Exact exponent for the number of persistent spins in the zero-temperature dynamics of the one-dimensional Potts model

For the zero-temperature Glauber dynamics of theq-state Potts model, the fractionr(q, t) of spins which never flip up to timet decays like a power lawr(q, t)t ^–(q) when the initial condition is random. By mapping the problem onto an exactly soluble one-species coagulation model (A+AA) or alternatively by transforming the problem into a free-fermion model, we obtain the exact expression of (q) for all values ofq. The exponent (q) is in general irrational, (3)=0.53795082..., (4)=0.63151575..., ..., with the exception ofq=2 andq=, for which (2)=3/8 and ()=1.     

Measurement of the2H(d, γ)4He reaction at intermediate excitation energies

The²H(d, )⁴He differential cross section was measured at deuteron laboratory energies of 20, 24, and 28 MeV between _cm=45° and _cm=135°. AtE _d =28 MeV a complete angular distribution was determined and fitted with Legendre polynomials. The ratioR=d/d (_cm=90°)/d/d (_cm=135°) was measured for each deuteron energy.     

Homogeneous and hypersurface-homogeneous shear-free perfect fluids in general relativity

Shear-free, general-relativistic perfect fluids are investigated in the case where they are either homogeneous or hypersurface-homogeneous (and, in particular, spatially homogeneous). It is assumed that the energy density and the presurep of the fluid are related by a barotropic equation of statep = p(), where +p 0. Under such circumstances, it follows that either the fluid's volume expansion rate or the fluid's vorticity (i.e., rotation) must vanish. In the homogeneous case, this leads to only two possibilities: either = = 0 (the Einstein static solution), or 0, = 0 (the Gödel solution). In the hypersurface-homogeneous case, the situation is more complicated: either = 0, 0 (as exemplified,inter alia, by the Friedmann-Robertson-Walker models), or 0, = 0 (which pertains, for example, in general stationary cylindrically symmetric fluids with rigid rotation, or = = 0 (as occurs for static spherically symmetric solutions). Each possibility is further subdivided in an invariant way, and related to the studies of other authors, thereby unifying and extending these earlier works.     

Inductive limit automorphisms of the irrational rotation algebra

It is shown that the flip automorphismUU ^*,VV ^* of the irrational rotation algebra A is an inductive limit automorphism. Here, the algebra A is generated by unitariesU, V satisfyingVU=e²ⁱ UV, where is an irrational number. Recently, Elliott and Evans proved that A can be approximated by unital subalgebras isomorphic to a direct sum of two matrix algebras over , the algebra of continuous functions on the unit circle. This is the central result which they used to obtain their structure theorem on A; namely, that A is the inductive limit of an increasing sequence of subalgebras each isomorphic to a direct sum of two matrix algebras over . In their proof, they devised a subtle construction of two complementary towers of projections. In the present paper it is shown that the two towers can be chosen so that each summand of their approximating basic building blocks is invariant under the flip automorphism and, in particular, that the unit projection of the first summand is unitarily equivalent to the complement of the unit of the second by a unitary which is fixed under the flip. Also, an explicit computation of the flip on the approximating basic building blocks of A is given. Further, combining this result along with others, including a theorem of Su and a spectral argument of Bratteli, Evans, and Kishimoto, a two-tower proof is obtained of the fact established by Bratteli and Kishimoto that the fixed point subalgebra B (under the flip) is approximately finite dimensional. Also used here is the fact that B has the cancellation property and is gifted with four basic unbounded trace functionals. The question is raised whether other finite order automorphisms of A (arising from a matrix in SL(2,)) are inductive limit automorphisms - or evenalmost inductive limit automorphisms in the sense of Voiculescu.Research partly supported by NSERC grant OGP0169928     

States of one-dimensional Coulomb systems as simple examples of θ vacua and confinement

The one-dimensional Coulomb system is known to have equilibrium states with nonvanishing electric field. These states are shown here to be analogous, and related, to the vacua which have been discussed for gauge theories in two or more space-time dimensions. The system exhibits confinement of fractional charges, which we dicuss with the purpose of offering a simple example of the-vacua phenomenology. Precise relations and connections between one-dimensional Coulomb gases and two-dimensional Abelian gauge theories, and quantum-mechanical matter systems, are discussed.Supported in part by National Science Foundation Grant PHY-2825390 A01.     

A relation between a.c. spectrum of ergodic Jacobi matrices and the spectra of periodic approximants

We study ergodic Jacobi matrices onl ²(Z), and prove a general theorem relating their a.c. spectrum to the spectra of periodic Jacobi matrices, that are obtained by cutting finite pieces from the ergodic potential and then repeating them. We apply this theorem to the almost Mathieu operator: (H _{, ,} u)(n)=u(n+1)+u(n–1)+ cos(2n+)u(n), and prove the existence of a.c. spectrum for sufficiently small , all irrational 's, and a.e. . Moreover, for 0<2 and (Lebesgue) a.e. pair , , we prove the explicit equality of measures: |_ac|=||=4 –2.Work partially supported by the US-Israel BSF     

Zero-Dimensional Spectral Measures for Quasi-Periodic Operators with Analytic Potential

We prove that for quasiperiodic operators with potential V(n)=f(+n), f analytic, the spectral measures are zero-dimensional for large, any irrational . It extends a result of Jitomirskaya and Last to the case of any analytic f.     

Isotropic spherical coordinates

The method of using regularization to analyze singularities is applied to the Schwarzschild metric in isotropic spherical coordinates (3). It is found that there arises a singularity at the gravitational radius which does not satisfy the conditions of physical realizability (T =T ,T ₀ ⁰ =T =0). Consequently, this metric cannot be considered as corresponding to pure vacuum.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 84–87, April, 1987.     

Some experimental data about the two contributions to magnetoresistance for n-type silicon crystal at 125 K

The transverse magnetoresistance (MR) was measured versus magnetic field strengthB at different rotational angles between the directions of bothB and currentI for n-type silicon crystal with charge carrier concentration of 1·8×10¹⁵cm^–3. The direction of the current through the two samples was chosen so that the angles between the current vector and [100] crystallographic axis were 50° and 70°, respectively. These measurements were done under weak electric and magnetic fields atT=125 K. It was found that the MR exhibits two types of anomalous effects, one of them at two opposite directions ofB at different, and the other at the same angles, when=50° and=70°. This shows that the anomalous behaviour of MR is not onlyB and dependent, but depends also on the current direction. Also the values ofB which are separated between the negative and positive parts of MR curves at the same depend on the magnitude of. These results may be attributed to the anomalous motion of charge carriers ink-space as a result of deviation of current direction from the symmetry axis.     

Fatigue Crack Propagation in Copper Bicrystals Having the Grain Boundaries of Σ3 Vicinal Domain

The criterion for occurrence of intergranular fatigue cracking in copper has been investigated from the view point of both the grain boundary (GB) character and the cyclic deformation property of constituent grains. The copper bicrystals were prepared to have several orientation relationships close to 3(1 1 1) coherent twin (3 vicinal domain) so as to change the GB character rapidly with increasing deviation angles || from the 3 relation. These bicrystals were shaped to single-edge-notched specimens in which a GB plane was perpendicular to the tensile axis. The fatigue crack propagation tests were carried out in air at room temperature. The specimens having deviation angles || less than 3° involved no intergranular fatigue cracking. When the || values were ranged from 3° to 5°, the ratio of the intergranular cracking increased. In the specimens having the || values more than 9°, the intragranular cracking became predominate again. The increase in the intergranular cracking with increasing deviation angle at the || values less than 5° could be understood in terms of the increasing GB susceptibility to the GB damage due to air environment. On the other hand, the intragranular cracking at the || values more than 9° could be attributed to the formation of the persistent slip bands in the constituent grains and subsequent crack propagation preferentially along them.     

Thermodynamic Properties of a Simple Model of Like-Charged Attracting Rods

We study the thermodynamic properties of a simple model for the possible mechanism of attraction between like charged rod-like polyions inside a polyelectrolyte solution. We consider two polyions in parallel planes, with Z charges each, in a solution containing multivalent counterion of valence . The model is solved exactly for Z13 for a general angle between the rods and supposing that n counterions are condensed onto each polyion. The free energy has two minima, one at =0 (parallel rods) and another at =/2 (perpendicular rods). The stability of the parallel and perpendicular configurations is analyzed.     

Three-Mode Entangled State Representation of Continuum Variables and Optical Four-Wave Mixing

We establish a new three-mode entangled state representation , of continuum variables, which make up a complete set. Using optical four-wave mixing and a beam splitter transform we can prepare , . Based on , a new number-difference--operational-phase uncertainty relation is established and the corresponding squeezing dynamics is discussed.     

On the global behaviour of symmetric Skyrmions

It is shown that the chiral angle, (r), of the hedgehog (symmetric) Skyrmions with an arbitrary baryon number, is a strictly decreasing or increasing function. For large values of r>0, (r) is strictly convex or concave. As r, (r) and (r) approach their limit values at the rate Or ^- for any (0,2).     

Zero measure spectrum for the almost Mathieu operator

We study the almost Mathieu operator: (H _{, ,} u)(n)=u(n+1)+u(n-1)+ cos (2n+)u(n), onl ² (Z), and show that for all ,, and (Lebesgue) a.e. , the Lebesgue measure of its spectrum is precisely |4–2|. In particular, for ||=2 the spectrum is a zero measure cantor set. Moreover, for a large set of irrational 's (and ||=2) we show that the Hausdorff dimension of the spectrum is smaller than or equal to 1/2.Work partially supported by the GIF     

On the uniqueness of static perfect-fluid solutions in general relativity

Following earlier work of Masood-ul-Alam, we consider a uniqueness problem for non-rotating stellar models. Given a static, asymptotically flat perfectfluid spacetime with barotropic equation of state (p), and given another such spacetime which is spherically symmetric and has the same (p) and the same surface potential: we prove that both are identical provided (p) satisfies a certain differential inequality. This inequality is more natural and less restrictive than the conditions required by Masood-ul-Alam.Supported by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich, project P-7197     

Non-commutative spheres

LetA be the irrational rotation algebra, i.e. theC ^*-algebra generated by two unitariesU, V satisfyingVU=e ²ⁱ UV, with irrational, and consider the fixed point subalgebraB under the flip automorphismUU ^–1,VV ^–1. We prove thatB is an AF-algebra.Dedicated to Professor Huzihiro Araki on the occasion of his 60'th birthday     

Branched polymers in a wedge geometry in three dimensions

We investigate the statistical and dimensional properties of uniform star polymers attached by the branching vertex of degreef in a wedge geometry in three dimensions and described by the wedge angles and. We show that the growth constant is equal to ^f , where is the self-avoiding walk limit. Thef and (, ) dependences of the corresponding critical exponent _f (, ) are studied using Monte Carlo techniques. In the casef=1, our results are compared with existing predictions obtained from series expansion and renormalization group methods. We have also estimated the amplitudes for the mean square radius of gyration and the mean square end-to-end branch length. Our results for the ratio of the mean square radius of gyration of anf-star to that of a linear polymer of the same degree of polymerization attached in a similar wedge, and the analogous ratio for the mean square end-to-end branch length, are consistent with these ratios being lattice-independent quantities.     

Comments on time-differential perturbed angular correlation functions for static axial electric quadrupole interaction

A technique of computer aided derivation of analytical formulas has been applied to perturbed- angular correlation functions in case of the static axial electric quadrupole interaction in a single crystal. An arbitrary orientation of the EFG symmetry axis with respect to the detectors was considered. Explicit formulas for correlation functions in commonly used detector configurations= and=/2 have been obtained. Small corrections to the previously published formulas have been suggested.     

Conical Quantum Billiard

The conical quantum billiard is examined. Wavefunctions are obtained in an open domain which excludes the polar axis, involving associated Legendre functions of the first and second kind. The first excited state is three-fold degenerate. One wavefunction is nonnodal. The nodal surface of either of the other states is a bisecting plane which includes the axis of the cone. These nodal properties maintain for 0 < ₀ /2, where ₀ is the half vertex angle of the cone. At > /2, the nonnodal state acquires a nodal at = /2. Thus, as with the image problem in two dimensions, there is critical vertex angle about which the nodal structure of one of the eigenstates suffers a topological change. This nodal transition is accompanied by a geometrical transformation of the cone from convex to concave. Solutions obtained are valid for all conical quantum billiards to the limit of the spherical quantum billiard excluding the polar axis.     

On the concept of “nonlocalization” associated with the gravitational field

The concept of nonlocalization associated with the gravitational field, which is carried by the internal variable () annexed to each point, is considered in connection with the geometrical theory of gauge fields. Two concrete examples of nonlocalization are proposed by taking as a vector and a spinor, respectively.