The Standard System of Coherent States; Several Degrees of Freedom

1986 ◽  
pp. 48-53
Author(s):  
Askold Perelomov
Keyword(s):  
Coherent States ◽  
Degrees Of Freedom ◽  
Standard System

scholarly journals Entanglement in massive coupled oscillators

2011 ◽  
Vol 11 (3&4) ◽  
pp. 278-299
Author(s):  
Nathan L. Harshman ◽  
William F. Flynn
Keyword(s):  
Coupled Oscillators ◽  
Coherent States ◽  
Degrees Of Freedom ◽  
Classical Model ◽  
Reduced Density Matrix ◽  
One Dimension ◽  
Atomic Position ◽  
Pure States ◽  
Non Gaussian ◽  
Reduced Density

This article investigates entanglement of the motional states of massive coupled oscillators. The specific realization of an idealized diatomic molecule in one-dimension is considered, but the techniques developed apply to any massive particles with two degrees of freedom and a quadratic Hamiltonian. We present two methods, one analytic and one approximate, to calculate the interatomic entanglement for Gaussian and non-Gaussian pure states as measured by the purity of the reduced density matrix. The cases of free and trapped molecules and hetero- and homonuclear molecules are treated. In general, when the trap frequency and the molecular frequency are very different, and when the atomic masses are equal, the atoms are highly-entangled for molecular coherent states and number states. Surprisingly, while the interatomic entanglement can be quite large even for molecular coherent states, the covariance of atomic position and momentum observables can be entirely explained by a classical model with appropriately chosen statistical uncertainty.

Dynamics of Open Quantum Systems Using Parametric Representation with Coherent States

2013 ◽  
Vol 20 (03) ◽  
pp. 1340002 ◽  
Author(s):  
Dario Calvani ◽  
Alessandro Cuccoli ◽  
Nikitas I. Gidopoulos ◽  
Paola Verrucchi
Keyword(s):  
Coherent States ◽  
Degrees Of Freedom ◽  
Irreversible Process ◽  
Open Quantum Systems ◽  
Parametric Representation ◽  
Quantum Systems ◽  
Entanglement Generation ◽  
Open Quantum ◽  
Alternative Description ◽  
Reduced Density

Open quantum systems and their dynamics are usually studied in terms of reduced density matrices. This approach allows a nonsymmetric description, which is useful when one of the two subsystems is to be considered an environment, at the expense of a loss of information, as tracing out the environmental degrees of freedom is an irreversible process. This has a series of consequences which can be severe. In this work we present an alternative description, which is still nonsymmetric but yet exact: It is based on a parametric representation of composite systems, as obtained by introducing environmental coherent states, such that the principal system get to be described by a set of pure states parametrically dependent on environmental variables. The representation allows one to relate properties which typically arise in studying systems with parametrically dependent Hamiltonians, such as the emergence of geometrical phases, with features which specifically characterize open quantum systems, such as decoherence and entanglement generation.

scholarly journals Free Coherent States and Distributions on p-Adic Numbers

1998 ◽  
Vol 01 (02) ◽  
pp. 349-355 ◽  
Author(s):  
S. V. Kozyrev
Keyword(s):  
Coherent States ◽  
Degrees Of Freedom ◽  
Space Of Distributions

Free coherent states for a system with p degrees of freedom are defined. An isomorphism between the space free coherent states and the space of distributions on p-adic disk is constructed.

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.

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.

Das Experten-Novizen-Paradigma und die Vertrauenskrise in der Psychologie

2016 ◽  
Vol 23 (4) ◽  
pp. 131-140 ◽  
Author(s):  
Philip Furley ◽  
Karsten Schul ◽  
Daniel Memmert
Keyword(s):  
Degrees Of Freedom

Zusammenfassung. Das Ziel des vorliegenden Beitrages ist es anhand eines vielverwendeten Paradigmas in der Sportwissenschaft – dem Experten-Novizen-Vergleich – zu prüfen, ob die momentane Vertrauenskrise in der Psychologie ebenfalls die Sportpsychologie betreffen könnte. Anhand einer exemplarischen Studie zeigen wir, dass es innerhalb dieses Paradigmas zu kontroversen Befunden kommt, welche durch die vermuteten Ursachen der Vertrauenskrise (Researcher Degrees of Freedom, kleine Stichprobengrößen) erklärt sein könnten. Zusätzlich argumentieren wir, dass weitere Faktoren (Konfundierung, Stichprobengrößen, Rosenthal Effekt, Expertise-Definition) innerhalb dieses Paradigmas die Reproduzierbarkeit von Erkenntnissen in Frage stellen. Wir diskutieren mögliche Maßnahmen, wie die dargestellten Probleme des Experten-Novizen-Paradigmas in zukünftigen Forschungsarbeiten gelöst werden können.

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