Exact Charged 2-Body Motion and the Static Balance Condition in Lineal Gravity

We find an exact solution to the charged 2-body problem in $(1+1)$ dimensional lineal gravity which provides the first example of a relativistic system that generalizes the Majumdar-Papapetrou condition for static balance.Comment: latex,7 pages, 2 figure

Exact Solution for Relativistic Two-Body Motion in Dilaton Gravity

We present an exact solution to the problem of the relativistic motion of 2 point masses in $(1+1)$ dimensional dilaton gravity. The motion of the bodies is governed entirely by their mutual gravitational influence, and the spacetime metric is likewise fully determined by their stress-energy. A Newtonian limit exists, and there is a static gravitational potential. Our solution gives the exact Hamiltonian to infinite order in the gravitational coupling constant.Comment: 6 pages, latex, 3 figure

Self-energy and Fermi surface of the 2-dimensional Hubbard model

We present an exact diagonalization study of the self-energy of the two-dimensional Hubbard model. To increase the range of available cluster sizes we use a corrected t-J model to compute approximate Greens functions for the Hubbard model. This allows to obtain spectra for clusters with 18 and 20 sites. The self-energy has several `bands' of poles with strong dispersion and extended incoherent continua with k-dependent intensity. We fit the self-energy by a minimal model and use this to extrapolate the cluster results to the infinite lattice. The resulting Fermi surface shows a transition from hole pockets in the underdoped regime to a large Fermi surface in the overdoped regime. We demonstrate that hole pockets can be completely consistent with the Luttinger theorem. Introduction of next-nearest neighbor hopping changes the self-energy stronlgy and the spectral function with nonvanishing next-nearest-neighbor hopping in the underdoped region is in good agreement with angle resolved photoelectron spectroscopy.Comment: 17 pages, 18 figure

Theory of the waterfall phenomenon in cuprate superconductors

Based on exact diagonalization and variational cluster approximation calculations we study the relationship between charge transfer models and the corresponding single band Hubbard models. We present an explanation for the waterfall phenomenon observed in angle resolved photoemission spectroscopy (ARPES) on cuprate superconductors. The phenomenon is due to the destructive interference between the phases of the O2p orbitals belonging to a given Zhang-Rice singlet and the Bloch phases of the photohole which occurs in certain regions of k-space. It therefore may be viewed as a direct experimental visualisation of the Zhang-Rice construction of an effective single band model for the CuO2 plane.Comment: 11 pages, 9 Postscript figure

Exact Relativistic Two-Body Motion in Lineal Gravity

We consider the N-body problem in (1+1) dimensional lineal gravity. For 2 point masses (N=2) we obtain an exact solution for the relativistic motion. In the equal mass case we obtain an explicit expression for their proper separation as a function of their mutual proper time. Our solution gives the exact Hamiltonian to infinite order in the gravitational coupling constant.Comment: latex, 11 pages, 2 figures, final version to appear in Phys. Rev. Let

Possibility of synthesizing doubly closed superheavy nucleus

The possibility of synthesizing a doubly magic superheavy nucleus, $^{298}114_{184}$, is investigated on the basis of fluctuation-dissipation dynamics. In order to synthesize this nucleus, we must generate more neutron-rich compound nuclei because of the neutron emissions from excited compound nuclei. The compound nucleus $^{304}114$ has two advantages to achieving a high survival probability. First, because of small neutron separation energy and rapid cooling, the shell correction energy recovers quickly. Secondly, owing to neutron emissions, the neutron number of the nucleus approaches that of the double closed shell and the nucleus obtains a large fission barrier. Because of these two effects, the survival probability of $^{304}114$ does not decrease until the excitation energy $E^{*}= 50$ MeV. These properties lead to a rather high evaporation reside cross section.Comment: 5 pages, 6 figure

Spin and charge dynamics of the t-J model at intermediate electron densities: absence of spin-charge separation

We present an exact diagonalization study of the dynamical spin and density correlation functions in small clusters of 2D t-J model for intermediate and low electron densities, rho<0.7. Both correlation functions agree remarkably well with the convolution of the single-particle spectral function, i.e. the simplest estimate within the Fermi liquid picture. Deviations from the convolution are shown to originate from symmetry-related selection rules, which are unaccounted for in the convolution estimate. Comparing the momentum distribution in the final states of the low lying spin and charge excitations to that of the ground state we establish that for all fillings under consideration the low energy peaks in both correlation functions originate from particle-hole excitations, as expected in a Fermi liquid.Comment: RevTex-file (4.5 PRB-pages) + 9 figures attached as compressed postscript file

Exact Solution for the Metric and the Motion of Two Bodies in (1+1) Dimensional Gravity

We present the exact solution of two-body motion in (1+1) dimensional dilaton gravity by solving the constraint equations in the canonical formalism. The determining equation of the Hamiltonian is derived in a transcendental form and the Hamiltonian is expressed for the system of two identical particles in terms of the Lambert $W$ function. The $W$ function has two real branches which join smoothly onto each other and the Hamiltonian on the principal branch reduces to the Newtonian limit for small coupling constant. On the other branch the Hamiltonian yields a new set of motions which can not be understood as relativistically correcting the Newtonian motion. The explicit trajectory in the phase space $(r, p)$ is illustrated for various values of the energy. The analysis is extended to the case of unequal masses. The full expression of metric tensor is given and the consistency between the solution of the metric and the equations of motion is rigorously proved.Comment: 34 pages, LaTeX, 16 figure