Interplanar binding in graphite studied with the Englert-Schwinger equation

A model of a graphite crystal is used which consists of a set of parallel slabs of positive charge immersed in an electron sea. The density of electrons in the region between slabs is calculated from the Englert-Schwinger equation. That equation improves Thomas-Fermi theory by including exchange and inhomogeneity corrections to the kinetic energy. The results are in semiquantitative agreement with empirical data and are slightly better than previous calculations of the interplanar binding of graphite

Measuring a photonic qubit without destroying it

Measuring the polarisation of a single photon typically results in its destruction. We propose, demonstrate, and completely characterise a \emph{quantum non-demolition} (QND) scheme for realising such a measurement non-destructively. This scheme uses only linear optics and photo-detection of ancillary modes to induce a strong non-linearity at the single photon level, non-deterministically. We vary this QND measurement continuously into the weak regime, and use it to perform a non-destructive test of complementarity in quantum mechanics. Our scheme realises the most advanced general measurement of a qubit: it is non-destructive, can be made in any basis, and with arbitrary strength.Comment: 4 pages, 3 figure

Atoms and Quantum Dots With a Large Number of Electrons: the Ground State Energy

We compute the ground state energy of atoms and quantum dots with a large number N of electrons. Both systems are described by a non-relativistic Hamiltonian of electrons in a d-dimensional space. The electrons interact via the Coulomb potential. In the case of atoms (d=3), the electrons are attracted by the nucleus, via the Coulomb potential. In the case of quantum dots (d=2), the electrons are confined by an external potential, whose shape can be varied. We show that the dominant terms of the ground state energy are those given by a semiclassical Hartree-exchange energy, whose N to infinity limit corresponds to Thomas-Fermi theory. This semiclassical Hartree-exchange theory creates oscillations in the ground state energy as a function of N. These oscillations reflect the dynamics of a classical particle moving in the presence of the Thomas-Fermi potential. The dynamics is regular for atoms and some dots, but in general in the case of dots, the motion contains a chaotic component. We compute the correlation effects. They appear at the order N ln N for atoms, in agreement with available data. For dots, they appear at the order N.Comment: 30 pages, 1 figur

Hidden Symmetries and Dirac Fermions

In this paper, two things are done. First, we analyze the compatibility of Dirac fermions with the hidden duality symmetries which appear in the toroidal compactification of gravitational theories down to three spacetime dimensions. We show that the Pauli couplings to the p-forms can be adjusted, for all simple (split) groups, so that the fermions transform in a representation of the maximal compact subgroup of the duality group G in three dimensions. Second, we investigate how the Dirac fermions fit in the conjectured hidden overextended symmetry G++. We show compatibility with this symmetry up to the same level as in the pure bosonic case. We also investigate the BKL behaviour of the Einstein-Dirac-p-form systems and provide a group theoretical interpretation of the Belinskii-Khalatnikov result that the Dirac field removes chaos.Comment: 30 page

Symmetric coupling of four spin-1/2 systems

We address the non-binary coupling of identical angular momenta based upon the representation theory for the symmetric group. A correspondence is pointed out between the complete set of commuting operators and the reference-frame-free subsystems. We provide a detailed analysis of the coupling of three and four spin-1/2 systems and discuss a symmetric coupling of four spin-1/2 systems.Comment: 20 pages, no figure

Quantitative wave-particle duality and non-erasing quantum erasure

The notion of wave-particle duality may be quantified by the inequality V^2+K^2 <=1, relating interference fringe visibility V and path knowledge K. With a single-photon interferometer in which polarization is used to label the paths, we have investigated the relation for various situations, including pure, mixed, and partially-mixed input states. A quantum eraser scheme has been realized that recovers interference fringes even when no which-way information is available to erase.Comment: 6 pages, 4 figures. To appear in Phys. Rev.

Enhancing Acceleration Radiation from Ground-State Atoms via Cavity Quantum Electrodynamics

When ground state atoms are accelerated through a high Q microwave cavity, radiation is produced with an intensity which can exceed the intensity of Unruh acceleration radiation in free space by many orders of magnitude. The cavity field at steady state is described by a thermal density matrix under most conditions. However, under some conditions gain is possible, and when the atoms are injected in a regular fashion, the radiation can be produced in a squeezed state

Source Vacuum Fluctuations of Black Hole Radiance

The emergence of Hawking radiation from vacuum fluctuations is analyzed in conventional field theories and their energy content is defined through the Aharonov weak value concept. These fluctuations travel in flat space-time and carry transplanckian energies sharply localized on cisplanckian distances. We argue that these features cannot accommodate gravitational nonlinearities. We suggest that the very emission of Hawking photons from tamed vacuum fluctuations requires the existence of an exploding set of massive fields. These considerations corroborate some conjectures of Susskind and may prove relevant for the back-reaction problem and for the unitarity issue.Comment: 33 pages, ULB-TH 03/94, 5 figures not included, available on request from F.E. (problem with truncation of long lines

Five Lectures On Dissipative Master Equations

1 First Lecture: Basics 1.1 Physical Derivation of the Master Equation 1.2 Some Simple Implications 1.3 Steady State 1.4 Action to the Left 2 Second Lecture: Eigenvalues and Eigenvectors of L 2.1 A Simple Case First 2.2 The General Case 3 Third Lecture: Completeness of the Damping Bases 3.1 Phase Space Functions 3.2 Completeness of the Eigenvectors of L 3.3 Positivity Conservation 3.4 Lindblad Form of Liouville Operators 4 Fourth Lecture: Quantum-Optical Applications 4.1 Periodically Driven Damped Oscillator 4.2 Conditional and Unconditional Evolution 4.3 Physical Signicance of Statistical Operators 5 Fifth Lecture: Statistics of Detected Atoms 5.1 Correlation Functions 5.2 Waiting Time Statistics 5.3 Counting StatisticsComment: 58 pages, 10 figures; book chapter to appear in ``Coherent Evolution in Noisy Environments'', Lecture Notes in Physics, (Springer Verlag, Berlin-Heidelberg-New York). Notes of lectures given in Dresden,23-27 April 200