Global Order-Value Optimization by means of a Multistart Harmonic Oscillator Tunneling Strategy

From the Baltic to the South China Sea, newly assertive authoritarian states sense an opportunity to resurrect old empires or build new ones at America's expense. Hoping that U.S. decline is real, nations such as Russia, Iran, and China are testing Washington's resolve by targeting vulnerable allies at the frontiers of American power. This book explains why the United States needs a new grand strategy that uses strong frontier alliance networks to raise the costs of military aggression in the new century. The book describes the aggressive methods which rival nations are using to test American power in strategically critical regions throughout the world. It shows how rising and revisionist powers are putting pressure on our frontier allies—countries like Poland, Israel, and Taiwan—to gauge our leaders' commitment to upholding the American-led global order. To cope with these dangerous dynamics, nervous U.S. allies are diversifying their national-security “menu cards” by beefing up their militaries or even aligning with their aggressors. The book reveals how numerous would-be great powers use an arsenal of asymmetric techniques to probe and sift American strength across several regions simultaneously, and how rivals and allies alike are learning from America's management of increasingly interlinked global crises to hone effective strategies of their own. The book demonstrates why the United States must strengthen the international order that has provided greater benefits to the world than any in history.

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Rosen-Chambers Variation Theory of Linearly-Damped Classic and Quantum Oscillator

JOURNAL OF ADVANCES IN PHYSICS ◽

10.24297/jap.v4i1.6966 ◽

2014 ◽

Vol 4 (1) ◽

pp. 404-426

Author(s):

Vincze Gy. Szasz A.

Keyword(s):

Harmonic Oscillator ◽

Classical Mechanics ◽

Universal Time ◽

Variation Theory ◽

Quantum Oscillator ◽

Variation Principle ◽

Poisson Brackets ◽

Mathematical Meaning ◽

Damped Harmonic Oscillator ◽

Damped Oscillator

Phenomena of damped harmonic oscillator is important in the description of the elementary dissipative processes of linear responses in our physical world. Its classical description is clear and understood, however it is not so in the quantum physics, where it also has a basic role. Starting from the Rosen-Chambers restricted variation principle a Hamilton like variation approach to the damped harmonic oscillator will be given. The usual formalisms of classical mechanics, as Lagrangian, Hamiltonian, Poisson brackets, will be covered too. We shall introduce two Poisson brackets. The first one has only mathematical meaning and for the second, the so-called constitutive Poisson brackets, a physical interpretation will be presented. We shall show that only the fundamental constitutive Poisson brackets are not invariant throughout the motion of the damped oscillator, but these show a kind of universal time dependence in the universal time scale of the damped oscillator. The quantum mechanical Poisson brackets and commutation relations belonging to these fundamental time dependent classical brackets will be described. Our objective in this work is giving clearer view to the challenge of the dissipative quantum oscillator.

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