The Spin-Statistics Relation and Noncommutative Quantum Field Theory

The efforts of combining quantum theory with general relativity have been great and marked by several successes. One field where progress has lately been made is the study of noncommutative quantum field theories that arise as a low energy limit in certain string theories. The idea of noncommutativity comes naturally when combining these two extremes and has profound implications on results widely accepted in traditional, commutative, theories. In this work I review the status of one of the most important connections in physics, the spin-statistics relation. The relation is deeply ingrained in our reality in that it gives us the structure for the periodic table and is of crucial importance for the stability of all matter. The dramatic effects of noncommutativity of space-time coordinates, mainly the loss of Lorentz invariance, call the spin-statistics relation into question. The spin-statistics theorem is first presented in its traditional setting, giving a clarifying proof starting from minimal requirements. Next the notion of noncommutativity is introduced and its implications studied. The discussion is essentially based on twisted Poincaré symmetry, the space-time symmetry of noncommutative quantum field theory. The controversial issue of microcausality in noncommutative quantum field theory is settled by showing for the first time that the light wedge microcausality condition is compatible with the twisted Poincaré symmetry. The spin-statistics relation is considered both from the point of view of braided statistics, and in the traditional Lagrangian formulation of Pauli, with the conclusion that Pauli's age-old theorem stands even this test so dramatic for the whole structure of space-time.

Shape-Dependent Confinement in Ultrasmall Zero-, One-, and Two-Dimensional PbS Nanostructures

Spatial dimensionality affects the degree of confinement when an electron-hole pair is squeezed from one or more dimensions approaching the bulk exciton Bohr radius (alpha(B)) limit. The etectron-hole interaction in zero-dimensional (0D) dots, one-dimensional (1D) rods/wires, and two-dimensional (2D) wells/sheets should be enhanced by the increase in confinement dimensions in the order 0D > 1D > 2D. We report the controlled synthesis of PbS nanomateriats with 0D, 1D, and 2D forms retaining at least one dimension in the strongly confined regime far below alpha(B) (similar to 10 nm for PbS) and provide evidence through varying the exciton-phonon coupling strength that the degree of confinement is systematically weakened by the loss of confinement dimension. Geometry variations show distinguishable far-field optical polarizations, which could find useful applications in polarization-sensitive devices.

Line tension of a two dimensional gas-liquid interface

In two dimensional (2D) gas-liquid systems, the reported simulation values of line tension are known to disagree with the existing theoretical estimates. We find that while the simulation erred in truncating the range of the interaction potential, and as a result grossly underestimated the actual value, the earlier theoretical calculation was also limited by several approximations. When both the simulation and the theory are improved, we find that the estimate of line tension is in better agreement with each other. The small value of surface tension suggests increased influence of noncircular clusters in 2D gas-liquid nucleation, as indeed observed in a recent simulation.

Intersoliton forces in weak-coupling quantum field theories

We offer a procedure for evaluating the forces exerted by solitons of weak-coupling field theories on one another. We illustrate the procedure for the kink and the antikink of the two-dimensional φ4 theory. To do this, we construct analytically a static solution of the theory which can be interpreted as a kink and an antikink held a distance R apart. This leads to a definition of the potential energy U(R) for the pair, which is seen to have all the expected features. A corresponding evaluation is also done for U(R) between a soliton and an antisoliton of the sine-Gordon theory. When this U(R) is inserted into a nonrelativistic two-body problem for the pair, it yields a set of bound states and phase shifts. These are found to agree with exact results known for the sine-Gordon field theory in those regions where U(R) is expected to be significant, i.e., when R is large compared to the soliton size. We take this agreement as support that our procedure for defining U(R) yields the correct description of the dynamics of well-separated soliton pairs. An important feature of U(R) is that it seems to give strong intersoliton forces when the coupling constant is small, as distinct from the forces between the ordinary quanta of the theory. We suggest that this is a general feature of a class of theories, and emphasize the possible relevance of this feature to real strongly interacting hadrons.

Patient exposure monitoring and radiation qualities in two-dimensional digital x-ray imaging

The methods for estimating patient exposure in x-ray imaging are based on the measurement of radiation incident on the patient. In digital imaging, the useful dose range of the detector is large and excessive doses may remain undetected. Therefore, real-time monitoring of radiation exposure is important. According to international recommendations, the measurement uncertainty should be lower than 7% (confidence level 95%). The kerma-area product (KAP) is a measurement quantity used for monitoring patient exposure to radiation. A field KAP meter is typically attached to an x-ray device, and it is important to recognize the effect of this measurement geometry on the response of the meter. In a tandem calibration method, introduced in this study, a field KAP meter is used in its clinical position and calibration is performed with a reference KAP meter. This method provides a practical way to calibrate field KAP meters. However, the reference KAP meters require comprehensive calibration. In the calibration laboratory it is recommended to use standard radiation qualities. These qualities do not entirely correspond to the large range of clinical radiation qualities. In this work, the energy dependence of the response of different KAP meter types was examined. According to our findings, the recommended accuracy in KAP measurements is difficult to achieve with conventional KAP meters because of their strong energy dependence. The energy dependence of the response of a novel large KAP meter was found out to be much lower than with a conventional KAP meter. The accuracy of the tandem method can be improved by using this meter type as a reference meter. A KAP meter cannot be used to determine the radiation exposure of patients in mammography, in which part of the radiation beam is always aimed directly at the detector without attenuation produced by the tissue. This work assessed whether pixel values from this detector area could be used to monitor the radiation beam incident on the patient. The results were congruent with the tube output calculation, which is the method generally used for this purpose. The recommended accuracy can be achieved with the studied method. New optimization of radiation qualities and dose level is needed when other detector types are introduced. In this work, the optimal selections were examined with one direct digital detector type. For this device, the use of radiation qualities with higher energies was recommended and appropriate image quality was achieved by increasing the low dose level of the system.

Graphene-like two-dimensional ionic boron with double dirac cones at ambient condition

Recently, partially ionic boron (γ-B28) has been predicted and observed in pure boron, in bulk phase and controlled by pressure [Nature, 457 (2009) 863]. By using ab initio evolutionary structure search, we report the prediction of ionic boron at a reduced dimension and ambient pressure, namely, the two-dimensional (2D) ionic boron. This 2D boron structure consists of graphene-like plane and B2 atom pairs, with the P6/mmm space group and 6 atoms in the unit cell, and has lower energy than the previously reported α-sheet structure and its analogues. Its dynamical and thermal stability are confirmed by the phonon-spectrum and ab initio molecular dynamics simulation. In addition, this phase exhibits double Dirac cones with massless Dirac fermions due to the significant charge transfer between the graphene-like plane and B2 pair that enhances the energetic stability of the P6/mmm boron. A Fermi velocity (vf) as high as 2.3 x 106 m/s, which is even higher than that of graphene (0.82 x 106 m/s), is predicted for the P6/mmm boron. The present work is the first report of the 2D ionic boron at atmospheric pressure. The unique electronic structure renders the 2D ionic boron a promising 2D material for applications in nanoelectronics.

A general treatment of two dimensional plane flows, for a micropolar fluid

In this paper we have studied the flow of a micropolar fluid, whose constitutive equations were given by Eringen, in two dimensional plane flow. In two notes, we have discussed the validity of the boundary condition v=a ω and its effect on the entire flow field. We have restricted our study to the case when Stokes' approximation is valid, i. e. slow motion for it is difficult to uncouple the equations in the most general case.

Simultaneous heat and mass transfer in unsteady free convection from two-dimensional and axisymmetric bodies

The unsteady laminar free convection boundary layer flows around two-dimensional and axisymmetric bodies placed in an ambient fluid of infinite extent have been studied when the flow is driven by thermal buoyancy forces and buoyancy forces from species diffusion. The unsteadiness in the flow field is caused by both temperature and concentration at the wall which vary arbitrarily with time. The coupled nonlinear partial differential equations with three independent variables governing the flow have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. Computations have been performed for a circular cylinder and a sphere. The skin friction, heat transfer and mass transfer are strongly dependent on the variation of the wall temperature and concentration with time. Also the skin friction and heat transfer increase or decrease as the buoyancy forces from species diffusion assist and oppose, respectively, the thermal buoyancy force, whereas the mass transfer rate is higher for small values of the ratio of the buoyancy parameters than for large values. The local heat and mass transfer rates are maximum at the stagnation point and they decrease progressively with increase of the angular position from the stagnation point.

Double diffusive unsteady free convection on two-dimensional and axisymmetric bodies in a porous medium

The unsteady laminar free convection flow of an incompressible electrically conducting fluid over two-dimensional and axisymmetric bodies embedded in a highly porous medium with an applied magnetic field has been studied. The unsteadiness in the flow field is caused by the variation of the wall temperature and concentration with time. The coupled nonlinear partial differential equations with three independent variables have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. It is observed that the skin friction, heat transfer and mass transfer increase with the permeability parameter but decrease with the magnetic parameter. The results are strongly dependent on the variation of wall temperature and concentration with time. The skin friction and heat transfer increase or decrease as the buoyancy forces from species diffusion assist or oppose the thermal buoyancy force. However, the mass transfer is found to be higher for small values of the ratio of the buoyancy parameters than for large values

Ordering near the percolation threshold in models of two-dimensional interacting bosons with quenched dilution

Randomly diluted quantum boson and spin models in two dimensions combine the physics of classical percolation with the well-known dimensionality dependence of ordering in quantum lattice models. This combination is rather subtle for models that order in two dimensions but have no true order in one dimension, as the percolation cluster near threshold is a fractal of dimension between 1 and 2: two experimentally relevant examples are the O(2) quantum rotor and the Heisenberg antiferromagnet. We study two analytic descriptions of the O(2) quantum rotor near the percolation threshold. First a spin-wave expansion is shown to predict long-ranged order, but there are statistically rare points on the cluster that violate the standard assumptions of spin-wave theory. A real-space renormalization group (RSRG) approach is then used to understand how these rare points modify ordering of the O(2) rotor. A new class of fixed points of the RSRG equations for disordered one-dimensional bosons is identified and shown to support the existence of long-range order on the percolation backbone in two dimensions. These results are relevant to experiments on bosons in optical lattices and superconducting arrays, and also (qualitatively) for the diluted Heisenberg antiferromagnet La-2(Zn,Mg)(x)Cu1-xO4.

Unsteady mixed convection over two-dimensional and axisymmetric bodies

The unsteady laminar incompressible mixed convection flow over a two-dimensional body (cylinder) and an axisymmetric body (sphere) has been studied when the buboyancy forces arise from both thermal and mass diffusion and the unsteadiness in the flow field is introduced by the time dependent free stream velocity. The nonlinear partial differential equations with three independent variables governing the flow have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. The results indicate that for the thermally assisting flow the local skin friction, heat transfer and mass diffusion are enhanced when the buoyancy force from mass diffusion assists the thermal buoyancy force. But this trend is opposite for the thermally opposing flow. The point of zero skin friction moves upstream due to unsteadiness. No singularity is observed at the point of zero skin friction for unsteady flow unlike steady flow. The flow reversal is observed after a certain instant of time. The velocity overshoot occurs for assisting flows.

On the two-dimensional thermoelectric power in quantum wells of non-parabolic materials under magnetic quantization

We present a simplified theoretical formulation of the thermoelectric power (TP) under magnetic quantization in quantum wells (QWs) of nonlinear optical materials on the basis of a newly formulated magneto-dispersion law. We consider the anisotropies in the effective electron masses and the spin-orbit constants within the framework of k.p formalism by incorporating the influence of the crystal field splitting. The corresponding results for III-V materials form a special case of our generalized analysis under certain limiting conditions. The TP in QWs of Bismuth, II-VI, IV-VI and stressed materials has been studied by formulating appropriate electron magneto-dispersion laws. We also address the fact that the TP exhibits composite oscillations with a varying quantizing magnetic field in QWs of n-Cd3As2, n-CdGeAs2, n-InSb, p-CdS, stressed InSb, PbTe and Bismuth. This reflects the combined signatures of magnetic and spatial quantizations of the carriers in such structures. The TP also decreases with increasing electron statistics and under the condition of non-degeneracy, all the results as derived in this paper get transformed into the well-known classical equation of TP and thus confirming the compatibility test. We have also suggested an experimental method of determining the elastic constants in such systems with arbitrary carrier energy spectra from the known value of the TP. (C) 2010 Elsevier Ltd. All rights reserved.

Cell-dynamical simulation of magnetic hysteresis in the two-dimensional Ising system

We present results from numerical simulations using a ‘‘cell-dynamical system’’ to obtain solutions to the time-dependent Ginzburg-Landau equation for a scalar, two-dimensional (2D), (Φ2)2 model in the presence of a sinusoidal external magnetic field. Our results confirm a recent scaling law proposed by Rao, Krishnamurthy, and Pandit [Phys. Rev. B 42, 856 (1990)], and are also in excellent agreement with recent Monte Carlo simulations of hysteretic behavior of 2D Ising spins by Lo and Pelcovits [Phys. Rev. A 42, 7471 (1990)].

Evidence for decoupled two-dimensional vortex behavior of YBa2Cu3O7-delta in La0.7Sr0.3MnO3/YBa2Cu3O7-delta/La0.7Sr0.3MnO3 trilayer

We investigate the vortex behavior of YBa2Cu3O7-delta thin films sandwiched between two ferromagnetic layers (La0.7Sr0.3MnO3/YBa2Cu3O7-delta/La0.7Sr0.3MnO3). The magnetization study on La0.7Sr0.3MnO3/YBa2Cu3O7-delta/La0.7Sr0.3MnO3 trilayers conspicuously shows the presence of both ferromagnetic and diamagnetic phases. The magnetotransport study on the trilayers reveals a significant reduction in the activation energy (U) for the vortex motion in YBa2Cu3O7-delta. Besides, the ``U'' exhibits a logarithmic dependence on the applied magnetic field which directly indicates the existence of decoupled two-dimensional (2D) pancake vortices present in the CuO2 layers. The evidence of 2D decoupled vortex behavior in La0.7Sr0.3MnO3/YBa2Cu3O7-delta/La0.7Sr0.3MnO3 is believed to arise from (a) the weakening of superconducting coherence length along the c-axis and (b) enhanced intraplane vortex-vortex interaction due to the presence of ferromagnetic layers. (C) 2010 American Institute of Physics. doi: 10.1063/1.3524545]

Suppression of low-frequency noise in two-dimensional electron gas at degenerately doped Si:P delta layers

We report low-frequency 1/f-noise measurements of degenerately doped Si:P delta layers at 4.2 K. The noise was found to be over six orders of magnitude lower than that of bulk Si:P systems in the metallic regime and is one of the lowest values reported for doped semiconductors. The noise was nearly independent of magnetic field at low fields, indicating negligible contribution from universal conductance fluctuations. Instead, the interaction of electrons with very few active structural two-level systems may explain the observed noise magnitude.