Percolation in a dependent random environment

Draw planes in ℝ³ that are orthogonal to the x axis, and intersect the x axis at the points of a Poisson process with intensity λ; similarly, draw planes orthogonal to the y and z axes using independent Poisson processes (with the same intensity). Taken together, these planes naturally define a randomly stretched rectangular lattice. Consider bond percolation on this lattice where each edge of length 𝓁 is open with probability e^−𝓁, and these events are independent given the edge lengths. We show that this model exhibits a phase transition: for large enough λ there is an infinite open cluster a.s., and for small λ all open clusters are finite a.s. We prove this result using the method of paths with exponential intersection tails, which is not applicable in two dimensions. The question whether the analogous process in the plane exhibits a phase transition is open. © 2000 John Wiley & Sons, Inc. Random Struct. Alg., 16, 333–343, 2000     

Random walks in varying dimensions

We establish recurrence criteria for sums of independent random variables which take values in Euclidean lattices of varying dimension. In particular, we describe transient inhomogeneous random walks in the plane which interlace two symmetric step distributions of bounded support.Research partially supported by the U.S. Army Research Office through the Mathematical Sciences Institute of Cornell University.Research supported in part by National Science Foundation Grant No. DMS 9300191, by a Sloan Foundation Fellowship, and by a Presidential Faculty Fellowship.     

Nachweis und Bestimmung von Nitraten in der Milch

Ohne Zusammenfassung     

Edward Teller, the Hungarian, American and Jew, too

As explained on p. 57 of George Marx’ comprehensive treatiseThe Voice of the Martians [1] (a pun on Leo Szilárd’sVoice of the Dolphins [2]), the titleThe Martians refers to another Szilárd joke, namely to his reply to a question of Fermi’s. In end-of-the-Century parlance, Fermi’s question would be formulated as follows: —With the galaxy presumably full of planetary systems, thereby also of life and thus of intelligence, where are all those extraterrestrials? [3] — to which Szilárd answered —They are among us, but they call themselves Hungarian… — One of these individuals of high intellectual stature, is (“let him be distinguished by a long life” as we would add in such cases by Jewish custom)Edward Teller.     

Special analytical properties of ultrastrong coherent fields

Emerging ultrastrong-laser capabilities that can reveal details of vacuum structure have intensified research into the fundamentals of quantum electrodynamics. It has been more than half a century since relativistic nonperturbative methods were introduced into the study of strong-field phenomena. Much of the early progress remains of fundamental relevance, but is known to only a small group of researchers. The aim of this paper is to reveal some of that work and to show how it impacts on current investigations. A basic result is that it has been shown that strong, single-mode fields (i.e. laser fields) can be treated by relativistic quantum mechanics with results identical to fully quantized electrodynamics. Attention is drawn to the existence of a Volkov Green’s function that has a clear physical interpretation as predicting several series of relativistic Floquet sideband states. It is more transparent and informative than the Volkov Green’s function of Schwinger. It is also shown that the fundamental experiments performed at the Stanford Linear Accelerator Center in 1997 on photon-multiphoton pair production could not be a high-order perturbative result, as was presumed by the investigators. The intensity employed was beyond the radius of convergence of perturbation theory, and the seeming perturbative increase in rate with intensity is an artifact. Of particular significance is the demonstration that a free electron in a strong plane-wave field (a “Volkov electron”) exists in an intensity-dependent superposition of angular momentum states, and is no longer a simple spin-1/2 particle.     

The Direction of Time: Seven Arrows for One Stream? A Program

I review the role of entropy in the Second Law of Thermodynamics in providing time with a direction and explaining irreversibility. I then list seven seemingly different features, each characterizing an additional arrow. In one case, connected to Black Hole Physics, the arrow has been successfully merged with the thermodynamical and may serve as model; in another case, that of the Evolutionary drive, the adequate function has been identified as complexity. We define the aims of the program and also provide information for an alternative, geometrical (effective) approach.     

Leptogenesis from supersymmetry breaking

We show that soft supersymmetry breaking terms involving the heavy sneutrinos can lead to sneutrino-antisneutrino mixing and to new sources of CP violation, which are present even if a single generation is considered. These terms are naturally present in supersymmetric versions of leptogenesis scenarios, and they induce indirect CP violation in the decays of the heavy sneutrinos, eventually generating a baryon asymmetry. This new contribution can be comparable to or even dominate over the asymmetry produced in traditional leptogenesis scenarios.     

Two-channel Kondo effect in a modified single electron transistor

We suggest a simple system of two electron droplets which should display two-channel Kondo behavior at experimentally accessible temperatures. Stabilization of the two-channel Kondo fixed point requires fine control of the electrochemical potential in each droplet, which can be achieved by adjusting voltages on nearby gate electrodes. We study the conditions for obtaining this type of two-channel Kondo behavior, discuss the experimentally observable consequences, and explore the generalization to the multichannel Kondo case.     

The Sign and Micro-Origin of Complexity as Entropy (Conjectured Resolution of a Paradox)

Evolution produces ever more ordered matter, while also increasing its complexity all the time. There are various ways of measuring complexity, such as Kolmogorov's algorithmic complexity, drawn from information theory, and identified with entropy, enchancing irreversibility in harmony with the second law of thermodynamics. On the other hand, however, the creation of order should have reduced entropy; quoting Schroedinger, it represents "negentropy." To resolve this apparent contradiction we first review a similar set up (though with a totally different interaction) occurring in black holes, a model in which the physics are now explicit and fully understood at the quantum level.