On the failure of subadditivity of the Wigner-Yanase entropy

It was recently shown by Hansen that the Wigner-Yanase entropy is, for general states of quantum systems, not subadditive with respect to decomposition into two subsystems, although this property is known to hold for pure states. We investigate the question whether the weaker property of subadditivity for pure states with respect to decomposition into more than two subsystems holds. This property would have interesting applications in quantum chemistry. We show, however, that it does not hold in general, and provide a counterexample.Comment: LaTeX2e, 4 page

Spectral Correlations from the Metal to the Mobility Edge

We have studied numerically the spectral correlations in a metallic phase and at the metal-insulator transition. We have calculated directly the two-point correlation function of the density of states $R(s,s')$. In the metallic phase, it is well described by the Random Matrix Theory (RMT). For the first time, we also find numerically the diffusive corrections for the number variance $$ predicted by Al'tshuler and Shklovski\u{\i}. At the transition, at small energy scales, $R(s-s')$ starts linearly, with a slope larger than in a metal. At large separations $|s - s'| \gg 1$, it is found to decrease as a power law $R(s,s') \sim - c / |s -s'|^{2-\gamma}$ with $c \sim 0.041$ and $\gamma \sim 0.83$, in good agreement with recent microscopic predictions. At the transition, we have also calculated the form factor $\tilde K(t)$, Fourier transform of $R(s-s')$. At large $s$, the number variance contains two terms $= B ^\gamma + 2 \pi \tilde K(0) where$\tilde{K}(0)$is the limit of the form factor for$t \to 0$.Comment: 7 RevTex-pages, 10 figures. Submitted to PR

Scaling of Level Statistics at the Disorder-Induced Metal-Insulator Transition

The distribution of energy level separations for lattices of sizes up to 28$\times$28$\times$28 sites is numerically calculated for the Anderson model. The results show one-parameter scaling. The size-independent universality of the critical level spacing distribution allows to detect with high precision the critical disorder $W_{c}=16.35$. The scaling properties yield the critical exponent, $\nu =1.45 \pm 0.08$, and the disorder dependence of the correlation length.Comment: 11 pages (RevTex), 3 figures included (tar-compressed and uuencoded using UUFILES), to appear in Phys.Rev. B 51 (Rapid Commun.

Spin and Rotation in General Relativity

Rapporteur's Introduction to the GT8 session of the Ninth Marcel Grossmann Meeting (Rome, 2000); to appear in the Proceedings.Comment: LaTeX file, no figures, 15 page

Quantum coherence in the presence of unobservable quantities

State representations summarize our knowledge about a system. When unobservable quantities are introduced the state representation is typically no longer unique. However, this non-uniqueness does not affect subsequent inferences based on any observable data. We demonstrate that the inference-free subspace may be extracted whenever the quantity's unobservability is guaranteed by a global conservation law. This result can generalize even without such a guarantee. In particular, we examine the coherent-state representation of a laser where the absolute phase of the electromagnetic field is believed to be unobservable. We show that experimental coherent states may be separated from the inference-free subspaces induced by this unobservable phase. These physical states may then be approximated by coherent states in a relative-phase Hilbert space

Infinite spin particles

We show that Wigner's infinite spin particle classically is described by a reparametrization invariant higher order geometrical Lagrangian. The model exhibit unconventional features like tachyonic behaviour and momenta proportional to light-like accelerations. A simple higher order superversion for half-odd integer particles is also derived. Interaction with external vector fields and curved spacetimes are analyzed with negative results except for (anti)de Sitter spacetimes. We quantize the free theories covariantly and show that the resulting wave functions are fields containing arbitrary large spins. Closely related infinite spin particle models are also analyzed.Comment: 43 pages, Late

Universal Cubic Eigenvalue Repulsion for Random Normal Matrices

Random matrix models consisting of normal matrices, defined by the sole constraint $[N^{\dag},N]=0$, will be explored. It is shown that cubic eigenvalue repulsion in the complex plane is universal with respect to the probability distribution of matrices. The density of eigenvalues, all correlation functions, and level spacing statistics are calculated. Normal matrix models offer more probability distributions amenable to analytical analysis than complex matrix models where only a model wth a Gaussian distribution are solvable. The statistics of numerically generated eigenvalues from gaussian distributed normal matrices are compared to the analytical results obtained and agreement is seen.Comment: 15 pages, 2 eps figures. to appar in Physical Review

Wigner Functions on a Lattice

The Wigner functions on the one dimensional lattice are studied. Contrary to the previous claim in literature, Wigner functions exist on the lattice with any number of sites, whether it is even or odd. There are infinitely many solutions satisfying the conditions which reasonable Wigner functions should respect. After presenting a heuristic method to obtain Wigner functions, we give the general form of the solutions. Quantum mechanical expectation values in terms of Wigner functions are also discussed.Comment: 11 pages, no figures, REVTE

Covariant quantization of infinite spin particle models, and higher order gauge theories

Further properties of a recently proposed higher order infinite spin particle model are derived. Infinitely many classically equivalent but different Hamiltonian formulations are shown to exist. This leads to a condition of uniqueness in the quantization process. A consistent covariant quantization is shown to exist. Also a recently proposed supersymmetric version for half-odd integer spins is quantized. A general algorithm to derive gauge invariances of higher order Lagrangians is given and applied to the infinite spin particle model, and to a new higher order model for a spinning particle which is proposed here, as well as to a previously given higher order rigid particle model. The latter two models are also covariantly quantized.Comment: 38 pages, Late

Unrestricted Hartree-Fock theory of Wigner crystals

We demonstrate that unrestricted Hartree-Fock theory applied to electrons in a uniform potential has stable Wigner crystal solutions for $r_s \geq 1.44$ in two dimensions and $r_s \geq 4.5$ in three dimensions. The correlation energies of the Wigner crystal phases are considerably smaller than those of the fluid phases at the same density.Comment: 4 pages, 5 figure