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Quantum Spaces of Tribosystems
Published in Dmitry N. Lyubimov, Kirill N. Dolgopolov, L.S. Pinchuk, Quantum Effects in Tribology, 2017
Dmitry N. Lyubimov, Kirill N. Dolgopolov, L.S. Pinchuk
The states with the least uncertainty are most close to their classical analog, since the impact of the Heisenberg principle (3.33) is minimized. Such states, if the equalities q=q¯ $ q = \bar{q} $ and p=p¯ $ p = \bar{p} $ are met, are called coherent. In other words, coherent states are states of least uncertainty in the values of the coordinate and momentum at the given mean values. In terms of S. Doronin, “Coherent states are a superposition of pure states, i.e. overlapping of individual states that a closed system can be in. Coherence is a consistency of behavior of individual components of a physical system by means of nonlocal correlations” [40].
The Principles of Quantum Optics
Published in David N. Klyshko, Yuri Sviridov, Photons and Nonlinear Optics, 2018
David N. Klyshko, Yuri Sviridov
Among the various types of instantaneous states of the quantum oscillator, coherent states stand out as being, in a sense, closest to the state of a classical oscillator with a definite coordinate and velocity. The distribution of the number of photons in the z-state is Poisson; thus, the variance is coincident with the mean number of photons: () (ΔN2)z=〈N〉=|z|2⋅
Quantum Nonlinear Optics
Published in Peter E. Powers, Joseph W. Haus, Fundamentals of Nonlinear Optics, 2017
Peter E. Powers, Joseph W. Haus
The coherent state has the property that it is a minimum uncertainty state. Consider two conjugate observables, Q=12(a+a†),P=12i(a†−a).
Coupled supersymmetry and ladder structures beyond the harmonic oscillator
Published in Molecular Physics, 2018
Cameron L. Williams, Nikhil N. Pandya, Bernhard G. Bodmann, Donald J. Kouri
The quantum mechanical harmonic oscillator (QMHO) is an important part of quantum theory. It has close connections to classical mechanics through an associated family of coherent states that minimise the Heisenberg uncertainty principle for the position and momentum operators. Often, the harmonic oscillator is used as an approximation to describe quantum systems that oscillate about an equilibrium position. It is also fundamental in quantum field theory and related areas like BCS superconductivity in solid state theory [1]. In the position representation, measuring energy in units of , where is Planck's constant and ω is the angular frequency of the oscillator, the Hamiltonian of the QMHO is the Schrödinger operator The domain of this operator is most easily described in terms of the sequence of Hermite functions which form an orthonormal basis of eigenfunctions for the Hilbert space . Each function ψ in the domain of is given by a series expansion whose sequence of coefficients is such that the norm obtained after applying is finite, .
Self-Controlled Flashing Nuclear Fusion in Stationary Magnetized Low-Temperature Plasma
Published in Fusion Science and Technology, 2023
V. I. Vysotskii, M. V. Vysotskyy
The state of a quantum system, in which relations (6), (7), and (8) turn into equalities, is called coherent correlated state (CCS). In practice, the term “CCS” refers to any state with . According to the same interpretation, the quantum state that transforms relations (6), (7), and (8) into equalities is traditionally called the coherent state, which is a synonym for the “squeezed” state, which is characterized by the minimum product of dispersions and the maximum proximity to the classical state of a particle in a potential well.1,2