7,088 research outputs found
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 between
projectile and target (resp. ejectile and residual target) being contradictory
with full antisymmetrization between nucleons, an explicit antisymmetrization
projector must be included in the definition of the transition
operator, We derive the
suitably antisymmetrized mean field equations leading to a non perturbative
estimate of . The theory is illustrated by a calculation of forward
- 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
Constrained Orthogonal Polynomials
We define sets of orthogonal polynomials satisfying the additional constraint
of a vanishing average. These are of interest, for example, for the study of
the Hohenberg-Kohn functional for electronic or nucleonic densities and for the
study of density fluctuations in centrifuges. We give explicit properties of
such polynomial sets, generalizing Laguerre and Legendre polynomials. The
nature of the dimension 1 subspace completing such sets is described. A
numerical example illustrates the use of such polynomials.Comment: 11 pages, 10 figure
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