# E. Papp's research while affiliated with West University of Timisoara and other places

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## Publications (48)

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 tim...

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 i...

In this paper one deals with the derivation of probability amplitudes characterizing the photon assisted injection of electrons in a two-terminal quantum conductor. For this purpose one accounts for spatially constant but time dependent periodic voltages applied on an Ohmic contact. Resorting to the discrete Fourier transform provides the probabili...

Closed 1/N-energy-formulae for relativistic two-boson (m

In this paper one deals with the theoretical derivation of energy bands and of related wavefunctions characterizing quasi 1D semiconductor
heterostructures, such as InAs quantum wire
models. Such models get characterized this time by equal coupling strength superpositions of Rashba and Dresselhaus spin-orbit interactions of dimensionless magnitud...

In this paper one deals with the theoretical derivation of spin precession
effects in quasi 1D quantum wire models. Such models get characterized by equal
coupling strength superpositions of Rashba and Dresselhaus spin-orbit
interactions of dimensionless magnitude $a$ under the influence of in-plane
magnetic fields of magnitude $B$. Besides the wav...

The influence of Rashba and Dresselhaus spin–orbit interactions on the electronic properties of quasi one-dimensional systems like InAs quantum wires is discussed in the presence of in-plane magnetic fields. One shows that equal coupling strength conditions are provided specifically by the commutativity of two-dimensional constituents of velocity a...

The novel 1/N-energy solution to the Harper equation presented recently is applied to the derivation of thermodynamic properties of Bloch electrons on a two-dimensional lattice penetrated by a perpendicular uniform magnetic field. One procceeds by using an almost typical density of states such as proposed previously for a two-dimensional electron g...

Proofs are given for the first time that the energy-spectrum of the Harper-equation can be derived in a closed implicit form by using the one-dimensional limit of the 1/N-description. Explicitly solvable cases are discussed in some more detail for Δ=1. Here Δ expresses the Harper-parameter discriminating between metallic (Δ<1) and insulator (Δ>1) p...

An alternative wavefunction to the description of the dynamic localization of a charged particle moving on a one-dimensional lattice under the influence of a periodic time dependent electric field is written down. For this purpose the method of characteristics such as applied by Dunlap and Kenkre [Phys. Rev. B34, 3625 (1986)] has been modified by u...

Density of state calculation performed previously for the Harper-equation by Wannier, Obermair and Ray [Phys. Status SolidiB93, 337 (1979)] are updated analytically and numerically. One considers both the influence of anisotropy and commensurability parameters. The main point of our generalization is to account for a multiplicity parameter describi...

The 1/N approach to the Harper equation proposed previously is generalized towards performing the pertinent band-energy description. Leading forms and corrections proceeding to first order in the magnetic field are written down. The energy reflection symmetry has also been discussed.

In this paper one deals with a transparent derivation of dynamic localization conditions for the electron on the 1D lattice proceeding irrespective of the concrete form of the periodic modulation of the time dependent electric field. This amounts to account for periodic zero minima generated in the time dependence of the mean square displacement (M...

Proofs are given that SOq(N)-motivated q deformations of the expansion parameter of the 1/N method can be incorporated into symmetry transformations preserving the radial form of the Schrödinger equation. This opens the way to establish the q deformed energy and the corresponding 1/N equivalent potential. So far the number of space dimensions is su...

Using suitable magnetic flux operators established in terms of discrete deriva-tives leads to quantum-mechanical descriptions of LC-circuits with an external time dependent periodic voltage. This leads to second order discrete Schrödinger equations provided by discretization conditions of the electric charge. Neglecting the capacitance leads to a s...

In this paper one presents further details concerning the derivation of exact bound state energies characterizing a single electron moving on two-dimensional heterostructures under Rashba-and Dresselhaus spin-orbit interactions in the presence of a transversal magnetic field. One resorts to algebraic methods as well as to symmetry relationships con...

In this paper one deals with the derivation of approximations as well as of exact results concerning the energy of a planar electron subjected to both Rashba and Dresselhaus spin–orbit interactions under the influence of a transversal magnetic field and of an additional in-plane electric field. One begins by applying quickly tractable large n-appro...

Proofs are given that by resorting to the discretization of the superconducting phase variable leads to the conversion of the eigenvalue equation of a mesoscopic Josephson junction under a dc voltage into a generalized version of the Harper equation with anisotropy parameter. A full conversion proceeds, however, in terms of selected parameters. Cla...

Electrons on infinite coupled chains with nearest neighbour couplings under uniform electric and magnetic fields can be expressed as conditionally solvable systems, which concerns both discrete coordinate and wavenumber representations. We then have to account for multiparameter extra-conditions relying on the single chain phase of the system, whic...

The movement of the electrons under the simultaneous influence of a scalar periodic potential and of a uniform transversal magnetic field is described by the well-known second order discrete Harper equation. This equation originates from a two-dimensional energy dispersion law under the minimal substitution. Here one deals with the Harper model und...

In this paper we deal with the derivation of dynamic localization conditions for electrons on the one-dimensional (1D) lattice under the influence of ac electric and magnetic fields of the same frequency. We resort, for convenience, to a tight-binding single-band Hamiltonian. Our emphasis is on a more fundamental theoretical understanding by invest...

Coupled chains in electric and magnetic fields are discussed in terms of interplays between periodicity conditions and the factorization of the wavefunction in the wavenumber representation. Proceeding in this manner yields a quickly tractable matching condition providing the quantization rule to the alternative derivation of complex energy bands....

Applying the method of characteristics leads to wavefunctions and dynamic localization conditions for electrons on the one dimensional lattice under perpendicular time dependent electric and magnetic fields. Such conditions proceed again in terms of sums of products of Bessel functions of the first kind. However, this time one deals with both the n...

Coupled chains in longitudinal electric and transversal magnetic ﬁelds are able to be formulated as a conditionally solvable problem. This opens the way to the onset of Wannier-Stark resonances, such as discussed before [E. Papp et al, Physica B. 403, (2008) 3289]. However, such resonances proceed under well deﬁned relationships concerning the ener...

Coupled chains in longitudinal electric and transversal magnetic ﬁelds are able to be formulated as a conditionally solvable problem. This opens the way to the onset of Wannier-Stark resonances, such as discussed before [E. Papp et al, Physica B. 403, (2008) 3289]. However, such resonances proceed under well deﬁned relationships concerning the ener...

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 gene...

This paper deals with the total persistent current at
T = 0
produced by the exact energy solution of the Dirac electron moving on isolated 1D
Aharonov–Bohm rings. Leading contributions concerning the non-relativistic limit are
written down for large values of the electron number. Usual non-relativistic currents
get reproduced, but now in terms of...

In this paper one deals with the study of total persistent currents in
1D discretized isolated rings pierced by a magnetic flux at T = 0. One
starts from basic current formulae relying on suitable flux intervals of
unit length. Next one resorts to Fourier series, which results in
generalized current formulae proceeding for arbitrary values of the
m...

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 generaliza...

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 si...

One shows that the oscillations with respect to the magnetic flux in the one-dimensional discretized Aharonov–Bohm rings are sensitive with respect to the parity of the number of electrons Ne. Resorting to basic flux intervals of unit length indicates that the period of such oscillations is given by the flux quantum Φ0=hc/e and by 2Φ0 if Ne is odd...

Dynamic localization conditions proceeding beyond the nearest-neighbour description have
been established by applying the quasi-energy description. The general energy
dispersion laws one deals with concern a periodic but commensurable dc?ac field like
E0+E1f(t), for
which f(t) = f(t+T)
and ?B = P?/Q. Here and ? = 2?/T
stand for the Bloch and ac f...

The q-deformed radial Schrödinger equation written down before (E. Papp, Phys. Rev. A 52, 101 (1995)) is analyzed in terms of products between q-Laguerre polynomials and q-exponential functions. For this purpose Coulomb and harmonic oscillator potentials are considered. Eigenvalue equations are able to be handled quasiclassically, such that now the...

It is shown that the radial Schrödinger equation characterizing the isotropic harmonic oscillator is produced, to second order, by the continuous limit of the discrete equation concerning a suitable rescaled Meixner polynomial. Quantum numbers are established as they should be by virtue of pertinent matching conditions.

This Letter deals with the application of the virial and Hellmann–Feynman theorems to the Hermitian squared Hamiltonian characterizing the generalized version of the q-symmetrized Harper equation. This results in links between energy-eigenvalues and certain averages of selected Hamiltonian-terms, as usual.

The Δ ≠ 1 generalization of the q-symmetrized Harper equation is discussed in terms of wavefunctions expressed by Laurent series. Proceeding by recursion leads to a nontrivial Δ-dependent generalization of the characteristic energy polynomial, with a special emphasis on a continuous dependence on the commensurability parameter. The multiplicity par...

This paper deals with the application of the q calculus to second order q-difference equations, like the q symmetrized form of the Harper equation. One obtains three-term recurrence relations, for which a symmetrized version is written down. This opens the way to establish explicit energy results that are dependent on the commensurability parameter...

In this paper we deal with the quantum-mechanical description of
electrons on a noncommutative plane under the influence of a
transversal and homogeneous magnetic field. For this purpose the
noncommutativity has been implemented by resorting to the quantum
Euclidean space relying on the quantum group SOq(N) and to the
so-called noncommutative θ-for...

This paper deals with the application of relationships between Harper and Mathieu equations to the derivation of energy formulas. Establishing suitable matching conditions, one proceeds by inserting a concrete solution to the Mathieu equation into the Harper equation. For this purpose, one resorts to the nonlinear oscillations characterizing the Ma...

Proofs are given that exact solutions to the wavefunctions of the
Harper equation can be established in an explicit manner by resorting to
three-term recurrence relations implied by a q-calculus approach
proposed previously. The q-normalization of wavefunctions resulting in
the appearance of peaks is discussed. The exact Q = 6 energy solution
has a...

Available 1/N energy-formulae for attractive n2. We found that critical energies established before for repulsive n=3-potentials are able to be understood, within inherent degrees of complementarity, in terms of real valued ground state energy extrapolations. Duality transformations concerning n>2-potentials are discussed, too.

The 1/N approach to the Harper equation proposed previously is generalized towards performing the pertinent band-energy description. Leading forms and corrections proceeding to first order in the magnetic field are written down. The energy reflection symmetry has also been discussed.

This paper deals with the derivation of non-polynomial solutions to the q-difference form of the Harper equation. Only quasiclassical approximations proceeding this time to first and second orders are discussed. The exact non-polynomial zero-energy solution to the above q-difference equation has also been presented.

The novel 1/N-energy solution to the Harper equation presented recently is applied to the derivation of thermodynamic properties of Bloch electrons on a two-dimensional lattice penetrated by a perpendicular uniform magnetic field. One procceeds by using an almost typical density of states such as proposed previously for a two-dimensional electron g...

Proofs are given for the first time that the energy-spectrum of the Harper-equation can be derived in a closed implicit form by using the one-dimensional limit of the 1/N-description, Explicitly solvable cases are discussed in some more detail for Δ = 1 . Here Δ expresses the Harper-parameter discriminating between metallic ( Δ < 1 ) and insulator...

This paper deals with the derivation of concrete polynomial solutions to
the q-difference form of the Harper equation proposed recently [P. B.
Wiegmann and A. V. Zabrodin, Phys. Rev. Lett. 72, 1890 (1994)], now by
using the q-calculus in conjunction with quite directly solvable
recurrence relations. Regularity patterns and the onset of
level-struct...

An alternative approach to the dynamic localization of a charged particle moving on an one-dymensional lattice under the influence of a time dependent electric field is proposed. The present dynamic localization proceeds to leading order in terms of the large order zeros of the Bessel function J 0 (z), such as derived before by Dunlap and Kenkre, w...

## Citations

... The energy spectrum was obtained mainly by direct diagonalization of the Hamiltonian, while the energy eigenvalue polynomial was determined only for a few models [6]. Closed forms for the density of states functions (DOS) were also determined [3,7,8]. The DOS can be applied to deduce the thermodynamic properties while the number of electrons or chemical potential remains fixed [9]. ...

... Choosing β = P /Q, where P and Q are mutually prime integers, leads to solvable fixed-Q three-term recurrence relations for which q 2Q = 1. The energies then get produced by the roots of energy-polynomials such as P 1 (E 2 ; q) = 0 and EP 2 (E 2 ; q) = 0 proceeding for even and odd Qvalues, respectively, as shown, e.g., in [3]. Such polynomials exhibit the degrees (Q−i +1)/2 in E 2 , where i = 1, 2 are the corresponding subscripts. ...

... This amounts to reverse the usual k-wavenumber dependence of the energy in order to establish two correlated wavenumbers, say k + and k − , which are responsible for the description of propagation paths along the Ox-axis. Then the two dimensional rotation matrix 11 one looks for can be established in terms of displacements of length L acting along the two paths just referred to above 9,10 . However, several details referring to a systematic study of the parameter dependent spin precession angles are still desirable. ...

... There has also been a lot of interest in driven lattice systems (where the force is timedependent), and also in this context some findings beyond the nearest neighbor approximation are available, e.g. [30][31][32]. In the present work, we extend these results in two ways. ...

... Both Rashba and Dresselhaus interactions have been studied in Refs. (Florescu et al. 2004;Xiao and Deng 2010;Krstajic et al. 2011;Papp and Micu 2010). ...

... The electronic effects in mesoscopic systems can be studied in many cases by restricting to the non-relativistic quantum mechanics [1][2][3][4][5][6][7][8][9][10] based on the Schrödinger equation with suitable additional terms describing the spin-orbit interaction [11][12][13][14][15][16]. Nevertheless, there are nano-systems laying out some measurable relativistic effects that can be satisfactory explained considering the electrons as massless Dirac particles moving on lattices [17][18][19][20]. ...

... Our results for a significantly wide class of q-polynomials are potentially useful in some of these fields. With a view to motivating the interested readers toward the theory and widespread applications of various families of q-series, q-polynomials, as well as q-difference and q-derivative operators, we have chosen here to include references (see, for example, [33][34][35][36][37][38][39][40][41][42][43][44][45]) to various related developments in recent years. ...

... Experimental confirmations [8] and the identification of further manifestations of dynamic localization effects deserve further 030002-4 attention, too. Other issues like dynamic localization effects produced by superpositions of time dependent electric and magnetic fields [9], or the description of currents in the dynamic localization regime [10], are also worthy of being mentioned. ...

... Next one finds that the Hamiltonian (4) changes the sign under Hermitian conjugation (11) H + q = −H q , but a such rather intriguing result is able to be understood in terms of the ERS. This amounts to consider realizations like H q = H (+) ...

... This amounts to formulate the magnetic flux operator in terms of right-and left-hand discrete derivatives, as shown by (7) and (8). Such operators are not hermitian owing to the very incorporation of discrete derivatives, but a hermitian realization can be readily established by resorting to a subsequent symmetrization, such as displayed in (9). Proceeding in this manner one gets faced with a deformed canonical commutation relation between electric charge and magnetic flux such as given by (12). ...