The probability distribution of the velocities of gas molecules after collision with a rapidly moving rigid body

The above problem is met, for example, in the case of the collision of molecules of the atmosphere with an artificial earth satellite and leads to the problem of determining the probability distribution of the absolute value of the vector sum of a constant vector and a Maxwell vector (the latter being a vector, whose rectangular components are distributed normally, with the same standard deviation and mean value zero). The resultant probability density is given by equation (18), the complement to the distribution function by (24), the mean value by (27) and the variance by (31). These results are obtained by transforming the corresponding three-dimensional normal distribution to spherical co-ordinates and integrating over the co-ordinate angles and , which yields the required probability density; the other results are then obtained from it by the usual methods.

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, , (. . , ). (18), -(24), -(27) (31). , ; .

     

Maximal violation of Bell's inequalities is generic in quantum field theory

Under weak technical assumptions on a net of local von Neumann algebras {A(O)} in a Hilbert space , which are fulfilled by any net associated to a quantum field satisfying the standard axioms, it is shown that for every vector state in there exist observables localized in complementary wedge-shaped regions in Minkowski space-time that maximally violate Bell's inequalities in the state . If, in addition, the algebras corresponding to wedge-shaped regions are injective (which is known to be true in many examples), then the maximal violation occurs in any state on () given by a density matrix.     

A reinterpretation of von Neumann's theory of measurement

Von Neumann's theory of measurement in quantum mechanics is reinterpreted so that the experimental arrangement specifies the location of the cut by calling for the separate observation of the object and the measuring apparatus after the initial measurement interaction. The measurement ascertains which element of the mixture describing the final state of the apparatus is actually present. The relevance and feasibility of observing the final coherent state of the object plus apparatus is criticized and the paradoxes of Schrödinger's cat and Wigner's friend are discussed.Work performed under the auspices of the U.S. Atomic Energy Commission.     

The Feynman Path Integrals and Everett's Universal Wave Function

We study here the properties of some quantum mechanical wave functions, which, in contrast to the regular quantum mechanical wave functions, can be predetermined with certainty (probability 1) by performing dense measurements (or continuous observations). These specific certain states are the junction points through which pass all the diverse paths that can proceed between each two such neighboring sure points. When we compare the properties of these points to the properties of the well-known universal wave functions of Everett we find a strong similarity between these two apparently uncorrelated entities, and in this way find the same similarity between the Feynman path integrals and Everett's universal wave functions.     

An alternative approach to quantum phenomena

This paper outlines the qualitative foundations of a quasiclassical theory in which particles are pictured as spatially extended periodic excitations of a universal background field, interacting with each other via nonlinearity in the equations of motion for that field, and undergoing collapse to a much smaller volume if and when they are detected. The theory is based as far as possible directly on experiment, rather than on the existing quantum mechanical formalism, and it offers simple physical interpretations of such concepts as mass, 4-momentum, interaction, potentials, and quantization; it may lead directly to the standard equations of quantum theory, such as the multiparticle Schrödinger equation, without going through the conventional process of quantizing a classical theory. The theory also provides an alternative framework in which to discuss wave-particle duality and the quantum measurement problem; in particular, it is suggested that the unpredictability of quantum phenomena may arise from deterministic chaos in the behavior of the background field.     

The simplified Fermi accelerator in classical and quantum mechanics

We review the simplified classical Fermi acceleration mechanism and construct a quantum counterpart by imposing time-dependent boundary conditions on solutions of the free Schrödinger equation at the unit interval. We find similiar dynamical features in the sense that limiting KAM curves, respectively purely singular quasienergy spectrum, exist(s) for sufficiently smooth wall oscillations (typically ofC ² type). In addition, we investigate quantum analogs to local approximations of the Fermi map both in its quasiperiodic and irregular phase space regions. In particular, we find pure point q.e. spectrum in the former case and conjecture that random boundary conditions are necessary to model a quantum analog to the chaotic regime of the classical accelerator.     

Three-Mode Entangled State Representation of Continuum Variables and Optical Four-Wave Mixing

We establish a new three-mode entangled state representation , of continuum variables, which make up a complete set. Using optical four-wave mixing and a beam splitter transform we can prepare , . Based on , a new number-difference--operational-phase uncertainty relation is established and the corresponding squeezing dynamics is discussed.     

Renormalization group at criticality and complete analyticity of constrained models: A numerical study

We study the majority rule transformation applied to the Gibbs measure for the 2D Ising model at the critical point. The aim is to show that the renormalized Hamiltonian is well defined in the sense that the renormalized measure is Gibbsian. We analyze the validity of Dobrushin-Shlosman uniqueness (DSU) finite-size condition for the constrained models corresponding to different configurations of the image system. It is known that DSU implies, in our 2D case, complete analyticity from which, as recently shown by Haller and Kennedy. Gibbsianness follows. We introduce a Monte Carlo algorithm to compute an upper bound to Vasserstein distance (appearing in DSU) between finite-volume Gibbs measures with different boundary conditions. We get strong numerical evidence that indeed the DSU condition is verified for a large enough volumeV for all constrained models.     

The geometry of the quantum correction for topological σ-models

The ring (Frobenius algebra) of local observables for topological -models on ¹ with values in the grassmannianG(s, n) is known to be the same as the quotient of the homology ring of the target space by the (inhomogeneous) ideal generated by the so-called quantum correction. While the need for a quantum correction comes from algebraic motivations in field theory, the aim of this paper is to understand its geometric meaning. The simple examples of ^{1 n} models tell us that the quantum correction comes by restriction on the boundary of the moduli spaces which allows to compute intersections on moduli spaces of lower degrees. We will check this point of view for the case of ¹ G(s,n) models, yielding a proof of the algebraic result from physics in terms of the geometry of the -model itself.Work partially supported by National Project 40% Probabilistic and geometrical methods in Mathematical Physics and by CNR-Gruppo Nazionale di Fisica Matematica.     

A model of Piron's preparation-question structures in Ludwig's selection structures

We give a model of the basic Jauch-Piron (JP) approach to quantum physics, i.e., of preparation-question structure (with four basic axioms and without axioms C, P, A), in terms of Ludwig's selection structure; in the latter structure the primitive notion of individual sample of a physical entity is formally described (without making reference to any probability concept). Once we interpret Piron's concept of question in Ludwig's context of a selection structure, we find that there is no difficulty in formalizing notions such as performable together questions; moreover, results such as = or ()= can be formally proved. We develop the theory along the lines of the JP approach; the set of JP propositions is derived and it turns out to be a complete lattice, as happens in Piron's theory, but with a different physical interpretation of the lattice operations. Finally, we study some connections between the standard Ludwig foundation and our approach.     

The effect of microsegregation on the generation of dislocations in zinc single crystals

The applicability of Tiller's considerations on the production of dislocations is proved. The density of dislocations appearing during impurity microsegregation increases with increasing rate of growth as a consequence of the corresponding change in the effective distribution coefficient. The real value of C at the microsegregation boundaries is at least twice as great as the average value of the concentration of impurities in the crystal in question.

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The theory of the spinning impact of imperfectly elastic bodies

The first theoretical solution is given of the spinning impact of an imperfectly elastic sphere on a rigid, imperfectly rough plane. The method of solution is based on the general static theory of the impact of rough bodies, elaborated by one of the authors in 1952 [5]. The problem leads to a non-linear differential equation, which can be solved only by an approximate numerical method. The results of the theory are in good agreement with the experiments carried out in 1947 [4].

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In conclusion the authors thank Dr. Vaclav Goldbach, lecturer at our department, for valuable help in making the experimental apparatus and in carrying out the difficult measurements by the method described in section 3 of this paper. Our thanks also go to O. Brha for help in the graphical solution and drawing of the figures.     

C*-Algèbres des systèmes canoniques. I

The twisted convolution associated with the Weyl form of the canonical commutation relations forn degrees of freedom is decribed using ordinary convolution on a nilpotent central extension of additive phase space by the one-dimensional torus. Twisted convolution determines severalC*-algebras of quantum mechanical observables amongst which we study especially the algebra ₂( , ) consisting of the ₂-functions on phase space and mapped isometrically onto the Hilbert-Schmidt-operators by the Schrödinger representation. The two last sections of the paper deal with phase space quantum mechanics from the point of view of twisted convolution: theWigner-Moyal formalism and the entire function formalism ofBargmann andSegal.     

Металлографические методы определепия нлотности дислокаци й В монокристаллах германия

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СВЕТОСИЛА ЭЛЕКТРОНН О-ОПТИЧЕСКИХ СИСТЕМ

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Hilbert Space or Gel'fand Triplet. Time-Symmetric or Time-Asymmetric Quantum Mechanics

Intrinsic microphysical irreversibility is thetime asymmetry observed in exponentially decayingstates. It is described by the semigroup generated bythe Hamiltonian H of the quantum physical system, not by the semigroup generated by a Liouvillian Lwhich describes the irreversibility due to the influenceof an external reservoir or measurement apparatus. Thesemigroup time evolution generated by H is impossible in the Hilbert space (HS) theory, which allowsonly time-symmetric boundary conditions and a unitarygroup time evolution. This leads to problems with decayprobabilities in the HS theory. To overcome these and other problems (nonexistence of Dirac kets)caused by the Lebesgue integrals of the HS, one extendsthe HS to a Gel'fand triplet, which contains not onlyDirac kets, but also generalized eigenvectors of the self-adjoint H with complex eigenvalues(E_R – i/2) and a Breit-Wignerenergy distribution. These Gamow states^G have a time-asymmetric exponentialevolution. One can derive the decay probability of the Gamow state into the decay productsdescribed by from the basic formula of quantummechanics (t) = Tr(|^G ›‹^G|), which in HS quantum mechanicsis identically zero. From this result one derives the decay rate (t) and all the standard relations between(0), , and the lifetime_R used in the phenomenology of resonancescattering and decay. In the Born approximation oneobtains Dirac's Golden Rule.     

Contribution to the theory of single-mode laser modulation II. Conduction modulation

The problem of conduction modulation of laser radiation is considered. It is shown that acoustic wave interacting with photon field in active medium causes a periodic modulation of the number of quanta in the single-mode gas laser. The problem of modulation is solved quantum mechanically and it is shown that dielectric and conduction modulation give similar results.     

Quantum mechanics and the direction of time

In recent papers the authors have discussed the dynamical properties of large Poincaré systems (LPS), that is, nonintegrable systems with a continuous spectrum (both classical and quantum). An interesting example of LPS is given by the Friedrichs model of field theory. As is well known, perturbation methods analytic in the coupling constant diverge because of resonant denominators. We show that this Poincaré catastrophe can be eliminated by a natural time ordering of the dynamical states. We obtain then a dynamical theory which incorporates a privileged direction of time (and therefore the second law of thermodynamics). However, it is only in very simple situations that this time ordering can be performed in an extended Hilbert space. In general, we need to go to the Liouville space (superspace) and introduce a time ordering of dynamical states according to the number of particles involved in correlations. This leads then to a generalization of quantum mechanics in which the usual Heisenberg's eigenvalue problem is replaced by a complex eigenvalue problem in the Liouville space.     

The propagation of excitation energy in perturbed crystals

The process of the propagation of excitation energy in perturbed dielectric crystals with a weak bond between the atoms having zero permanent dipole moment is studied. It is shown that on certain assumptions this process of propagation can be regarded as the motion of a Frenkel exciton in the electrostatic field of the defect. Frenkel's exciton can be characterized in this case as a neutral polarizable particle having induced dipole moment equal to the change in the induced dipole moment of the crystal during the excitation of one of its atoms.

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Основные соотношени я длн построения механических селект оров нейтронов

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