AB effect and Aharonov-Susskind charge non-superselection

We consider a particle in a coherent superposition of states with different electric charge moving in the vicinity of a magnetic flux. Formally, it should acquire a (gauge-dependent) AB relative phase between the charge states, even for an incomplete loop. If measureable, such a geometric, rather than topological, AB-phase would seem to break gauge invariance. Wick, Wightman and Wigner argued that since (global) charge-dependent phase transformations are physically unobservable, charge state superpositions are unphysical (`charge superselection rule'). This would resolve the apparent paradox in a trivial way. However, Aharonov and Susskind disputed this superselection rule: they distinguished between such global charge-dependent transformations, and transformations of the relative inter-charge phases of two particles, and showed that the latter \emph{could} in principle be observable! Finally, the paradox again disappears once we considers the `calibration' of the phase measured by the Aharonov-Susskind phase detectors, as well as the phase of the particle at its initial point. It turns out that such a detector can only distinguish between the relative phases of two paths if their (oriented) difference forms a loop around the flux

Reduction of Effective Terahertz Focal Spot Size By Means Of Nested Concentric Parabolic Reflectors

An ongoing limitation of terahertz spectroscopy is that the technique is generally limited to the study of relatively large samples of order 4 mm across due to the generally large size of the focal beam spot. We present a nested concentric parabolic reflector design which can reduce the terahertz focal spot size. This parabolic reflector design takes advantage of the feature that reflected rays experience a relative time delay which is the same for all paths. The increase in effective optical path for reflected light is equivalent to the aperture diameter itself. We have shown that the light throughput of an aperture of 2 mm can be increased by a factor 15 as compared to a regular aperture of the same size at low frequencies. This technique can potentially be used to reduce the focal spot size in terahertz spectroscopy and enable the study of smaller samples

On the theory of electric dc-conductivity : linear and non-linear microscopic evolution and macroscopic behaviour

We consider the Schrodinger time evolution of charged particles subject to a static substrate potential and to a homogeneous, macroscopic electric field (a magnetic field may also be present). We investigate the microscopic velocities and the resulting macroscopic current. We show that the microscopic velocities are in general non-linear with respect to the electric field. One kind of non-linearity arises from the highly non-linear adiabatic evolution and (or) from an admixture of parts of it in so-called intermediate states, and the other kind from non-quadratic transition rates between adiabatic states. The resulting macroscopic dc-current may or may not be linear in the field. Three cases can be distinguished : (a) The microscopic non-linearities can be neglected. This is assumed to be the case in linear response theory (Kubo formalism, ...). We give arguments which make it plausible that often such an assumption is indeed justified, in particular for the current parallel to the field. (b) The microscopic non-linearitites lead to macroscopic non-linearities. An example is the onset of dissipation by increasing the electric field in the breakdown of the quantum Hall effect. (c) The macroscopic current is linear although the microscopic non-linearities constitute an essential part of it and cannot be neglected. We show that the Hall current of a quantized Hall plateau belongs to this case. This illustrates that macroscopic linearity does not necessarily result from microscopic linearity. In the second and third cases linear response theory is inadequate. We elucidate also some other problems related to linear response theory.Comment: 24 pages, 6 figures, some typing errors have been corrected. Remark : in eq. (1) of the printed article an obvious typing error remain

On the probabilistic description of a multipartite correlation scenario with arbitrary numbers of settings and outcomes per site

We consistently formalize the probabilistic description of multipartite joint measurements performed on systems of any nature. This allows us: (1) to specify in probabilistic terms the difference between nonsignaling, the Einstein- Podolsky-Rosen (EPR) locality and Bell's locality; (2) to introduce the notion of an LHV model for an S_{1}x...xS_{N}-setting N-partite correlation experiment, with outcomes of any spectral type, discrete or continuous, and to prove both general and specific "quantum" statements on an LHV simulation in an arbitrary multipartite case; (3) to classify LHV models for a multipartite quantum state, in particular, to show that any N-partite quantum state, pure or mixed, admits an Sx1x...x1 -setting LHV description; (4) to evaluate a threshold visibility for a noisy bipartite quantum state to admit an S_{1}xS_ {2}-setting LHV description under any generalized quantum measurements of two parties. In a sequel to this paper, we shall introduce a single general representation incorporating in a unique manner all Bell-type inequalities for either joint probabilities or correlation functions that have been introduced or will be introduced in the literature.Comment: 26 pages; added section Conclusions and some references for section

Quantum-Mechanical Dualities on the Torus

On classical phase spaces admitting just one complex-differentiable structure, there is no indeterminacy in the choice of the creation operators that create quanta out of a given vacuum. In these cases the notion of a quantum is universal, i.e., independent of the observer on classical phase space. Such is the case in all standard applications of quantum mechanics. However, recent developments suggest that the notion of a quantum may not be universal. Transformations between observers that do not agree on the notion of an elementary quantum are called dualities. Classical phase spaces admitting more than one complex-differentiable structure thus provide a natural framework to study dualities in quantum mechanics. As an example we quantise a classical mechanics whose phase space is a torus and prove explicitly that it exhibits dualities.Comment: New examples added, some precisions mad

Relaxation Phenomena in a System of Two Harmonic Oscillators

We study the process by which quantum correlations are created when an interaction Hamiltonian is repeatedly applied to a system of two harmonic oscillators for some characteristic time interval. We show that, for the case where the oscillator frequencies are equal, the initial Maxwell-Boltzmann distributions of the uncoupled parts evolve to a new equilibrium Maxwell-Boltzmann distribution through a series of transient Maxwell-Boltzmann distributions. Further, we discuss why the equilibrium reached when the two oscillator frequencies are unequal, is not a thermal one. All the calculations are exact and the results are obtained through an iterative process, without using perturbation theory.Comment: 22 pages, 6 Figures, Added contents, to appear in PR

Optimal Covariant Measurement of Momentum on a Half Line in Quantum Mechanics

We cannot perform the projective measurement of a momentum on a half line since it is not an observable. Nevertheless, we would like to obtain some physical information of the momentum on a half line. We define an optimality for measurement as minimizing the variance between an inferred outcome of the measured system before a measuring process and a measurement outcome of the probe system after the measuring process, restricting our attention to the covariant measurement studied by Holevo. Extending the domain of the momentum operator on a half line by introducing a two dimensional Hilbert space to be tensored, we make it self-adjoint and explicitly construct a model Hamiltonian for the measured and probe systems. By taking the partial trace over the newly introduced Hilbert space, the optimal covariant positive operator valued measure (POVM) of a momentum on a half line is reproduced. We physically describe the measuring process to optimally evaluate the momentum of a particle on a half line.Comment: 12 pages, 3 figure

Transition to Landau Levels in Graphene Quantum Dots

We investigate the electronic eigenstates of graphene quantum dots of realistic size (i.e., up to 80 nm diameter) in the presence of a perpendicular magnetic field B. Numerical tight-binding calculations and Coulomb-blockade measurements performed near the Dirac point exhibit the transition from the linear density of states at B=0 to the Landau level regime at high fields. Details of this transition sensitively depend on the underlying graphene lattice structure, bulk defects, and localization effects at the edges. Key to the understanding of the parametric evolution of the levels is the strength of the chiral-symmetry breaking K-K' scattering. We show that the parametric variation of the level variance provides a quantitative measure for this scattering mechanism. We perform measurements of the parametric motion of Coulomb blockade peaks as a function of magnetic field and find good agreement. We thereby demonstrate that the magnetic-field dependence of graphene energy levels may serve as a sensitive indicator for the properties of graphene quantum dots and, in further consequence, for the validity of the Dirac-picture.Comment: 10 pages, 11 figures, higher quality images available on reques

Design of a fault tolerant airborne digital computer. Volume 1: Architecture

This volume is concerned with the architecture of a fault tolerant digital computer for an advanced commercial aircraft. All of the computations of the aircraft, including those presently carried out by analogue techniques, are to be carried out in this digital computer. Among the important qualities of the computer are the following: (1) The capacity is to be matched to the aircraft environment. (2) The reliability is to be selectively matched to the criticality and deadline requirements of each of the computations. (3) The system is to be readily expandable. contractible, and (4) The design is to appropriate to post 1975 technology. Three candidate architectures are discussed and assessed in terms of the above qualities. Of the three candidates, a newly conceived architecture, Software Implemented Fault Tolerance (SIFT), provides the best match to the above qualities. In addition SIFT is particularly simple and believable. The other candidates, Bus Checker System (BUCS), also newly conceived in this project, and the Hopkins multiprocessor are potentially more efficient than SIFT in the use of redundancy, but otherwise are not as attractive

5-State Rotation-Symmetric Number-Conserving Cellular Automata are not Strongly Universal

We study two-dimensional rotation-symmetric number-conserving cellular automata working on the von Neumann neighborhood (RNCA). It is known that such automata with 4 states or less are trivial, so we investigate the possible rules with 5 states. We give a full characterization of these automata and show that they cannot be strongly Turing universal. However, we give example of constructions that allow to embed some boolean circuit elements in a 5-states RNCA