Metastability and nucleation for the Blume-Capel model. Different mechanisms of transition

We study metastability and nucleation for the Blume-Capel model: a ferromagnetic nearest neighbor two-dimensional lattice system with spin variables taking values in {–1,0, +1}. We consider large but finite volume, small fixed magnetic fieldh, and chemical potential in the limit of zero temperature; we analyze the first excursion from the metastable –1 configuration to the stable +1 configuration. We compute the asymptotic behavior of the transition time and describe the typical tube of trajectories during the transition. We show that, unexpectedly, the mechanism of transition changes abruptly when the lineh=2 is crossed.     

AN EXTENSION OF “POPPER'S EXPERIMENT” CAN TEST INTERPRETATIONS OF QUANTUM MECHANICS

Karl Popper proposed a way to test whether a proposed relation of a quantum-mechanical state to perceived reality in the Copenhagen interpretation (CI) of quantum mechanics—namely that the state of a particle is merely an expression of what is known about the system—is in agreement with all experimental facts. A conceptual flaw in Popper's proposal is identified and an improved version of his experiment (called Extension step 1)—which fully serves its original purpose—is suggested. The main purpose of this paper is to suggest to perform this experiment. The results of this experiment predicted under the alternative assumptions that the CI or the many-worlds interpretation (MWI) is correct are shown to be identical. Only after a further modification (called Extension step 2) (the use of an ion isolated from the macroscopic environment as particle detector) the predictions using the respective interpretations become qualitatively different. This is because what is known by a human observer H can fail as a basis for the prediction of the statistical distribution of measurement results within the MWI in special cases: The temporal evolution of a system un-entangled with H (like the isolated ion) can depend on another system's state components that are entangled with states ortogonal to H. Thus—within the CI—for H they are known not to exist. Yet H can infer their existence by studying the evolution of the ion.     

The modular group and super-KMS functionals

Every normal, faithful, self-adjoint functional on a von Neumann algebraA canonically determines a one-parameter-weakly continuous *-automorphism group (the analog of the modular group) and a canonical ₂ grading onA, commuting with . We show that the functional satisfies the weak super-KMS property with respect to and Furthermore, we prove that and are the unique pair of a-weakly continuous one-parameter *-automorphism group and a grading of the algebra, commuting with each other, with respect to which is weakly super-KMS. The above results thus provide a complete extension of the theory of Tomita and Takesaki to the nonpositive case.Supported in part by the National Science Foundation under Grant DMS-8922002.     

Luminescence of Higher Plants upon Excitation by Laser Radiation with Different Energy and Time Parameters

The luminescence response of the leaves of higher plants exposed to laser radiation with different energy and time parameters has been investigated at a wavelength of 685 nm. The plants were irradiated by laser radiation at 1060, 632, and 530 nm. Radiation at = 632 nm was used as the control. It is shown that radiation at = 1060 nm suppresses photosynthesis, whereas that at = 530 nm stimulates it.     

Physical properties of some McVittie metrics

A class of McVittie's new nonquadratic solutions is investigated in some detail with regard to its physical properties. It is found that decreasing pressure and density are not compatible with center regularity for these perfect fluid spheres. It is further seen that for gaseous spheres (i.e., the density drops to zero at the outer boundary of the sphere together with the pressurep) oscillatory motions arenot possible. For these gaseous models the pressure and the density are both positive inside the outer surface, and their respective gradients are negative. For the outer gaseous shells models are constructed where for a certain time interval the pressure is increasing for contracting models. Without any restriction with respect to time, for these shell models it found that the density is increasing for contracting models, and the adiabatic speed of sound is less than the speed of light. It is also found that the trace of the energy-momentum tensor is positive, the total mass is negative, and for collapsing shells the rate of change of circumference as measured by an observer riding on the shell is an increasing function of time. However, all these models have the strange geometric feature that the physical radius is a decreasing function of comoving radial coordinate.     

Exponential decay near resonance,without analyticity

We consider a quantum mechanical model which displays the behaviour associated with having a resonance or metastable state. The Hamiltonian depends on a parameter . When =0, there is an eigenstate ₀; when 0, ₀ dissolves into the continuous spectrum, showing approximate exponential decay. We prove this result without using dilatation analyticity. The model describes a two-state atom coupled to the quantized radiation field. The state space of the field is truncated, so that only the vacuum and one-photon states are included.This work was partially supported by NSF Grant DMS-8922941     

A kinetic equation with kinetic entropy functions for scalar conservation laws

We construct a nonlinear kinetic equation and prove that it is welladapted to describe general multidimensional scalar conservation laws. In particular we prove that it is well-posed uniformly in — the microscopic scale. We also show that the proposed kinetic equation is equipped with a family of kinetic entropy functions — analogous to Boltzmann's microscopicH-function, such that they recover Krushkov-type entropy inequality on the macroscopic scale. Finally, we prove by both — BV compactness arguments in the multidimensional case and by compensated compactness arguments in the one-dimensional case, that the local density of kinetic particles admits a continuum limit, as it converges strongly with 0 to the unique entropy solution of the corresponding conservation law.Research was supported in part by the National Aeronautics and Space Administration under NASA Contract No. NAS1-18605 while the authors were in residence at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA 23665. Additional support for the second author was provided by U.S.-Israel BSF Grant No. 85-00346. Part of this research was carried out while the first author was visiting Tel-Aviv University     

The unrestricted Hartree-Fock method

The unrestricted Hartree-Fock method is important for discussing several effects, including the spin density produced in the core of an atom by exchange with an unfilled valence electron shell. The method allows electrons with and spins to have slightly different orbitals due to the differing exchange interaction, but ignores the fact that this automatically results in gaining also some in-out correlation energy. The validity of the method must therefore be questioned, since correlation is in general the larger effect. It is shown that in atomic calculations the method gives results which are in fact correct to a good order of approximation. However, the interplay of spin polarisation and correlation is such that in some molecular or other systems the method would fail.     

Vlasov hydrodynamics of a quantum mechanical model

We derive the Vlasov hydrodynamics from the microscopic equations of a quantum mechanical model, which simulates that of an assembly of gravitating particles. In addition we show that the local microscopic dynamics of the model corresponds, on a suitable time-scale, to that of an ideal Fermi gas.Work supported in part by Fonds zur Förderung der wissenschaftlichen Forschung in Osterreich, Project number 3569     

Periodic Motion of Atoms Near a Charged Wire

We study the classical motion of an atom in the vicinity of an infinite straight wire which carries an oscillating uniform charge. This system has been proposed as a mechanism for trapping cold neutral atoms. The parameters of the problem are the magnitude Q and frequency of oscillation of the charge, the mass M and polarizability of the atom, and the angular momentum L of the atom about the wire. For 0 and 2MQ ² greater than, but close to, L ², we prove that the atom's radial motion is periodic (with period 2/), and that the atom moves in a helical path around the wire. For 2MQ ² L ² we prove that the atom must either collide with the wire or else escape to infinity in the radial direction.     

Theory of electronic transport in two-dimensional systems in the presence of magnetic fields

The paper of three parts is focused on the Landauer-Büttiker approach to the study of transport in two-dimensional electron systems, with particular attention to the influence of an external magnetic field. In the previous part the total conductance of such a system was shown to be proportional to the transmission current. In the present part we give a detailed proof, based on the linear response theory, to the last statement. The value of the magnetic field may be arbitrary and possible inhomogeneity of the electric field is also considered.The author wishes to thank to Professor P. Steda and Professor L. Smrka for discussions and encouragement.     

HNC calculations of the partial structure factors of molten AgI

We have calculated the pair distribution functions and partial structure factors of molten AgI within the hypernetted chain (HNC) approximation. We have assumed that the effective interionic pair potentials are the same in the liquid and solid states, and have used the potentials constructed by Parrinello et al., which they used to describe both -AgI and the phase transition in AgI. The structure of molten AgI exhibits features similar to those of molten CuCl. Both of these salts melts from a superionic phase.     

Effect of uniaxial stresses on the character of the first-order antiferromagnetic phase transition in an Mn-8 at. % Ge alloy

The method of neutron diffraction is used to construct temperature dependences of the intensity of 110 antiferromagnetic reflection under the influence of compressive stresses = 0–150 MPa along [001]. Application of the stresses leads to an increase in the transition temperature, the transition being delayed in proportion to the increase in the load. On the other hand, the loading leads to a reduction in the magnetization jump for the antiferromagnetic sublattices. Thus, at > 100 MPa, the antiferromagnetic transformation takes on features of a second-order phase transformation. The transition which takes place in the stressed state is characterized by smoother rearrangment of short-order antiferromagnetic order into long-range order, as is evidenced by erosion of the transition boundary. The model proposed here — which does not ascribe the usual effect to uniaxial stresses on the antiferromagnetic transition in -Mn alloys — is based on the anomalous temperature dependence of the elastic constants.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 92–97, March, 1987.     

“Projective relativity” and magnetohydrodynamics

The geometrical structure of the Castelnuovo space-time and the Fantappié group are analyzed with the Inönj-Wigner method of contraction of a group with respect to the various subgroups. If we utilize the two vectorsposition andvelocity, we can study the structure of the magnetohydrodynamics tensor. It follows that from projective magnetohydrodynamics we can deduce as limiting cases four theories (two by two duals in the sense of the classical projective geometry).     

Diffusion of positive muons and other light particles in metals

The paper gives a survey of the principal techniques available for the experimental determination of the diffusivityD ⁺(T) of positive muons in crystals (Gurevich technique, trapping, longitudinal muon-spin relaxation, transverse muon-spin relaxation in superconductors) and discusses their strengths and weaknesses. The main theoretical ideas of the quantum theory of diffusion are outlined and the distinction between different mechanisms is emphasized. It is argued that at high temperaturesT the so-called adiabatic regime with a preexponential factor of the diffusivity of the order of magnitude _D d ² ( _D = Debye frequency of the host crystal,d=jump distance of the muons) always exists. In the fcc metals and in the case of¹H in Nb it is followed by a so-called Flynn-Stoneham regime at intermediate temperatures, whereas for ⁺ in Nb and-Fe such a regime is not observed. Instead, in these cases the adiabatic regime appears to go over directly to the few-phonon regime of incoherent tunnelling between adjacent ground states, leading to the one-phononD ⁺ ~T law at low temperatures.The metal best-studied with regard to muon diffusion,-Fe, is used to illustrate the theoretical analysis of experimental results in some detail. In an Appendix the theoretical expressions required for the quantitative determination ofD ⁺ by the Gurevich technique are collected.     

Testing non-commutative QED \gamma\gamma\gamma and \gamma\gamma\gamma\gamma couplings at LHC

In this work, we investigate the sensitivity of the process at LHC for the photonic 3- and 4-point functions that appear in non-commutative QED. We show that this process serves to study the behavior of the space-space as well as of the space-time non-commutativity. We also show that this process can probe the non-commutative scale in the range of a few TeV.Received: 9 February 2004, Revised: 27 February 2004, Published online: 8 April 2004     

Short-range order in binary alloys taking into account formation of structural domains

A model is proposed for representing microinhomogeneities of disordered alloys as cubic structural domains. The concept of an effective atom introduced in this article made it possible to express the relation between property and composition in terms of property parameters of nearest atom pairs, the domain size, and the short-range parameter of the first coordination sphere ₁. Using as an example the concentration dependence of the Young modulus, the thermal linear expansion coefficient, and the magnetic anisotropy constant we have determined the property parameters of atom pairs and the composition dependence of ₁ and of the domain size of disordered alloys of the Ni_1-cFe_c, system (0c0.25).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 59–64, September, 1977.     

Physical Gauge in the Problem of Dynamical Chiral Symmetry Breaking in QED in a Magnetic Field

We describe how the choice of an appropriate (physical) gauge leads to the solution of a nonperturbative problem in quantum electrodynamics: dynamical chiral symmetry breaking in QED in a constant magnetic field.     

Deducing the Schrödinger equation from minimum χ2

The most unbiased probabilistic model for the possible values of a characteristic of a quantum system subject to the constraints represented by some known mean values characterizes the system in a steady-state condition. We suppose that random fluctuations alter such a steady-state condition. The probability distribution of the possible deviations from the steady-state condition is estimated by minimizing Pearson's ² subject to the mean fluctuations available. The optimum Pearson function ^* may be interpreted as the wave function of the system and in the case of the harmonic oscillator, the free particle in a box, and the hydrogen atom, the prediction based on it is compatible with that provided by the solution of the corresponding Schrödinger equations.     

Method for obtaining high phase space density in a surface-mounted atom trap

We describe a method for obtaining a high phase space density of alkali atoms in a surface-mounted microscopic atom trap created above a transparent conductor or permanent magnet on a substrate prism. We show that the peak value of the phase space density can locally reach the level of 10^-2 when the microtrap is loaded with atoms from a gravito-optical surface trap. Initial spin polarization of the atoms is not required. PACS 32.80.Pj; 39.25.+k; 03.75.Be