Exact Momentum Research Articles

Exact momentum distribution of the U=

The Lanczos method has been used to obtain the evolution after hole doping of the momentum distribution of a one-band Hubbard model of infinite U on a 4\ifmmode\times\else\texttimes\fi{}4 cluster of the square lattice. Our results show that the corner of the Brillouin zone is progressively emptied as holes are introduced into the half-filled system because only one electron per k point is allowed in this situation. On the other hand, the behavior in the dilute limit is more conventional: approximately two electrons per k point occupy the lower part of the one-electron band.

Some topics in the molecular dynamics ensemble

The molecular dynamics method generates averages in an ensemble with constant particle number, volume, energy, and total momentum. For this ensemble, we obtain the exact ideal gas partition function and momentum distribution function, show that a ’’correction’’ applied in the past to equation-of-state data of hard core particles is not needed, and rederive a known relationship between potential energy fluctuations and the heat capacity.

Volume-averaged Expression of Two-phase Flow

In this paper, a two-phase flow with randomly distributed particles is considered. The Navier-Stokes equation is integrated over the control volume fixed to the absolute co-ordinates, and then an exact volume-averaged momentum equation is derived. We remove the difficulty of mathematical treatment due to the random particle distribution by using a smooth weight-function. By the above volume-averaged equation, we can explain some phenomena of two-phase flow. As an example, the apparent viscosity of the two-phase parallel flow, where the particle concentration is distributed arbitrarily in the plane perpendicular to the flow direction, is obtained theoretically and compared with the summarized experimental data.

Interaction of a low density runaway beam with cavity modes

An idealized problem is investigated which illustrates the role of wave-particle interactions in the evolution of runaway beams. The model considers the interaction between a weak cold beam, driven by an external static electric field E, and waves quantized by the geometry. The waves may correspond to Gould–Trivelpiece modes fixed by the length of the experimental device, or to the finite length of the experimental device, or to the finite Fourier modes encountered in computer simulations. The physics consists of the sweeping of the accelerated beam through the resonance provided by each cavity mode. This process is formulated in analogy with the O’Neil–Winfrey–Malmberg problem but uses a spatially averaged description based on the exact energy and momentum conservation laws with the dynamics simplified through a WKB representation of the dispersion relation. This model shows that the beam can be clamped in velocity with the momentum push being transferred to the waves. The model has been extended to the relativistic and multi-mode cases. For E=0 the nonrelativistic results are in good agreement with the work of O’Neil, et al., while in the relativistic case the model reproduces the nontrivial features of the computer study by Lampe and Sprangle.

Semiclassical treatment of bound state systems. II. Trajectory calculations using the exact quantum momentum

Equations of motion based upon the exact solution of the Milne equation are used to perform trajectory calculations. Using the trajectory information we calculate charge densities for N fermions in a harmonic oscillator potential in a semiclassical approximation. The charge densities so obtained are in almost exact agreement with exact calculation within the outermost density maxima. Outside this region the differences between the approximate and exact densities are essentially independent of the number of fermions in the system.

Exact momentum and energy balances and entropy production in phenomenological irreversible thermodynamics of a continuous system

Exact momentum and energy balances and entropy production in phenomenological irreversible thermodynamics of a continuous system

Exact and approximate angular momentum projection for light nuclei

Angular momentum projection is carried out in an exact way on Slater determinant wave functions for the axially symmetric nuclei 8Be and 12C and the asymmetric 4p-4h state in 16O. In the latter case, it is shown that the projected energies and the B(E2, 2 + → 0 +) value for the K = 0 band in the 4p-4h state are consistent with the Brown and Green model. An approximate method for the calculation of the projected energies is given for the axially symmetric cases. Using this method, one obtains the binding energies of the projected states easily and with good accuracy. The excitation energies are less well reproduced.

Orbits in Fixed Field Alternating Gradient Synchrotron

An analytical investigation has been made of the motion of a charged particle in an axially symmetric steady magnetic field. For a given momentum, expressions for the shape of the equilibrium orbit and betatron oscillation frequencies have been derived in terms of the field index k, the spiral parameter K, and the set of field coefficients gnm. These algebraic results have been programmed for the IBM704 computer. For a 500 MeV fixed field alternating gradient (FFAG) synchrotron designed as an injector,1 computations yield radial and vertical tunes averaged with respect to momentum of Δr = 3.23, ≤z = 2.37 with variations of |νr| Ζ 0.0001, |Δνz| Ζ 0.0004 depending on the exact momentum. For comparison, Runge-Kutta evaluations which require a factor of six longer computing times yield average tunes of νr = 3.22 and νz = 2.49.

Possible exact momentum pair-breaking mechanism due to UMKLAPP processes in superconductors

We would like to show that it is possible to obtain non exact opposite momentum pairings in the presence of an external magnetic field if the electrons in superconductors are strongly coupled to the transverse phonons as well as to the longitudinal phonons usually assumed in the BCS-Bogoliubov's [1] theory.