On the possible emergence of nonstatic quantum waves in a static environment

Choi, Jeong Ryeol

doi:10.1007/s11071-021-06222-8

Cited by 10 publications

(50 citation statements)

References 29 publications

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“…For a specific mode of a wave, we can write the vector potential as A(r, t) = u(r)q(t) [23] where u(r) is the position function which is determined by a boundary condition, whereas q(t) is quadrature which exhibits the time behavior of the amplitude of the wave. The harmonic oscillator description of quantum wave functions q|ψ n (t) for a light wave can be represented in terms of e −W(t)q 2 /2 [12], where W(t) is a time function. Because W(t) is a complex number in general, it can be divided into real (W R (t)) and imaginary parts (W I (t)):…”

Section: Measure Of Nonstaticitymentioning

confidence: 99%

“…Hence, W I (t) is responsible for the appearance of the nonstatic character in the waves. If we define D(t) = W I /W R , the root-mean-square (RMS) value of D(t) is the quantitative measure D of nonstaticity [12]. In this work, we are interested in the effects of D(t) on nonstatic behavior of the quantum waves.…”

Section: Measure Of Nonstaticitymentioning

confidence: 99%

“…Although the environment of the waves treated in Ref. [12] is static, we do not restrict to a static environment in this work.…”

Section: Measure Of Nonstaticitymentioning

confidence: 99%

“…In our recent work [12], it has been shown that nonstatic waves can also arise even in a transparent medium whose parameters do not vary. In this case, the shape of light waves varies over time in a unique regular way as a manifestation of their nonstatic features.…”

Section: Introductionmentioning

confidence: 99%

“…Nonstatic quantum light waves have been a focus of active research in optics and related subjects during several decades [5][6][7][8][9][10][11][12]. In particular, the manipulation and application of such waves are important in nano-optics according to their extensive role in nano science and technology [13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

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Characteristics of Nonstatic Quantum Light Waves: The Principle for Wave Expansion and Collapse

Choi

2021

Photonics

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Nonstatic quantum light waves arise in time-varying media in general. However, from a recent report, it turned out that nonstatic waves can also appear in a static environment where the electromagnetic parameters of the medium do not vary in time. Such waves in Fock states exhibit a belly and a node in turn periodically in the graphic of their evolution. This is due to the wave expansion and collapse in quadrature space, which manifest a unique nonstaticity of the wave. The principle for wave expansion and collapse is elucidated from rigorous analyses for the basic nonstatic waves which are dissipative and amplifying ones. The outcome of wave nonstaticity can be interpreted in terms of the coefficient of the quadratic exponent in the exponential function appearing in the wave eigenfunction; if the imaginary part of the coefficient is positive, the wave expands, whereas the wave collapses when it is negative. Using this principle, we further analyze novel nonstatic properties of light waves which exhibit complicated time behaviors, i.e., for the case that the waves not only undergo the periodical change of nodes and bellies but their envelopes exhibit gradual dissipation/expansion as well.

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Section: Measure Of Nonstaticitymentioning

confidence: 99%

Section: Measure Of Nonstaticitymentioning

confidence: 99%

“…Although the environment of the waves treated in Ref. [12] is static, we do not restrict to a static environment in this work.…”

Section: Measure Of Nonstaticitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Characteristics of Nonstatic Quantum Light Waves: The Principle for Wave Expansion and Collapse

Choi

2021

Photonics

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Quantum confinement detection using a coupled Schrödinger system

2023

Nonlinear Dyn

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Machine learning techniques have provided valuable insights into understanding the fundamental principles of physics. Recent studies have demonstrated the ability of deep neural networks (DNNs) to learn a wide range of differential equations (DEs) and classical Hamiltonian mechanics systems. This has led to the emergence of solving the inverse problem associated with partial differential equations using DNNs. In this paper, we propose a novel method for detecting quantum confinement by numerically solving the Schrödinger system on manifolds with nonlinear coupling. Our method exhibits remarkable performance in identifying various quantum phenomena. Moreover, our research introduces a promising approach for principled modeling and prediction in quantum processes. By combining deep learning with traditional models, our hybrid model leverages the strengths of both approaches, enhancing computational efficiency and enabling meaningful predictions for complex quantum physical processes. The integration of multiple deep learning principles with quantum physics enables effective handling of large datasets and addresses inverse challenges related to intricate dynamical systems and physical phenomena.

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Analysis of light-wave nonstaticity in the coherent state

Choi

2021

Sci Rep

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The characteristics of nonstatic quantum light waves in the coherent state in a static environment is investigated. It is shown that the shape of the wave varies periodically as a manifestation of its peculiar properties of nonstaticity like the case of the Fock-state analysis for a nonstatic wave. A belly occurs in the graphic of wave evolution whenever the wave is maximally displaced in the quadrature space, whereas a node takes place every time the wave passes the equilibrium point during its oscillation. In this way, a belly and a node appear in turn successively. Whereas this change of wave profile is accompanied by the periodic variation of electric and magnetic energies, the total energy is conserved. The fluctuations of quadratures also vary in a regular manner according to the wave transformation in time. While the resultant time-varying uncertainty product is always larger than (or, at least, equal to) its quantum-mechanically allowed minimal value ($$\hbar /2$$ ħ / 2 ), it is smallest whenever the wave constitutes a belly or a node. The mechanism underlying the abnormal features of nonstatic light waves demonstrated here can be interpreted by the rotation of the squeezed-shape contour of the Wigner distribution function in phase space.

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On the possible emergence of nonstatic quantum waves in a static environment

Cited by 10 publications

References 29 publications

Characteristics of Nonstatic Quantum Light Waves: The Principle for Wave Expansion and Collapse

Characteristics of Nonstatic Quantum Light Waves: The Principle for Wave Expansion and Collapse

Quantum confinement detection using a coupled Schrödinger system

Analysis of light-wave nonstaticity in the coherent state

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