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.     

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.     

Spacetime and future quantum theory

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

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.     

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.     

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.     

Topological quantum field theory

A twisted version of four dimensional supersymmetric gauge theory is formulated. The model, which refines a nonrelativistic treatment by Atiyah, appears to underlie many recent developments in topology of low dimensional manifolds; the Donaldson polynomial invariants of four manifolds and the Floer groups of three manifolds appear naturally. The model may also be interesting from a physical viewpoint; it is in a sense a generally covariant quantum field theory, albeit one in which general covariance is unbroken, there are no gravitons, and the only excitations are topological.On leave from Department of Physics, Princeton University. Research supported in part by NSF Grants No. 80-19754, 86-16129, 86-20266     

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.     

Axioms for quantum theory

The first three of these axioms describe quantum theory and classical mechanics as statistical theories from the very beginning. With these, it can be shown in which sense a more general than the conventional measure theoretic probability theory is used in quantum theory. One gets this generalization defining transition probabilities on pairs of events (not sets of pairs) as a fundamental, not derived, concept. A comparison with standard theories of stochastic processes gives a very general formulation of the non existence of quantum theories with hidden variables. The Cartesian product of probability spaces can be given a natural algebraic structure, the structure of an orthocomplemented, orthomodular, quasi-modular, not modular, not distributive lattice, which can be compared with the quantum logic (lattice of all closed subspaces of an infinite dimensional Hubert space). It is shown how our given system of axioms suggests generalized quantum theories, especially Schrödinger equations, for phase space amplitudes.     

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.