arXiv subjects
Publications and source records attributed to A. Zee.
I discuss various thoughts, old and new, about the cosmological constant (or dark energy) paradox. In particular, I suggest the possibility that the cosmological ``constant'' may decay as $Λ\sim α^2 m_N^3 / τ$, where $τ$ is the age of the universe.
Does the existence of dark energy suggest that there is more to the graviton than we think we know?
We propose parametrizations of the neutrino mixing matrix. We discuss several Ansatzes: in some of them $V_{e3}=0$ but in others $V_{e3}$ typically ``comes out'' to be of order $\simeq 0.05.$
We discuss an Ansatz for the neutrino mixing matrix and speculate on the form and origin of the neutrino mass matrix.
We develop simple models for the global spread of infectious diseases, emphasizing human mobility via air travel and the variation of public health infrastructure from region to region. We derive formulas relating the total and peak number of infections in two countries to the rate of travel between them and their respective epidemiological parameters.
It is well known that the neutrino mass matrix contains more parameters than experimentalists can hope to measure in the foreseeable future even if we impose CP invariance. Thus, various authors have proposed ansatzes to restrict the form of the neutrino mass matrix further. Here we propose that $m_{ν_1} + m_{ν_2} + m_{ν_3} = 0$; this ``zero sum'' condition can occur in certain class of models, such as models whose neutrino mass matrix can be expressed as commutator of two matrices. With this condition, the absolute neutrino mass can be obtained in terms of the mass-squared differences. When combined with the accumulated experimental data this condition predicts two types of mass hierarchies, with one of them characterized by $m_{ν_3} \approx -2m_{ν_1} \approx -2 m_{ν_2} \approx 0.063$ eV, and the other by $m_{ν_1} \approx -m_{ν_2} \approx 0.054$ eV and $m_{ν_3} \approx 0.0064$ eV. The mass ranges predicted is just below the cosmological upper bound of 0.23 eV from recent WMAP data and can be probed in the near future. We also point out some implications for direct laboratory measurement of neutrino masses, and the neutrino mass matrix.
We argue that the accumulated neutrino data, including recent results from KamLAND and K2K, point to a neutrino mixing matrix with (V_{11}, V_{21}, V_{31}; V_{21}, V_{22}, V_{32}; V_{13}, V_{23}, V_{33}) = (-2/\sqrt{6}, 1/\sqrt{6}, 1/\sqrt{6}; 1/\sqrt{3}, 1/\sqrt{3}, 1/\sqrt{3}; 0, 1/\sqrt{2}, -1/\sqrt{2}). We propose some simple neutrino mass matrices which predict such a mixing matrix.
A non-Hermitean random matrix model proposed a few years ago has a remarkably intricate spectrum. Various attempts have been made to understand the spectrum, but even its dimension is not known. Using the Dyson-Schmidt equation, we show that the spectrum consists of a non-denumerable set of lines in the complex plane. Each line is the support of the spectrum of a periodic Hamiltonian, obtained by the infinite repetition of any finite sequence of the disorder variables. Our approach is based on the ``theory of words.'' We make a complete study of all 4-letter words. The spectrum is complicated because our matrix contains everything that will ever be written in the history of the universe, including this particular paper.
Barn owls hunt in the dark by using cues from both sight and sound to locate their prey. This task is facilitated by topographic maps of the external space formed by neurons (e.g., in the optic tectum) that respond to visual or aural signals from a specific direction. Plasticity of these maps has been studied in owls forced to wear prismatic spectacles that shift their visual field. Adaptive behavior in young owls is accompanied by a compensating shift in the response of (mapped) neurons to auditory signals. We model the receptive fields of such neurons by linear filters that sample correlated audio-visual signals, and search for filters that maximize the gathered information, while subject to the costs of rewiring neurons. Assuming a higher fidelity of visual information, we find that the corresponding receptive fields are robust and unchanged by artificial shifts. The shape of the aural receptive field, however, is controlled by correlations between sight and sound. In response to prismatic glasses, the aural receptive fields shift in the compensating direction, although their shape is modified due to the costs of rewiring.
We discuss and review the basic physics that leads to superfluidity/superconductivity in certain quantum Hall states, in particular the so-called double-layered (mmm) state. In the K-matrix description of the quantum correlation in quantum Hall states, those states with det(K)=0 contain a special correlation that leads to superfluidity/superconductivity. We propose a four-terminal measurement to test the DC Josephson-like effect in interlayer tunneling, so that the superfluidity/superconductivity in the (mmm) states can be settled experimentally.
Using 2D quantum spin-1/2 model as a concrete example, we studied the relation between gapless fermionic excitations (spinons) and quantum orders in some spin liquid states. Using winding number, we find the projective symmetry group that characterizes the quantum order directly determines the pattern of Fermi points in the Brillouin zone. Thus quantum orders provide an origin for gapless fermionic excitations.
We study static fermion bags in the 1+1 dimensional Gross-Neveu and Nambu-Jona-Lasinio models. It has been known, from the work of Dashen, Hasslacher and Neveu (DHN), followed by Shei's work, in the 1970's, that the self-consistent static fermion bags in these models are reflectionless. The works of DHN and of Shei were based on inverse scattering theory. Several years ago, we offered an alternative argument to establish the reflectionless nature of these fermion bags, which was based on analysis of the spatial asymptotic behavior of the resolvent of the Dirac operator in the background of a static bag, subjected to the appropriate boundary conditions. We also calculated the masses of fermion bags based on the resolvent and the Gelfand-Dikii identity. Based on arguments taken from a certain generalized one dimensional supersymmetric quantum mechanics, which underlies the spectral theory of these Dirac operators, we now realize that our analysis of the asymptotic behavior of the resolvent was incomplete. We offer here a critique of our asymptotic argument.
We formulate the RNA folding problem as an $N\times N$ matrix field theory. This matrix formalism allows us to give a systematic classification of the terms in the partition function according to their topological character. The theory is set up in such a way that the limit $N\to \infty$ yields the so-called secondary structure (Hartree theory). Tertiary structure and pseudo-knots are obtained by calculating the $1/N^2$ corrections to the partition function. We propose a generalization of the Hartree recursion relation to generate the tertiary structure.
The localization behavior of noninteracting two-dimensional electrons in a random potential and strong magnetic field is of fundamental interest for the physics of the quantum Hall effect. In order to understand the emergence of power-law delocalization near the discrete extended-state energies $E_n = \hbar ω_c (n+{1/2})$, we study a generalization of the disorder-averaged Liouvillian framework for the lowest Landau level to $N$ flavors of electron densities (N=1 for the physical case). We find analytically the large-N limit and 1/N corrections for all disorder strengths: at $N = \infty$ this gives an estimate of the critical conductivity, and at order 1/N an estimate of the localization exponent $ν$. The localization properties of the analytically tractable $N \gg 1$ theory seem to be continuously connected to those of the exact quantum Hall plateau transition at $N = 1$.
Recently, an analytic method was developed to study in the large $N$ limit non-hermitean random matrices that are drawn from a large class of circularly symmetric non-Gaussian probability distributions, thus extending the existing Gaussian non-hermitean literature. One obtains an explicit algebraic equation for the integrated density of eigenvalues from which the Green's function and averaged density of eigenvalues could be calculated in a simple manner. Thus, that formalism may be thought of as the non-hermitean analog of the method due to Brézin, Itzykson, Parisi and Zuber for analyzing hermitean non-Gaussian random matrices. A somewhat surprising result is the so called "Single Ring" theorem, namely, that the domain of the eigenvalue distribution in the complex plane is either a disk or an annulus. In this paper we extend previous results and provide simple new explicit expressions for the radii of the eigenvalue distiobution and for the value of the eigenvalue density at the edges of the eigenvalue distribution of the non-hermitean matrix in terms of moments of the eigenvalue distribution of the associated hermitean matrix. We then present several numerical verifications of the previously obtained analytic results for the quartic ensemble and its phase transition from a disk shaped eigenvalue distribution to an annular distribution. Finally, we demonstrate numerically the "Single Ring" theorem for the sextic potential, namely, the potential of lowest degree for which the "Single Ring" theorem has non-trivial consequences.
We study the quantum Hall transition using the density-density correlation function. We show that in the limit h->0 the electron density moves along the percolating trajectories, undergoing normal diffusion. The localization exponent coincides with its percolation value ν=4/3. The framework provides a natural way to study the renormalization group flow from percolation to quantum Hall transition. We also confirm numerically that the critical conductivity of a classical limit of quantum Hall transition is σ_{xx} = \sqrt{3}/4.
Euclidean random matrices appear in a broad class of physical problems involving disorder. The problem of determining their spectra can be mapped, using the replica method, into the study of a scalar field theory with an interaction of the type e^(psi^2). We apply the instanton method to study their spectral tails.
We introduce a new brane-world model in which the bulk solution consists of outgoing plane waves. This is an exact solution to string theory with no naked singularities. The recently discussed self-tuning mechanism to cancel the cosmological constant on a brane is naturally incorporated. We show that even if the vacuum energy on the brane changes, e.g. due to a phase transition, the brane geometry remains insensitive to the local vacuum energy. We also consider the static self-tuning branes introduced earlier, and find a solution in which the brane geometry starts to contract when the vacuum energy on the brane changes.