Quasiclassical Correlation Functions from the Wigner Density Using the Stability Matrix

2019 ◽  
Vol 59 (5) ◽  
pp. 2165-2174 ◽  
Author(s):  
Amartya Bose ◽  
Nancy Makri
Keyword(s):  
Correlation Functions ◽  
Stability Matrix ◽  
The Stability

scholarly journals Heavy handed quest for fixed points in multiple coupling scalar theories in the ε expansion

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Hugh Osborn ◽  
Andreas Stergiou
Keyword(s):  
Fixed Points ◽  
Index Case ◽  
Symmetric Tensors ◽  
Number Of Solutions ◽  
Stability Matrix ◽  
Negative Eigenvalues ◽  
Large Numbers ◽  
Quadratic Invariants ◽  
Scalar Theories ◽  
The Stability

Abstract The tensorial equations for non trivial fully interacting fixed points at lowest order in the ε expansion in 4 − ε and 3 − ε dimensions are analysed for N-component fields and corresponding multi-index couplings λ which are symmetric tensors with four or six indices. Both analytic and numerical methods are used. For N = 5, 6, 7 in the four-index case large numbers of irrational fixed points are found numerically where ‖λ‖2 is close to the bound found by Rychkov and Stergiou [1]. No solutions, other than those already known, are found which saturate the bound. These examples in general do not have unique quadratic invariants in the fields. For N ⩾ 6 the stability matrix in the full space of couplings always has negative eigenvalues. In the six index case the numerical search generates a very large number of solutions for N = 5.

Application of the two-dimensional Newcomb problem to compute the stability matrix of external MHD modes in a tokamak

2004 ◽  
Vol 46 (11) ◽  
pp. 1699-1721 ◽  
Author(s):  
Nobuyuki Aiba ◽  
Shinji Tokuda ◽  
Tomoko Ishizawa ◽  
Masao Okamoto
Keyword(s):  
Two Dimensional ◽  
Stability Matrix ◽  
Newcomb Problem ◽  
The Stability

On the Stability of Large Discrete Buckling Structures

1983 ◽  
Vol 50 (1) ◽  
pp. 230-232 ◽  
Author(s):  
A. Maher
Keyword(s):  
Buckling Load ◽  
Critical Buckling Load ◽  
Stability Matrix ◽  
The Stability

An approximate applicable method is presented for the computation of the critical buckling load of a moderately large complicated assembly in terms of traces of successive powers of the stability matrix. The method is based on the use of the bound approach of reference [1, 2]. An illustrative example and comparison with known results are given.

NEW CHARACTERISERS OF BIFURCATIONS FROM KINK SOLUTIONS IN A COUPLED SINE CIRCLE MAP LATTICE

2001 ◽  
Vol 11 (09) ◽  
pp. 2501-2508 ◽  
Author(s):  
GAURI R. PRADHAN ◽  
NEELIMA GUPTE
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Spatial Period ◽  
Circle Map ◽  
Stability Matrix ◽  
Different Types ◽  
The Stability ◽  
Bifurcation Behavior ◽  
Solution Changes

Kink solutions in coupled sine circle map lattices demonstrate interesting bifurcation behavior. These are illustrated by the study of spatial period two kink solutions for this system. Different types of spatiotemporal solutions such as temporally frozen kinks, spatiotemporally synchronized solutions and kink induced temporally intermittent solutions appear in different regions of parameter space for this system and bifurcations are seen from one type of solution to another. The upper boundaries of the regions where the kinks are stable can be picked up by linear stability analysis. However, the eigenvalues of the stability matrix do not cross the unit circle along the lower stability boundaries, although the nature of the solution changes. Thus linear stability analysis is not sufficient to identify these lower boundaries. Hence we have proposed new characterisers which are capable of identifying such boundaries. Our identifiers successfully pick up the lower boundaries missed by linear stability analysis as well as the upper boundaries. Our characterisers could be of utility in other situations as well.

Monte Carlo Renormalization of the 3-D-Ising Model and the Analyticity of Block-Spin Transformations

1991 ◽  
Vol 02 (01) ◽  
pp. 487-490 ◽  
Author(s):  
T.S. SMIT ◽  
J.R. HERINGA ◽  
H.W.J. BLÖTE ◽  
A. COMPAGNER ◽  
Y.T.J.C. FONK ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Correlation Functions ◽  
Coupling Constants ◽  
Nearest Neighbour ◽  
Cubic Lattices ◽  
Simple Cubic ◽  
Lattice Size ◽  
The Stability ◽  
Derivatives Of ◽  
Monte Carlo Renormalization Group

We present a new analysis on Monte Carlo Renormalization Group (MCRG) results obtained earlier by means of the Delft Ising System Processor (DISP). The MCRG data involve a total of 57 coupling constants, 36 even and 21 odd. Simulations were carried out for simple cubic lattices with 643, 323 and 163 spins. The RG transformation is assumed to be analytic. A number of relations exist between correlation functions at different renormalization levels. Some of these involve the derivatives of the stability matrix. These correlation functions enable an analysis of the so-called regular part of the RG transformation. If the Hamiltonian of the original lattice only contains nearest-neighbour couplings then the regular contributions to the specific heat and the magnetic susceptibility can be easily determined. These contributions must depend only weakly on the initial lattice size, at least if the RG transformation is analytic. We investigated whether this is indeed true when the majority-rule is applied. New simulations involving higher-order correlations will enable us to study the analytic contributions in more detail.

scholarly journals Simplified calculation of the stability matrix for semiclassical propagation

2000 ◽  
Vol 113 (21) ◽  
pp. 9390-9392 ◽  
Author(s):  
Sophya Garashchuk ◽  
John C. Light
Keyword(s):  
Stability Matrix ◽  
The Stability ◽  
Simplified Calculation
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