Scientific uses of the MANIAC

This is the story of how Nick Metropolis came to build the MANIAC and about the scientific uses to which it was put in the early days of electronic computing. Among the illustrious scientists attracted to the MANIAC were Fermi, Teller, von Neumann, Bethe, Gamow, and Ulam. Many of the scientific contributions were “firsts” that had a profound influence on subsequent developments over a wide spectrum of scientific activities. These included the pion-proton phase shift analysis, the nonlinear coupled oscillators, the study of the genetic code, importance sampling, two-dimensional hydrodynamics, Monte Carlo calculation of nuclear cascades, universalities of iterative functions and “anticlerical” chess.     

Cellular processing and satistical mechanics

A general model of multiprocessing and multiprocessor systems is given in terms of random fields and statistical mechanics. This model is called cellular processing which is a special application of cellular automata of von Neumann and Ulam. Cellular processing includes several well-known topics, such as image processing, VLSI optimization, and artificial intelligence.     

中子弹与中子弹中的物理学

简述了美国研制中子弹的历史背景，中子弹的简要发展史，详细阐释了中子弹的两个重要特性；强辐射与低爆炸威力，并与普通裂变弹作了对比，在分析中子弹特性的基础上，讲述了中子弹的物理原理，即中子弹是一种以氘氚聚变反应释放的高能中子为主杀务因素的特殊设计的低威力氢弹，最后，文章阐述了中子弹的功用与局限以及中子弹的防御措施。     

团簇物理的新进展(Ⅱ)——关于原子团簇和原子核的相似点和不同点

本文重点讨论金属原子团簇和原子核两费米子体系之间相似之处,如饱和性、壳结构、集体振荡、Ｊａｈｎ－Ｔｅｌｅｒ效应,裂变和聚合反应等,以及由于两者凝聚力的本质差别所造成的不同点。     

Generalization of the von Neumann theorem to nonreproducible measurements in quantum field theory. III

The consequences of a Theorem, which is a generalization of the fundamental von Neumann theorem on the reduction of a wave packet, and a Corollary of this theorem, which has a deep fundamental significance, are discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 85–91, November, 1978.     

Lattice Boltzmann model for combustion and detonation

In this paper we present a lattice Boltzmann model for combustion and detonation. In this model the fluid behavior is described by a finite-difference lattice Boltzmann model by Gan et al. [Physica A, 2008, 387: 1721]. The chemical reaction is described by the Lee-Tarver model [Phys. Fluids, 1980, 23: 2362]. The reaction heat is naturally coupled with the flow behavior. Due to the separation of time scales in the chemical and thermodynamic processes, a key technique for a successful simulation is to use the operator-splitting scheme. The new model is verified and validated by well-known benchmark tests. As a specific application of the new model, we studied the simple steady detonation phenomenon. To show the merit of LB model over the traditional ones, we focus on the reaction zone to study the non-equilibrium effects. It is interesting to find that, at the von Neumann peak, the system is nearly in its thermodynamic equilibrium. At the two sides of the von Neumann peak, the system deviates from its equilibrium in opposite directions. In the front of von Neumann peak, due to the strong compression from the reaction product behind the von Neumann peak, the system experiences a sudden deviation from thermodynamic equilibrium. Behind the von Neumann peak, the release of chemical energy results in thermal expansion of the matter within the reaction zone, which drives the system to deviate the thermodynamic equilibrium in the opposite direction. From the deviation from thermodynamic equilibrium, Δ _m *, defined in this paper, one can understand more on the macroscopic effects of the system due to the deviation from its thermodynamic equilibrium.     

Fritz Lange, Klaus Fuchs, and the Remigration of Scientists to East Germany

I describe the social and political framework in the German Democratic Republic (GDR) in which the remigration of scientists and other scholars to East Germany occurred after the Second World War, between 1946 and 1959. Since these included only a small number of scientists, I illustrate the problems they encountered and the opportunities they were provided during their reintegration into GDR society by discussing in some detail the cases of two physicists, Fritz Lange (1899–1987) and Klaus Fuchs (1911–1988), both of whom remigrated to East Germany in 1959 but from very different countries, the Soviet Union and Great Britain, and under dramatically different circumstances.     

Stable equivalence of the weak closures of free groups convolution algebras

We prove in this paper that the von Neumann algebras associated to the free non-commutative groups are stably isomorphic, i.e. that they are isomorphic when tensorized by the algebra of all linear bounded operators on a separable, infinite dimensional Hilbert space. This gives positive evidence for an old question, due to R.V. Kadison (see also S. Sakai's book on W^*-algebras), whether the von Neumann algebras associated to free groups are isomorphic or not.     

Field algebras do not leave field domains invariant

It is proved that von Neumann algebras associated to Op*-algebra (P, D) cannot leave the domainD ofP invariant if they are type I or type III factors or finite direct sums of such factors. Hence it follows that in quantum field theory global and local von Neumann field algebras in typical cases do not leave invariant the definition domain of Wightman fields.     

Von Neumann entropy in a Rashba-Dresselhaus nanodot; dynamical electronic spin-orbit entanglement

The main purpose of the present article is to report the characteristics of von Neumann entropy, thereby, the electronic hybrid entanglement, in the heterojunction of two semiconductors, with due attention to the Rashba and Dresselhaus spin-orbit interactions. To this end, we cast the von Neumann entropy in terms of spin polarization and compute its time evolution; with a vast span of applications. It is assumed that gate potentials are applied to the heterojunction, providing a two dimensional parabolic confining potential (forming an isotropic nanodot at the junction), as well as means of controlling the spin-orbit couplings. The spin degeneracy is also removed, even at electronic zero momentum, by the presence of an external magnetic field which, in turn, leads to the appearance of Landau states. We then proceed by computing the time evolution of the corresponding von Neumann entropy from a separable (spin-polarized) initial state. The von Neumann entropy, as we show, indicates that electronic hybrid entanglement does occur between spin and two-dimensional Landau levels. Our results also show that von Neumann entropy, as well as the degree of spin-orbit entanglement, periodically collapses and revives. The characteristics of such behavior; period, amplitude, etc., are shown to be determined from the controllable external agents. Moreover, it is demonstrated that the phenomenon of collapse-revivals’ in the behavior of von Neumann entropy, equivalently, electronic hybrid entanglement, is accompanied by plateaus (of great importance in quantum computation schemes) whose durations are, again, controlled by the external elements. Along these lines, we also make a comparison between effects of the two spin-orbit couplings on the entanglement (von Neumann entropy) characteristics. The finer details of the electronic hybrid entanglement, which may be easily verified through spin polarization measurements, are also accreted and discussed. The novel results of the present article, with potent applications in the field of quantum information processing, provide a deeper understanding of the electronic von Neumann entropy and hybrid entanglement that occurs in two-dimensional nanodots.     

Golden-Thompson and Peierls-Bogolubov inequalities for a general von Neumann algebra

Some inequalities for a general von Neumann algebra, which reduces to Golden-Thomspon and Peierls-Bogolubov inequalities when the von Neumann algebra has a trace, are proved.     

Bell’s inequality, Einstein, Podolsky, Rosen arguments and von Neumann’s projection postulate

This paper is devoted to analysis of the role of projection postulate in Einstein, Podolsky, and Rosen-EPR [1] argument against completeness of QM. It will be shown that the EPR considerations do not match with von Neumann’s quantum measurement theory (QMT). The root of EPR’s conclusion on incompleteness of QM is the misuse of von Neumann’s projection postulate. EPR applied this postulate to observables with degenerate spectra (which is totally forbidden by von Neumann’s axiomatics of QM). Consequences for Bell’s inequality and quantum information theory are analyzed. This paper might stimulate discussion on the role of projection postulate in quantum information theory, especially quantum cryptography and teleportation.     

Universal local symmetries and nonsuperposition in classical mechanics

In the Hilbert space formulation of classical mechanics, pioneered by Koopman and von Neumann, there are potentially more observables than in the standard approach to classical mechanics. In this Letter, we show that actually many of those extra observables are not invariant under a set of universal local symmetries which appear once the Koopman and von Neumann formulation is extended to include the evolution of differential forms. Because of their noninvariance, those extra observables have to be removed. This removal makes the superposition of states in the Koopman and von Neumann formulation, and as a consequence also in classical mechanics, impossible.     

Critical high density Fission-Fusion Plasmas

The implosion-induced compression of a pellet consisting of fissionable material, such as U 233, U 235 or Pu 239, to high densities by a laser-, relativistic electron-, or ion-beam is expected to lead to very small critical masses which can be furthermore substantially reduced by simultaneously compressing the pellet together with a neutron reflector. This method opens the prospect for micro-fission-explosions to be used for controlled power production as for a safe fast breeder reactor or for rocket propulsion. Furthermore, if the neutron reflector consists of thermonuclear material, such as T—D, the method can be used for the controlled release of thermonuclear energy. There the fission chain reaction not only will assist in the ignition of the thermonuclear reaction but in turns the fusion neutrons will accelerate the fission chain reaction to a very fast pace. In this case therefore, the fission chain reaction and the fusion thermonuclear reaction are coupled together with an expected greatly increased energy output.     

A New Inequality for the von Neumann Entropy

Strong subadditivity of von Neumann entropy, proved in 1973 by Lieb and Ruskai, is a cornerstone of quantum coding theory. All other known inequalities for entropies of quantum systems may be derived from it. Here we prove a new inequality for the von Neumann entropy which we prove is independent of strong subadditivity: it is an inequality which is true for any four party quantum state, provided that it satisfies three linear relations (constraints) on the entropies of certain reduced states.     

Entanglement in the supermolecular dimer [Mn4]2

This paper investigates the entanglement in the supermolecular dimer [Mn4]2 consisting of a pair of single molecular magnets with antiferromagnetic exchange-coupllng J. The conventional yon Neumann entropy as a function of the exchange-coupling is calculated explicitly for all eigenstates with the quantum number range from M = M1 ＋ M2 = -9 to 0. It is shown that the yon Neumann entropy is not a monotonic function of the coupling strength. However, it is significant that the entropy of entanglement has the maximum values and the minimum values for most eigenstates, which is extremely useful in the quantum computing. It also presents the time-evolution of entanglement from various initial states. The results are useful in the design of devices based on the entanglement of two molecular magnets.     

De Morgan Property for Effect Algebras of von Neumann Algebras

It is shown that the unit interval of a von Neumann algebra is a Sum Brouwer–Zadeh algebra when equipped with another unary operation sending each element to the complement of its range projection. The main result of this Letter says that a von Neumann algebra is finite if and only if the corresponding Brouwer–Zadeh structure is de Morgan or, equivalently, if the range projection map preserves infima in the unit interval. This provides a new characterization of finiteness in the Murray–von Neumann structure theory of von Neumann algebras in terms of Brouwer–Zadeh structures.     

A Conversation with Robert F. Christy – Part II

Robert F. Christy, Institute Professor of Theoretical Physics Emeritus at Caltech, recalls his wartime work at Los Alamos on the critical assembly for the plutonium bomb (“the Christy bomb”); the Alamogordo test, July 16, 1945; the postwar concerns of ALAS (Association of Los Alamos Scientists); his brief return to the University of Chicago and move to Caltech; friendship with and later alienation from Edward Teller; work with Charles and Tommy Lauritsen and William A. Fowler in Caltech’s Kellogg Radiation Laboratory; Freeman Dyson’s Orion Project; work on the meson and RR Lyrae stars; fellowship at Cambridge University; 1950s Vista Project at Caltech; his opposition to the Strategic Defense Initiative; and his post-retirement work for the National Research Council’s Committee on Dosimetry and on inertial-confinement fusion.     

Endomorphism semigroups and lightlike translations

Borchers and Wiesbrock have studied the one-parameter semigroups of endomorphisms of von Neumann algebras that appear as lightlike translations in the theory of algebras of local observables, showing that they automatically transform under the appropriate modular automorphisms as under velocity transformations. Here, these results are abstracted and analyzed as essentially operator-theoretic. Criteria are then established for a spatial derivation of a von Neumann algebra to generate a one-parameter semigroup of endomorphisms, and all of this is combined to establish a von Neumann-algebraic converse to the Borchers and Wiesbrock results. This sort of analysis is then applied to questions of isotony and covariance for local algebras, to show that Poincaré covariance together with a domain condition for the translations can imply isotony.This research was partly supported by a fellowship from the Consiglio Nazionale delle Ricerche.     

Resonance Theory for Schrödinger Operators

Given a family of isometries in a tracial von Neumann algebra M, a unital subalgebra B⊂M and a completely-positive map we define the free Fisher information of relative to B and η. Using this notion, we define the free dimension of relative to B, id. Let R be a measurable equivalence relation on a finite measure space X. Let M be the von Neumann algebra associated to R, and let be the canonical diffuse subalgebra. If are partial isometries arising from a treeing of this equivalence relation, then is equal to the cost of the equivalence relation in the sense of Gaboriau and Levitt. Received: 11 September 1999/Accepted: 10 November 2000