arXiv subjects
Publications and source records attributed to Feng Pan.
A complete analysis of entangled triqubit pure states is carried out based on a new simple entanglement measure. An analysis of all possible extremally entangled pure triqubit states with up to eight terms is shown to reduce, with the help of SLOCC transformations, to three distinct types. The analysis presented are most helpful for finding different entanglement types in multipartite pure state systems.
A simple entanglement measure for multipartite pure states is formulated based on the partial entropy of a series of reduced density matrices. Use of the proposed new measure to distinguish disentangled, partially entangled, and maximally entangled multipartite pure states is illustrated.
The quantum critical behavior of the Bose-Hubbard model for a description of two coupled Bose-Einstein condensates is studied within the framework of an algebraic theory. Energy levels, wavefunction overlaps with those of the Rabi and Fock regimes, and the entanglement are calculated exactly as functions of the phase parameter and the number of bosons. The results show that the system goes though a phase transition and that the critical behavior is enhanced in the thermodynamic limit.
We study binding energies in three isotopic chains ($^{100-130}$Sn, $^{152-181}$Yb, and $^{181-202}$Pb) using the extended pairing model with Nilsson single-particle energies. The exactly solvable nature of the model means that the pairing strength G(A) required to reproduce the experimental binding energies can be determined uniquely. The valence space consists of the neutron single-particle levels between two closed shells corresponding to the magic numbers 50-82 and 82-126. In all three isotopic chains, log(G(A)) has a smooth quadratic behavior for even as well as odd nucleon numbers A; log(G(A)) for even and odd A are very similar. Remarkably, G(A) for all the Pb isotopes can be also described by a two parameter expression that is inversely proportional to the dimensionality of the model space.
The influence of the intruder level on nuclear deformation is studied within the framework of the nucleon-pair shell model truncated to an SD-pair subspace. The results suggest that the intruder level has a tendency to soften the deformation and plays an important role in determining the onset of rotational behavior.
A mixed-symmetry nuclear shell-model scheme for carrying out calculations in regimes where there is a competition between two or more modes is proposed. A one-dimensional toy model is used to demonstrate the concept. The theory is then applied to $^{24}Mg$ and $^{44}Ti$. For lower pf-shell nuclei such as $^{44-48}Ti$ and $^{48}Cr$ there is strong SU(3) symmetry breaking due to the spin-orbit interaction. However, the quadrupole collectivity as measured by B(E2) transition strengths in the yrast band remain high even though SU(3) appears to be broken. Some results for the so-called X(5) symmetry that falls along the U(5) $\leftrightarrow$ SU(3) leg of the Interacting Boson Model are also considered. The results show that the mixed-symmetry concept is effective, even when strong symmetry breaking occurs.
A Nilsson mean-field plus extended pairing interaction Hamiltonian with many-pair interaction terms is proposed. Eigenvalues of the extended pairing model are easy to obtain. Our investigation shows that one- and two-body interactions continue to dominate the dynamics for relatively small values of the pairing strength. As the strength of the pairing interaction grows, however, the three- and higher many-body interaction terms grow in importance. A numerical study of even-odd mass differences in the $^{154-171}$Yb isotopes shows that the extended pairing model is applicable to well-deformed nuclei.
Induced representations of Brauer algebra $D_{f}(n)$ from $S_{f_{1}}\times S_{f_{2}}$ with $f_{1}+f_{2}=f$ are discussed. The induction coefficients (IDCs) or the outer-product reduction coefficients (ORCs) of $S_{f_{1}}\times S_{f_{2}}\uparrow D_{f}(n)$ with $f\leq 4$ up to a normalization factor are derived by using the linear equation method. Weyl tableaus for the corresponding Gel'fand basis of SO(n) are defined. The assimilation method for obtaining CG coefficients of SO(n) in the Gel'fand basis for no modification rule involved couplings from IDCs of Brauer algebra are proposed. Some isoscalar factors of $SO(n)\supset SO(n-1)$ for the resulting irrep $[λ_{1},~λ_{2},~ λ_{3},~λ_{4},\dot{0}]$ with $\sum\limits_{i=1}^{4}λ_{i}\leq .
A new simple Young diagrammatic method for Kronecker products of O(n) and Sp(2m) is proposed based on representation theory of Brauer algebras. A general procedure for the decomposition of tensor products of representations for O(n) and Sp(2m) is outlined, which is similar to that for U(n) known as the Littlewood rules together with trace contractions from a Brauer algebra and some modification rules given by King.
A new method for deriving universal Ř matrices from braid group representation is discussed. In this case, universal Ř operators can be defined and expressed in terms of products of braid group generators. The advantage of this method is that matrix elements of Ř are rank independent, and leaves multiplicity problem concerning coproducts of the corresponding quantum groups untouched. As examples, Ř matrix elements of $[1]\times [1]$, $[2]\times [2]$, $[1^{2}]\times [1^{2}]$, and $[21]\times [21]$ with multiplicity two for $A_{n}$, and $[1]\times [1]$ for $B_{n}$, $C_{n}$, and $D_{n}$ type quantum groups, which are related to Hecke algebra and Birman-Wenzl algebra, respectively, are derived by using this method.
An exact, number-conserving solution to the generalized, orbit-dependent pairing problem is derived by introducing an infinite-dimensional algebra. A method for obtaining eigenvalues and eigenvectors of the corresponding Hamiltonian is also given. The relevance of the orbit-dependent pairing solution is demonstrated by comparing predictions of the model with shell-model calculations.
An infinite dimensional algebra, which is useful for deriving exact solutions of the generalized pairing problem, is introduced. A formalism for diagonalizing the corresponding Hamiltonian is also proposed. The theory is illustrated with some numerical examples.
A complementary group to SU(n) is found that realizes all features of the Littlewood rule for Kronecker products of SU(n) representations. This is accomplished by considering a state of SU(n) to be a special Gel'fand state of the complementary group {\cal U}(2n-2). The labels of {\cal U}(2n-2) can be used as the outer multiplicity labels needed to distinguish multiple occurrences of irreducible representations (irreps) in the SU(n)\times SU(n)\downarrow SU(n) decomposition that is obtained from the Littlewood rule. Furthermore, this realization can be used to determine SU(n)\supset SU(n-1)\times U(1) Reduced Wigner Coefficients (RWCs) and Clebsch-Gordan Coefficients (CGCs) of SU(n), using algebraic or numeric methods, in either the canonical or a noncanonical basis. The method is recursive in that it uses simpler RWCs or CGCs with one symmetric irrep in conjunction with standard recoupling procedures. New explicit formulae for the multiplicity for SU(3) and SU(4) are used to illustrate the theory.
A general procedure for the derivation of SU(3)\supset U(2) reduced Wigner coefficients for the coupling (λ_{1}μ_{1})\times (λ_{2}μ_{2})\downarrow (λμ)^η, where ηis the outer multiplicity label needed in the decomposition, is proposed based on a recoupling approach according to the complementary group technique given in (I). It is proved that the non-multiplicity-free reduced Wigner coefficients of SU(n) are not unique with respect to canonical outer multiplicity labels, and can be transformed from one set of outer multiplicity labels to another. The transformation matrices are elements of SO(m), where m is the number of occurrence of the corresponding irrep (λμ) in the decomposition (λ_{1}μ_{1})\times (λ_{2}μ_{2})\downarrow (λμ). Thus, a kind of the reduced Wigner coefficients with multiplicity is obtained after a special SO(m) transformation. New features of this kind of reduced Wigner coefficients and the differences from the reduced Wigner coefficients with other choice of the multiplicity label given previously are discussed. The method can also be applied to the derivation of general SU(n) Wigner or reduced Wigner coefficients with multiplicity. Algebraic expression of another kind of reduced Wigner coefficients, the so-called reduced auxiliary Wigner coefficients for SU(3)\supset U(2), are also obtained.