosecond or femtosecond laser pulses

A study of the emissions, for high atomic density potassium, under nanosecond (ns) or femtosecond (fs) two-photon excitation is presented. It is shown that the parametric emissions (connected to the |6S_1/2〉↔|5P_3/2〉↔|4S_1/2〉 transitions) strongly depend on the excitation intensity and they have a nonlinear and a linear response region, in both kinds of excitation. In the ns excitation, the calculated results of a four-level atomic configuration agree well with the experimental ones, in the case of the path-1 parametric emissions (|6S_1/2〉↔|5P_3/2〉↔|4S_1/2〉) for certain excitation and atomic density parameters. Also, the fields of the atomic path-2 (|6S_1/2〉↔|4P_3/2〉↔|4S_1/2〉) are numerically shown to be amplified spontaneous emission (ASE) or cascade ASE without population inversion, due to the population transfer to the |6S_1/2〉 level initially and its subsequent collapse to the lower levels. In the fs excitation, only parametric emissions are observed from both atomic paths and there are not yet numerical calculations available to compare with. However, there is strong similarity of the experimental ns and fs results for the path-1 parametric emissions.     

The Asymptotic Limits of Zero Modes of Massless Dirac Operators

Asymptotic behaviors of zero modes of the massless Dirac operator H = α · D + Q(x) are discussed, where α = (α₁, α₂, α₃) is the triple of 4 × 4 Dirac matrices, , and Q(x) = (q _jk (x)) is a 4 × 4 Hermitian matrix-valued function with | q _jk (x) | ≤ C 〈x〉^−ρ, ρ > 1. We shall show that for every zero mode f, the asymptotic limit of |x|² f (x) as |x| → + ∞ exists. The limit is expressed in terms of the Dirac matrices and an integral of Q(x) f (x).      

A Link between Quantum Logic and Categorical Quantum Mechanics

Abramsky and Coecke (Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science, pp. 415–425, IEEE Comput. Soc., New York, 2004) have recently introduced an approach to finite dimensional quantum mechanics based on strongly compact closed categories with biproducts. In this note it is shown that the projections of any object A in such a category form an orthoalgebra Proj  A. Sufficient conditions are given to ensure this orthoalgebra is an orthomodular poset. A notion of a preparation for such an object is given by Abramsky and Coecke, and it is shown that each preparation induces a finitely additive map from Proj  A to the unit interval of the semiring of scalars for this category. The tensor product for the category is shown to induce an orthoalgebra bimorphism Proj  A×Proj  B→Proj (A ⊗ B) that shares some of the properties required of a tensor product of orthoalgebras. These results are established in a setting more general than that of strongly compact closed categories. Many are valid in dagger biproduct categories, others require also a symmetric monoidal tensor compatible with the dagger and biproducts. Examples are considered for several familiar strongly compact closed categories.     

The Unusual Magnetic Resonance Properties of Trigonal Prismatic Tc and Re Complexes

The electron paramagnetic resonance (EPR) spectra of the trigonal prismatic complexes Tc(abt)₃, Tc(bdt)₃, Re(abt)₃ and Re(bdt)₃ (abt, O-aminobenzenethiol; bdt, benzene-1,2-dithiol) in dilute frozen solution are interpreted in terms of an axially symmetric spin Hamiltonian, with g values close to two, principal hyperfine couplings of |A ^Tc| ~ 5–12 × 10⁻⁴ cm⁻¹, nuclear quadrupole couplings of |P ^Tc| ~ 0.3–0.35 × 10⁻⁴ cm⁻¹ and the unusual values 5 × 10⁻⁴ cm⁻¹ ~ |A _zz ^Re| < |P ^Re| ~ |A _xx ^Re| ~ |A _yy ^Re| ~ 25 × 10⁻⁴ cm⁻¹. Similar magnitudes of the parameters have been obtained by simulation of the previously published spectra of Re(pda)₃, Re(tdt)₃ and Re(pdt)₃ (pda, O-phenylenediamine; tdt, toluene-3,4-dithiol; pdt, cis-1,2-diphenylethene-1,2-dithiol) by other authors. The unexpectedly large value of P relative to A is a common feature of all the Re tris-dithiolato and related trigonal prismatic complexes studied by EPR and is attributed to the high degree of delocalization of the unpaired electron onto the ligands and the distortion of the electron charge cloud. These factors are less evident in the complexes Tc(abt)₃ and Tc(bdt)₃. Intermolecular dipolar interactions, narrowed by weak exchange, are responsible for some of the spectral features observed in the solid state and concentrated (≫1 mM) frozen solutions, although there is no evidence for specific solute–solute interactions.