Generalized point interactions in one-dimensional quantum mechanics

There is a four-parameter family of point interactions in one-dimensional quantum mechanics. They represent all possible self-adjoint extensions of the kinetic energy operator. If time-reversal invariance is imposed, the number of parameters is reduced to three. One of these point interactions is the familiar delta function potential but the other generalized ones do not seem to be widely known. We present a pedestrian approach to this subject and comment on a recent controversy in the literature concerning the so-called delta' interaction. We emphasize that there is little resemblance between the delta' interaction and what its name suggests.

Fermi pseudo-potential and energy-dependent point interactions in one dimension

There are point interactions in one dimension that can be interpreted as self-adjoint extensions (SAEs) of the kinetic energy [KE] operator. Here, we report the results obtained in two recent papers cited in [1]. In the first, we consider point interactions in one dimension in the form of the Fermi pseudo-potential, in one and two-channel cases. In the second, we consider a new type of point interactions that are self-adjoint and effectively energy-dependent. © 2005 American Institute of Physics.

Four-point one-loop amplitude computation in the pure spinor formalism

The massless 4-point one-loop amplitude computation in the pure spinor formalism is shown to agree with the computation in the RNS formalism. © SISSA 2006.

Correspondence between the one-loop three-point vertex and the Y and Delta electric resistor networks

Different mathematical methods have been applied to obtain the analytic result for the massless triangle Feynman diagram yielding a sum of four linearly independent (LI) hypergeometric functions of two variables F-4. This result is not physically acceptable when it is embedded in higher loops, because all four hypergeometric functions in the triangle result have the same region of convergence and further integration means going outside those regions of convergence. We could go outside those regions by using the well-known analytic continuation formulas obeyed by the F-4, but there are at least two ways we can do this. Which is the correct one? Whichever continuation one uses, it reduces a number of F-4 from four to three. This reduction in the number of hypergeometric functions can be understood by taking into account the fundamental physical constraint imposed by the conservation of momenta flowing along the three legs of the diagram. With this, the number of overall LI functions that enter the most general solution must reduce accordingly. It remains to determine which set of three LI solutions needs to be taken. To determine the exact structure and content of the analytic solution for the three-point function that can be embedded in higher loops, we use the analogy that exists between Feynman diagrams and electric circuit networks, in which the electric current flowing in the network plays the role of the momentum flowing in the lines of a Feynman diagram. This analogy is employed to define exactly which three out of the four hypergeometric functions are relevant to the analytic solution for the Feynman diagram. The analogy is built based on the equivalence between electric resistance circuit networks of types Y and Delta in which flows a conserved current. The equivalence is established via the theorem of minimum energy dissipation within circuits having these structures.

One-dimensional point interaction with Griffiths' boundary conditions

Griffiths proposed a pair of boundary conditions that define a point interaction in one dimensional quantum mechanics. The conditions involve the nth derivative of the wave function where n is a non-negative integer. We re-examine the interaction so defined and explicitly confirm that it is self-adjoint for any even value of n and for n = 1. The interaction is not self-adjoint for odd n > 1. We then propose a similar but different pair of boundary conditions with the nth derivative of the wave function such that the ensuing point interaction is self-adjoint for any value of n.

Asymptotic freedom, dimensional transmutation, and an infrared conformal fixed point for the δ-function potential in one-dimensional relativistic quantum mechanics

We consider the Schrödinger equation for a relativistic point particle in an external one-dimensional δ-function potential. Using dimensional regularization, we investigate both bound and scattering states, and we obtain results that are consistent with the abstract mathematical theory of self-adjoint extensions of the pseudodifferential operator H=p2+m2−−−−−−−√. Interestingly, this relatively simple system is asymptotically free. In the massless limit, it undergoes dimensional transmutation and it possesses an infrared conformal fixed point. Thus it can be used to illustrate nontrivial concepts of quantum field theory in the simpler framework of relativistic quantum mechanics.

The ENP in practice - the European Union's policy towards Russia, Ukraine, Belarus and Moldova one year after the publication of the Strategy Paper. OSW Point of View, June 2005

Clear qualitative changes have taken place in relations between the European Union and its Eastern neighbours over the past year. The European Neighbourhood Policy (ENP) has been playing a significant part in the context of these changes. In the cases of Moldova and Ukraine, which are the countries interested in enhancing co-operation with the EU, the ENP has provided a formula that allows taking steps to implement this objective. The ENP has also contributed to "outlining an alternative" to Belarus' current self-isolation. However, the ENP has first of all given a clear message to Russia by specifying the EU's interests and objectives concerning Eastern Europe. The ENP has clearly stated that the EU wants to build democracy and a free market in those countries, and has signalled that the European Union intends to discuss the issues concerning the countries directly with them, and not through Moscow's offices.

A selection of one hundred of Perrin's fables : accompanied with a key, containing the text, a literal and a free translation arranged in such a manner as to point out the difference between the French and the English idiom : also a figured pronunciation of the French, according to the best French works extant on the subject : the whole preceded by a short treatise on the sounds of the French language, compared with those of the English /

Mode of access: Internet.

Orbital multicriticality in spin-gapped quasi-one-dimensional antiferromagnets

Motivated by the quasi-one-dimensional antiferromagnet CaV(2)O(4), we explore spin-orbital systems in which the spin modes are gapped but orbitals are near a macroscopically degenerate classical transition. Within a simplified model we show that gapless orbital liquid phases possessing power-law correlations may occur without the strict condition of a continuous orbital symmetry. For the model proposed for CaV(2)O(4), we find that an orbital phase with coexisting order parameters emerges from a multicritical point. The effective orbital model consists of zigzag-coupled transverse field Ising chains. The corresponding global phase diagram is constructed using field theory methods and analyzed near the multicritical point with the aid of an exact solution of a zigzag XXZ model.

Continuous structural transitions in quasi-one-dimensional classical Wigner crystals

We study the structural phase transitions in confined systems of strongly interacting particles. We consider infinite quasi-one-dimensional systems with different pairwise repulsive interactions in the presence of an external confinement following a power law. Within the framework of Landau's theory, we find the necessary conditions to observe continuous transitions and demonstrate that the only allowed continuous transition is between the single-and the double-chain configurations and that it only takes place when the confinement is parabolic. We determine analytically the behavior of the system at the transition point and calculate the critical exponents. Furthermore, we perform Monte Carlo simulations and find a perfect agreement between theory and numerics.

No relationship found between point heteroplasmy in mitochondrial DNA control region and age range, sex and haplogroup in human hairs

The analysis of heteroplasmy (presence of more than one type of mitochondrial DNA in an individual) is used as a tool in human identification studies, anthropology, and most currently in studies that relate heteroplasmy with longevity. The frequency of heteroplasmy and its correlation with age has been analyzed using different tissues such as blood, muscle, heart, bone and brain and in different regions of mitochondrial DNA, but this analysis had never been performed using hair samples. In this study, samples of hair were sequenced in order to ascertain whether the presence or not of heteroplasmy varied according to age, sex and origin of haplogroup individuals. The samples were grouped by age (3 groups), gender (male and female) and haplogroup of origin (European, African and Native American), and analyzed using the chi-square statistical test (chi(2)). Based in statistical results obtained, we conclude that there is no relationship between heteroplasmy and sex, age and haplogroup origin using hair samples.

Relationship between Rheological Properties and One-Step W/O/W Multiple Emulsion Formation

Formation of a normal (not temporary) W/O/W multiple emulsion via the one-step method as a result of the simultaneous occurrence of catastrophic and transitional phase inversion processes has been recently reported. Critical features of this process include the emulsification temperature (corresponding to the ultralow surface tension point), the use of a specific nonionic surfactant blend and the surfactant blend/oil phase ratio, and the addition of the surfactant blend to the oil phase. The purpose of this study was to investigate physicochemical properties in an effort to gain a mechanistic understanding of the formation of these emulsions. Bulk, surface, and interfacial theological properties of adsorbed nonionic surfactant (CremophorRH40 and Span80) films were investigated under conditions known to affect W/O/W emulsion formation. Bulk viscosity results demonstrated that CremophorRH40 has a higher mobility in oil compared than in water, explaining the significance of the solvent phase. In addition, the bulk viscosity profile of aqueous solutions containing CremophorRH40 indicated a phase transition at around 78 +/- 2 degrees C, which is in agreement with cubic phase formation in the Winsor III region. The similarity in the interfacial elasticity values of CremophorRH40 and Span80 indicated that canola oil has a major effect on surface activity, showing the significance of vegetable oil. The highest interfacial shear elasticity and viscosity were observed when both surfactants were added to the oil phase, indicating the importance of the microstructural arrangement. CremophorRH40/Span80 complexes tended to desorb from the solution/solution interface with increasing temperature, indicating surfactant phase formation as is theoretically predicted in the Winsor III region. Together these interfacial and bulk rheology data demonstrate that one-step W/O/W emulsions form as a result of the simultaneous occurrence of phase-transition processes in the Winsor III region and explain the critical formulation and processing parameters necessary to achieve the formation of these normal W/O/W emulsions.

Influence of Phase Inversion on the Formation and Stability of One-Step Multiple Emulsions

A novel method of preparation of water-in-oil-in-micelle-containing water (W/O/W(m)) Multiple emulsions using the one-step emulsification method is reported. These multiple emulsions were normal (not temporary) and stable over a 60 day test period. Previously, reported multiple emulsion by the one-step method were abnormal systems that formed at the inversion point of simple emulsion (where there is an incompatibility in the Ostwald and Bancroft theories, and typically these are O/W/O systems). Pseudoternary phase diagrams and bidimensional process-composition (phase inversion) maps were constructed to assist in process and composition optimization. The surfactants used were PEG40 hydrogenated castor oil and sorbitan oleate, and mineral and vegetables oils were investigated. Physicochemical characterization studies showed experimentally, for the First time, the significance of the ultralow surface tension point oil multiple emulsion formation by one-step via phase inversion processes. Although the significance of ultralow surface tension has been speculated previously, to the best of our knowledge, this is the first experimental confirmation. The multiple emulsion system reported here was dependent not only upon the emulsification temperature, but also upon the component ratios, therefore both the emulsion phase inversion and the phase inversion temperature were considered to fully explain their formation. Accordingly, it is hypothesized that the formation of these normal multiple emulsions is not a result of a temporary incompatibility (at the inversion point) during simple emulsion preparation, as previously reported. Rather, these normal W/O/W(m) emulsions are a result of the simultaneous occurrence of catastrophic and transitional phase inversion processes. The formation of the primary emulsions (W/O) is in accordance with the Ostwald theory and the formation of the multiple emulsions (W/O/W(m)) is in agreement with the Bancroft theory.

Bimanual aiming and overt attention: one law for two hands

Reaching to interact with an object requires a compromise between the speed of the limb movement and the required end-point accuracy. The time it takes one hand to move to a target in a simple aiming task can be predicted reliably from Fitts' law, which states that movement time is a function of a combined measure of amplitude and accuracy constraints (the index of difficulty, ID). It has been assumed previously that Fitts' law is violated in bimanual aiming movements to targets of unequal ID. We present data from two experiments to show that this assumption is incorrect: if the attention demands of a bimanual aiming task are constant then the movements are well described by a Fitts' law relationship. Movement time therefore depends not only on ID but on other task conditions, which is a basic feature of Fitts' law. In a third experiment we show that eye movements are an important determinant of the attention demands in a bimanual aiming task. The results from the third experiment extend the findings of the first two experiments and show that bimanual aiming often relies on the strategic co-ordination of separate actions into a seamless behaviour. A number of the task specific strategies employed by the adult human nervous system were elucidated in the third experiment. The general strategic pattern observed in the hand trajectories was reflected by the pattern of eye movements recorded during the experiment. The results from all three experiments demonstrate that eye movements must be considered as an important constraint in bimanual aiming tasks.

Contradiction of quantum mechanics with local hidden variables for quadrature phase amplitude measurements

We demonstrate a contradiction of quantum mechanics with local hidden variable theories for continuous quadrature phase amplitude (position and momentum) measurements. For any quantum state, this contradiction is lost for situations where the quadrature phase amplitude results are always macroscopically distinct. We show that for optical realizations of this experiment, where one uses homodyne detection techniques to perform the quadrature phase amplitude measurement, one has an amplification prior to detection, so that macroscopic fields are incident on photodiode detectors. The high efficiencies of such detectors may open a way for a loophole-free test of local hidden variable theories.