Quantum field theory on a growing lattice

We construct the classical and canonically quantized theories of a massless scalar field on a background lattice in which the number of points--and hence the number of modes--may grow in time. To obtain a well-defined theory certain restrictions must be imposed on the lattice. Growth-induced particle creation is studied in a two-dimensional example. The results suggest that local mode birth of this sort injects too much energy into the vacuum to be a viable model of cosmological mode birth.Comment: 28 pages, 2 figures; v.2: added comments on defining energy, and reference

Theory of combined exciton-cyclotron resonance in a two-dimensional electron gas: The strong magnetic field regime

I develop a theory of combined exciton-cyclotron resonance (ExCR) in a low-density two-dimensional electron gas in high magnetic fields. In the presence of excess electrons an incident photon creates an exciton and simultaneously excites one electron to higher-lying Landau levels. I derive exact ExCR selection rules that follow from the existing dynamical symmetries, magnetic translations and rotations about the magnetic field axis. The nature of the final states in the ExCR is elucidated. The relation between ExCR and shake-up processes is discussed. The double-peak ExCR structure for transitions to the first electron Landau level is predicted.Comment: 5 pages, 3 figures, replaced with the published versio

Shake-up Processes in a Low-Density Two-Dimensional Electron Gas: Spin-Dependent Transitions to Higher Hole Landau Levels

A theory of shake-up processes in photoabsorption of an interacting low-density two-dimensional electron gas (2DEG) in strong magnetic fields is presented. In these processes, an incident photon creates an electron-hole pair and, because of Coulomb interactions, simultaneously excites one particle to higher Landau levels (LL's). In this work, the spectra of correlated charged spin-singlet and spin-triplet electron-hole states in the first hole LL and optical transitions to these states (i.e., shake-ups to the first hole LL) are studied. Our results indicate, in particular, the presence of optically-active three-particle quasi-discrete states in the exciton continuum that may give rise to surprisingly sharp Fano resonances in strong magnetic fields. The relation between shake-ups in photoabsorption of the 2DEG and in the 2D hole gas (2DHG), and shake-ups of isolated negative X^- and positive X^+ trions are discussed.Comment: 8 pages, 8 figures. References updated, one figure added (Fig. 6). Accepted in Phys. Rev.

The quantum speed up as advanced knowledge of the solution

With reference to a search in a database of size N, Grover states: "What is the reason that one would expect that a quantum mechanical scheme could accomplish the search in O(square root of N) steps? It would be insightful to have a simple two line argument for this without having to describe the details of the search algorithm". The answer provided in this work is: "because any quantum algorithm takes the time taken by a classical algorithm that knows in advance 50% of the information that specifies the solution of the problem". This empirical fact, unnoticed so far, holds for both quadratic and exponential speed ups and is theoretically justified in three steps: (i) once the physical representation is extended to the production of the problem on the part of the oracle and to the final measurement of the computer register, quantum computation is reduction on the solution of the problem under a relation representing problem-solution interdependence, (ii) the speed up is explained by a simple consideration of time symmetry, it is the gain of information about the solution due to backdating, to before running the algorithm, a time-symmetric part of the reduction on the solution; this advanced knowledge of the solution reduces the size of the solution space to be explored by the algorithm, (iii) if I is the information acquired by measuring the content of the computer register at the end of the algorithm, the quantum algorithm takes the time taken by a classical algorithm that knows in advance 50% of I, which brings us to the initial statement.Comment: 23 pages, to be published in IJT

Automatic regularization by quantization in reducible representations of CCR: Point-form quantum optics with classical sources

Electromagnetic fields are quantized in manifestly covariant way by means of a class of reducible representations of CCR. $A_a(x)$ transforms as a Hermitian four-vector field in Minkowski four-position space (no change of gauge), but in momentum space it splits into spin-1 massless photons (optics) and two massless scalars (similar to dark matter). Unitary dynamics is given by point-form interaction picture, with minimal-coupling Hamiltonian constructed from fields that are free on the null-cone boundary of the Milne universe. SL(2,C) transformations and dynamics are represented unitarily in positive-norm Hilbert space describing $N$ four-dimensional oscillators. Vacuum is a Bose-Einstein condensate of the $N$-oscillator gas. Both the form of $A_a(x)$ and its transformation properties are determined by an analogue of the twistor equation. The same equation guarantees that the subspace of vacuum states is, as a whole, Poincar\'e invariant. The formalism is tested on quantum fields produced by pointlike classical sources. Photon statistics is well defined even for pointlike charges, with UV/IR regularizations occurring automatically as a consequence of the formalism. The probabilities are not Poissonian but of a R\'enyi type with $\alpha=1-1/N$. The average number of photons occurring in Bremsstrahlung splits into two parts: The one due to acceleration, and the one that remains nonzero even if motion is inertial. Classical Maxwell electrodynamics is reconstructed from coherent-state averaged solutions of Heisenberg equations. Static pointlike charges polarize vacuum and produce effective charge densities and fields whose form is sensitive to both the choice of representation of CCR and the corresponding vacuum state.Comment: 2 eps figures; in v2 notation in Eq. (39) and above Eq. (38) is correcte

Double-slit interference pattern from single-slit screen and its gravitational analogues

The double slit experiment (DSE) is known as an important cornerstone in the foundations of physical theories such as Quantum Mechanics and Special Relativity. A large number of different variants of it were designed and performed over the years. We perform and discuss here a new verion with the somewhat unexpected results of obtaining interference pattern from single-slit screen. This outcome, which shows that the routes of the photons through the array were changed, leads one to discuss it, using the equivalence principle, in terms of geodesics mechanics. We show using either the Brill's version of the canonical formulation of general relativity or the linearized version of it that one may find corresponding and analogous situations in the framework of general relativity.Comment: 51 pages, 12 Figures five of them contain two subfigures and thus the number of figures is 17, 1 Table. Some minor changes introduced, especially, in the reference

Binding Energy of Charged Excitons in ZnSe-based Quantum Wells

Excitons and charged excitons (trions) are investigated in ZnSe-based quantum well structures with (Zn,Be,Mg)Se and (Zn,Mg)(S,Se) barriers by means of magneto-optical spectroscopy. Binding energies of negatively () and positively (X+) charged excitons are measured as functions of quantum well width, free carrier density and in external magnetic fields up to 47 T. The binding energy of shows a strong increase from 1.4 to 8.9 meV with decreasing quantum well width from 190 to 29 A. The binding energies of X+ are about 25% smaller than the binding energy in the same structures. The magnetic field behavior of and X+ binding energies differ qualitatively. With growing magnetic field strength, increases its binding energy by 35-150%, while for X+ it decreases by 25%. Zeeman spin splittings and oscillator strengths of excitons and trions are measured and discussed

A Dodecalogue of Basic Didactics from Applications of Abstract Differential Geometry to Quantum Gravity

We summarize the twelve most important in our view novel concepts that have arisen, based on results that have been obtained, from various applications of Abstract Differential Geometry (ADG) to Quantum Gravity (QG). The present document may be used as a concise, yet informal, discursive and peripatetic conceptual guide-cum-terminological glossary to the voluminous technical research literature on the subject. In a bonus section at the end, we dwell on the significance of introducing new conceptual terminology in future QG research by means of `poetic language'Comment: 16 pages, preliminary versio

The 50% advanced information rule of the quantum algorithms

The oracle chooses a function out of a known set of functions and gives to the player a black box that, given an argument, evaluates the function. The player should find out a certain character of the function through function evaluation. This is the typical problem addressed by the quantum algorithms. In former theoretical work, we showed that a quantum algorithm requires the number of function evaluations of a classical algorithm that knows in advance 50% of the information that specifies the solution of the problem. Here we check that this 50% rule holds for the main quantum algorithms. In the structured problems, a classical algorithm with the advanced information, to identify the missing information should perform one function evaluation. The speed up is exponential since a classical algorithm without advanced information should perform an exponential number of function evaluations. In unstructured database search, a classical algorithm that knows in advance 50% of the n bits of the database location, to identify the n/2 missing bits should perform Order(2 power n/2) function evaluations. The speed up is quadratic since a classical algorithm without advanced information should perform Order(2 power n) function evaluations. The 50% rule identifies the problems solvable with a quantum sped up in an entirely classical way, in fact by comparing two classical algorithms, with and without the advanced information.Comment: 18 pages, submitted with minor changes to the International Journal of Theoretical Physic

Revisiting Zitterbewegung

The Dirac wave equation for the electron soon lead to the recognition of the Zitterbewegung. This was studied both by Schrodinger and Dirac. Later there were further elegant and sometimes dissenting insights, from different authors. We briefly review some of these developments. However in more recent times with dark energy and noncommutative spacetime coming to centre stage, the earlier studies of Zitterbewegung become questionable.Comment: 14 pages; late