Herman-Kluk semiclassical dynamics in action-angle representation: New approaches to mapping quantum degrees of freedom

2006 ◽  
Vol 124 (20) ◽  
pp. 204112 ◽  
Author(s):  
Rajdeep Saha ◽  
M. Ovchinnikov
Keyword(s):  
Degrees Of Freedom ◽  
New Approaches ◽  
Semiclassical Dynamics

scholarly journals Hidden Nambu mechanics II: Quantum/semiclassical dynamics

2019 ◽  
Vol 2019 (12) ◽  
Author(s):  
Atsushi Horikoshi
Keyword(s):  
Time Evolution ◽  
Quantum Dynamics ◽  
Degrees Of Freedom ◽  
Hamiltonian Dynamics ◽  
Extended Phase ◽  
Nambu Mechanics ◽  
Mechanical Structure ◽  
Wave Packet Dynamics ◽  
Semiclassical Dynamics ◽  
Metastable Potential

Abstract Nambu mechanics is a generalized Hamiltonian dynamics characterized by an extended phase space and multiple Hamiltonians. In a previous paper [Prog. Theor. Exp. Phys. 2013, 073A01 (2013)] we revealed that the Nambu mechanical structure is hidden in Hamiltonian dynamics, that is, the classical time evolution of variables including redundant degrees of freedom can be formulated as Nambu mechanics. In the present paper we show that the Nambu mechanical structure is also hidden in some quantum or semiclassical dynamics, that is, in some cases the quantum or semiclassical time evolution of expectation values of quantum mechanical operators, including composite operators, can be formulated as Nambu mechanics. We present a procedure to find hidden Nambu structures in quantum/semiclassical systems of one degree of freedom, and give two examples: the exact quantum dynamics of a harmonic oscillator, and semiclassical wave packet dynamics. Our formalism can be extended to many-degrees-of-freedom systems; however, there is a serious difficulty in this case due to interactions between degrees of freedom. To illustrate our formalism we present two sets of numerical results on semiclassical dynamics: from a one-dimensional metastable potential model and a simplified Henon–Heiles model of two interacting oscillators.

Kinematic Structure and Functional Analysis of Shaft Couplings Involving Pode Joints

1983 ◽  
Vol 105 (4) ◽  
pp. 672-680 ◽  
Author(s):  
E. Akbil ◽  
T. W. Lee
Keyword(s):  
Functional Analysis ◽  
Degrees Of Freedom ◽  
Systematic Approach ◽  
Degree Of Freedom ◽  
Graph Representation ◽  
Kinematic Structure ◽  
Mobility Analysis ◽  
New Approaches ◽  
New Concepts ◽  
Basic Concepts

This paper introduces some basic concepts and new approaches regarding the kinematic structure and functional analysis of mechanisms. The theory and approach are illustrated on shaft couplings involving pode joints. Kinematic structure of pode joints is given and some new concepts, such as multiple contacting points and effective and idle degrees-of-freedom, are introduced. A systematic approach which includes a modified graph representation and a modified degree-of-freedom equation is presented. Using this approach the mobility analysis of a class of difficult and complex mechanisms can be treated. Several specific examples are presented to illustrate the basic theory.

Semiclassical dynamics in up to 15 coupled vibrational degrees of freedom

1997 ◽  
Vol 106 (12) ◽  
pp. 4832-4839 ◽  
Author(s):  
Mark L. Brewer ◽  
Jeremy S. Hulme ◽  
David E. Manolopoulos
Keyword(s):  
Degrees Of Freedom ◽  
Semiclassical Dynamics

New Approaches to the Modal Analysis for Machine Tool Structure

1984 ◽  
Vol 106 (1) ◽  
pp. 40-47 ◽  
Author(s):  
Shinyi Wang ◽  
Hisayoshi Sato ◽  
Masanori O-Hori
Keyword(s):  
Machine Tool ◽  
Modal Analysis ◽  
Impulse Response ◽  
Degrees Of Freedom ◽  
Computation Time ◽  
Measured Data ◽  
Sufficient Accuracy ◽  
New Approaches ◽  
Curve Fit ◽  
Machine Tool Structure

Three new approaches to modal analysis using impulse response were developed to identify the vibration characteristics of machine tool structure. The methods are based on the principle of minimizing the sum of squares of the differences between the measured data and the analytical expression. One of the methods successfully simplified the algorithm of the curve fit procedure and the computation time was significantly economized, so that it could be carried out by a microcomputer with sufficient accuracy for the system having about 30-degrees-of-freedom.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

Beyond autism: Challenging unexamined assumptions about social motivation in typical development

2019 ◽  
Vol 42 ◽  
Author(s):  
Karen Bartsch ◽  
David Estes
Keyword(s):  
Social Interest ◽  
Social Motivation ◽  
Typical Development ◽  
Typically Developing ◽  
New Approaches

Abstract In challenging the assumption of autistic social uninterest, Jaswal & Akhtar have opened the door to scrutinizing similar unexamined assumptions embedded in other literatures, such as those on children's typically developing behaviors regarding others’ minds and morals. Extending skeptical analysis to other areas may reveal new approaches for evaluating competing claims regarding social interest in autistic individuals.

Representing utility and deploying the body

2020 ◽  
Vol 43 ◽  
Author(s):  
David Spurrett
Keyword(s):  
Functional Activity ◽  
Degrees Of Freedom ◽  
The Body ◽  
Target Article ◽  
Processing Demands ◽  
The Many

Abstract Comprehensive accounts of resource-rational attempts to maximise utility shouldn't ignore the demands of constructing utility representations. This can be onerous when, as in humans, there are many rewarding modalities. Another thing best not ignored is the processing demands of making functional activity out of the many degrees of freedom of a body. The target article is almost silent on both.

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