Symmetric Superposition Research Articles

Superposition states through correlations of the second kind

We introduce model systems, embedded in R2, for joint systems consisting of two entangled spin-1/2 entities in superposition states: one in a symmetric superposition state, one in an antisymmetric superposition state. We study these model systems and compare them with a model system for a spin-1 quantum entity. All this leads to a new way of looking at the tensor product of Hilbert spaces within the context of quantum mechanics, and thus also to a new approach for the description of joint systems in quantum mechanics.

Quantum bound states in a double-bend quantum channel

By use of the mode-matching technique the quantum bound states in a double-bend quantum channel of finite length connecting to two 2D electron gas reservoirs have been investigated in detail. The conductance G of the quantum system is calculated as a function of Fermi energy and the electron density associated with bound states. It is found that there exists one resonant peak in G corresponding to resonant tunneling via one quasibound state below the first conductance plateau for the quantum channel with double-bend continuity and two resonant peaks in G corresponding to resonant tunneling via two quasibound states which are symmetric and antisymmetric superposition of two local bound states localized at two right-angle bends below the first conductance plateau for the quantum channel with double-bend discontinuity. At finite temperature the results are compared with experimental results and are found to explain them well.

Pattern formation in icosahedral virus capsids: the papova viruses and Nudaurelia capensis beta virus

The capsids of the spherical viruses all show underlying icosahedral symmetry, yet they differ markedly in capsomere shape and in capsomere position and orientation. The capsid patterns presented by the capsomere shapes, positions, and orientations of three viruses (papilloma, SV40, and N beta V) have been generated dynamically through a bottom-up procedure which provides a basis for understanding the patterns. A capsomere shape is represented in two-dimensional cross-section by a mass or charge density on the surface of a sphere, given by an expansion in spherical harmonics, and referred to herein as a morphological unit (MU). A capsid pattern is represented by an icosahedrally symmetrical superposition of such densities, determined by the positions and orientations of its MUs on the spherical surface. The fitness of an arrangement of MUs is measured by an interaction integral through which all capsid elements interact with each other via an arbitrary function of distance. A capsid pattern is generated by allowing the correct number of approximately shaped MUs to move dynamically on the sphere, positioning themselves until an extremum of the fitness function is attained. The resulting patterns are largely independent of the details of both the capsomere representation and the interaction function; thus the patterns produced are generic. The simplest useful fitness function is sigma 2, the average square of the mass (or charge) density, a minimum of which corresponds to a "uniformly spaced" MU distribution; to good approximation, the electrostatic free energy of charged capsomeres, calculated from the linearized Poisson-Boltzmann equation, is proportional to sigma 2. With disks as MUs, the model generates the coordinated lattices familiar from the quasi-equivalence theory, indexed by triangulation numbers. Using fivefold MUs, the model generates the patterns observed at different radii within the T = 7 capsid of papilloma and at the surface of SV40; threefold MUs give the T = 4 pattern of Nudaurelia capensis beta virus. In all cases examined so far, the MU orientations are correctly found.

Chiralvs. symmetric states in optical isomers

An extension of a recent model explaining the stability of chiral molecules is presented here. From the comparison between the energy reduction produced by the adoption of a chiral form and that produced by a symmetric superposition of chiral states it is concluded that the true fundamental state of the chiral molecules is the chiral one, which eliminates the well-known «optical-isomers paradox». Also, a discussion on the main differences between the approach used here and the previous attempts of explanation based in the double-well model is made.

Vacuum structure in quantum gravity

The physical interpretation of the Eguchi-Hanson (EH) instanton solution is suggested. This solution describes the tunneling transition which connects vacua with opposite orientations. The diagonal vacuum states are symmetric and antisymmetric superpositions of states with a given orientation. The EH instantons lead to appearance of the induced Einstein term and of the large induced cosmological term in the effective action of the conformal gravity theory.

Precision of linear and angular bisecting of graticules in sighting and measuring telescopes

1. The angular rhombic, square, and zig-zag graticules have large measurement ranges and serve to test precisely coaxiality, linearity, and flatness of products by means of sighting and measuring telescopes type PPS-11 and cathetometers KM-7 at distances up to 30 m. 2. The graticules with linear bisectors and concentric circumferences are limited for precise measurements to values on the telescope graduated barrels not exceeding 2 mm and on the graticule scale up to 1 mm. 3. The confidence errors in sighting graticules with linear and angular bisectors does not exceed 2″ for measuring telescopes type PPS-11 and cathetometers KM-7. 4. The best relationship between the linear and angular graticule bisector widths for a symmetrical superposition upon it of the sighting telescope's cross-hair visible image should be 3∶1.