DRIVEN MESOSCOPIC ELECTRIC CIRCUITS

2008 ◽  
Vol 22 (01) ◽  
pp. 51-60 ◽  
Author(s):  
F. KHEIRANDISH ◽  
H. PAHLAVANI
Keyword(s):  
Quantum Theory ◽  
Energy Spectrum ◽  
Algebraic Approach ◽  
Electric Circuit ◽  
External Source ◽  
Persistent Current ◽  
Time Dependent ◽  
Quantum Ring ◽  
Electric Circuits

The quantum theory for a mesoscopic electric circuit with charge discreteness is investigated. The persistent current on a quantum ring using an algebraic approach have been obtained. The energy spectrum and the persistent current of a quantum LC-design mesoscopic circuit, with a time-dependent external source, have been found.

The persistent current and energy spectrum on a driven mesoscopic LC-circuit with Josephson junction

2018 ◽  
Vol 32 (06) ◽  
pp. 1850066
Author(s):  
Hassan Pahlavani
Keyword(s):  
Energy Spectrum ◽  
Josephson Junction ◽  
Electric Circuit ◽  
External Source ◽  
Electrical Circuit ◽  
Persistent Current ◽  
Time Dependent ◽  
Coupling Energy ◽  
Junction Device ◽  
Lc Circuit

The quantum theory for a mesoscopic electric circuit including a Josephson junction with charge discreteness is studied. By considering coupling energy of the mesoscopic capacitor in Josephson junction device, a Hamiltonian describing the dynamics of a quantum mesoscopic electric LC-circuit with charge discreteness is introduced. We first calculate the persistent current on a quantum driven ring including Josephson junction. Then we obtain the persistent current and energy spectrum of a quantum mesoscopic electrical circuit which includes capacitor, inductor, time-dependent external source and Josephson junction.

QUANTIZATION OF MESOSCOPIC QUARTZ PIEZOELECTRIC CRYSTAL EQUIVALENT CIRCUIT

2011 ◽  
Vol 25 (11) ◽  
pp. 847-853 ◽  
Author(s):  
ZHAN-YUAN YAN ◽  
JIN-YING MA ◽  
XIAO-HONG ZHANG
Keyword(s):  
Quantum Theory ◽  
Energy Spectrum ◽  
Finite Difference ◽  
Equivalent Circuit ◽  
Quantum Fluctuation ◽  
Integrate Circuit ◽  
New Method ◽  
Piezoelectric Crystal ◽  
Electric Circuits ◽  
Perturbative Method

In the framework of an advanced quantum theory for mesoscopic electric circuits in accord with the discreteness of electric charges, a mesoscopic quartz piezoelectric crystal equivalent circuit is quantized. To resolve the finite difference Schrödinger equation, an improved parameter perturbative method is proposed when WKB and perturbative method are inapplicable. With this method, the energy spectrum and wavefunctions of the system are obtained and used to calculate current quantum fluctuation as an application. The new method would be helpful to the application of the mesoscopic circuits quantum theory. Besides, the detail characters of energy spectrum and wavefunctions in the system would be helpful to the design of integrate circuit.

MESOSCOPIC CIRCUIT WITH LINEAR DISSIPATION

2002 ◽  
Vol 16 (26) ◽  
pp. 975-979 ◽  
Author(s):  
TING LU ◽  
YOU-QUAN LI
Keyword(s):  
Quantum Theory ◽  
Magnetic Flux ◽  
Electric Circuit ◽  
Energy Spectra ◽  
Electric Circuits ◽  
Symmetry Hypothesis ◽  
Main Ideas ◽  
Further Development

We firstly demonstrate the main ideas of quantum theory for mesoscopic electric circuits, which we proposed several years ago. In the theory, the importance of the charge discreteness in a mesoscopic electric circuit is addressed. As a further development, we discuss the mesoscopic electric circuit in the presence of linear dissipation as well as magnetic flux. We propose a quantum Kirchoff equation for the LCR circuit and discuss the oscillations for different criterion factors. We also solve the energy spectra and eigenvalues of the physical current under a soluble symmetry hypothesis.

The quantum dynamics of a mesoscopic driven RLC circuit consisting of a linear inductor, a linear resistor and a nonlinear capacitor

2021 ◽  
Author(s):  
A. Zamani ◽  
H. Pahlavani
Keyword(s):  
Quantum Dynamics ◽  
Dynamical Behavior ◽  
Electric Circuit ◽  
External Source ◽  
Electrical Circuit ◽  
Persistent Current ◽  
Nonlinear Parameters ◽  
Quantum Dynamical ◽  
Rlc Circuit ◽  
Cubic Polynomial

The nonlinear capacitor that obeys of a cubic polynomial voltage–charge relation (usually a power series in charge) is introduced. The quantum theory for a mesoscopic electric circuit with charge discreteness is investigated, and the Hamiltonian of a quantum mesoscopic electrical circuit comprised by a linear inductor, a linear resistor and a nonlinear capacitor under the influence of a time-dependent external source is expressed. Using the numerical solution approaches, a good analytic approximate solution for the quantum cubic Duffing equation is found. Based on this, the persistent current is obtained antically. The energy spectrum of such nonlinear electrical circuit has been found. The dependency of the persistent current and spectral property equations to linear and nonlinear parameters is discussed by the numerical simulations method, and the quantum dynamical behavior of these parameters is studied.

Parametric inference in Markov branching processes with time-dependent random immigration rate

1985 ◽  
Vol 22 (03) ◽  
pp. 503-517
Author(s):  
Helmut Pruscha
Keyword(s):  
Point Processes ◽  
Traditional Approach ◽  
Branching Processes ◽  
External Source ◽  
Time Dependent ◽  
Parametric Inference ◽  
Asymptotic Results ◽  
Subcritical Case ◽  
Immigration Rate ◽  
Pearson Type

The present paper deals with continuous-time Markov branching processes allowing immigration. The immigration rate is allowed to be random and time-dependent where randomness may stem from an external source or from state-dependence. Unlike the traditional approach, we base the analysis of these processes on the theory of multivariate point processes. Using the tools of this theory, asymptotic results on parametric inference are derived for the subcritical case. In particular, the limit distributions of some parametric estimators and of Pearson-type statistics for testing simple and composite hypotheses are established.

scholarly journals Sequential Reasoning in Electricity: Developing and Using a Three-Tier Multiple Choice Test

2017 ◽  
Vol 8 ◽  
Author(s):  
Hildegard Urban
Keyword(s):  
Multiple Choice ◽  
Electric Circuit ◽  
Choice Test ◽  
School Students ◽  
Reliable Measure ◽  
Electric Circuits ◽  
Multiple Choice Tests ◽  
Qualitative Understanding ◽  
In Series ◽  
Testing Electricity

Electricity is one of the areas in physics most studied in terms of learning difficulties. Misconceptions are strongly-held, stable cognitive structures, which differ from expert conception and affect how students understand scientific explanations. Therefore, there is a need for tests of conceptual understanding tests which are useful in diagnosing the nature of students’ misconceptions related to simple electric circuits and, in consequence, can serve as a valid and reliable measure of students’ qualitative understanding of simple electric circuits. As ordinary multiple choice tests with one-tier may overestimate the students’ correct as well as wrong answers, two- and three-tier tests were developed by researchers. Although, there is much research related to students’ conceptions in basic electricity, there is a lack of instruments for testing basic electricity concepts of students at grade 7, especially addressing an electric circuit as a system for a simple circuit of resistors and lamps in series. To address this gap, the context of the present study is an extension to the development of an already existing instrument developed by the author for testing electricity concepts of students at grade 7, specifically focusing on only two specific aspects in depth: first, to develop three-tier items for figuring out sequential reasoning, and second, to distinguish between misconceptions and lack of knowledge. The participants of the study included 339 secondary school students from grade 7 to 12 after instruction on electricity. Surprisingly, there are no dependences on students’ misconceptions either according to their gender or to their age. In conclusion, the findings of the study suggest that four items for uncovering students’ sequential reasoning can serve as a valid and reliable measure of students’ qualitative understanding of the systemic character of an electric circuit.

CONSTANT ELASTICITY OF VARIANCE OPTION PRICING MODEL WITH TIME-DEPENDENT PARAMETERS

2000 ◽  
Vol 03 (04) ◽  
pp. 661-674 ◽  
Author(s):  
C. F. LO ◽  
P. H. YUEN ◽  
C. H. HUI
Keyword(s):  
Option Pricing ◽  
Algebraic Approach ◽  
Time Dependent ◽  
Model Parameters ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Pricing Options ◽  
Term Structures ◽  
Option Values

This paper provides a method for pricing options in the constant elasticity of variance (CEV) model environment using the Lie-algebraic technique when the model parameters are time-dependent. Analytical solutions for the option values incorporating time-dependent model parameters are obtained in various CEV processes with different elasticity factors. The numerical results indicate that option values are sensitive to volatility term structures. It is also possible to generate further results using various functional forms for interest rate and dividend term structures. Furthermore, the Lie-algebraic approach is very simple and can be easily extended to other option pricing models with well-defined algebraic structures.

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