ON THE SEPARATION METHOD FOR THE NUCLEAR MANY-BODY PROBLEM

1965 ◽  
Vol 43 (4) ◽  
pp. 605-618 ◽  
Author(s):  
M. Razavy ◽  
S. J. Stack
Keyword(s):  
Wave Function ◽  
Long Range ◽  
Body Wave ◽  
Outer Part ◽  
Separation Distance ◽  
Many Body ◽  
Range Interaction ◽  
Method Of Calculation ◽  
Reaction Matrix ◽  
Range Part

A method of calculation of the nuclear reaction matrix is proposed in which the interaction is divided into two parts. The long-range part of the interaction together with the kinetic energy forms the unperturbed Hamiltonian and the short-range interaction is treated as a perturbation. The separation distance is so chosen that the perturbation produces no energy shift, but modifies the many-body wave function. For the special case where the outer part of the interaction is sufficiently weak, a plane-wave approximation is used for the unperturbed wave function, with the result that the diagonal elements of the reaction matrix are given by the first Born approximation of the long-range part of the potential. An iteration scheme is set up to compute the dividing point of the interaction. Such properties of nuclear matter as saturation, binding energy, and rearrangement energy are discussed in terms of the separation distance and its derivatives. Finally, this method is compared with those of Moszkowski and Scott (1960) and Bethe et al. (1963).

Electron correlation and many-body wave function of semiconductor heterojunction

1989 ◽  
Vol 6 (8) ◽  
pp. 370-373
Author(s):  
Wang Hongwei ◽  
Feng Weiguo ◽  
Mao Huiming ◽  
Sun Xin
Keyword(s):  
Wave Function ◽  
Electron Correlation ◽  
Body Wave ◽  
Many Body

EXISTENCE OF FOUR DISTINCT PHASES IN ONE DIMENSIONAL MANY-BODY SYSTEMS WITH LONG-RANGE INTERACTION: QUANTUM KOSTERLITZ–THOULESS TRANSITIONS

2001 ◽  
Vol 15 (06n07) ◽  
pp. 175-182
Author(s):  
KAZUMOTO IGUCHI
Keyword(s):  
Long Range ◽  
Luttinger Liquid ◽  
Scaling Theory ◽  
Wigner Crystal ◽  
Many Body ◽  
Range Interaction ◽  
One Dimensional ◽  
Ground State Wavefunction ◽  
Long Range Interaction ◽  
Many Body Systems

We conceptually study the existence of four distinct quantum phases: the Luttinger liquid, the Wigner crystal, the Coulomb plasma and the molecular crystal in one-dimensional many-body systems with long-range interaction. We show that the anomaly of the ground state wavefunction indicates a quantum Kosterlitz–Thouless transition at zero temperature, which separates into two regimes of the Luttinger liquid and the Wigner crystal. We also postulate a scaling theory which discriminate the four phases using the Kosterlitz–Thouless scaling theory.

q-Gaussian approximants mimic non-extensive statistical-mechanical expectation for many-body probabilistic model with long-range correlations

Open Physics ◽  
2009 ◽  
Vol 7 (3) ◽  
Author(s):  
William Thistleton ◽  
John Marsh ◽  
Kenric Nelson ◽  
Constantino Tsallis
Keyword(s):  
Long Range ◽  
Gaussian Distribution ◽  
Random Variables ◽  
Present System ◽  
Many Body ◽  
Scale Invariant ◽  
Range Interaction ◽  
Multivariate Gaussian Distribution ◽  
Long Range Correlations ◽  
Long Range Interactions

AbstractWe study a strictly scale-invariant probabilistic N-body model with symmetric, uniform, identically distributed random variables. Correlations are induced through a transformation of a multivariate Gaussian distribution with covariance matrix decaying out from the unit diagonal, as ρ/r α for r =1, 2, ..., N-1, where r indicates displacement from the diagonal and where 0 ⩽ ρ ⩽ 1 and α ⩾ 0. We show numerically that the sum of the N dependent random variables is well modeled by a compact support q-Gaussian distribution. In the particular case of α = 0 we obtain q = (1-5/3 ρ) / (1- ρ), a result validated analytically in a recent paper by Hilhorst and Schehr. Our present results with these q-Gaussian approximants precisely mimic the behavior expected in the frame of non-extensive statistical mechanics. The fact that the N → ∞ limiting distributions are not exactly, but only approximately, q-Gaussians suggests that the present system is not exactly, but only approximately, q-independent in the sense of the q-generalized central limit theorem of Umarov, Steinberg and Tsallis. Short range interaction (α > 1) and long range interactions (α < 1) are discussed. Fitted parameters are obtained via a Method of Moments approach. Simple mechanisms which lead to the production of q-Gaussians, such as mixing, are discussed.

Wave equation for dissipative systems derived from a quantized many-body problem

1980 ◽  
Vol 58 (7) ◽  
pp. 1019-1025 ◽  
Author(s):  
M. Razavy
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Body Problem ◽  
Body Wave ◽  
Time Dependent ◽  
Dissipative Systems ◽  
Many Body ◽  
Dependent Part ◽  
The Many

A classical many-body problem composed of an infinite number of mass points coupled together by springs is quantized. The masses and the spring constants in this system are chosen in such a way that the motion of each particle is exponentially damped. Because of the quadratic form of the Hamiltonian, the many-body wave function of the system can be written as a product of two terms: a time-dependent phase factor which contains correlations between the classical motions of the particles, and a stationary state solution of the Schrödinger equation. By assuming a Hartree type wave function for the many-particle Schrödinger equation, the contribution of the time-dependent part to the single particle wave function is determined, and it is shown that the time-dependent wave function of each mass point satisfies the nonlinear Schrödinger–Langevin equation. The characteristic decay time of any part of the subsystem, in this model, is related to the stiffness of the springs, and is the same for all particles.

scholarly journals Convergence of many-body wave-function expansions using a plane-wave basis: From homogeneous electron gas to solid state systems

2012 ◽  
Vol 86 (3) ◽  
Author(s):  
James J. Shepherd ◽  
Andreas Grüneis ◽  
George H. Booth ◽  
Georg Kresse ◽  
Ali Alavi
Keyword(s):  
Wave Function ◽  
Solid State ◽  
Plane Wave ◽  
Body Wave ◽  
Electron Gas ◽  
Many Body
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