Showing papers by "California Institute of Technology published in 1982"

A single quantum cannot be cloned

Abstract: If a photon of definite polarization encounters an excited atom, there is typically some nonvanishing probability that the atom will emit a second photon by stimulated emission. Such a photon is guaranteed to have the same polarization as the original photon. But is it possible by this or any other process to amplify a quantum state, that is, to produce several copies of a quantum system (the polarized photon in the present case) each having the same state as the original? If it were, the amplifying process could be used to ascertain the exact state of a quantum system: in the case of a photon, one could determine its polarization by first producing a beam of identically polarized copies and then measuring the Stokes parameters1. We show here that the linearity of quantum mechanics forbids such replication and that this conclusion holds for all quantum systems.

Quantum limits on noise in linear amplifiers

Abstract: How much noise does quantum mechanics require a linear amplifier to add to a signal it processes? An analysis of narrow-band amplifiers (single-mode input and output) yields a fundamental theorem for phase-insensitive linear amplifiers; it requires such an amplifier, in the limit of high gain, to add noise which, referred to the input, is at least as large as the half-quantum of zero-point fluctuations. For phase-sensitive linear amplifiers, which can respond differently to the two quadrature phases ("$cos\ensuremath{\omega}t$" and "$sin\ensuremath{\omega}t$"), the single-mode analysis yields an amplifier uncertainty principle---a lower limit on the product of the noises added to the two phases. A multimode treatment of linear amplifiers generalizes the single-mode analysis to amplifiers with nonzero bandwidth. The results for phase-insensitive amplifiers remain the same, but for phase-sensitive amplifiers there emerge bandwidth-dependent corrections to the single-mode results. Specifically, there is a bandwidth-dependent lower limit on the noise carried by one quadrature phase of a signal and a corresponding lower limit on the noise a high-gain linear amplifier must add to one quadrature phase. Particular attention is focused on developing a multimode description of signals with unequal noise in the two quadrature phases.

Environment-induced superselection rules

Abstract: We show how the correlations of a quantum system with other quantum systems may cause one of its observables to behave in a classical manner. In particular, "reduction of the wave packet," postulated by von Neumann to explain definiteness of an outcome of an individual observation, can be explained when a realistic model of an apparatus is adopted. Instead of an isolated quantum apparatus with a number of states equal to the number of possible distinct outcomes of the measurement, discussed by von Neumann, we consider an apparatus interacting with other physical systems, described here summarily as "environment." The interaction of the quantum apparatus with the environment results in correlations. Correlations impose effective superselection rules which prevent apparatus from appearing in a superposition of states corresponding to different eigenvalues of the privileged pointer observable. It is the propagation of the correlations with the pointer basis states which is ultimately responsible for the choice of the pointer observable. It can be thought of as a process of amplification in which the state of many distinct physical systems becomes correlated with the pointer basis state. Whether these environment systems are regarded as a part of the apparatus setup, or as a part of its environment is irrelevant. What is crucial is the redundancy of the record concerning the pointer observable which is imprinted into the correlations. Eigenspaces of the pointer observable provide a natural basis for the pointer of the quantum apparatus and determine the to-be-measured observable of the quantum system. Decay of those elements of the apparatus-system density matrix, which are off-diagonal in the pointer observable, is caused by the natural evolution of the combined system-apparatus-environment object. For a hypothetical finite environment with $N$ distinct eigenvalues of the apparatus-environment interaction Hamiltonian, off-diagonal terms will decay to become of the order of ${N}^{\ensuremath{-}\frac{1}{2}}$, and will recur only on a Poincar\'e time scale. No recurrences will be observed in realistic circumstances. As the correlations spread through the environment on a time scale typically much shorter than the recurrence time scale calculated for the environment already correlated with the pointer observable, the measurement becomes effectively irreversible. Relevance of this model of the measurement process for the understanding of the second law of thermodynamics and its relation to Bohr's "irreversible act of amplification" is briefly discussed. The emergence of the pointer observable can be interpreted as a clue about the resolution of the measurement problem in case of no environment. It points towards the possibility that properties of quantum systems have no absolute meaning. Rather, they must be always characterized with respect to other physical systems.

A Generalization of Algebraic Surface Drawing

Abstract: The mathematical description of three dimensional surfaces usually falls in one of two classifications: parametric and algebraic. The form is defined as all points which satisfy some equation: F(x,y,z)=0. This form is ideally suited for image space shaded picture drawing, the pixel coordinates are substituted for x and y and the equation is solved for z. Algorithms for drawing such objects have been developed primarily for first and second order polynomial functions. This paper presents a new algorithm applicable to other functional forms, in particular to the summation of several gaussian density distributions. The algorithm was created to model electron density maps of molecular structures but can be used for other artistically interesting shapes.

A new look at the saturn system: the voyager 2 images.

Abstract: Voyager 2 photography has complemented that of Voyager I in revealing many additional characteristics of Saturn and its satellites and rings. Saturn's atmosphere contains persistent oval cloud features reminiscent of features on Jupiter. Smaller irregular features track out a pattern of zonal winds that is symmetric about Saturn's equator and appears to extend to great depth. Winds are predominantly eastward and reach 500 meters per second at the equator. Titan has several haze layers with significantly varying optical properties and a northern polar "collar" that is dark at short wavelengths. Several satellites have been photographed at substantially improved resolution. Enceladus' surface ranges from old, densely cratered terrain to relatively young, uncratered plains crossed by grooves and faults. Tethys has a crater 400 kilometers in diameter whose floor has domed to match Tethys' surface curvature and a deep trench that extends at least 270° around Tethys' circumference. Hyperion is cratered and irregular in shape. Iapetus' bright, trailing hemisphere includes several dark-floored craters, and Phoebe has a very low albedo and rotates in the direction opposite to that of its orbital revolution with a period of 9 hours. Within Saturn's rings, the "birth" of a spoke has been observed, and surprising azimuthal and time variability is found in the ringlet structure of the outer B ring. These observations lead to speculations about Saturn's internal structure and about the collisional and thermal history of the rings and satellites.

Ion-supported tori and the origin of radio jets

Abstract: While apparently supplying tremendous power to their extended radio-emitting regions, the nuclei of most radio galaxies emit little detectable radiation. It is proposed that at the centre of each is a spinning black hole surrounded by a torus of gas too hot and tenuous to radiate efficiently. The torus anchors magnetic fields which extract rotational energy from the hole in the form of two collimated beams of relativistic particles and fields. These in turn drive the observed radio jets and hot spots. A large supply of accreting gas is thus unnecessary and radio galaxies may be interpreted as starved quasars.

Water in silicate glasses: An infrared spectroscopic study

Abstract: Infrared and near-infrared transmission spectra have been taken on 19 volcanic and synthetic silicate glasses with known H2O contents (0.06–6.9 wt. %). Absorption peaks were observed at wavelengths of 1.41 μm, 1.91 μm, 2.22 μm, 2.53 μm, and 2.8 μm. These peaks have been attributed to the first overtone of the OH stretching vibration, the combination stretching+bending mode of H2O molecules, the combination stretching+bending mode of X-OH groups, a combination mode of the fundamental OH stretch+a low energy lattice vibration, and the fundamental OH stretching mode, respectively. Molar absorptivities of the peaks have been determined to be 0.2, 1.8, 1.0, 0.9, and 67 l/mol-cm. These values apply over the full range of glass compositions studied (albite, rhyolite, basalt).

The anatomy of A-, B-, and Z-DNA

Abstract: Recent advances in DNA synthesis methods have made it possible to carry out single-crystal x-ray analyses of double-stranded DNA molecules of predetermined sequence, with 4 to 12 base pairs. At least one example has been examined from each of the three known families of DNA helix: A, B, and Z. Each family has its own intrinsic restrictions on chain folding and structure. The observed solvent positions in these crystal structures have confirmed earlier fiber and solution measurements, and have led to proposals explaining the transitions from B to A and from B to Z helices. Prospects are improving for an understanding of the mode of bending of DNA in chromatin, and the way in which specific DNA sequences are recognized by drug molecules and repressor proteins.

Light reflection functions for simulation of clouds and dusty surfaces

Abstract: The study of the physical process of light interacting with matter is an important part of computer image synthesis since it forms the basis for calculations of intensities in the picture. The simpler models used in the past are being augmented by more complex models gleaned from the physics literature. This paper is another step in the direction of assimilating such knowledge. It concerns the statistical simulation of light passing through and being reflected by clouds of similar small particles. (It does not, however, address the cloud structure modeling problem). By extension it can be applied to surfaces completely covered by dust and is therefore a physical basis for various theories of diffuse reflection.

Subsurface Valleys and Geoarcheology of the Eastern Sahara Revealed by Shuttle Radar

Abstract: The shuttle imaging radar (SIR-A) carried on the space shuttle Columbia in November 1981 penetrated the extremely dry Selima Sand Sheet, dunes, and drift sand of the eastern Sahara, revealing previously unknown buried valleys, geologic structures, and possible Stone Age occupation sites. Radar responses from bedrock and gravel surfaces beneath windblown sand several centimeters to possibly meters thick delineate sand- and alluvium-filled valleys, some nearly as wide as the Nile Valley and perhaps as old as middle Tertiary. The now-vanished major river systems that carved these large valleys probably accomplished most of the erosional stripping of this extraordinarily flat, hyperarid region. Underfit and incised dry wadis, many superimposed on the large valleys, represent erosion by intermittent running water, probably during Quaternary pluvials. Stone Age artifacts associated with soils in the alluvium suggest that areas near the wadis may have been sites of early human occupation. The presence of old drainage networks beneath the sand sheet provides a geologic explanation for the locations of many playas and present-day oases which have been centers of episodic human habitation. Radar penetration of dry sand and soils varies with the wavelength of the incident signals (24 centimeters for the SIR-A system), incidence angle, and the electrical properties of the materials, which are largely determined by moisture content. The calculated depth of radar penetration of dry sand and granules, based on laboratory measurements of the electrical properties of samples from the Selima Sand Sheet, is at least 5 meters. Recent (September 1982) field studies in Egypt verified SIR-A signal penetration depths of at least 1 meter in the Selima Sand Sheet and in drift sand and 2 or more meters in sand dunes.

A molecular map of the immune response region from the major histocompatibility complex of the mouse

Abstract: A stretch of 200 kilobases (kb) of DNA from the I region of the mouse major histocompatibility complex has been cloned and characterized. It contains the genes for the biochemically defined class II proteins Eα, Eβ and Aβ. DNA blot analyses suggest that the I region may contain only 6–8 class II genes. Correlation of our molecular map with the genetic map of the I region confines two of the five I subregions, I–J and I–B, to less than 3.4 kb of DNA at the 3′ end of the Eβ gene where a hotspot for recombination has been observed. Indeed, the I–A and I–E subregions may be contiguous. If so, the I–B and I–J subregions are not encoded in the I region between the I–A and I–E subregions.

Instability of flat space at finite temperature

Abstract: The instabilities of quantum gravity are investigated using the path-integral formulation of Einstein's theory. A brief review is given of the classical gravitational instabilities, as well as the stability of flat space. The Euclidean path-integral representation of the partition function is employed to discuss the instability of flat space at finite temperature. Semiclassical, or saddle-point, approximations are utilized. We show how the Jeans instability arises as a tachyon in the graviton propagator when small perturbations about hot flat space are considered. The effect due to the Schwarzschild instanton is studied. The small fluctuations about this instanton are analyzed and a negative mode is discovered. This produces, in the semiclassical approximation, an imaginary part of the free energy. This is interpreted as being due to the metastability of hot flat space to nucleate black holes. These then evolve by evaporation or by accretion of thermal gravitons, leading to the instability of hot flat space. The nucleation rate of black holes is calculated as a function of temperature.

Large N limits as classical mechanics

Abstract: This paper discusses the sense in which the large $N$ limits of various quantum theories are equivalent to classical limits. A general method for finding classical limits in arbitrary quantum theories is developed. The method is based on certain assumptions which isolate the minimal structure any quantum theory should possess if it is to have a classical limit. In any theory satisfying these assumptions, one can generate a natural set of generalized coherent states. These coherent states may then be used to construct a classical phase space, derive a classical Hamiltonian, and show that the resulting classical dynamics is equivalent to the limiting form of the original quantum dynamics. This formalism is shown to be applicable to the large $N$ limits of vector models, matrix models, and gauge theories. In every case, one can explicitly derive a classical action which contains the complete physics of the $N=\ensuremath{\infty}$ theory. "Solving" the $N=\ensuremath{\infty}$ theory requires minimizing the classical Hamiltonian, and this has been possible only in simple theories. The relation between this approach and other methods which have been proposed for deriving large $N$ limits is discussed in detail.

Hotspots, polar wander, Mesozoic convection and the geoid

Abstract: The geoid bears little relation to present tectonic features of the Earth other than trenches and hotspots. The Mesozoic supercontinent of Pangea, however, apparently occupied a central position in the Atlantic–African geoid high. This and the equatorial Pacific geoid high contain most of the world's hotspots. The plateaus and rises which are now in the western Pacific formed in the Pacific geoid high and this may have been the early Mesozoic–late Palaeozoic position of a large part of Asia and other fragments of the Pacific rim continents. The major global geoid highs were regions of extensive Cretaceous volcanism and may be the former sites of continental aggregations and mantle insulation and, therefore, hotter-than-normal mantle. The pent-up heat causes rifts and hotspots and results in uplift, magmatism, fragmentation and dispersal of the continents and the subsequent formation of plateaus, aseismic ridges and seamount chains which cause a global rise in sea-level. Convection in the upper mantle caused by such lateral temperature gradients is intrinsically episodic. A geoid anomaly of 50 m can be formed in about 100 Myr by continental insulation. We show here that such geoid anomalies are long-lived and may be used to remove the ambiguity in early Mesozoic–late Palaeozoic plate reconstructions. Geoid highs control the rotation axis of the Earth and, in effect, bring long-lived continental aggregations to the Equator. Many aspects of continental geology such as vertical-tectonics and episodicity of magmatism and transgressions can be explained by continental insulation.

Some effects of disconnecting the cerebral hemispheres

Abstract: To start by looking back a little, recall that even a small brain lesion, if critically located in the left or language hemisphere, may selectively destroy a person's ability to read, while at the same time sparing speech and the ability to converse. The printed page continues to be seen, but the words have lost their meaning. This condition typically follows from focal damage to the angular gyrus in the left hemisphere. It also results from lesions interruptingt he neural input to this left angular gyrus from the visual or calcarine cortical areas (1, 2). It is natural to conclude in such cases that the left hemisphere is responsible for reading while the undamaged right hemisphere, in contrast, must be "wordblind" or incapable of seeing meaning in the printed word.

Monthly Mean Sea-Level Variability Along the West Coast of North America

Abstract: Linear statistical estimators are used to examine 29 years of nonseasonal, monthly-mean, tide-gauge sea-level data along the west coast of North America. The objective is exploration of the structure, and causes of nearshore ocean variability over time scales of months to years at 20 stations from Alaska to Mexico. North of San Francisco, 50–60% of the sea-level variability reflects a simple inverse barometric response to local atmospheric pressure. These inverted barometer effects account for only 10–15% of the variance at stations to the south. The dominant signal of inverse-barometer-corrected sea level represents a nearly uniform rise or fall of sea level everywhere along the eastern rim of the North Pacific. The interannual aspects of this large-scale sea-level variability are closely related to El Nino occurrences in the eastern tropical Pacific which appear to propagate poloward with phase speeds of ∼40 cm s−1. Higher frequency aspects of this large-scale sea-level variability appear to re...

Lion roars and nonoscillatory drift mirror waves in the magnetosheath

Abstract: It is shown that Extremely Low Frequency, or 'lion' roars are closely coupled to quasi-periodic, large scale magnetosheath structures. Because the latter are waves generated by the drift mirror instability, an attempt is made to identify and describe the magnetic and plasma features associated with this instability. Observations and analyses of the large scale structures using ISEE 1 and 2 data for the earth's magnetosheath and Pioneer 11 data for Jupiter and Saturn are presented, along with the background of the drift mirror waves. The cyclotron and drift mirror instabilities occurring in the magnetosheath are natural relaxation processes which reduce the plasma pressure anisotropies created by preferential heating of the solar wind plasma as it passes through the bow shock, as well as the compression occurring when the plasma and fields approach the near-subsolar magnetopause.

The Dynamics of Planetary Rings

Abstract: The discovery of ring systems around Uranus and Jupiter, and the Pioneer and Voyager spacecraft observations of Saturn, have shown that planetary rings are both more common and more complex than previously suspected. These ring systems, interesting in their own right, also serve as prototypes for more massive disk systems such as accretion disks and spiral galaxies occurring elsewhere in astronomy. Disks and rings are a natural consequence of dissipation in rotating systems. A cloud of debris surrounding a spherical planet settles into a flat circular ring because interparticle collisions dissipate energy but conserve total angular momentum. Since planets are oblate, only the component of angular momentum along the spin axis is conserved, and the flat ring lies in the equatorial plane. Collisions redistribute angular momentum among the particles and the ring spreads, transferring mass inward and angular momentum outward (Lynden-Bell & Pringle 1974). However, the spreading process occurs on a much longer timescale than the flattening process since the collision speeds in a flat ring are much lower than the orbital speeds (see Sections 2.2 and 5. 3). Spreading can be slowed by gravitational interactions with satellites; nevertheless, a ring cannot live forever and an important constraint on possible ring models is that they yield survival times at least comparable to the age of the solar system (cf. Sections 5, 6). This review was written in October 1981, shortly after the Voyager 2 encounter with Saturn. Analysis of the data from the Voyager encounters is not yet complete. Therefore the emphasis in this review is on the basic physical processes that occur in planetary rings, rather than on a detailed confrontation of theoretical predictions with observation. Table 1 lists some of the important properties of the planets with known ring systems. For the sake of brevity we shall refer to a series of papers we have written on rings (Goldreich & Tremaine 1978a, b, c, 1979a, b, c, 1980, 1981) as GT 1, . . . , GT 8.

Chemical Composition of Acid Fog

Abstract: Fog water collected at three sites in Los Angeles and Bakersfield, California, was found to have higher acidity and higher concentrations of sulfate, nitrate, and ammonium than previously observed in atmospheric water droplets. The pH of the fog water was in the range of 2.2 to 4.0. The dominant processes controlling the fog water chemistry appear to be the condensation and evaporation of water vapor on preexisting aerosol and the scavenging of gas-phase nitric acid.