Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Progress of Theoretical and Experimental Physics

Tsallis, Rényi, and Shannon entropies for time-dependent mesoscopic RLC circuits

V. Aguiar, I. Guedes, I. A. Pedrosa

Published Nov 1, 2015• 5 citations
Publisher

Abstract

We calculate information measures using the Tsallis, Rényi, and Shannon entropies for two classes (Lane–Emden and Caldirola–Kanai) of time-dependent mesoscopic RLC circuits. To determine the expressions for the entropies, we used the dynamical invariant method to obtain the exact Schrödinger wave function |$\big (\psi _n (x,t)\big )$|⁠. For the state |$n=0$|⁠, all the expressions found are given in terms of |$\rho $|⁠, a c-number quantity satisfying a nonlinear differential equation. For the Caldirola–Kanai system, the entropies do not vary with time, but decrease with increasing damping factor. For the Lane–Emden system, the entropies decrease with increasing time. We also analyze the behavior of the Shannon and Rényi lengths in the charge and magnetic flux spaces and compare them with the respective standard deviations.

DOI
10.1093/ptep/ptv146

Related papers

Quantum Description of a Mesoscopic RLC Circuit

I. A. Pedrosa, Anderson Pereira Pinheiro

We present a quantum description of a mesoscopic RLC circuit. Based on the Caldirola-Kanai Hamiltonian and quantum invariant method we solve the Schrödinger equation for this circuit and write the corresponding wave functions in terms of a particular solution of the Milne-Pinney equation. In addition, we construct coherent and squeezed states for the quantized RLC circuit and evaluate the quantum fluctuations of the charge and the magnetic flux as well as the uncertainty product. Subject Index: 060, 064 The study of mesoscopic systems has attracted a lot of attention in the litera-ture in the last few years.1)–19) The great interest in these systems is motived partly because of the rapid development of nanophysics and nanoelectronics and partly because in the manufacture of electronics devices the miniaturization of integrated

Progress of Theoretical Physics•Jun 1, 2011•29 citations

Quantum description of a time-dependent mesoscopic RLC circuit

I. A. Pedrosa

In this paper, we present a comprehensive quantum description of a mesoscopic RLC circuit with time-dependent resistance, inductance and capacitance. Based on the dynamical invariant method and using quadratic invariants, we derive exact nonstationary quantum states for this circuit and write them in terms of solutions of the Milne–Pinney equation. Afterwards, we use quadratic invariants to construct coherent states for this quantized system and employ them to investigate quantum properties of the RLC circuit. In particular, we show that the product of the quantum fluctuations of the charge and the magnetic flux does not satisfy the minimum uncertainty relation.

Physica Scripta•Nov 1, 2012•7 citations

Dinâmica quântica de um circuito RLC mesoscópico

Anderson Pereira Pinheiro

In this work we present a quantum description of a mesoscopic RLC circuit without source. For this purpose, we model this system for that of a damped harmonic oscillator which is described by the Caldirola-Kanai Hamiltonian. Then, with the aid of the quantum invariant method we solve the Schrödinger equation associated with this Hamiltonian and write the corresponding wave functions in terms of a particular solution of the Milne-Pinney equation. We also construct coherent states for the RLC quantized, and evaluate the quantum fluctuations of the charge and the magnetic flux, as well as the corresponding product of uncertainty.

•Jun 30, 2011•0 citations

Fisher information of quantum damped harmonic oscillators

V. Aguiar, I. Guedes

We calculate the time-dependent Fisher information in position and momentum for the lowest lying state of two classes of quantum damped (Lane–Emden (LE) and Caldirola–Kanai (CK)) harmonic oscillators. The expressions of and are written in terms of a c-number quantity satisfying a nonlinear differential equation. Analytical solutions of were obtained. For the LE and CK oscillators, we observe that increases while decreases with increasing time. The product increases and tends to a constant value in the limit for the LE oscillator, while it is time-independent for the CK oscillator. Moreover, for the CK oscillator the product decreases as the damping increases. Relations among the Fisher information, Leipnik and Shannon entropies, and the Stam and Cramer–Rao inequalities are given. A discussion on the squeezing phenomenon in position for the oscillators is presented.

Physica Scripta•Mar 27, 2015•23 citations

Dissipative in quantum mesoscopic RLC circuits

Hassan Pahlavani, Razmjou Arash

The quantum theory for a mesoscopic electric circuit with charge discreteness is investigated. Taking the Caldirola-Kanai Hamiltonian in studding quantum mechanics of dissipative systems, we obtain the persistent current and the energy spectrum of a damped quantum LC-design mesoscopic circuit under the influence of a time-dependent external field.

Iranian Journal of Physics Research•Jun 15, 2010•0 citations

Rényi and Tsallis information entropies for a harmonic position-dependent mass

Dorcas A. Addo, Daniel Sabi-Takou, Eugene Adjei +1 more

In this paper, we study Renyi and Tsallis information entropies for a Hamiltonian system with position-dependent mass confined in harmonic oscillator potential. Gegenbauer polynomials are used to obtain the position eigenfunction of such a system, and the modified Bessel function of the second kind is used to determine the equivalent momentum eigenfunction. By means of probability densities of both representations, we analytically and numerically evaluate the Heisenberg-like uncertainty of this system. Because the Renyi and Tsallis information entropies in position representation are described by integral functionals of the Gegenbauer polynomials, these quantities are much more difficult to calculate. To get around this problem, we evaluate these information entropies at the system s asymptotical limit, which corresponds to the behavior of an undeformed harmonic oscillator. Nevertheless, no approximation method is used to obtain the Tsallis and Renyi information entropies in momentum representation. In both representations, we find that these information entropies approach the Shannon entropy when the entropic parameter alpha-> 1 and are closed to the results of similar models of the literature. Finally, we evaluate the related entropic uncertainty relations numerically to validate the latter obersevations.

quant-pharXiv:2609.17941•Sep 17, 2026•0 citations
We calculate information measures using the Tsallis, Rényi, and Shannon entropies for two classes (Lane–Emden and Caldirola–Kanai) of time-dependent mesoscopic RLC circuits. To determine the expressions for the entropies, we used the dynamical invariant method to obtain the exact Schrödinger wave function |(ψn(x,t))\big (\psi _n (x,t)\big )(ψn​(x,t))|⁠. For the state |n=0n=0n=0|⁠, all the expressions found are given in terms of |ρ\rho ρ|⁠, a c-number quantity satisfying a nonlinear differential equation. For the Caldirola–Kanai system, the entropies do not vary with time, but decrease with increasing damping factor. For the Lane–Emden system, the entropies decrease with increasing time. We also analyze the behavior of the Shannon and Rényi lengths in the charge and magnetic flux spaces and compare them with the respective standard deviations.
We present a quantum description of a mesoscopic RLC circuit. Based on the Caldirola-Kanai Hamiltonian and quantum invariant method we solve the Schrödinger equation for this circuit and write the corresponding wave functions in terms of a particular solution of the Milne-Pinney equation. In addition, we construct coherent and squeezed states for the quantized RLC circuit and evaluate the quantum fluctuations of the charge and the magnetic flux as well as the uncertainty product. Subject Index: 060, 064 The study of mesoscopic systems has attracted a lot of attention in the litera-ture in the last few years.1)–19) The great interest in these systems is motived partly because of the rapid development of nanophysics and nanoelectronics and partly because in the manufacture of electronics devices the miniaturization of integrated
In this paper, we present a comprehensive quantum description of a mesoscopic RLC circuit with time-dependent resistance, inductance and capacitance. Based on the dynamical invariant method and using quadratic invariants, we derive exact nonstationary quantum states for this circuit and write them in terms of solutions of the Milne–Pinney equation. Afterwards, we use quadratic invariants to construct coherent states for this quantized system and employ them to investigate quantum properties of the RLC circuit. In particular, we show that the product of the quantum fluctuations of the charge and the magnetic flux does not satisfy the minimum uncertainty relation.
In this work we present a quantum description of a mesoscopic RLC circuit without source. For this purpose, we model this system for that of a damped harmonic oscillator which is described by the Caldirola-Kanai Hamiltonian. Then, with the aid of the quantum invariant method we solve the Schrödinger equation associated with this Hamiltonian and write the corresponding wave functions in terms of a particular solution of the Milne-Pinney equation. We also construct coherent states for the RLC quantized, and evaluate the quantum fluctuations of the charge and the magnetic flux, as well as the corresponding product of uncertainty.
We calculate the time-dependent Fisher information in position and momentum for the lowest lying state of two classes of quantum damped (Lane–Emden (LE) and Caldirola–Kanai (CK)) harmonic oscillators. The expressions of and are written in terms of a c-number quantity satisfying a nonlinear differential equation. Analytical solutions of were obtained. For the LE and CK oscillators, we observe that increases while decreases with increasing time. The product increases and tends to a constant value in the limit for the LE oscillator, while it is time-independent for the CK oscillator. Moreover, for the CK oscillator the product decreases as the damping increases. Relations among the Fisher information, Leipnik and Shannon entropies, and the Stam and Cramer–Rao inequalities are given. A discussion on the squeezing phenomenon in position for the oscillators is presented.
In this paper, we study Renyi and Tsallis information entropies for a Hamiltonian system with position-dependent mass confined in harmonic oscillator potential. Gegenbauer polynomials are used to obtain the position eigenfunction of such a system, and the modified Bessel function of the second kind is used to determine the equivalent momentum eigenfunction. By means of probability densities of both representations, we analytically and numerically evaluate the Heisenberg-like uncertainty of this system. Because the Renyi and Tsallis information entropies in position representation are described by integral functionals of the Gegenbauer polynomials, these quantities are much more difficult to calculate. To get around this problem, we evaluate these information entropies at the system s asymptotical limit, which corresponds to the behavior of an undeformed harmonic oscillator. Nevertheless, no approximation method is used to obtain the Tsallis and Renyi information entropies in momentum representation. In both representations, we find that these information entropies approach the Shannon entropy when the entropic parameter alpha-> 1 and are closed to the results of similar models of the literature. Finally, we evaluate the related entropic uncertainty relations numerically to validate the latter obersevations.