Trees at an Interface

A lattice tree at an interface between two solvents of different quality is examined as a model of a branched polymer at an interface. Existence of the free energy is shown, and the existence of critical lines in its phase diagram is proven. In particular, there is a line of first order transitions separating a positive phase from a negative phase (the tree being predominantly on either side of the interface in these phases), and a curve of localization–delocalization transitions which separate the delocalized positive and negative phases from a phase where the tree is localized at the interface. This model is generalized to a branched copolymer which is examined in a certain averaged quenched ensemble. Existence of a thermodynamic limit is shown for this model, and it is also shown that the model is self-averaging. Lastly, a model of branched polymers interacting with one another through a membrane is considered. The existence of a limiting free energy is shown, and it is demonstrated that if the interaction is strong enough, then the two branched polymers will adsorb on one another.     

A fluid generalization of membranes

In a certain sense a perfect fluid is a generalization of a point particle. This leads to the question as to what is the corresponding generalization for extended objects. Here the lagrangian formulation of a perfect fluid is much generalized by replacing the product of the co-moving vector which is a first fundamental form by higher dimensional first fundamental forms; this has as a particular example a fluid which is a classical generalization of a membrane; however there is as yet no indication of any relationship between their quantum theories.     

Enhancement of an Instability by Internal Feedbacks in a Plasma

The electron-ion instability is excited in counterstreaming ion beams and plasma system. The instability is a new type of standing oscillations whose wavelength is given by D/n, where D is the distance between boundaries and n is an integer. The amplitude is controlled by a difference between the velocities of the beams, which changes the phase of a feedback loop. The internal feedback is caused by a reflected wave and by a coupling between the boundaries. Temporal evolution of the instability is measured and is found to agree with numerical solutions of the Van der Pol equation including a feedback term. A measured growth rate is proportional to the square of the oscillation amplitude.     

Poisson brackets and the Feynman problem

A derivation of a pair of Maxwell equations which is based on the concept of a Poisson structure on a manifold is given. The idea is geometric in character, and is extended to a generalized algebra. The special case of the dynamics for a particle in a Yang-Mills field is obtained as a consequence of the generalized case.     

On the fluctuation enhanced conductivity of a superconductor: The correct evaluation of the Maki graph

According to Maki, a particular diagram—the Maki graph—gives a contribution to the fluctuation enhanced conductivity of a superconductor which is infinite in the case of a thin film. It is shown that this result is spurious and that it is due to a breakdown of the standard Green function impurity technique. A new method is developed which is strictly based on the Boltzmann equation. It is shown that the temperature dependent contribution of the Maki graph to the conductivity is negligibly small in a dirty metal.     

Design of a Reflective Aspherical Surface of a Compact Beam-Shaping Device

A compact beam-shaping device with a reflective aspherical surface is proposed. The device converts a circular symmetric Gaussian beam from a laser into a uniform distribution on a target plane. The device consists of a laser, a reflective aspherical surface formed on the base plane inclined by 45° against the optical axis, and a spacer. The surface is designed for an optical device used as a transmitter of indoor wireless optical communication, which is one of the promising applications. The designed surface is obtained by approximation using polynomial. Beam shaping of a simulated surface and a uniform intensity distribution on the target plane is obtained. The intensity distribution generated by the surface is numerically simulated and evaluated if the surface is misaligned. It is clarified that the generated distribution is tolerable for the misalignment.     

Focusing of an X-ray spherical wave by a uniaxially bent crystal: Johann scheme and logarithmic spiral

Focusing of a spherical wave in the well-known Johann scheme is considered theoretically. An analytical formula for the size of the crystal bent surface reflecting radiation in the Johann scheme is derived. The intensity distribution near the focus is found. The spherical aberration of the diffracted beam is analyzed. Back scattering is shown to minimize the aberration. Spectral characteristics of an Johann spectrometer are discussed. The focusing of a spherical wave by a crystal bent into a logarithmic spiral is considered. It is shown that the Johann scheme is a specific case of a logarithmic spiral.     

The interaction between a disclination in a nematic liquid crystal and a rubbed surface

For the case of a rubbed surface with a finite anisotropic surface tension, a model is developed for the structure and energy of a surface disclination and of an edge disclination near the surface. It is found that there is an energy barrier against detaching a disclination from the surface, and also that there is a critical distance within which a disclination is attracted, and beyond which it is repelled, by the surface. These properties may provide a measurement of the anisotropy of the surface tension.     

A Minimal Framework for Non-Commutative Quantum Mechanics

Deformation quantisation is applied to ordinary Quantum Mechanics by introducing the star product in a configuration space combining a Riemannian structure with a Poisson one. A Hilbert space compatible with such a configuration space is designed. The dynamics is expressed by a Hermitian Hamiltonian containing a scalar potential and a one-form potential. As a simple illustration, it is shown how a particular type of non-commutativity of the star product is interpretable as generating the Zeeman effect of ordinary Quantum Mechanics.     

Distribution corresponding to classical thermodynamics

A distribution corresponding to classical thermodynamics is constructed. The concept of degrees of freedom is generalized and a concept of temperature-dependent number of collective degrees of freedom is introduced. A relationship between the theory of numbers and mesoscopic physics is established. A geometric interpretation of spinodal as a curve of maximum entropy and as a catastrophe in a quasi-static Caratheodory process is given. A concept of local ideal gas is introduced. The phase transition of fluids to a dispersed system is determined. The distribution obtained is numerically compared with the distribution for a van der Waals gas in the Hougen-Watson diagram.     

Displacement measurement technique for beam kinematics

It is proposed to develop a digital image correlation procedure that is suitable for beams whose kinematics is described by an Euler–Bernoulli hypothesis. As a direct output, the degrees of freedom corresponding to flexural and axial loads are directly measured. The performance of the correlation algorithm is evaluated by using a picture of a cantilever beam experiment. One load level is analyzed with the present algorithm. The latter is validated by comparing the displacement field with that given by a finite element based correlation algorithm. It is also shown that a locally buckled zone is detectable with the present procedure.     

Relativistic motion of a free particle in a uniform gravitational field

The problem of the motion of a free particle in a uniform gravitational field is considered. A relativistic solution based on the assumption that the motion is a consequence of the curvature of spacetime is obtained. The results are compared with various results based on the assumption that spacetime is flat in a region in which the gravitational field is uniform. In the curved spacetime approach, if a particle is projected from a point in a uniform gravitational field, the vertical distance covered by the particle in infinite coordinate time is infinite, but the horizontal distance covered and the elapsed proper time of the particle are finite. If spacetime is assumed to be flat and the gravitational motion of a particle a consequence of a relativistic force proportional to the relative mass of the particle, then the results obtained for the motion of a particle in a uniform gravitational field are close to the curved spacetime results. All other assumptions, including the assumption that the motion of a particle in a uniform gravitational field is equivalent to the motion of a particle in a uniformly accelerating frame of reference, lead to results in serious disagreement with the curved spacetime results.     

Wigner function and the entanglement of a quantized Bessel-Gaussian vortex state of a quantized radiation field

A new kind of quantum non-Gaussian state with a vortex structure,termed a Bessel-Gaussian vortex state,is constructed,which is an eigenstate of the sum of squared annihilation operators a2+b2.The Wigner function of the quantum vortex state is derived and exhibits negativity which is an indication of nonclassicality.It is also found that a quantized vortex state is always in entanglement.And a scheme for generating such quantized vortex states is proposed.     

Quantum Monte Carlo study of hard-core bosons in Creutz ladder with zero flux

The quantum phase of hard-core bosons in Creutz ladder with zero flux is studied.For a specific regime of the parameters(t_x=t_p,t_y0),the exact ground-state is found analytically,which is a dimerized insulator with one electron bound in each rung of the ladder.For the case t_x,t_y,t_p0,the system is exactly studied using quantum Monte Carlo(QMC)method without a sign problem.It is found that the system is a Mott insulator for small t_p and a quantum phase transition to a superfluid phase is driven by increasing t_p.The critical t~c _pis determined precisely by a scaling analysis.Since it is possible that the Creutz ladder is realized experimentally,the theoretical results are interesting to the cold-atom experiments.     

Bose-Einstein condensation and the glassy state

The distinction between a classical glass and a classical liquid is difficult, since both are disordered. The difference is in the fact that a glass is frozen while the liquid is not. In this Letter an equilibrium measure is suggested that distinguishes between a glass and a liquid. The choice of this measure is based on the idea that in a system which is not frozen symmetry under permutation of particles is physically relevant, because particles can be permuted by actual physical motion. This is not the case in a frozen system. In this Letter it is shown how to generalize naturally the quantum mechanical concept of Bose condensed fraction to classical systems in order to distinguish between the glass and the liquid. It is finite in the liquid and zero in the frozen state. The actual value of the condensed fraction in the liquid may serve also as a measure of the glassiness in the liquid.     

Integrability of Characteristic Hamiltonian Systems on Simple Lie Groups with Standard Poisson Lie Structure

Phase space of a characteristic Hamiltonian system is a symplectic leaf of a factorizable Poisson Lie group. Its Hamiltonian is a restriction to the symplectic leaf of a function on the group which is invariant with respect to conjugations. It is shown in this paper that such a system is always integrable.     

Multiple-reflection effects in hadron-nucleus scattering: (I). Cluster expansion of the optical potential

A basic assumption underlying the high-energy hadron-nucleus optical potential is that no target nucleon is struck more than once. Although this condition is satisfied at high energy, such is not the case in the vicinity of medium-energy resonances, where the amplitude for the projectile to undergo multiple reflections between two target nucleons is quite large. As a remedy for this problem, the multiple-scattering series is rearranged such that the optical potential can be expressed as a cluster expansion. The lowest order optical potential is modified by a two-body cluster term, which is a sum of all possible reflections of the projectile between a pair of target nucleons. This term is evaluated for a model potential within the formalism of Foldy and Walecka: it is substantially smaller than the contribution of a single reflection, and its overall effect is small under certain additional restrictions. If the independent-pair picture of nuclei is valid, then the three-body cluster term may be small, and the lowest order Glauber optical potential can provide a self-consistent picture of hadron-nucleus interactions, even though a term-by-term expansion of the multiple-scattering series does not provide such assurance.     

On the width of a ray

Consistent with earlier work by Kravtsov and Orlov, a simple general expression for the width of a Fresnel zone deltar(F) in a smooth inhomogeneous environment is derived; this is the diffractive contribution to the width of a ray. In a stratified environment at long range, the general Fresnel zone width expression is shown to reduce approximately to one that is proportional to [equation in text] where alpha is the ray stability parameter, sigma is the acoustic frequency, r is the range from the source to the field point of interest, and R is the source to receiver range. In a stratified environment on which a weak small-scale perturbation is superimposed, deterministic rays in the background environment that connect fixed end points break up into bundles of micromultipaths at moderate to long range and a second, scattering-induced, contribution deltar(s) to the width of a ray must be considered. It is shown that deltar(s) is proportional to /alpha/r(R-r) and argued that in a micromultipathing environment the total effective width of a background ray is deltar(tot)= [equation in text] . Theoretical predictions are shown to agree well with travel-time sensitivity kernel calculations.     

Detailed field model for DH stripe lasers

The field problem for DH stripe lasers is solved, using a two-dimensional model; the field variation perpendicular to the junction plane is found from a slab model, whereas the transverse variation is calculated using a method applicable to any complex permittivity profile. The origin of transverse variations in the permittivity is described by including current spreading, temperature variations and the carrier profile. The permittivity is used directly and not fitted by a parabola or a step. The fact that a large fraction of the intensity may be propagating in then-andp-layers, is taken into account by introduction of an effective permittivity. The model is applied to a practical example, and the threshold current is found as a function of active-layer thickness and stripe width. It is described how the model can be used both below and above the threshold.