Continuum Singularities of a Mean Field Theory of Collisions

Consider a complex energy $z$ for a $N$-particle Hamiltonian $H$ and let $\chi$ be any wave packet accounting for any channel flux. The time independent mean field (TIMF) approximation of the inhomogeneous, linear equation $(z-H)|\Psi>=|\chi>$ consists in replacing $\Psi$ by a product or Slater determinant $\phi$ of single particle states $\phi_i.$ This results, under the Schwinger variational principle, into self consistent TIMF equations $(\eta_i-h_i)|\phi_i>=|\chi_i>$ in single particle space. The method is a generalization of the Hartree-Fock (HF) replacement of the $N$-body homogeneous linear equation $(E-H)|\Psi>=0$ by single particle HF diagonalizations $(e_i-h_i)|\phi_i>=0.$ We show how, despite strong nonlinearities in this mean field method, threshold singularities of the {\it inhomogeneous} TIMF equations are linked to solutions of the {\it homogeneous} HF equations.Comment: 21 pages, 14 figure

Multifractality and intermediate statistics in quantum maps

We study multifractal properties of wave functions for a one-parameter family of quantum maps displaying the whole range of spectral statistics intermediate between integrable and chaotic statistics. We perform extensive numerical computations and provide analytical arguments showing that the generalized fractal dimensions are directly related to the parameter of the underlying classical map, and thus to other properties such as spectral statistics. Our results could be relevant for Anderson and quantum Hall transitions, where wave functions also show multifractality.Comment: 4 pages, 4 figure

Anticoherence of spin states with point group symmetries

We investigate multiqubit permutation-symmetric states with maximal entropy of entanglement. Such states can be viewed as particular spin states, namely anticoherent spin states. Using the Majorana representation of spin states in terms of points on the unit sphere, we analyze the consequences of a point-group symmetry in their arrangement on the quantum properties of the corresponding state. We focus on the identification of anticoherent states (for which all reduced density matrices in the symmetric subspace are maximally mixed) associated with point-group symmetric sets of points. We provide three different characterizations of anticoherence, and establish a link between point symmetries, anticoherence and classes of states equivalent through stochastic local operations with classical communication (SLOCC). We then investigate in detail the case of small numbers of qubits, and construct infinite families of anticoherent states with point-group symmetry of their Majorana points, showing that anticoherent states do exist to arbitrary order.Comment: 15 pages, 5 figure

Antisymmetrization of a Mean Field Calculation of the T-Matrix

The usual definition of the prior(post) interaction $V(V^\prime )$ between projectile and target (resp. ejectile and residual target) being contradictory with full antisymmetrization between nucleons, an explicit antisymmetrization projector ${\cal A}$ must be included in the definition of the transition operator, $T\equiv V^\prime{\cal A}+V^\prime{\cal A}GV.$ We derive the suitably antisymmetrized mean field equations leading to a non perturbative estimate of $T$. The theory is illustrated by a calculation of forward $\alpha$-$\alpha$ scattering, making use of self consistent symmetries.Comment: 30 pages, no figures, plain TeX, SPHT/93/14

Existence of a Density Functional for an Intrinsic State

A generalization of the Hohenberg-Kohn theorem proves the existence of a density functional for an intrinsic state, symmetry violating, out of which a physical state with good quantum numbers can be projected.Comment: 6 page

Fragments entomologiques : vorgelegt in der Sitzung vom 4. December 1861

Tête un peu moins large que le thorax, un peu luisante, finement et peu densement ponctuée, toute noire; les poils du vertex et des joues plus abondants, fauves, ceux de la face plus courts, plus rares, et roux; le chaperon presque nu, inégalement ponctué, subrugueux, tronqué droit au bout et margué d'une ligne enfoncée parallèle au bord: flagellum des antennes d'un noir de poix, le premier article long et mince, les autres plus épais, formant une massue longue et faiblement comprimée. ..

Multifractality of quantum wave packets

We study a version of the mathematical Ruijsenaars-Schneider model, and reinterpret it physically in order to describe the spreading with time of quantum wave packets in a system where multifractality can be tuned by varying a parameter. We compare different methods to measure the multifractality of wave packets, and identify the best one. We find the multifractality to decrease with time until it reaches an asymptotic limit, different from the mulifractality of eigenvectors, but related to it, as is the rate of the decrease. Our results could guide the study of experimental situations where multifractality is present in quantum systems.Comment: 6 pages, 4 figures, final version including a new figure (figure 1

Open problems in nuclear density functional theory

This note describes five subjects of some interest for the density functional theory in nuclear physics. These are, respectively, i) the need for concave functionals, ii) the nature of the Kohn-Sham potential for the radial density theory, iii) a proper implementation of a density functional for an "intrinsic" rotational density, iv) the possible existence of a potential driving the square root of the density, and v) the existence of many models where a density functional can be explicitly constructed.Comment: 10 page