With the help of the time-dependent Lagrangian for a damped harmonic oscillator, the quantization of mesoscopic RLC circuit in the context of a number-phase quantization scheme is realized and the corresponding Hamilt...With the help of the time-dependent Lagrangian for a damped harmonic oscillator, the quantization of mesoscopic RLC circuit in the context of a number-phase quantization scheme is realized and the corresponding Hamiltonian operator is obtained. Then the evolution of the charge number and phase difference across the capacity are obtained. It is shown that the number-phase analysis is useful to tackle the quantization of some mesoscopic circuits and dynamical equations of the corresponding operators.展开更多
The quantum phase properties of the generalized squeezed vacuum states associated with solvable quantum systems are studied by using the Pegg-Barnett formalism.Then,two nonclassical features,i.e.,squeezing in the numb...The quantum phase properties of the generalized squeezed vacuum states associated with solvable quantum systems are studied by using the Pegg-Barnett formalism.Then,two nonclassical features,i.e.,squeezing in the number and phase operators,as well as the number-phase Wigner function of the generalized squeezed states are investigated.Due to some actual physical situations,the present approach is applied to two classes of generalized squeezed states：solvable quantum systems with discrete spectra and nonlinear squeezed states with particular nonlinear functions.Finally,the time evolution of the nonclassical properties of the considered systems has been numerically investigated.展开更多
With respect to flows in a two-dimensional sudden expansion and contraction channel having a pair of cavities, numerical simulation was performed by imposing inlet/outlet boundary conditions giving a velocity distribu...With respect to flows in a two-dimensional sudden expansion and contraction channel having a pair of cavities, numerical simulation was performed by imposing inlet/outlet boundary conditions giving a velocity distribution to the inlet. Periodic flows have been reproduced, which have a discrete spectrum about frequency. A fundamental wave occupies most part of the disturbance components, but higher harmonic waves are also included. The disturbance is excited by Kelvin-Helmholtz instability in a cavity section, where only the fundamental wave is generated. A wavenumber is regulated by a channel length under a periodic boundary condition, but there is no restriction in a main flow direction under the inlet/outlet boundary conditions, and therefore, some wavenumbers can occur. Therefore, an arbitrary frequency component of disturbance is a synthesized wave composed of various wave numbers. There are two kinds of components constituting this synthesized wave: a maximum of a velocity distribution is near a wall and in the center of the channel, which are called as wall mode and central mode in linear stability analysis of the plane Poiseuille flow. The synthesized wave composed of some modes shows a tendency to lower wavenumbers at the center of the channel.展开更多
It is a fact that imaginary numbers do not have practical significance. But the role of imaginary numbers is very broad and enormous, due to the existence of Euler’s formula. Due to Euler’s formula, imaginary number...It is a fact that imaginary numbers do not have practical significance. But the role of imaginary numbers is very broad and enormous, due to the existence of Euler’s formula. Due to Euler’s formula, imaginary numbers have been applied in many theoretical theories. One of the biggest functions of imaginary numbers is to represent changes in phase, which is indispensable in signal analysis theory. The imaginary numbers in quantum mechanics pose a greater mystery: do the imaginary numbers really exist? This question still needs further scientific development to be answered.展开更多
文摘With the help of the time-dependent Lagrangian for a damped harmonic oscillator, the quantization of mesoscopic RLC circuit in the context of a number-phase quantization scheme is realized and the corresponding Hamiltonian operator is obtained. Then the evolution of the charge number and phase difference across the capacity are obtained. It is shown that the number-phase analysis is useful to tackle the quantization of some mesoscopic circuits and dynamical equations of the corresponding operators.
文摘The quantum phase properties of the generalized squeezed vacuum states associated with solvable quantum systems are studied by using the Pegg-Barnett formalism.Then,two nonclassical features,i.e.,squeezing in the number and phase operators,as well as the number-phase Wigner function of the generalized squeezed states are investigated.Due to some actual physical situations,the present approach is applied to two classes of generalized squeezed states：solvable quantum systems with discrete spectra and nonlinear squeezed states with particular nonlinear functions.Finally,the time evolution of the nonclassical properties of the considered systems has been numerically investigated.
文摘With respect to flows in a two-dimensional sudden expansion and contraction channel having a pair of cavities, numerical simulation was performed by imposing inlet/outlet boundary conditions giving a velocity distribution to the inlet. Periodic flows have been reproduced, which have a discrete spectrum about frequency. A fundamental wave occupies most part of the disturbance components, but higher harmonic waves are also included. The disturbance is excited by Kelvin-Helmholtz instability in a cavity section, where only the fundamental wave is generated. A wavenumber is regulated by a channel length under a periodic boundary condition, but there is no restriction in a main flow direction under the inlet/outlet boundary conditions, and therefore, some wavenumbers can occur. Therefore, an arbitrary frequency component of disturbance is a synthesized wave composed of various wave numbers. There are two kinds of components constituting this synthesized wave: a maximum of a velocity distribution is near a wall and in the center of the channel, which are called as wall mode and central mode in linear stability analysis of the plane Poiseuille flow. The synthesized wave composed of some modes shows a tendency to lower wavenumbers at the center of the channel.
文摘It is a fact that imaginary numbers do not have practical significance. But the role of imaginary numbers is very broad and enormous, due to the existence of Euler’s formula. Due to Euler’s formula, imaginary numbers have been applied in many theoretical theories. One of the biggest functions of imaginary numbers is to represent changes in phase, which is indispensable in signal analysis theory. The imaginary numbers in quantum mechanics pose a greater mystery: do the imaginary numbers really exist? This question still needs further scientific development to be answered.
