Analyzing the geometric phase for self-oscillations in field emission nanowire mechanical resonators

Choi, Jeong Ryeol; Ju, Sanghyun

doi:10.1007/s11071-019-05001-w

Cited by 4 publications

(2 citation statements)

References 33 publications

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“…In many cases, it enables us to derive quantum solutions of TDHSs. [ 31–34 ] From the Liouville‐von Neumann equation,

normald \overset{I}{true} / normald t = \partial \overset{I}{true} / \partial t + {(i ℏ)}^{- 1} false[\overset{I}{true}, {\hat{H}}_{q} false] = 0

, we can establish a linear invariant operator [ 31 ] of the system such that

\hat{I} = c \{X (t) [\hat{p} - p_{normalp} false(t false)] - i scriptA (t) [\hat{x} - x_{normalp} false(t false)]\} e^{i η (t)}

where c is a complex constant,

p_{normalp} false(t false)

is a particular solution of the classical equation of motion of the system in momentum space,

X false(t false) = \sqrt{X_{1}^{2} false(t false) + X_{2}^{2} false(t false)}

, and

\begin{matrix} true \\ right scriptA false(t false) & = & left \frac{Ω}{X false(t false)} - i m \exp_{q} (β t) \overset{X}{true} (t) \end{matrix}

\begin{matrix} true \\ right η false(t false) & = & left \frac{Ω}{m} \int_{0}^{t} \frac{d t^{'}}{X^{2} ...} \end{matrix}

…”

Section: Resultsmentioning

confidence: 99%

The Effects of Nonextensivity for a General Driven Dissipative Oscillator in the Coherent States

Choi

2021

Annalen der Physik

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The nonextensivity for a general quantum dissipative system driven by an external force is investigated. The dynamics of the system is characterized by a nonextensivity parameter q which indicates the degree of departure from extensivity for the system. The wave function of the system in the coherent state is derived with the aid of the linear invariant operator which obeys the Liouville–von Neumann equation. It is confirmed that, although the corresponding quantum energy dissipates with time like the classical energy, its time behavior is somewhat different from that of the usual dissipative systems depending on the scale of nonextensivity. The rate of such a dissipation becomes slightly larger as q increases. The effects of nonextensivity on other quantum characteristics of the system, such as fluctuations and uncertainty relations for canonical variables, are also analyzed rigorously. It is shown that the authors' results in the nonextensive regime recover to those of the well known standard ones in the limit q→1.

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“…In many cases, it enables us to derive quantum solutions of TDHSs. [ 31–34 ] From the Liouville‐von Neumann equation,

normald \overset{I}{true} / normald t = \partial \overset{I}{true} / \partial t + {(i ℏ)}^{- 1} false[\overset{I}{true}, {\hat{H}}_{q} false] = 0

, we can establish a linear invariant operator [ 31 ] of the system such that

\hat{I} = c \{X (t) [\hat{p} - p_{normalp} false(t false)] - i scriptA (t) [\hat{x} - x_{normalp} false(t false)]\} e^{i η (t)}

where c is a complex constant,

p_{normalp} false(t false)

is a particular solution of the classical equation of motion of the system in momentum space,

X false(t false) = \sqrt{X_{1}^{2} false(t false) + X_{2}^{2} false(t false)}

, and

\begin{matrix} true \\ right scriptA false(t false) & = & left \frac{Ω}{X false(t false)} - i m \exp_{q} (β t) \overset{X}{true} (t) \end{matrix}

\begin{matrix} true \\ right η false(t false) & = & left \frac{Ω}{m} \int_{0}^{t} \frac{d t^{'}}{X^{2} ...} \end{matrix}

…”

Section: Resultsmentioning

confidence: 99%

The Effects of Nonextensivity for a General Driven Dissipative Oscillator in the Coherent States

Choi

2021

Annalen der Physik

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“…For more recent advancements in quantum learning, please refer to [35,[37][38][39][40][41][42][43][44][45][46][47][48][49]. These studies highlight the latest developments in this rapidly evolving field.…”

Section: Quantum Mechanics Based On Machine Learningmentioning

confidence: 99%

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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Quantum Confinement Detection using a Coupled Schrödinger System

2023

Preprint

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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 Schr¨odinger 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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Analyzing the geometric phase for self-oscillations in field emission nanowire mechanical resonators

Cited by 4 publications

References 33 publications

The Effects of Nonextensivity for a General Driven Dissipative Oscillator in the Coherent States

The Effects of Nonextensivity for a General Driven Dissipative Oscillator in the Coherent States

Quantum confinement detection using a coupled Schrödinger system

Quantum Confinement Detection using a Coupled Schrödinger System

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