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Unformatted text preview: arXiv:cond-mat/0701572v1 [cond-mat.mes-hall] 24 Jan 2007 DYNAMIC LOCALIZATION EFFECTS IN L-RING CIRCUIT C.MICU (a), E. PAPP (b) , L. AUR (b) * (a) Physics Department, North University of Baia Mare, RO-430122, (b) Department of Theoretical Physics, West University of Timisoara, RO-300323 (Dated: August 22, 2007) 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 generaliza- tion 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. Keywords : Charge discretization; Quantum L-ring circuits; Persistent currents; Dynamic local- ization conditions; Quantum wires PACS numbers: I. INTRODUCTION Quantum circuits with charge discreteness have been the focus considerable interest during the last decade [1- 5]. It has been realized that quantum circuits are able to provide useful developments in the field of nanodevices, transmission lines as well as of molecular electronic cir- cuits [6-8]. The chargediscreteness referred to above gets incorporated in the eigenvalue equation Q | n > = nq e | n > (1) where n is an integer and where Q denotes the Hermitian operator of the electric charge. The elementary charge is denoted by q e . The common choice is to put q e = e , where e is the charge of the electron. The charge eigen- functions are orthonormalized , in which case the time dependent wavefunction describing the quantum circuit can be expressed as | ψ ( t ) > = summationdisplay n C n ( t ) | n > (2) where nǫ ( −∞ , ∞ ) We have also to keep in mind that usual derivatives have to be replaced by discrete ones when dealing with n- dependent functions. Proceeding in this manner leads to a discrete Schrodinger equation, as shown before [1-3]. On the other hand, the influence of the capacitance can be disregarded, which results in a discrete Schr¨odinger-equation concerning the L-ring cir- cuit. The interesting point is that this latter equation is equivalent, under suitable matching conditions, to the one describing the 1D conductor, i.e. to the electron on the 1D lattice under the influence of a time dependent electric field. This opens the way to a general derivationelectric field....
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This note was uploaded on 03/18/2012 for the course PHYSICS 303 taught by Professor Ihn during the Spring '12 term at Swiss Federal Institute of Technology Zurich.
- Spring '12
- Theoretical Physics