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

arXiv:cond-mat/0701572

Dynamic Localization Effects in L-Ring Circuit

C. Micu, É. Papp, L. Aur

Published Jan 24, 2007• 0 citations
arXivHTMLPDF

Abstract

Using suitable magnetic flux operators established in terms of discrete derivatives leads to quantum-mechanical descriptions of LC-circuits with an external time dependent periodic voltage. This leads to second order discrete Schrodinger equations provided by discretization conditions of the electric charge. Neglecting the capacitance leads to a simplified description of the L-ring circuit threaded by a related time dependent magnetic flux. The equivalence with electrons moving on one dimensional (1D) lattices under the influence of time dependent electric fields can then be readily established. This opens the way to derive dynamic localization conditions serving to applications in several areas, like the time dependent electron transport in quantum wires or the generation of higher harmonics by 1D conductors. Such conditions, which can be viewed as an exact generalization of the ones derived before by Dunlap and Kenkre [Phys. Rev. B 34, 3625(1986)], proceed in terms of zero values of time averages of related persistent currents over one period.

DOI
10.48550/arxiv.cond-mat/0701572

Related papers

The influence of the elementary charge on the canonical quantization of LC-circuits

Erhardt Papp, Dania Racolta, L. Aur +1 more

In this paper one deals with the quantization of mesoscopic LC-circuits under the influence of an external time dependent voltage. The canonically conjugated variables, such as given by the electric charge and the magnetic flux, get established by resorting to the Hamiltonian equations of motion provided by both Faraday and Kirchhoff laws. This time the discretization of the electric charge is accounted for, so that magnetic flux operators one looks for should proceed in terms of discrete derivatives. However, the flux operators one deals with are not Hermitian, which means that subsequent symmetrizations are in order. The eigenvalues characterizing such operators can be readily established in terms of twisted boundary conditions. Besides the discrete Schrödinger equation with nearest-neighbor hopping, a nontrivial next nearest neighbor generalization has also been established. Such issues open the way to the derivation of persistent currents in terms of effective k-dependent Hamiltonians. Handling the time dependent voltage within the nearest neighbor description leads to the derivation of dynamic localization effects in L-ring configurations, such as discussed before by Dunlap and Kenkre. The onset of the magnetic flux quantum has also been discussed in some more detail.

arXiv:1607.07356•AIP conference proceedings•Jan 1, 2017•0 citations

The quantization of mesoscopic LC-circuits. Basic ideas and applications

Erhardt Papp, Codruta Micu, Dania Racolta

In this paper one deals with the quantization of mesoscopic LC-circuits under the influence of an external time dependent voltage. The canonically conjugated variables, such as given by the electric charge and the magnetic flux get established by resorting to the hamiltonian equations of motion. This time the discretization of the electric charge is accounted for by working in combination with both right-hand and left-hand discrete derivatives. This results in the onset of related magnetic flux operators. Besides the discrete Schrödinger equation with nearest-neighbor hoppings, a nontrivial next nearest neighbor generalization has also been established. Handling the time dependent voltage within the nearest neighbor description opens the way to the derivation of dynamic localization effects in terms of the approach discussed before by Dunlap and Kenkre, L-ring configurations included.

AIP conference proceedings•Jan 1, 2015•3 citations

Generalized versus Selected Descriptions of Quantum LC-Circuits

É. Papp, C. Micu, O. Borchin

Proofs are given that the quantum-mechanical description of the LC-circuit with a time dependent external source can be readily established by starting from a more general discretization rule of the electric charge. For this purpose one resorts to an arbitrary but integer-dependent real function F(n) instead of n. This results in a nontrivial generalization of the discrete time dependent Schrödingerequation established before via F(n) = n, as well as to modified charge conservation laws. However, selected descriptions can also be done by looking for a unique derivation of the effective inductance. This leads to site independent inductances, but site dependent ones get implied by accounting for periodic solutions to F(n) in terms of Jacobian elliptic functions. Many-charge generalizations of quantum circuits, including the modified continuity equation for total charge and current densities, have also been discussed. Keywords: Quantum LC-circuits; Charge discretization; Discrete Schrödinger equations; Many-charge generalizations I.

Journal of Computational and Theoretical Nanoscience•Feb 1, 2010•2 citations

Generalized versus selected descriptions of quantum LC - circuits

É. Papp, C. Micu, O. Borchin +1 more

Proofs are given that the quantum-mechanical description of the LC -circuit with a time dependent external source can be readily established by starting from a more general discretization rule of the electric charge. For this purpose one resorts to an arbitrary but integer-dependent real function F(n) instead of n. This results in a nontrivial generalization of the discrete time dependent Schrodinger-equation established before via F(n)=n, as well as to modified charge conservation laws. However, selected descriptions can also be done by looking for a unique derivation of the effective inductance. This leads to site independent inductances, but site dependent ones get implied by accounting for periodic solutions to F(n) in terms of Jacobian elliptic functions. Many-charge generalizations of quantum circuits, including the modified continuity equation for total charge and current densities, have also been discussed.

arXiv:0710.2620•Oct 14, 2007•0 citations

Quantum LC - circuits with diffusive modification of the continuity equation

É. Papp, C. Micu, Borchin, O.

Proofs are given that the quantum-mechanical description of the LC-circuit with a time dependent external source can be readily established by starting from a general discretization rule of the electric charge. For this purpose one resorts to an arbitrary but integer-dependent real function F(n) instead of n. This results in a nontrivial generalization of the discrete time dependent Schrodinger-equation established before via F(n)=n. Such generalization leads to site-dependent hopping amplitudes as well as to diffusive modification of the continuity equation. One shows, in particular, that there are firm supports concerning rational multiples of the elementary electric charge.

arXiv:cond-mat/0702248•Feb 9, 2007•0 citations

Influence of a time-periodic magnetic flux on interacting electrons in a one-dimensional loop

Guido Burmeister, Klaus Maschke

We consider N strongly interacting electrons in a one-dimensional circular loop that is pierced by a time-periodic magnetic flux ${a(t)=a}_{0}{+a}_{1}(t)$ with the angular frequency $\ensuremath{\omega}.$ Similar to our previous work, where we have considered a static magnetic flux ${a}_{0},$ the electron positions are expressed in terms of collective and relative coordinates. Strong $e\ensuremath{-}e$ interaction can then be treated in a harmonic approximation for the relative motion. The presently searched solutions of the time-dependent Schr\"odinger equation for a time-periodic flux are given by the Floquet states. The Floquet states for a spatially constant one-particle potential form a complete set of Floquet-basis states, which is used to study the influence of the one-particle potential on the electronic states. While for a spatially constant one-particle potential the time-averaged observables, such as the electronic energy and the electronic current or angular momentum, depend solely on the time-averaged magnetic flux ${a}_{0},$ a spatially varying one-particle potential leads to pronounced resonances. In the case of moderate electronic relaxation, the stationary properties are determined by the Floquet state with lowest time-averaged energy. For the associated persistent angular momentum we predict jumps with heights proportional to the number of electrons N. We further show that, already by measuring the locations of these jumps in the ${(a}_{0},\ensuremath{\omega})$ plane, one could determine the number of electrons N as well as the effective $e\ensuremath{-}e$ interaction.

Physical review. B, Condensed matter•Apr 3, 2003•2 citations
Using suitable magnetic flux operators established in terms of discrete derivatives leads to quantum-mechanical descriptions of LC-circuits with an external time dependent periodic voltage. This leads to second order discrete Schrodinger equations provided by discretization conditions of the electric charge. Neglecting the capacitance leads to a simplified description of the L-ring circuit threaded by a related time dependent magnetic flux. The equivalence with electrons moving on one dimensional (1D) lattices under the influence of time dependent electric fields can then be readily established. This opens the way to derive dynamic localization conditions serving to applications in several areas, like the time dependent electron transport in quantum wires or the generation of higher harmonics by 1D conductors. Such conditions, which can be viewed as an exact generalization of the ones derived before by Dunlap and Kenkre [Phys. Rev. B 34, 3625(1986)], proceed in terms of zero values of time averages of related persistent currents over one period.
In this paper one deals with the quantization of mesoscopic LC-circuits under the influence of an external time dependent voltage. The canonically conjugated variables, such as given by the electric charge and the magnetic flux, get established by resorting to the Hamiltonian equations of motion provided by both Faraday and Kirchhoff laws. This time the discretization of the electric charge is accounted for, so that magnetic flux operators one looks for should proceed in terms of discrete derivatives. However, the flux operators one deals with are not Hermitian, which means that subsequent symmetrizations are in order. The eigenvalues characterizing such operators can be readily established in terms of twisted boundary conditions. Besides the discrete Schrödinger equation with nearest-neighbor hopping, a nontrivial next nearest neighbor generalization has also been established. Such issues open the way to the derivation of persistent currents in terms of effective k-dependent Hamiltonians. Handling the time dependent voltage within the nearest neighbor description leads to the derivation of dynamic localization effects in L-ring configurations, such as discussed before by Dunlap and Kenkre. The onset of the magnetic flux quantum has also been discussed in some more detail.
In this paper one deals with the quantization of mesoscopic LC-circuits under the influence of an external time dependent voltage. The canonically conjugated variables, such as given by the electric charge and the magnetic flux get established by resorting to the hamiltonian equations of motion. This time the discretization of the electric charge is accounted for by working in combination with both right-hand and left-hand discrete derivatives. This results in the onset of related magnetic flux operators. Besides the discrete Schrödinger equation with nearest-neighbor hoppings, a nontrivial next nearest neighbor generalization has also been established. Handling the time dependent voltage within the nearest neighbor description opens the way to the derivation of dynamic localization effects in terms of the approach discussed before by Dunlap and Kenkre, L-ring configurations included.
Proofs are given that the quantum-mechanical description of the LC-circuit with a time dependent external source can be readily established by starting from a more general discretization rule of the electric charge. For this purpose one resorts to an arbitrary but integer-dependent real function F(n) instead of n. This results in a nontrivial generalization of the discrete time dependent Schrödingerequation established before via F(n) = n, as well as to modified charge conservation laws. However, selected descriptions can also be done by looking for a unique derivation of the effective inductance. This leads to site independent inductances, but site dependent ones get implied by accounting for periodic solutions to F(n) in terms of Jacobian elliptic functions. Many-charge generalizations of quantum circuits, including the modified continuity equation for total charge and current densities, have also been discussed. Keywords: Quantum LC-circuits; Charge discretization; Discrete Schrödinger equations; Many-charge generalizations I.
Proofs are given that the quantum-mechanical description of the LC -circuit with a time dependent external source can be readily established by starting from a more general discretization rule of the electric charge. For this purpose one resorts to an arbitrary but integer-dependent real function F(n) instead of n. This results in a nontrivial generalization of the discrete time dependent Schrodinger-equation established before via F(n)=n, as well as to modified charge conservation laws. However, selected descriptions can also be done by looking for a unique derivation of the effective inductance. This leads to site independent inductances, but site dependent ones get implied by accounting for periodic solutions to F(n) in terms of Jacobian elliptic functions. Many-charge generalizations of quantum circuits, including the modified continuity equation for total charge and current densities, have also been discussed.
Proofs are given that the quantum-mechanical description of the LC-circuit with a time dependent external source can be readily established by starting from a general discretization rule of the electric charge. For this purpose one resorts to an arbitrary but integer-dependent real function F(n) instead of n. This results in a nontrivial generalization of the discrete time dependent Schrodinger-equation established before via F(n)=n. Such generalization leads to site-dependent hopping amplitudes as well as to diffusive modification of the continuity equation. One shows, in particular, that there are firm supports concerning rational multiples of the elementary electric charge.
We consider N strongly interacting electrons in a one-dimensional circular loop that is pierced by a time-periodic magnetic flux a(t)=a0+a1(t){a(t)=a}_{0}{+a}_{1}(t)a(t)=a0​+a1​(t) with the angular frequency $\ensuremath{\omega}.$ Similar to our previous work, where we have considered a static magnetic flux a0,{a}_{0},a0​, the electron positions are expressed in terms of collective and relative coordinates. Strong $e\ensuremath{-}e$ interaction can then be treated in a harmonic approximation for the relative motion. The presently searched solutions of the time-dependent Schr\"odinger equation for a time-periodic flux are given by the Floquet states. The Floquet states for a spatially constant one-particle potential form a complete set of Floquet-basis states, which is used to study the influence of the one-particle potential on the electronic states. While for a spatially constant one-particle potential the time-averaged observables, such as the electronic energy and the electronic current or angular momentum, depend solely on the time-averaged magnetic flux a0,{a}_{0},a0​, a spatially varying one-particle potential leads to pronounced resonances. In the case of moderate electronic relaxation, the stationary properties are determined by the Floquet state with lowest time-averaged energy. For the associated persistent angular momentum we predict jumps with heights proportional to the number of electrons N. We further show that, already by measuring the locations of these jumps in the ${(a}_{0},\ensuremath{\omega})$ plane, one could determine the number of electrons N as well as the effective $e\ensuremath{-}e$ interaction.