Quantum Physics

Imaging with a layered superlens is a spatial filtering operation characterized by the point spread function (PSF). We show that in the same optical system the image of a narrow sub-wavelength Gaussian incident field may be surprisingly dissimilar to the PSF, and the width of PSF is not a straightforward measure of resolution. FWHM or std. dev. of PSF give ambiguous information about the actual resolution, and imaging of objects smaller than the FWHM of PSF is possible. A multiscale analysis of imaging gives good insight into the peculiar scale-dependent properties of sub-wavelength imaging.

Optogenetics is an innovative technique for optical control of cells. This field has exploded over the past decade or so and has given rise to great advances in neuroscience. A variety of applications both from the basic and applied research have emerged, turning the early ideas into a powerful paradigm for cell biology, neuroscience and medical research. This review aims at highlighting the basic concepts that are essential for a comprehensive understanding of optogenetics and some important biological/biomedical applications. Further, emphasis is placed on advancement in optogenetics-associated light-based methods for controlling gene expression, spatially-controlled optogenetic stimulation and detection of cellular activities.

We propose a non-deterministic CNOT gate based on a quantum cloner, a quantum switch based on all optical routing of single photon by single photon, a quantum-dot spin in a double-sided optical microcavity with two photonic qubits, delay lines and other linear optical photonic devices. Our CNOT provides a fidelity of 78% with directly useful outputs for a quantum computing circuit and requires no ancillary qubits or electron spin measurements.

It was proved that balance equations for systems with corpuscular structure can be derived if a kinematic description by piece-wise analytic functions is available . This article presents a rigorous derivation of an one-dimensional hydrodynamic model for the stock price evolution. The kinematic description is given by a set of time functions describing the evolution of the stock price.

We theoretically study the stacked optical transients generated from a series of square pulses passing through a cold atomic ensemble. Using the hybrid analysis and fast Fourier transform, we identify the stacked coherent transients [Europhys. Lett. 4, 47 (1987)] as optical precursors. With slow-light and electromagnetically induced transparency, we obtain nearly 700% transmitted intensity at the transient spikes resulting from the interference between the delayed main field and the stacked optical precursors.

The recent interest in precursors has been fuelled by the possibility of using them for the efficient transmission of information through absorbing media at radio or optical frequencies. Here we demonstrate that the low attenuation experienced by the Brillouin precursor is attributed to the inherently low absorption of dispersive media near DC, a characteristic already exploited with communications systems using the extremely low frequency (ELF) band. Pulses, regardless of their temporal width and carrier frequency, always obey Beer's law as long as they propagate in the linear time invariant regime. We conclude with an FDTD simulation of the Maxwell-Bloch equations that shows how optical coherent bleaching effects, which take place in the linear time variant regime of the Lorentz oscillator model, can cause sustained deviations from Beer's law over relatively long distances of water.

We study optical precursors when a step-modulated pulse propagates through collections of cold potassium atoms. Here, we expand on our previous report on the direct observation of optical precursors [PRL 96, 143901, (2006)], giving more experimental details and extending our work to the case of an off-resonance carrier frequency. The transmitted pulse consists of a severalnanosecond-long spike occurring immediately after the front. The spike begins with nearly 100% transmission, consisting of both the Sommerfeld and Brillouin precursors, and subsequently decays to a constant value expected from Beer's Law of absorption. For the case of an off-resonance carrier frequency, we observe interference between the optical precursors and the main signal, causing modulation due to the detuning of the carrier frequency from the medium resonance frequency. Precursors may be useful for imaging applications requiring penetrating optical radiation, such as in biological systems, or in optical communication systems.

We have performed an isospin analysis of single-pion production processes in antiprotonnucleon scattering from threshold to 2.90 GeV/c. Reactions used are pp-+Bprr", iippn-and Bn-$ppn-. Results show that u 1, the total 2 = 1 cross section, rises rapidly from threshold to reach a broad maximum around 2.5 GeV/c and o D, the Z = 0 cross section, rises from threshold and continues on a linearly rising trend at least up to 2.90 GeV/c. In the region of 2.9 GeV/c, crl and o0 have comparable values, thus suggesting that considerable amount of Z= 3 Nz and !&t states is produced even in this low momentum region. We further determine that single pion production processes are not the source of the a0 (2375,190) enhancement observed in the pp and Bd total cross sections and may account for as much as 25 f 8% of the z1 (2350,140) enhancement.

• The temporal series of the volatility and the return for the model is analyzed. • The distribution of the returns is verified and the power of the long tail distribution gotten. • The Hurst index is calculated using the rescaled range analysis.

Evaluation of link prediction methods is a hard task in very large complex networks because of the inhibitive computational cost. By setting a lower bound of the number of common neighbors (CN), we propose a new framework to efficiently and precisely evaluate the performances of CN-based similarity indices in link prediction for very large heterogeneous networks. Specifically, we propose a fast algorithm based on the parallel computing scheme to obtain all the node pairs with CN values larger than the lower bound. Furthermore, we propose a new measurement, called selfpredictability, to quantify the performance of the CN-based similarity indices in link prediction, which on the other side can indicate the link predictability of a network.

Structural controllability, which is an interesting property of complex networks, attracts many researchers from various fields. The maximum matching algorithm was recently applied to explore the minimum number of driver nodes, where control signals are injected, for controlling the whole network. Here we study the controllability of directed Erdös-Rényi and scale-free networks under attacks and cascading failures. Results show that degree-based attacks are more efficient than random attacks on network structural controllability. Cascade failures also do great harm to network controllability even if they are triggered by a local node failure.

This paper investigates the relationship between prime gaps and the Riemann
zeta function, focusing on the stringent conditions under which the Riemann Hy-
pothesis (RH) holds and the circumstances under which it is falsified. Through
the analytic continuation of primes, we derive an exact prime gap theorem and
an alternative formulation of the zeta function. A key result reveals that a zero is
generated independently of 𝑠
, providing a potential counterexample to RH. This
challenges the assumption that all nontrivial zeta zeros lie on the critical line
ℜ(𝑠)=1
2 . Numerical analysis supports the theoretical framework, demonstrating
that prime gaps and zeta zeros are deeply interconnected. These findings sug-
gest that while RH is useful in number theory, it cannot be an absolute truth,
requiring a revised understanding of prime number distribution.

C. Cálculo analítico de la función de agrupamiento a dos puntos para N = 2 v des y por otro se realizará el tradicional análisis de fluctuaciones espectrales con el objetivo de, relacionando ambos enfoques, construir un modelo de colectividades tridiagonales que reproduzca la estadística espectral que las caracteriza en caos cuántico.

In the presented study, firstly the microstructural features of the PVP-Cu 2 Te interlayer was evaluated by employing XRD and SEM approaches and the PVP-Cu 2 Te is formed on the p-Si wafer. Secondly, both the forward and reverse biases current-voltage and capacitance/conductance-frequency characteristics of the prepared Al/p-Si (MS) and Al/(PVP-Cu 2 Te)/p-Si (MPS) structures have been analyzed to compare the organic interlayer effect. Basic electrical parameters for reverse-saturation current (I o ), ideality factor (n), and zero-bias BH (Φ Bo ) were calculated as 2.3 × 10 -6 A, 2.38, and 0.576 eV for MS and 2.2 × 10 -8 A, 1.85, and 0.692 eV for MPS structures, respectively. Apparently, Io value for MPS is almost two order lower than MS structure. Besides, organic interlayer usage enhances the performance of MPS structure in respect of high BH, high-rectifying ratio, lowseries (R s ) resistance, and low-leakage current. When the experimental and theoretical field-lowering coefficients compared, Poole-Frenkel emission (PFE) is dominated for two structures at reverse bias zone.

The eigenstates of general complex linear combination of SU (1, 1) generators (su c (1, 1) algebraic coherent states (ACS)) are constructed and discussed. It is shown that in the case of quadratic boson representation ACS can exhibit strong both linear and quadratic amplitude squeezing. ACS for a given Lie group algebra contain the corresponding Perelomov CS with maximal symmetry.

Overcomplete families of states of the type of Barut-Girardello coherent states (BG CS) are constructed for noncompact algebras u(p, q) and sp(N, C) in quadratic bosonic representation. The sp(N, C) BG CS are obtained in the form of multimode ordinary Schrödinger cat states. A set of such macroscopic superpositions is pointed out which is overcomplete in the whole N mode Hilbert space (while the associated sp(N, C) representation is reducible). The multimode squared amplitude Schrödinger cat states are introduced as macroscopic superpositions of the obtained sp(N, C) BG CS.

It is shown that any two Hamiltonians H(t) and H'(t) of N dimensional quantum systems can be related by means of time-dependent canonical transformations (CT). The dynamical symmetry group of system with Hamiltonian H(t) coincides with the invariance group of H(t). Quadratic Hamiltonians can be diagonalized by means of linear time-dependent CT. The diagonalization can be explicitly carried out in the case of stationary and some nonstationary quadratic H. Linear CT can diagonalize the uncertainty matrix \sigma(\rho) for canonical variables p_k, q_j in any state \rho, i.e., \sigma(\rho) is symplectically congruent to a diagonal uncertainty matrix. For multimode squeezed canonical coherent states (CCS) and squeezed Fock states with equal photon numbers in each mode \sigma is symplectic itself. It is proved that the multimode Robertson uncertainty relation is minimized only in squeezed CCS.

A sufficient condition for a state |\psi> to minimize the Robertson-Schr\"{o}dinger uncertainty relation for two observables A and B is obtained which for A with no discrete spectrum is also a necessary one. Such states, called generalized intelligent states (GIS), exhibit arbitrarily strong squeezing (after Eberly) of A and B. Systems of GIS for the SU(1,1) and SU(2) groups are constructed and discussed. It is shown that SU(1,1) GIS contain all the Perelomov coherent states (CS) and the Barut and Girardello CS while the Bloch CS are subset of SU(2) GIS.

We propose a new model for description of electrons beam dynamics in Free Electron Laser (FEL) undulator, based on the method of linear time-dependent invariants of quantum-mechanical charge particle. The magnetic field has periodic structure along the undulator. For this problem, described by time-dependent quadratic Hamiltonian, we obtain exact solution. The time-evolutions of the tree quantum fluctuations: covariance cov(q,p), var(q) and var(p) for the charge particle in this case are also determined. This research will help to optimize the FEL undulator: for example, using a 2.5 GeV linear electron accelerator it will be possible to emit radiation at 1.5 nm and shorter length. This method could be applicable also to any device with periodic structure of applied field (e.g. Tokamak, cyclic accelerators) for the case of charge non-relativistic quantum particles.

Integrals of motion and statistical properties of quantized electromagnetic field (e.-m. field) in time-dependent linear dielectric and conductive media are considered, using Choi-Yeon quantization, based on Caldirola-Kanai type Hamiltonian. Eigenstates of quadratic and linear invariants are constructed, the solutions being expressed in terms of a complex parametric function that obeys classical oscillator equation with time-varying frequency. The time evolutions of initial Glauber coherent states and Fock states are considered. The medium conductivity and the time-dependent electric permeability are shown to generate squeezing and non-vanishing covariances. In the time-evolved coherent and squeezed states all the second statistical moments of the electric and magnetic field components are calculated and shown to mminimize the Robertson-Schrödinger uncertainty relation.

The problem of diagonalization of Hamiltonians of N -dimensional boson systems by means of time-dependent canonical transformations (CT) is considered, the case of quadratic Hamiltonians being treated in greater detail. The unitary generator of time-dependent CT which can transform any Hamiltonian to that of a system of uncoupled stationary oscillators is constructed. The close relationship between methods of canonical transformations, time-dependent integrals of motion and dynamical symmetry is noted. The diagonalization and symplectic properties of the uncertainty matrix for 2N canonical observables are studied. It is shown that the normalized uncertainty matrix is symplectic for the squeezed multimode Glauber coherent states and for the squeezed Fock states with equal photon numbers in each mode. The Robertson uncertainty relation for the dispersion matrix of canonical observables is shown to be minimized in squeezed coherent states only.

An introductory survey on the Schroedinger uncertainty relation and its minimization states is presented with minimal number of formulas and some historical points. The case of the two canonical observables, position and momentum, is discussed in greater detail: basic properties of the two subsets of minimization states (canonical squeezed and coherent states) are reviewed and compared. The case of two non-canonical observables is breafly outlined. Stanfard SU(1,1) and SU(2) group-related coherent states can be defined as states that minimize Schroedinger inequality for the three pairs of generators simultaneously. The symmetry of the Heisenberg and Schroedinger relations is also discussed, and two natural generalizations to the cases of several observables and several states are noted.

Diagonalization of uncertainty matrix and minimization of Robertson inequality for n observables are considered. It is proved that for even n this relation is minimized in states which are eigenstates of n/2 independent complex linear combinations of the observables. In case of canonical observables this eigenvalue condition is also necessary. Such minimizing states are called Robertson intelligent states (RIS). The group related coherent states (CS) with maximal symmetry (for semisimple Lie groups) are particular case of RIS for the quadratures of Weyl generators. Explicit constructions of RIS are considered for operators of su(1, 1), su(2), h N and sp(N, R) algebras. Unlike the group related CS, RIS can exhibit strong squeezing of group generators. Multimode squared amplitude squeezed states are naturally introduced as sp(N, R) RIS. It is shown that the uncertainty matrices for quadratures of q-deformed boson operators a q,j (q > 0) and of any k power of a j = a 1,j are positive definite and can be diagonalized by symplectic linear transformations.

A scheme for construction of uncertainty relations (UR) for n observables and m states is presented. Several lowest order UR are displayed and briefly discussed. For two states |ψ and |φ and canonical observables the (entangled) extension of Heisenberg UR reads [∆p(ψ)] 2 [∆q(φ)] 2 +[∆p(φ)] 2 [∆q(ψ)] 2 ≥ 1/2. Some possible applications of the new inequalities are noted.

The Barut-Girardello coherent states (BG CS) representation is extended to the noncompact algebras u(p, q) and sp(N, R) in (reducible) quadratic boson realizations. The sp(N, R) BG CS take the form of multimode ordinary Schrödinger cat states. Macroscopic superpositions of 2 n-1 sp(N, R) CS (2 n canonical CS, n = 1, 2, . . .) are pointed out which are overcomplete in the N -mode Hilbert space and the relation between the canonical CS and the u(p, q) BG-type CS representations is established. The sets of u(p, q) and sp(N, R) BG CS and their discrete superpositions contain many states studied in quantum optics (even and odd N -mode CS, pair CS) and provide an approach to quadrature squeezing, alternative to that of intelligent states. New subsets of weakly and strongly nonclassical states are pointed out and their statistical properties (first-and second-order squeezing, photon number distributions) are discussed. For specific values of the angle parameters and small amplitude of the canonical CS components these states approaches multimode Fock states with one, two or three bosons/photons. It is shown that eigenstates of a squared non-Hermitian operator A 2 (generalized cat states) can exhibit squeezing of the quadratures of A.

A complete set of solutions |z,u,v>_{sa} of the eigenvalue equation (ua^2+va^{dagger 2})|z,u,v> = z|z,u,v> ([a,a^{dagger}]=1) are constructed and discussed. These and only these states minimize the Schr\"{o}dinger uncertainty inequality for the squared amplitude (s.a.) quadratures. Some general properties of Schr\"{o}dinger intelligent states (SIS) |z,u,v> for any two observables X, Y are discussed, the sets of even and odd s.a. SIS |z,u,v;+,-> being studied in greater detail. The set of s.a. SIS contain all even and odd coherent states (CS) of Dodonov, Malkin and Man'ko, the Perelomov SU(1,1) CS and the squeezed Hermite polynomial states of Bergou, Hillery and Yu. The even and odd SIS can exhibit very strong both linear and quadratic squeezing (even simultaneously) and super- and subpoissonian statistics as well. A simple sufficient condition for superpoissonian statistics is obtained and the diagonalization of the amplitude and s.a. uncertainty matrice...

Kolmogorov complexity is a measure of the information contained in a binary string. We investigate here the notion of quantum Kolmogorov complexity, a measure of the information required to describe a quantum state. We show that for any definition of quantum Kolmogorov complexity measuring the number of classical bits required to describe a pure quantum state, there exists a pure n-qubit state which requires exponentially many bits of description. This is shown by relating the classical communication complexity to the quantum Kolmogorov complexity. Furthermore we give some examples of how quantum Kolmogorov complexity can be applied to prove results in different fields, such as quantum computation and thermodynamics, and we generalize it to the case of mixed quantum states.

Kolmogorov complexity is a measure of the information contained in a binary string. We investigate here the notion of quantum Kolmogorov complexity, a measure of the information required to describe a quantum state. We show that for any definition of quantum Kolmogorov complexity measuring the number of classical bits required to describe a pure quantum state, there exists a pure n-qubit state which requires exponentially many bits of description. This is shown by relating the classical communication complexity to the quantum Kolmogorov complexity. Furthermore, we give some examples of how quantum Kolmogorov complexity can be applied to prove results in different fields, such as quantum computation and thermodynamics, and we generalize it to the case of mixed quantum states.

The thermal-to-percolative crossover exponent φ, well-known for ferromagnetic systems, is studied extensively for Edwards-Anderson spin glasses. The scaling of defect energies are determined at the bond percolation threshold pc, using an new algorithm. Simulations extend to system sizes above N = 10 8 in dimensions d = 2, . . . , 7. The results can be related to the behavior of the transition temperature Tg ∼ (p -pc) φ between the paramagnetic and the glassy regime for p ց pc. In three dimensions, where our simulations predict φ = 1.127(5), this scaling form for Tg provides a rare experimental test of predictions arising from the equilibrium theory of low-temperature spin glasses. For dimension near and above the upper critical dimension, the results provide a new challenge to reconcile mean-field theory with finite-dimensional properties.

We apply to nucleon decay the knowledge about the short-distance structure of baryon wave functions gleaned from QCD form factor calculations and the J/$ --) pp decay rate. We review the uncertainties arising when current algebra and PCAC are aused to relate N + z+ meson decay rates to (OlqqqjN) matrix elements. We show that the relevant matrix elements are not directly related to those of the leading twist operators "measured" in conventional high momentum transfer physics, but argue for -an indirect relation based on models that fit both form factor and J/q decay data. We use these inputs to calculate the p * e+s" decay rate in minimal SU(5) and other grand unified theories (GUTS) for a specified value of the heavy vector boson mass mx. Our results combined with the recent experimental lower limit on this mode indicate that rnx > 2 X 10 l5 GeV in the minimal SU(5) GUT, and we derive analogous bounds for super-symmetric GUTS. Our calculated lifetime for a given value of rnx is considerably shorter than previous estimates made using non-relativistic SU(6) or the bag model, a difference traceable to the different normalizations of 2 and 3 quark wave functions at short distances.

Mass mixing and CP violation in the B°-B ° system are studied in the standard six-quark model. The mass and width differences are obtained by reliable methods, and their radiative corrections included to leading logarithm. Constraints on the Kobayashi-Maskawa parameters are rederived in order to permit a quantitative account of B ° phenomenology. Strong evidence against the observability of CP violation in B°-B ° mixing is presented. * These fractions are based on solid-angle restrictions and detector efficiencies associated with the CLEO detector, * An analysis of KM parameters in the presence of such corrections has been performed in ref. [28]. See also ref. [29].

New application of our AI Abstract Engineering techniques in quantum theory of entanglement is considered. We design AI experiment with Conway’s quantum particle equipped with mathematical free will ( predicted by Conway’s Strong Free Will Theorem (2009)) based on GRPO - model used in AI.

The structure and mechanism of the formation of superlattices lamellae in microporous polyole fine (polyethylene and polypropylene) films obtained by polymer melt extrusion followed by annealing, uniaxial extension, and thermal fixation stages have been studied by scanning electron and atomic force microscopy. It has been shown that oriented anisometric particles, i.e., lamellae aggregates, are formed in films as the spin draw ratio λ f increases. At the stage of uniaxial extension (pore formation) of annealed films, a particle ensemble transforms to spatial superlattices of lamellae. Numerical processing of electron micros copy images of the film surface show that the nonmonotonic dependences of the correlation length of density fluctuations and the ratios of the alternation period of particles along extension to their thickness on the parameter λ f correspond to a unified mechanism of lamellae ordering.

Microporous films of polyolefins, namely, polyethylene and polypropylene, have been prepared using the process based on the extrusion of the melt with the subsequent annealing, uniaxial extension, and thermal fixation. The influence of the conditions used for preparation of the films on their morphology, porosity, number and sizes of through flow channels, and mechanical properties has been investigated. It has been found that a significant influence on the characteristics of the porous structure of the films is exerted by the degree of orientation of the melt at extrusion, the annealing temperature, and the degree of uniaxial extension of the films. The threshold values of these parameters, at which through flow channels are formed in the films, have been determined. It has been shown using filtration porosimetry that polyethylene films have a higher permeability to liquids as compared to the polypropylene samples (240 and 180 L/(m 2 h atm), respectively). The porous structure of the polyethylene films is characterized by larger sizes of through pores than those of the polypropylene samples (the average pore sizes are 210 and 160 nm, respectively), whereas the polypropylene films contain a larger number of through flow channels.

The surface structure of polypropylene and polyethylene microporous films prepared by the extrusion of the polymer melt with the subsequent stages of annealing, uniaxial extension, and thermal fixa tion of the samples has been analyzed using scanning electron microscopy. It has been shown that percolation through pores corresponds to the axial texture of the surface with the channel structure described by the frac tal cluster model. The transition from open pores (through flow channels) to closed pores leads to the forma tion of surface regions with a biaxial texture. An increase in the density of the solid phase cluster is accompa nied by the formation of a homogeneous biaxial texture with a period of alternation of the density in two mutually perpendicular directions, one of which coincides with the direction of orientation of the films.

In this work we present a keV-scale sterile-neutrino search with a low-tritium-activity data set of the KATRIN experiment, acquired in a commissioning run in 2018. KATRIN performs a spectroscopic measurement of the tritium $$\upbeta $$ β -decay spectrum with the main goal of directly determining the effective electron anti-neutrino mass. During this commissioning phase a lower tritium activity facilitated the measurement of a wider part of the tritium spectrum and thus the search for sterile neutrinos with a mass of up to $$1.6\, \textrm{keV}$$ 1.6 keV . We do not find a signal and set an exclusion limit on the sterile-to-active mixing amplitude of $$\sin ^2\theta < 5\times 10^{-4}$$ sin 2 θ < 5 × 10 - 4 ($$95\%$$ 95 % C.L.) at a mass of 0.3 keV. This result improves current laboratory-based bounds in the sterile-neutrino mass range between 0.1 and 1.0 keV.

Permutation and its partial transpose play important roles in quantum information theory. The Werner state is recognized as a rational solution of the Yang-Baxter equation, and the isotropic state with an adjustable parameter is found to form a braid representation. The set of permutation's partial transposes is an algebra called the "PPT" algebra which guides the construction of multipartite symmetric states. The virtual knot theory having permutation as a virtual crossing provides a topological language describing quantum computation having permutation as a swap gate. In this paper, permutation's partial transpose is identified with an idempotent of the Temperley-Lieb algebra. The algebra generated by permutation and its partial transpose is found to be the Brauer algebra. The linear combinations of identity, permutation and its partial transpose can form various projectors describing tangles; braid representations; virtual braid representations underlying common solutions of the braid relation and Yang-Baxter equations; and virtual Temperley-Lieb algebra which is articulated from the graphical viewpoint. They lead to our drawing a picture called the "ABPK" diagram describing knot theory in terms of its corresponding algebra, braid group and polynomial invariant. The paper also identifies nontrivial unitary braid representations with universal quantum gates, and derives a Hamiltonian to determine the evolution of a universal quantum gate, and further computes the Markov trace in terms of a universal quantum gate for a link invariant to detect linking numbers.

Fix integers g ≥ 3 and r ≥ 2, with r ≥ 3 if g = 3. Given a compact connected Riemann surface X of genus g, let M DH (X) denote the corresponding SL(r, C) Deligne-Hitchin moduli space. We prove that the complex analytic space M DH (X) determines (up to an isomorphism) the unordered pair {X, X}, where X is the Riemann surface defined by the opposite almost complex structure on X.

Field theories naturally give rise to multiple jets of hadrons in short-distance processes, such as e+e -annihilation. In particular, a low-energy jet of hadrons distributed in some cone of opening angle 6 would be naively expected to evolve at high energies into multiple jets within the angle 6. We explore to what extent this will happen in quantum chromodynamics. * Permanent address. ** Jet opening angles decrease very roughly as Nhadrons/Eje t. * To ensure that the quanta are made at short distances we think of Ej~ t -~ ~/~ (in e + e-) or Ejet = (PT)jet (in pp---~high-pT jets ). ** Extracted from the work of Polyakov [4]. (This proliferation can be nicely interpreted as a branching process [5] .) It is by now common wisdom that this conjectural picture should in some way apply to QCD. *** We will not discuss the case where one observes some' fixed number of jets at large fixed angles to one another. The probability of such a configuration vanishes roughly as a power of 1/In E. * We always measure p2 in units of A2~ (1 GeV)2. In this section we ignore the difference between q--* qG and G--* GG. The picture does not warrant any better. ** For reasons of symmetry we assume that each breakup is into two partons of essentially equal p2. * The azimuthal angle of the partons is entirely random. ** We choose a u-quark jet for all partons. This should be acceptable, as we are interested in calorimetric properties, not flavor. * Quantities such as (p~-Had), which are not linear as is (45), are probably more sensitive to perturbative broadening.

The path integral approach to representing braid group is generalized for particles with spin. Introducing the notion of charged winding number in the super-plane, we represent the braid group generators as homotopically constrained Feynman kernels. In this framework, super Knizhnik-Zamolodchikov operators appear naturally in the Hamiltonian, suggesting the possibility of spinning nonabelian anyons. We then apply our formulation to the study of fractional quantum Hall effect (FQHE). A systematic discussion of the ground states and their quasi-hole excitations is given. We obtain Laughlin, Halperin and Moore-Read states as exact ground state solutions to the respective Hamiltonians associated to the braid group representations. The energy gap of the quasi-excitation is also obtainable from this approach.

The adsorption of chiral D-(-)-tartaric acid is studied on a Pd(111) substrate using a combination of temperature-programmed desorption (TPD) and reflection-absorption infrared spectroscopy (RAIRS). It is found that reaction at room temperature occurs predominantly via deprotonation of the carboxylic acid groups. Bitartrate species form at ~300 K at low coverages while monotartrate species predominate at higher coverages since the removal of the second proton is inhibited by surface crowding. It also appears that the bitartrate can rehydrogenate on heating to reform some monotartrate species. The hydrogens deriving from the carboxylate group desorbs at ~315 K, and the mono-and bitartrate species are stable to ~390 K where they decompose to evolve hydrogen, carbon dioxide and some water. Carbon monoxide is also formed and evolves in a desorption-rate limited state at ~450 K. Biacidic, second-layer D-(-)-tartaric acid adsorbs at higher coverages and initially desorbs in a state at ~329 K shifting to higher temperatures as the second-layer coverage increases, indicative of attractive interactions between adsorbates. A decomposition intermediate is detected by dosing D-(-)-tartaric acid at low temperatures (~100 K) and heating to ~300 K or by dosing at ~300 K and heating to ~320 K, and is characterized by modes at ~1313, 1261, 1202 and 1116 cm -1 assigned to δ CH modes and a ν CO alc vibration suggesting that the intermediate may form by the removal of the \COO group.

We report the observation of two-photon f luorescence excitation in a continuous-wave (cw) single-beam gradient force optical trap and demonstrate its use as an in situ probe to study the physiological state of an optically confined sample. In particular, a cw Nd : YAG (1064-nm) laser is used simultaneously to conf ine, and excite visible f luorescence from submicrometer regions of, cell specimens. Two-photon f luorescence emission spectra are presented for motile human sperm cells and immotile Chinese hamster ovary cells that have been labeled with nucleic acid (Propidium Iodide) and pH-sensitive (Snarf) f luorescent probes. The resulting spectra are correlated to light-induced changes in the physiological state experienced by the trapped cells. This spectral technique should prove extremely useful for monitoring cellular activity and the effects of conf inement by optical tweezers.

We report on cell damage of single cells confined in continuous-wave (cw), near-infrared (NIR) multimode optical traps as a result of multiphoton absorption phenomena. Trapping beams at NIR wavelengths less than 800 nm are capable of damaging cells through a two-photon absorption process. Cell damage is more pronounced in multimode cw traps compared with single-frequency true cw NIR traps because of transient power enhancement by longitudinal mode beating. Partial mode locking in tunable cw Ti:sapphire lasers used as trapping beam sources can produce unstable subnanosecond pulses at certain wavelengths that amplify multiphoton absorption effects significantly. We recommend the use of single-frequency long-wavelength NIR trapping beams for optical micromanipulation of vital cells.