Stationary non-equilibrium states of infinite harmonic systems

We investigate the existence, properties and approach to stationary non-equilibrium states of infinite harmonic crystals. For classical systems these stationary states are, like the Gibbs states, Gaussian measures on the phase space of the infinite system (analogues results are true for quantum systems). Their ergodic properties are the same as those of the equilibrium states: e.g. for ordered periodic crystals they are Bernoulli. Unlike the equilibrium states however they are not stable towards perturbations in the potential.We are particularly concerned here with states in which there is a non-vanishing steady heat flux passing through every point of the infinite system. Such superheat-conducting states are of course only possible in systems in which Fourier's law does not hold: the perfect harmonic crystal being an example of such a system. For a one dimensional system, we find such states (explicitely) as limits, whent, of time evolved initial states _i in which the left and right parts of the infinite crystal are in equilibrium at different temperatures, _L ^–L _R ^–1 , and the middle part is in an arbitrary state. We also investigate the limit of these stationary (t) states as the coupling strength between the system and the reservoirs goes to zero. In this limit we obtain a product state, where the reservoirs are in equilibrium at temperatures _L ^–1 and _R ^–1 and the system is in the unique stationary state of the reduced dynamics in the weak coupling limit.On leave of absence from the Fachbereich Physik der Universität München. Work supported by a Max Kade Foundation FellowshipResearch supported in part by NSF Grant MPS75-20638     

High-temperature series for scalar-field Lattice models: Generation and analysis

An implementation of the free-embedding scheme for high-temperature series generation on the body-centered cubic family of lattices in arbitrary dimensiond is, described. Series to order 21 in inverse temperature are tabulated for several scalar field models, both for the magnetic susceptibility and for the second moment of the spin correlation function. The critical behavior of a family of 3-dimensional double Gaussian models, which interpolate continuously between the spin-1/2 Ising model and the Gaussian model, is analyzed in detail away from the Gaussian model limit using confluent inhomogeneous secondorder differential approximants. With our best estimate of the correction-to-scaling exponent,=0.52±0.03, the leading exponents for the susceptibility and correlation length for this family are consistent with universality and are given by=1.237±0.002 and =0.630±0.0015, respectively, and=2–/=0.0359±0.0007.     

On the electromagnetic structure of elementary particles

Using modern similarity and dimensionality methods, criteria of similarity are derived and used as transformations, which effect the conversion from one natural system of units to another. The exclusion principles thus defined are used to determine the powers of the similarity criteria in quantitative relations.Systems of units of the fermion and boson types are used in the simplest identification of the parameters corresponding to elementary particles.A set of electric and magnetic physical constants with dimensionality length, area, and volume, is obtained and successfully unified within the limits of a vortex ring, the maximum dimensions of which are defined by the Compton wavelength, and the minimum by the classical radius of the particle. The vortex ring model is in accordance with the latest experimental data, and it enables the behavior of the incident and target particles in the scattering process to be predicted.In modern theoretical physics the elementary particles are still considered as essentially structureless point formations, and hence it is impossible to give a purely theoretical treatment of the structure of the particles. Thus the various attempts in this direction (Hofstadter, Blokhintsev) have a polyphenomenological character and are internally inconsistent. (The search for the structure of an elementary particle is carried out on the assumption that it is not elementary, since truly elementary particles are defined as point size.) The author recognizes the need for an original approach to the structure of elementary particles, based on a method of study adequate for the problem. Such a method is the theory of dimensionality and similarity (Sedov, Gukhman, and Kirpichev), which serves as a scientific basis of a physical experiment (Kirpichev), or as the scientific basis for a model of the phenomena, insofar as the criteria of similarity are a reflection of the physical model of the process (Gukhman).It is a pleasure to thank Academician L. I. Sedov and Professor K. A. Putilov for valuable criticism and advice, and Professor A. S. Irisov and V. V. Lokhin for useful discussions.     

Zeros of the partition function and Gaussian inequalities for the plane rotator model

The partition function for ferromagnetic plane rotators in a complex external field , with ¦Im ¦ ¦Re ¦, is bounded below in modulus by its value at =0. The proof is based on complex combinations of duplicated variables which are positive definite on a subgroup of the configuration group. In the isotropic situation (and =0), the associated Gaussian inequalities imply that all truncated correlation functions decay at least as the two-point function.     

Particle velocities faster than the speed of light

In connection with another article by the author, we show how it might be possible to travel faster than the speed of light. We show that for clocks and rods moving faster than the speed of light, we get instead of time dilation and Lorentz contraction, respectively, time contraction and Lorentz expansion, respectively. It is shown that this paper is in confirmation with earlier articles dealing with this subject.     

More inequalities for critical exponents

A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequalitydv +2 2–. Others are 1 1 +v, 1 1 , 1,d 1 + 1/ (for d),dv, ₃ + (for d), ₄ , and _{2m 2m+2} (form 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.NSF Predoctoral Fellow (1976–1979). Research supported in part by NSF Grant PHY 78-23952.     

An experiment to test an explanation of a possible violation of quantum theory

An experiment to test a possible explanation of the Schmidt backwards causation results is suggested. The experiment might distinguish between many- and one- world interpretations of quantum theory.     

Standpoint cosmology

An unorthodox cosmology is based on a notion of standpoint, distinguishing past from future, realized through Hilbert-space representation of the complex conformai group for 3+1spacetime and associated coherent states. Physical (approximate) symmetry attaches to eight-parameter complex Poincaré displacements, interpretable as growth of standpoint age (one parameter), boost of matter energy-momentum in standpoint rest frame (three parameters) and displacement of matter location in a compact U(1)O(4)/O(3) spacetime attached to standpoint (four parameters). An initial condition (at big bang) is characterized by a huge dimensionless parameter that breaks dilation invariance. Four major length scales are recognized, called Planck, particle, lab, and Hubble, with separations controlled by ; all physical concepts, including spacetime, depend on wideness of scale separation.     

Motion of a test body in Taub space

We examine the motion of a test body in a static Taub space. It is shown that in the case of a fall to a gravitating plane, the test body on approach cannot have velocity greater than the velocity of light, measured by the clock of a distant observer or in its proper reference frame. The greater the velocity of a body receding from the plane, the greater the height to which it rises over the gravitating plane, however, the maximal height of its rise equals x=1/, i.e., the weaker the gravitational field, the greater the height ¦x¦ to which the body rises. We give a qualitative analysis of the arbitrary motion of a test body in a static Taub space.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 27–32, February, 1989.     

Замечание К теории по степенного возникновения подви жных слоев в плазме инертных газов

[1] t _B , t _B . , t _B , . .

---

A note on the theory of the successive production of moving striations in the plasma of inert gases

Approximate expressions are derived on the basis of Pekárek's theoretical paper [1] for the period of the maximum t_B of a wave packet produced by the passage of a wave of stratification before the aperture of a photomultiplier, and for its time width in the half-height t_B. The relaxation time of a wave of stratification, following from the theory [1], can thus be calculated by means of the experimentally measured velocity of motion of the maximum of a wave packet u and its width t_B. The calculation is supplemented by numerical data on the magnitude of errors committed by using approximate expressions.

     

ПРОВОДИМОСТЬ СРЕДНЕ Й ЧАСТИ КАНАЛА КОНДЕНСИРОВАННЫХ РА ЗРНДОВ

. , . . - , 500 10 000 30 500 . - , .     

The conceptual analysis (CA) method in theories of microchannels: Application to quantum theory. Part I. Fundamental concepts

A method is proposed that should facilitate the construction of theories of submicroscopic particles (denoted as theories of microchannels) in a way similar to the use of group-theoretical methods. The conceptual analysis (CA) method is based on the analysis of the basic concepts of a theory; it permits a determination of necessary conditions imposed on the mathematical apparatus (of the theory) which then appear as a mathematical representation of the structures obtained in a formal scheme of a theory. A pertinent conceptual analysis leads to a new definition (relativization) of the concept empirical implication. The approach may be characterized as realistic and operational. The application of the CA method is illustrated on the example of quantum theory. In Part I the algebraic structure of a partially ordered, up-ward directed, bounded set is deduced from the rudimentary concepts. In Parts II and III, we shall deduce the Hilbert-space structure (well established in quantum mechanics) from postulates on some essential idealizations accepted in the theory. Whereas Part II is concerned with the idealizations of existing quantum theories based on the Hilbert-space formalism, Part I may be considered as a general basis for a wider class of theories.Dedicated to Prof. G. Ludwig on the occasion of his 60th birthday.     

Quantitative method for determination of fibre texture in wires I. Principle of method and analytical expression of absorption factor

An X-ray diffraction method is described for the quantitative determination of the fibre texture in cylindrical specimens (wires), which does not require specimen preparation. The integrated intensity of the diffracted radiation from a certain atomic plane is measured in the direction parallel to the plane determined by the axis of the wire and by the direct beam for different orientations of the axis of the wire. These measurements can be carried out in practice using an X-ray counter diffractometer or Weissenberg goniometer. The pole figure is determined from the dependence of the diffracted intensity on the orientation of the wire after correcting the intensities for the absorption of radiation in the specimen. The geometric arrangement enables the absorption factor to be calculated analytically. Its form was verified experimentally by measuring the dependence of the intensity of the 220 reflection on the orientation of the axis of a cylindrical specimen of Al containing randomly oriented crystals.

---

I.

( ), . , , , . . , . . 220 .

---

---

The author wishes to thank Z. iký for help in carrying out the measurements and calculations.     

Quantum-Monte-Carlo simulations for fermionic systems

The paper gives a general idea of Quantum-Monte-Carlo simulations for fermionic systems in higher dimensions. A basic trick is provided to avoid the minus-sign problems which in some form lead to unsurmountable difficulties in simulations, for example at lower temperatures and for larger system sizes.     

Anti-photon

It should be apparent from the title of this article that the author does not like the use of the word photon, which dates from 1926. In his view, there is no such thing as a photon. Only a comedy of errors and historical accidents led to its popularity among physicists and optical scientists. I admit that the word is short and convenient. Its use is also habit forming. Similarly, one might find it convenient to speak of the aether or vacuum to stand for empty space, even if no such thing existed. There are very good substitute words for photon, (e.g., radiation or light), and for photonics (e.g., optics or quantum optics). Similar objections are possible to use of the word phonon, which dates from 1932. Objects like electrons, neutrinos of finite rest mass, or helium atoms can, under suitable conditions, be considered to be particles, since their theories then have viable non-relativistic and non-quantum limits. This paper outlines the main features of the quantum theory of radiation and indicates how they can be used to treat problems in quantum optics.It is a pleasure to join in the 60th birthday celebration of the Director, Herbert Walther, of the Max-Planck-Institute for Quantum Optics at Garching, and wish him much happiness and many more years of his very great scientific creativity.     

Double quantum transitions in paramagnetic resonance

The theory of double quantum transitions of the M=±2 type, with regard to inhomogeneously broadened spin systems is studied in this paper with the approximation ²T₂T₃ 1. We suppose that the inhomogeneous broadening is formed by an inhomogeneous crystal field. The obtained results describe the magnitude of absorption as a function of the h.f. power and also describe the shape of the absorption curve. It is demonstrated that in inhomogeneously broadened spin systems the absorption curve of double quantum transitions has the form of the difference of two different Lorentz's curves and that at the saturation ( ²T₂T₁ 1) the absorption increases with the cube of the h.f. field intensity. The shape of the curves is expressed by means of phenomenological relaxation constants of the system.

---

M=±2 ²T₂T₃ 1. , - . . , ( ²T₂T₁ 1) . .

     

The temperature vibrations of urea molecules

The structural and dynamic parameters of urea at 112°K and 295°K were determined by the least squares method. The characteristic temperature of the torsional optical vibrations of a molecule about a C-O bond was determined and is in good agreement with the value determined by Raman scattering. The fractional X-coordinate of the nitrogen atom corrected for torsional vibrations was determined and it was found that the magnitude of the projection of the C-N bond in the given temperature range changes only within the limits of observational errors. A new method, called temperature difference synthesis, is described and it is shown that it is suitable for rapid qualitative determination of the thermal anisotropy of the vibrations of atoms in a crystal lattice.

---

112°K 295°K. C-O , , . X- , C-N . , , , .

     

Dark body and black hole horizons

The formula for the horizon of a Newtonian dark body is given and compared to that of a relativistic black hole: a Newtonian dark body has at least one hair.     

On the asymptotics of occurrence times of rare events for stochastic spin systems

We consider translation-invariant attractive spin systems. LetT _,x ^v be the first time that the average spin inside the hypercube reaches the valuex when the process is started from an invariant measure with density smaller thanx. We obtain sufficient conditions for (1) ¦¦^–1 logT _,x ^v (x) in distribution as ¦¦ , and ¦¦^–1 logT _,x ^v (x) as ¦¦ , where (x):= –lim ¦¦^–1 log {(average spin inside ) x. And (2)T _,x ^v /ET _,x ^v converges to a unit mean exponential random variable as ¦¦ . Both (1) and (2) are proven under some type of rapid convergence to equilibrium. (1) is also proven without extra conditions for Ising models with ferromagnetic pair interactions evolving according to an attractive reversible dynamics; in this case is a thermodynamic function. We discuss also the case of finite systems with boundary conditions and what can be said about the state of the system at the timeT _,x ^v .On leave from São Paulo University.     

К ВОПРОСУ O КРИТИЧЕСКО Й ЧАСТОТЕ ПРИ ПРЕРЫВИСТОМ ОСВЕ ЩЕНИИ

c , c n , n AgBr. .