Large charge fluctuations in classical Coulomb systems

The typical fluctuation of the net electric chargeQ contained in a subregion of an infinitely extended equilibrium Coulomb system is expected to grow only as S, whereS is the surface area of. For some cases it has been previously shown thatQ/S has a Gaussian distribution as ¦¦. Here we study the probability law for larger charge fluctuations (large-deviation problem). We discuss the case when both ¦¦ andQ are large, but now withQ of an order larger than S. For a given value ofQ, the dominant microscopic configurations are assumed to be those associated with the formation of a double electrical layer along the surface of. The probability law forQ is then determined by the free energy of the double electrical layer. In the case of a one-component plasma, this free energy can be computed, for large enoughQ, by macroscopic electrostatics. There are solvable two-dimensional models for which exact microscopic calculations can be done, providing more complete results in these cases. A variety of behaviors of the probability law are exhibited.     

Focusing effects in the synthetic aperture radar imaging of ocean waves

We derive the properties of the image obtained for an ocean wave whose cross-section may be given byσ _w(x,y,y) and surface profile byh(x,y,t).σ _w andh are functions representing the wave phenomena, but whose exact properties are determined by the ocean wave surface properties, for an ocean wavelength ofλ _w, heightH, and orbital frequency ω. We calculate the effect of defocusing of the wave image due to its temporal motion, and derive both the resolution of the radar system if no focus compensation is provided in the processor and the necessary distance the azimuth telescope has to be moved to provide diffraction-limited imaging. We illustrate these results for data taken by the JPL synthetic aperture radar over Hurricane Gloria on September 30, 1976, and the ERIM radar over Marineland, Florida, on December 15, 1975. This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract NAS 7-100, sponsored by the special programs office and the Seesat program office under Mr. F.C. Williams and Mr. S.W. McCandless of the National Aeronautics and Space Administration.     

Long range interactions between some charged solitons

A procedure is offered for evaluating the forces between classical, charged solitons at large distances. This is employed for the solitons of a complex, scalar two-dimensional field theory with a U(1) symmetry, that leads to a conserved chargeQ. These forces are the analogues of the strong interaction forces. The potential,U(Q, R), is found to be attractive, of long range, and strong when the coupling constants in the theory are small. The dependence ofU(Q, R) onQ, the sum of the charges of the two interacting solitons (Q will refer to isospin in the SU(2) generalisation of the U(1) symmetric theory) is of importance in the theory of strong interactions; group theoretical considerations do not give such information. The interaction obtained here will be the leading term in the corresponding quantum field theory when the coupling-constants are small.     

Algebras in higher-dimensional statistical mechanics - the exceptional partition (mean field) algebras

We determine the structure of the partition algebraP _n(Q) (a generalized Temperley-Lieb algebra) for specific values ofQ , focusing on the quotient which gives rise to the partition function ofn siteQ-state Potts models (in the continuousQ formulation) in arbitrarily high lattice dimensions (the mean field case). The algebra is nonsemisimple iffQ is a nonnegative integer less than 2n-1. We determine the dimension of the key irreducible representation in every specialization.Work supported by the Packard Foundation.     

Running coupling: does the coupling between dark energy and dark matter change sign during the cosmological evolution?

In this paper we put forward a running coupling scenario for describing the interaction between dark energy and dark matter. The dark sector interaction in our scenario is free of the assumption that the interaction term Q is proportional to the Hubble expansion rate and the energy densities of dark sectors. We only use a time-variable coupling b(a) (with a the scale factor of the universe) to characterize the interaction Q. We propose a parametrization form for the running coupling b(a)=b ₀ a+b _e (1−a) in which the early-time coupling is given by a constant b _e , while today the coupling is given by another constant, b ₀. For investigating the feature of the running coupling, we employ three dark energy models, namely, the cosmological constant model (w=−1), the constant w model (w=w ₀), and the time-dependent w model (w(a)=w ₀+w ₁(1−a)). We constrain the models with the current observational data, including the type Ia supernova, the baryon acoustic oscillation, the cosmic microwave background, the Hubble expansion rate, and the X-ray gas mass fraction data. The fitting results indicate that a time-varying vacuum scenario is favored, in which the coupling b(z) crosses the noninteracting line (b=0) during the cosmological evolution and the sign changes from negative to positive. The crossing of the noninteracting line happens at around z=0.2–0.3, and the crossing behavior is favored at about 1σ confidence level. Our work implies that we should pay more attention to the time-varying vacuum model and seriously consider the phenomenological construction of a sign-changeable or oscillatory interaction between dark sectors.     

Noncommutative Supergeometry and Duality

We introduce a notion of Q-algebra that can be considered as a generalization of the notion of Q-manifold (a supermanifold equipped with an odd vector field obeying {Q,Q} =0). We develop the theory of connections on modules over Q-algebras and prove a general duality theorem for gauge theories on such modules. This theorem contains as a simplest case SO(d,d, Z)-duality of gauge theories on noncommutative tori.     

A BRST-like operator for space with zero curvature but non-zero torsion tensor

A new type of BRST-like operatorQ has been constructed for spaces with zero Riemann curvature tensor but with non-zero torsion. It is invariant under local coordinate transformation, and its proof depends upon the validity of the first Bianchi identity. Also, there exists a supersymmetry associated withQ. Finally, the cohomology induced byQ has been investigated.     

Chaotic properties of multipoint correlation functions of an Ising model with long-range interactions on the Sierpiński—Gasket lattice

A class of multispin correlation functions of an Ising model with ferromagnetic nearest neighbor interactionsK and constant (distance-independent) long-range interactionsQ ₁=Q,l=1,2,..., on the Sierpiski-gasket lattice is considered. Using an exact method for calculating thermodynamic functions of hierarchically constructed Ising systems, it is shown that, for a set of values ofQ and for almost all values ofK, someM _k-spin correlation functions, whereM _k=3 ^k +3 withk=1,2,...,n andn=1,2,... being the order of lattice construction, change chaotically asn, k, and therebyM _k increase to infinity. Accordingly, in the thermodynamic limit, these correlation functions prove to be nonanalytic for appropriate values ofQ andK. SinceM _k-point correlation functions withk being finite, i.e., correlation functions involving finite numbers of spins, remain analytic asn tends to infinity, there is a smooth crossover between analytic properties of correlation functions of the two types.     

A comparison of high statistics measurements of the proton and deuteron structure functions

We present a detailed comparison of high statistics measurements of the structure functionF ₂(x, Q ²) from deep inelastic scattering of charged leptons on hydrogen and deuterium targets. It is found that the CERN results from the EMC and BCDMS Collaborations are both compatible with the lowQ ² electron scattering results from SLAC after an adjustment of the relative normalizations. We discuss the residual discrepancy between EMC and BCDMS which persists after this renormalization and find that the SLAC data are in better agreement with the steeperx dependence of the BCDMS results. A phenomenological parametrization ofF ₂(x, Q ²) is given.     

Invariant states and conditional expectations of the anticommutation relations

The groupG of unitary elements of a maximal abelian von Neumann algebra on a separable, complex Hilbert spaceH acts as a group of automorphisms on the CAR algebraA(H) overH. It is shown that the set ofG-invariant states is a simplex, isomorphic to the set of regular probability measures on aw*-compact setS ofG-invariant generalized free states. The GNS Hilbert space induced by an arbitraryG-invariant state onA(H) supports a *-representation ofC(S); the canonical map ofA(H) intoC(S) can then be locally implemented by a normal,G-invariant conditional expectation.     

Measurement of electric quadrupole moments of neutron-rich nuclei14B and15B

The experimental study of nuclear moments of several neutron-rich nuclei, using the phenomenon of ejectile spin polarization in the projectile fragmentation reaction, is reported. The spin-polarized fragments¹⁴B and¹⁵B were produced in the fragmentation of¹⁸O projectiles on a Nb target at 64.7 MeV/u. They were implanted into a Mg single crystal, and the quadrupole momentsQ were determined by the-NMR method. The results, ¦Q(¹⁴B)¦ =29.84 ±0.75 mb and ¦Q(¹⁵B)¦=38.01 ±1.08 mb, are compared with theoretical models. Shell model calculations in a 0 model space, using effective charges commonly accepted in this mass region, predict values about 40% larger than the experimentalQ(¹⁵B). Agreement is obtained when a much smaller effective charge for neutrons is employed. The method was also applied to the measurement of the magnetic moments of¹⁷N and¹⁷B. The result reveals an important contribution of configurations with excess neutrons coupled to formJ =2⁺.     

Entropy dissipation and moment production for the Boltzmann equation

LetH(f/M)=flog(f/M)dv be the relative entropy off and the Maxwellian with the same mass, momentum, and energy, and denote the corresponding entropy dissipation term in the Boltzmann equation byD(f)=Q(f,f) logf dv. An example is presented which shows that |D(f)/H(f/M)| can be arbitrarily small. This example is a sequence of isotropic functions, and the estimates are very explicitly given by a simple formula forD which holds for such functions. The paper also gives a simplified proof of the so-called Povzner inequality, which is a geometric inequality for the magnitudes of the velocities before and after an elastic collision. That inequality is then used to prove that f(v) |v|^s dt<C(t), wheref is the solution of the spatially homogeneous Boltzmann equation. HereC(t) is an explicitly given function dependings and the mass, energy, and entropy of the initial data.     

Hypergeometric series in a series expansion of the directed-bond percolation probability on the square lattice

The asymmetric directed-bond percolation (ADBP) problem with an asymmetry parameterk is introduced and some rigorous results are given concerning a series expansion of the percolation probability on the square lattice. It is shown that the first correction term,d _n,1 (k) is expressed by Gauss' hypergeometric series with a variablek. Since the ADBP includes the ordinary directed bond percolation as a special case withk=1, our results give another proof for the Baxter-Guttmann's conjecture thatd _n,1(1) is given by the Catalan number, which was recently proved by Bousquet-Mélou. Direct calculations on finite lattices are performed and combining them with the present results determines the first 14 terms of the series expansion for percolation probability of the ADBP on the square lattice. The analysis byDlog Padé approximations suggests that the critical value depends onk, while asymmetry does not change the critical exponent of percolation probability.     

Production rate and decay lifetime measurements ofBs0 mesons at LEP usingDs and? mesons

The study of the properties of inclusive production ofD _s mesons and of events in which a and a muon are present in the same jet provides two independent measurements of the probability,f _s ^w , for a heavy quark to hadronize into a strangeB orD meson. The data sample analysed corresponds to 243,000 hadronicZ ⁰ decays. The combined value of these measurements isf _s ^w =0.19±0.06±0.08. From the flight distance distributions ofD _s and of (-lepton) secondary vertices, with the lepton emitted at high transverse momentum relative to the jet axis, two values are obtained for theB _s ⁰ meson lifetime. Combining these measurements with a previous result based on the study ofD _s- events, theB _s ⁰ meson lifetime is measured to be: 0.96±0.37 ps.     

The low temperature quadrupole orientation of103Ru in ruthenium

The quadrupole frequencyv _Q =e ² qQ/h of¹⁰³Ru (Z=44,N=59) in a ruthenium single crystal has been measured using the technique of low temperature quadrupole orientation to bev _Q (¹⁰³RuRu)=−14.7(5) MHz. Temperatures below 2 mK were reached in this experiment using a PrNi₅ demagnetization stage attached to a³He−⁴He dilution refrigerator. Using the measured magnitude of the RuRu electric field gradient (EFG) at low temperatures |eq(RuRu)|=1.02(3)×10¹⁷ V.cm⁻² [1] and adopting the sign ofeq(RuRu) to be negative from systematics, this result yields a value for the ground-state electric quadrupole moment of¹⁰³Ru ofQ(¹⁰³Ru)=+0.59(2) b. This moment may be interpreted using the weak coupling model of de-Shalit [2]. A Korringa constant for¹⁰³RuRu ofC _K=39(6) Ks was measured in this experiment. Taking advantage of a small iridium contamination of the ruthenium single crystal, the quadrupole moment of the¹⁹²Ir ground state was determined to beQ(¹⁹²Ir)=+2.12(25) b. The sign of the IrRu electric field gradient was found to be negative as a result of this work.     

Mass spectral condition for leptons and quarks

Consideration is given to the mass spectral conditiona(a,_m)a =a _m, wherea is the annihilation operator forQ=–1 states in the Hilbert space of leptons and quarks anda _m is the commutator resolvent ofa with respect tom. It is observed that this spectral condition, which simply requires a to be a congruent automorph ofa _m , implies that the third-, fourth-, and fifth-generationQ=-1 leptons have the masses 1788.03 MeV, 42.1649 GeV, and 1.33422 TeV, respectively. With the assumption that the mass spectral condition also holds forQ=0 states in the Hilbert space, one obtains new theoretical upper and lower bounds on the neutrino masses.     

Quasi-free “second quantization”

Araki and Wyss considered in 1964 a mapAQ(A) of one-particle trace-class observables on a complex Hilbert-space into the fermionC*-algebraU() over . In particular they considered this mapping in a quasi-free representation.We extend the mapAQ(A) in a quasi-free representation labelled byT, 0TI, to allAB()_sa such that tr(T A(1–T)A)< withQ(A) now affiliated with the algebra. This generalizes some well-known results of Cook on the Fock-representationT=0.     

Spin susceptibilities for the Hubbard model in a band approach

The properties of spin excitations superposed on a uniform ground state with antiferromagnetic (or spiral) spin structure are studied in a 2D Hubbard model. Expressions are derived for the spin susceptibility in the random phase approximation (RPA) using split Hubbard bands as a zeroth approximation. The calculated collective modes with dispersion ω(Q)=c|Q−(π, π)| near Q∼(π, π) reproduce well the characteristics of the spin excitations observed in undoped cuprates. For doped systems with an antiferromagnetic structure of the ground state, calculating X″(Q,ω→0) gives the same mode with a peak at Q∼(π, π), regardless of the type of Fermi surface. It is shown that in doped systems with a spiral ground state spin structure, X″(Q,ω→0) peaks occur with incommensurate quasimomenta Q that are coupled to the spirality vector. Zh. éksp. Teor. Fiz. 116, 1058–1080 (September 1999)     

Gauge theory in deformed $$ \mathcal{N} $$ = (1, 1) superspace

We review the non-anticommutative Q-deformations of = (1, 1) supersymmetric theories in four-dimensional Euclidean harmonic superspace. These deformations preserve chirality and harmonic Grassmann analyticity. The associated field theories arise as a low-energy limit of string theory in specific backgrounds and generalize the Moyal-deformed supersymmetric field theories. A characteristic feature of the Q-deformed theories is the half-breaking of supersymmetry in the chiral sector of the Euclidean superspace. Our main focus is on the chiral singlet Q-deformation, which is distinguished by preserving the SO(4) ∼ Spin(4) “Lorentz” symmetry and the SU(2) R-symmetry. We present the superfield and component structures of the deformed = (1, 0) supersymmetric gauge theory as well as of hypermultiplets coupled to a gauge superfield: invariant actions, deformed transformation rules, and so on. We discuss quantum aspects of these models and prove their renormalizability in the Abelian case. For the charged hypermultiplet in an Abelian gauge superfield background we construct the deformed holomorphic effective action. The text was submitted by the authors in English.