Eigenenergy Spectrum Research Articles

The multiquantum intensity-dependent Jaynes–Cummings model with the counterrotating terms

Abstract In this paper we have investigated the eigen energy spectrum of the k-photon intensity-dependent Jaynes–Cummings (JC) model without the rotating-wave approximation (RWA). Our analysis shows that for k⩾2 the k-photon intensity-dependent JC model without the RWA does not have eigenstates in the Hilbert space spanned by the photon number states, i.e. the model becomes ill-defined. Hence, the k-photon intensity-dependent JC model without the RWA is qualitatively different from the RWA counterpart which is valid for all values of k and the coupling parameter. As a consequence, previous studies of the effects of the counterrotating terms in the k-photon intensity-dependent JC model for k⩾2 are all invalid.

Exact eigenstates of the two-photon Jaynes-Cummings model with the counter-rotating term

We have investigated the eigenenergy spectrum of the two-photon Jaynes-Cummings (JC) model with and without the rotating-wave approximation (RWA). Our analysis has indicated that the counter-rotating term dramatically changes the nature of the RWA energy spectrum and that the non-RWA spectrum can be approximated by the RWA spectrum only in the range of a sufficiently small coupling constant. Furthermore, unlike the one-photon counterpart, the two-photon JC model without the RWA is well defined only if the coupling parameter is below a certain critical value. As a result, the dynamics of the two-photon JC model without the RWA is significantly different from its RWA counterpart. For instance, the counter-rotating term can dramatically enhance the field squeezing effect. Besides, we would expect that the quantum dynamics of the two-photon JC model without the RWA is qualitatively different from that of the usual one-photon case.

Nonlinear multiquantum Jaynes-Cummings model with counter-rotating terms

In this paper we have investigated the eigenenergy spectrum of the nonlinear k-quantum Jaynes-Cummings (JC) model without the rotating-wave approximation (RWA). Our analysis has shown that the nonlinear k-quantum JC model without the RWA does not have eigenstates in the Hilbert space spanned by the number states, i.e. the model becomes ill-defined. Hence, the nonlinear k-quantum JC model without the RWA is qualitatively different from the RWA counterpart which is valid for all values of k and the coupling parameter. In other words, the counter-rotating terms do drastically alter the nature of the system.

Edge state formation in magnetic quantum structures

The formation of magnetic edge states is investigated for magnetic quantum structures with inhomogeneous magnetic fields such as a magnetic quantum dot ( B=0 for r< r 0 and B≠0 elsewhere) and a magnetic quantum ring ( B=0 for r 1< r< r 2 and B≠0 elsewhere). It is found that the eigenenergy spectra for these structures critically depend on the number of missing flux quanta and eigenstates which are composed of bulk Landau levels and magnetic edge states. The magnetic edge states correspond well with the classical particle trajectories which circulate either clockwise or counterclockwise along the boundary between magnetic domains.

Conductance oscillations related to the eigenenergy spectrum of a quantum dot in weak magnetic fields.

The electron transport through a quantum dot, defined by the electrostatic potential of four Schottky gates on top of a GaAs-${\mathrm{Ga}}_{\mathit{x}}$${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As heterostructure, was studied experimentally. The dot was connected to the surrounding two-dimensional electron gas by two variable quantum point contacts. The conductance, measured either as a function of gate voltage or magnetic field, showed characteristic variations: conductance maxima recurrently appear when the gate voltage is varied and conductance maxima are observed to shift approximately linearly in position when the magnetic field is varied. The measurement is compared with a transport model, where the eigenenergy spectrum is calculated for an isolated perfectly circular disk, with qualitative agreement regarding the characteristic variations of conductance and in Fourier power spectra of magnetoconductance. The conductance variations are related to the density of states at the Fermi energy. They cannot be attributed to single levels because the number of electrons in the dot was too large (approximately 1700 electrons), but originate from a shell structure with coincident energy levels.

Corner transfer matrix of an asymmetric six-vertex model

We consider a free Fermion six-vertex model with asymmetrically chosen vertex weights from the point of view of its corner transfer matrix. The generator of the corner transfer matrix then corresponds to a quantum XY spin chain Hamiltonian in an inhomogeneous magnetic field. The diagonalisation of the Hamiltonian employs orthogonal polynomials. The eigenenergy spectrum is related to the zeros of the asymptotic expansion of these polynomials. Lastly we identify a critical region in the phase diagram of the model which is spanned by the magnetic field and the parameter describing the strength of the inhomogeneity.

The Casimir Effect in Dielectrics

Abstract The Casimir force in one dimension between two dielectrics with arbitrary position-dependent refractive index is calculated. A numerical procedure is developed, including renormalization and regularization, to calculate this force and the temperature correction. The force is directly derived from the electromagnetic mode structure and the corresponding eigenenergy spectrum. Some essential differences between one- and three-dimensional results are discussed.

Edge-state properties and bulk eigenenergy spectra of periodically modulated two-dimensional electron systems in a magnetic field.

Edge-state properties and bulk eigenenergy spectra of periodically modulated two-dimensional electron systems in a magnetic field.

Evidence of resonant intersubband optical phonon scattering in quantum wires

Under certain biasing conditions, the intersubband energy separation in a quantum wire can match the optical phonon energy, thereby enhancing the scattering of charge carriers. We provide direct theoretical evidence that an anomalous negative differential transconductance (NDT) recently observed in an array of quantum wires at high temperatures is caused by resonant intersubband optical phonon scattering. Self-consistent 2D solutions of the Schrodinger and Poisson equations with a subsequent Monte Carlo analysis of intersubband scattering reveal a strong resonant polar optic phonon coupling between subbands at the gate bias indicated by the experimental data. The peak-to-valley ratio of the NDT exhibits a maximum near 170 K, thereby confirming the predictions of several theoretical investigations. The observation of resonant scattering is only possible because the quasi-1D form of Gauss's law shows an opposite trend to that for 2D systems in the dependence of the eigenenergy spectrum on gate bias.

Intersubband optic phonon resonances in electrostatically confined quantum wires

We investigate the occurrence of resonant intersubband optic phonon scattering in an array of quantum wires at high temperatures. Self-consistent solutions of the Schrödinger and Poisson equations with a subsequent Monte Carlo analysis of intersubband scattering reveal a strong resonant polar optic phonon coupling between subbands at the gate bias indicated by the experimental data. The observation of resonant scattering is only possible because the quasi-1D form of Gauss’ law shows an opposite trend to that for 2D systems in the dependence of the eigenenergy spectrum on gate bias.

An eigenvalue moment method analysis of theV(x) = [ω2/2]x2+ αx3+ βx4anharmonic oscillator

The anharmonic oscillator potential V(x) = [ω2/2]x 2 + αx 3 + βx 4 has been studied in terms of a hypervirial-Padé analysis (Lai, C. S., and Madan, M. P., 1985, Molec. Phys., 54, 669) and improved perturbative expansions (Fernandez, F. M., Meson, A. M., and Castro, E. A., 1985, Molec. Phys., 58, 365). We compare these results with those of a recently developed technique, the eigenvalue moment method, which is fundamentally simple and capable of yielding converging bounds to the low lying eigenenergies. It is concluded that hypervirial-Padé approaches can be inadequate in ‘high precision’ analysis of eigenenergy spectra.

Electron energy levels in a quantum well within an in-plane magnetic field

The exact eigenenergy spectrum of an electron is calculated in a quantum well within an in-plane magnetic field. The numerical solutions for the excited energy states as well as the ground-state energy are found for various quantum-well widths and barrier heights. The cyclotron orbits are considerably affected by the quantum well. The energy levels higher than the potential height of the quantum well and the energy levels lower than the potential height of the quantum well show quite different behaviors. These are explained with the properties of the combined potential and the wave function inherent to the system.

High energy vibrational states of cyanoacetylene: Variational and perturbative analysis of an anharmonic normal mode

The high energy vibrational eigenstates of cyanoacetylene are calculated with variational and perturbation theory, using a new empirical potential energy function. A detailed analysis of the eigenstates reveals that the HC bond in HCCCN is not a good local mode, even as a zeroth-order description, due predominantly to the linear geometry of the molecule. A unique anharmonic normal mode description is developed and applied to calculate accurately the eigenenergy spectrum with second-order perturbation theory. An indirect coupling scheme is presented which accounts for mixing of nearly degenerate but uncoupled high energy zeroth-order states. These results are used to account for spectral congestion in the experimental high energy spectrum of cyanoacetylene.