Laser theory for semiconductor quantum dots in microcavities

Quantum dots (QDs) used as active material in microresonators are currently of strong topical interest due to breakthroughs in growth and device structuring. From the theory side, however, atomic models are still used to analyse the emission from these semiconductor systems, despite known differences between QDs and atoms. We introduce a semiconductor laser theory based on a microscopic approach with the goal of better describing the characteristic behaviour of QD-based laser devices and to show differences from predictions based on atomic models.     

Position and quantum theory

It is customarily maintained that the concept of unmeasured (i.e., unobserved) position is without meaning in quantum theory. However, the vast literature on the subject, as shown here through the typical example of the double-slit experiment, really does not provide an iron-clad proof that this is indeed so. The question of the possible meaning of unobserved position is thus open. The problem is then resolved by showing quite rigorously that, after all, unobserved position is meaningless in quantum theory. The criterion for unobserved position to be meaningful in any theory (probabilistic or not) is taken to be that the probability density for position must satisfy the Einstein-Chapman-Kolmogorov equation with a positive-semidefinite kernel which is also properly normalized.     

Pruned quantum theory

Comments are given on controversial problems of interpretation of quantum mechanics and quantal measurements.     

Discrete quantum theory

This paper is concerned with tracing the implications of two ideas as they affect quantum theory. One, which descends from Leibniz and Mach, is that there is no space-time continuum, but that which are involved are spacial and temporal relations involving the distant matter of the universe. The other is that our universe is finite. The picture of the world to which we are led is that of an enormous space-time Feynman diagram whose vertices are events. A consequence of finiteness is that between each pair of events, along a world line, there can be only finitely many intermediate events. A further change is that we are no longer required to believe that particles need be anywhere between events. The paper takes up nonrelativistic quantum theory in a way that is consistent with these ideas. By considering analogies between the Wiener and the Feynman integrals, and between the Wiener process and related discrete processes, there is obtained a straightforward theory for the Feynman integral. Propagators are worked out for many of the cases relevant to the nonrelativistic theory.The paper shows that, even when there are, along each world-line, no more than one event per Compton wavelength, agreement is good with the usual Schrödinger theory.Research supported in part by the NSF.     

Spacetime and future quantum theory

Space and time are discussed in connection with the future of quantum theory.     

Simplicial gauge theory and quantum gauge theory simulation

We propose a general formulation of simplicial lattice gauge theory inspired by the finite element method. Numerical tests of convergence towards continuum results are performed for several SU(2) gauge fields. Additionally, we perform simplicial Monte Carlo quantum gauge field simulations involving measurements of the action as well as differently sized Wilson loops as functions of β.     

Cosmic numbers and quantum theory

The cosmic numbers are considered, with emphasis on the relationN ². (HereN is the number of nucleons in the universe, and, its radius in atomic units.) This relation is interpreted in terms of a quantum mechanical model.     

History and many-worlds quantum theory

We suggest that, contrary to what is sometimes stated, the only way we can make reliable statements about history, using information available at the present, is to use unitary evolution backwards in time. We give some discussion of how this might work in practice, and point out that additional inputs, e.g. certain prejudices, are also required.     

High magnetic field investigations of quantum dots

We have performed systematic investigations of the Coulomb blockade oscillations observed in a single quantum dot defined in the plane of a two-dimensional electron gas. At high magnetic fields these oscillations reflect the inner electronic structure of the dot, showing both a significant periodic amplitude modulation as well as a systematic variation of the conductance oscillation period. The former results from the modulation of the coupling of the electronic states in the dot with the leads, and can be readily explained within an activated transport model. The latter effect reflects the detailed electronic structure of the quantum dot and permits a comparison with the structure calculated within a simple capacitance model. The experimental results are in excellent qualitative agreement with the theoretical model, however a detailed quantitative comparison must include both the additional coupling of the dot to its environment as well as the gate voltage dependence of the dot structure itself.PACS: 73.20.Dx; 72.20. My.     

Performance investigations of quantum dot infrared photodetectors

Quantum dot infrared photodetectors (QDIPs) have already attracted more and more attention in recent years due to a high photoconductive gain, a low dark current and an increased operating temperature. In the paper, a device model for the QDIP is proposed. It is assumed that the total electron transport and the self-consistent potential distribution under the dark conditions determine the dark current calculation of QDIP devices in this model. The model can be used for calculating the dark current, the photocurrent and the detectivity of QDIP devices, and these calculated results show a good agreement with the published results, which illustrate the validity of the device model.     

Hyperfunction quantum field theory

The quantum field theory in terms of Fourier hyperfunctions is constructed. The test function space for hyperfunctions does not containC functions with compact support. In spite of this defect the support concept ofH-valued Fourier hyperfunctions allows to formulate the locality axiom for hyperfunction quantum field theory.     

Quaternionic quantum field theory

We show that a quaternionic quantum field theory can be formulated when the numbers of bosonic and fermionic degrees of freedom are equal and the fermions, as well as the bosons, obey a second order wave equation. The theory takes the form of either a functional integral with quaternion-imaginary Lagrangian, or a Schrödinger equation and transformation theory for quaternion-valued wave functions, with a quaternion-imaginary Hamiltonian. The connection between the two formulations is developed in detail, and many related issues, including the breakdown of the correspondence principle and the Hilbert space structure, are discussed.     

Point-form quantum field theory

We examine canonical quantization of relativistic field theories on the forward hyperboloid, a Lorentz-invariant surface of the form x_μx^μ = τ². This choice of quantization surface implies that all components of the 4-momentum operator are affected by interactions (if present), whereas rotation and boost generators remain interaction free—a feature characteristic of Dirac’s “point-form” of relativistic dynamics. Unlike previous attempts to quantize fields on space-time hyperboloids, we keep the usual plane-wave expansion of the field operators and consider evolution of the system generated by the 4-momentum operator. We verify that the Fock-space representations of the Poincaré generators for free scalar and spin-1/2 fields look the same as for equal-time quantization. Scattering is formulated for interacting fields in a covariant interaction picture and it is shown that the familiar perturbative expansion of the S-operator is recovered by our approach. An appendix analyzes special distributions, integrals over the forward hyperboloid, that are used repeatedly in the paper.     

Contextual quantum process theory

A logically complete interpretation of quantum mechanics is given in terms of a theory of quantum processes.Research performed during stays at Utrecht State University, at the Institute for the History and Foundations of Science and at the Department of Philosophy.