A probabilistic analysis of the difficulties of unifying quantum mechanics with the theory of relativity

A procedure is given for the transformation of quantum mechanical operator equations into stochastic equations. The stochastic equations reveal a simple correlation between quantum mechanics and classical mechanics: Quantum mechanics operates with “optimal estimations,” classical mechanics is the limit of “complete information.” In this connection, Schrödinger's substitution relationsp _x → -i? ?/?x, etc, reveal themselves as exact mathematical transformation formulas. The stochastic version of quantum mechanical equations provides an explanation for the difficulties in correlating quantum mechanics and the theory of relativity: In physics “time” is always thought of as a numerical parameter; but in the present formalism of physics “time” is described by two formally totally different quantities. One of these two “times” is a numerical parameter and the other a random variable. This last concept of time shows all the properties required by the theory of relativity and is therefore to be considered as the relativistic time.     

Finite-temperature quantum field theory in Minkowski space

We formulate finite-temperature quantum field theories in Minkowski space (real time) using Feynman path integrals. We show that at non-zero temperature a new field arises which plays the role of a ghost field and is necessary for unambiguous Feynman rules. Consequently, the finite-temperature Lagrangian is different from the zero-temperature one and a new, discrete Z₂ symmetry arises. We discuss the functional formalism and spontaneous symmetry breakdown at finite temperature and also the possibility of spontaneous breakdown of the (thermal) Z₂ symmetry.     

Equilibrium and non-equilibrium hard thermal loop resummation in the real time formalism

We investigate the use of the hard thermal loop (HTL) resummation technique in non-equilibrium field theory. We use the Keldysh representation of the real time formalism (RTF). We derive the HTL photon self energy and the resummed photon propagator. We show that no pinch singularities appear in the non-equilibrium HTL effective propagator. We discuss a possible regularization mechanism for these singularities at higher orders. As an example of the application of the HTL resummation method within the RTF we discuss the damping rate of a hard electron. Received: 9 April 1998 / Published online: 21 September 1998     

Dynamics of and radiation from superconducting strings and springs

We present a detailed study of the dynamics of and radiation from superconducting strings. We derive an approximate local action for a current-carrying vortex line and present some exact solutions to its equation of motion. These include stable static “springs” and oscillating “kinky” loops. For one of these “kinky” loops we are able to calculate the radiation exactly, and find (in contrast to previous work) the result is finite. We also argue that the non-local electromagnetic self-interaction of a loop causes the kinks to slowly straighten out. Finally, we discuss the loss of current at “cusp-like” regions and show that the shrinking of loops generally leads to current loss rather than gain.     

Structure-dependent optical anisotropy of porphyrin Langmuir–Schaefer films

We have studied the optical anisotropy of Langmuir–Schaefer layers of PdC₁₀OAP porphyrin, deposited onto gold substrates with thickness in the range 0–16 monolayers (ML). Deposition has been carried out at two values of the surface pressure Π, corresponding to different layer structures. In one case (Π=30 mN/m), molecules are well ordered in stacks oriented edge-on with respect to the substrate. In the other (Π=10 mN/m), a complex reorganization of the system happens several days after deposition, to form a mesoscopic two-dimensional lattice. The spectra measured by reflectance anisotropy spectroscopy (RAS) in two cases are clearly characterized. In the former, the line shape is dominated by a characteristic, large structure appearing in coincidence with the Soret band of the molecule, the development of which from a “peak-like” to a “derivative-like” appearance occurs at a well-defined critical thickness Θ_c (8 ML). In the latter, the line shape is always “peak-like”. We explain both line shapes in terms of morphological characteristics of the layer, occurring at different thickness values. The present results clearly show the potential of RAS to characterize efficiently the deposition of organic materials, and suggest that in short time it will be used as an in situ and real time spectroscopy, as already done in inorganic growth.     

Fully Developed Turbulence and the Multifractal Conjecture

We review the Parisi-Frisch (Proc. Int. School of Physics “E. Fermi”, pp. 84–87, North-Holland, Amsterdam, 1985) MultiFractal formalism for Navier-Stokes turbulence with particular emphasis on the issue of statistical fluctuations of the dissipative scale. We do it for both Eulerian and Lagrangian Turbulence. We also show new results concerning the application of the formalism to the case of Shell Models for turbulence. The latter case will allow us to discuss the issue of Reynolds number dependence and the role played by vorticity and vortex filaments in real turbulent flows.     

Electron spin resonance and antiferromagnetic resonance of single crystals of yttrium doped with gadolinium

The nonlinear interaction of oscillation modes is investigated on the basis of Lagrangian formalism. Equations describing the changes of the bound mode amplitudes versus time, are obtained. It is shown that the energy transformation between different modes is of a periodic nature: if in the initial moment of time an appreciable part of the energy is contained, for example, in them-th mode, then after a period of timeTt (called a time of nonlinear interaction) the energy will be transformed to then-th mode. Expressions forT _t for cases with the interaction of two and three modes are obtained. As a particular case the process of nonlinear interaction of the electron “transverse” and “longitudinal” oscillations in the highfrequency hybrid resonance region of a “weakly” inhomogeneous plasma was investigated.     

Surface wave at grazing-incidence Mössbauer diffraction

Dynamical theory of Mössbauer diffraction in the presence of hyperfine interaction for TRBD-geometry are developed. We show that “dispersion surfaces interaction” must be taken into account by exact solution of boundary condition if χ > 10^-4. We fined out that the oversurface diffracted wave intensity reaches maximum value at ? ～ ?_c and reveal an unusual angular dependence.     

Duality and quantum-algebra symmetry of the AN−1(1) open spin chain with diagonal boundary fields

We show that the transfer matrix of the A_N−1⁽¹⁾ open spin chair with diagonal boundary fields has the symmetry U_q(SU(l)) × U_q(SU(N−l)) × U(1), as well as a “duality” symmetry which maps l ↔ N − l. We exploit these symmetries to compute exact boundary S-matrices in the regime with q real.     

Self-consistent calculation of the optical potential and ground-state properties of nuclear matter

On the basis of the Green-function formalism, we performed a self-consistent calculation of the self-energy ∑(k, ω) of a particle interacting with the infinite nuclear medium. The function ∑(k, ω) was mapped out in the energy-momentum plane, and the single-particle energy ω(k), momentum distribution ?(k) and the “on-shell” part of the self-energy, ∑(k, ω(k)), were defined, from which all physical properties followed. In particular we investigated the ground-state properties of nuclear matter in two Λ-approximations of the T-matrix. In one, the intermediate two-particle propagator, Λ₀₀, represented free-particle propagation; in the other, called Λ₁₁, intermediate states included both interacting particles and holes. Pauli principle effects were included in both approximations. The second approximation was expected to be conserving because it included a large part of the rearrangement effects which, we found, contributed ～6 MeV per particle to the average energy and ～28 MeV to the singleparticle energy at zero momentum. The Hugenholtz-van Hove theorem was nearly satisfied, with only 1 MeV separating the chemical potential from the average energy. We also studied, in the Λ₀₀-approximation, the optical potential for the scattering of a particle by a large nucleus; it was directly related to the “on-shell” part of the self-energy. It was found that, below 100 MeV, the real part varied as (?90 + 0.584E) [MeV], and the imaginary part as (2.4 + 0.009 E) [MeV].     

Supergraphity: (II). Manifestly covariant rules and higher-loop finiteness

We continue our discussion of the background field formalism in supersymmetric theories, deriving new covariant Feynman rules for chiral superfields. As a result, we obtain improved power-counting rules for both simple and extended supersymmetry which can be used to make the following statements: If the corresponding extended superfield formalism exist, (a) N=2 supersymmetric Yang-Mills theory is finite beyond one loop, (b) N=4 Yang-Mills is finite at all loops, and (c) N=8 supergravity is finite through six loops. We also find that in simple super-Yang-Mills the radiative corrections to the Fayet-Iliopoulos (“D”) term, which are known to vanish for higher loops, also vanish automatically at one loop for arbitrary couplings.     

Statistical approach to the kinetics of nonuniform fluids

We present a new formalism in Fourier space for the study of spatially nonuniform fluids in nonequilibrium states which generalizes previous work on uniform fluids. Starting from the Liouville equation we obtain a hierarchy of equations for the reduced distribution functions which gives their rate of change at any given order of the system mean density as a sum of a finite number of terms. Using a finite-ranged repulsive interaction potential we derive, as a first application of the formalism, the Boltzmann integrodifferential equation for an infinite system which is initially in a “weakly” inhomogeneous state. This is accomplished introducing an initial statistical assumption, namely initial molecular chaos; this condition is seen to hold during the time evolution described by the resulting kinetic equation.     

A calculation of low-energy πN partial waves based on fixed-t analyticity

The real parts of πN partial waves from threshold to 500 MeV/c and below threshold down to the nucleon-exchange cut are calculated from “partial-wave relations” which are obtained by a projection of fixed-t dispersion relations. The formalism proposed by earlier authors was modified such that the method can also be applied to the isospin-even amplitudes. Except for the partial waves P13, D13, D33 and D35, the results are compatible with the KH80 partial-wave solution. The agreement with our new fits to the partial-wave dispersion relation is reasonable, except for D33 and D35. Our results are useful as a starting solution and as constraints in partial-wave analyses. They show to what extent the “experimental” partial-wave amplitudes are compatible with various analyticity constraints. For further applications, we have calculated the coefficients of a threshold expansion which converges up to 320 MeV/c, provided one considers the one-nucleon contribution separately.     

Excitation of the Classical Electromagnetic Field in a Cavity Containing a Thin Slab with a Time-Dependent Conductivity

We derive an exact infinite set of coupled ordinary differential equations describing the evolution of the modes of the classical electromagnetic field inside an ideal cavity containing a thin slab with the time-dependent conductivity σ(t) and dielectric permittivity ε(t) for the dispersion-less media. We analyze this problem in connection with the attempts to simulate the so-called dynamical Casimir effect in three-dimensional electromagnetic cavities containing a thin semiconductor slab periodically illuminated by strong laser pulses. Therefore, we assume that functions σ(t) and δε(t) = ε(t) ? ε(0) are different from zero during short time intervals (pulses) only. Our main goal here is to find the conditions under which the initial nonzero classical field could be amplified after a single pulse (or a series of pulses). We obtain approximate solutions to the dynamical equations in the cases of “small” and “big” maximal values of the functions σ(t) and δε(t). We show that the single-mode approximation used in the previous studies can be justified in the case of “small” perturbations, but the initially excited field mode cannot be amplified in this case if the laser pulses generate free carriers inside the slab. The amplification could be possible, in principle, for extremely high maximum values of conductivity and the concentration of free carries (the model of an “almost ideal conductor”) created inside the slab under the crucial condition providing the negativity of the function δε(t). This result follows from a simple approximate analytical solution confirmed by exact numerical calculations. However, the evaluation shows that the necessary energy of laser pulses must be, probably, unrealistically high.     

A study of Fe-doped Bi-Sr-Ca-Cu superconductors

We have substituted 1.5% of Fe for Cu in several “2212” and “2223” Bi-Sr-Ca-Cu superconductors. All of the samples show a reduction ofT _c about 13 K due to the Fe impurities. Mössbauer measurements at room temperature reveal the structural characteristics such as stacking faults and intergrowth of different phases in these Bi-based compounds on the microscopic scale. The susceptibility ofT _c to Fe-doping in the Bi-“2212” or “2223” system is comparable to that of the “123” system but much smaller than that of the “214” system. The interplanar correlation existing in the “123” and the Bi-“2212” and “2223” systems seems to play an important role in sustaining the high temperature superconductivity and weakening the detrimental effect of impurity elements on superconductivity in these two systems.     

Glueball singularity,flavour loops and the Harari-Freund picture

We discuss several points concerning the structure of the cylinder term in the dual topological expansion. Using dual field theory as a guide, we concentrate on the possibility of a two-singularity scheme à la Harari-Freund. We start from results obtained previously at the lowest order in ?=N _f /N _c and study what can be the role of flavour-loop corrections in the real world where ?～1. It is argued that, in spite of the actual value of ?, precise mechanisms exist which can weaken the role of the flavour-loop corrections in the kinematical region where “soft” dynamics dominates. We also claim that theS-matrix at largeN _c (?≈-0) incorporates already many realistic features, and we refute some objections recently raised against the Harari-Freund picture.     

Pseudoscalars and vector mesons in a unitary and self-consistently broken SU(6) W scheme

We estimate hadronic self-energy effects to “bare” pseudoscalar (P) and vector (V) meson states due to theP→PV→P, P→VV→P, V→ PP→V, V→PV→V andV→VV→V loops. We simulate higher order diagrams by consistently requiring external and internal particles to have the same mass. We find good agreement with all the experimental masses (exceptm _π), widths and mixing angles. The “bare”P andV states are heavy (≈1.26 GeV) and degenerate up to a smallm _s?m_u quark mass difference term. The “bare” coupling constants for thePPV, PVV andVVV vertices obey exact OZI rule and almost exact SU(6) _W symmetry. We use a common cut-off ofk _cm?0.7 GeV/c corresponding to a harmonic oscillator radius of ?0.7 fm for all SU(6) _W related thresholds except for the pion.     

Fine structure of the diffraction cone: Manifestation of <Emphasis Type="Italic">t</Emphasis>-channel unitarity

We show that the deviation from exponential behavior of the diffraction cone observed near t = ?0.1 GeV² both at the ISR and the LHC (so-called break) follows from a two-pion loop in the t-channel, imposed by unitarity. By using a simple Regge-pole model we extrapolate the “break” from the ISR energy region to that of the LHC.     

Comments on the electric modulus formalism model and superior alternatives to it for the analysis of the frequency response of ionic conductors

Because of the past and continuing wide usage of the 1973 original modulus formalism (OMF) model for analyzing dispersive frequency-response data of ion-conducting materials, it is important to discuss and demonstrate its theoretical and experimental inadequacies to help avoid its future use and to describe and illustrate important alternatives to it. The OMF fits data with a K1 response model alone, one indirectly derived from stretched-exponential temporal behavior, while the corrected modulus formalism (CMF) involves the composite CK1 model, one that includes in addition a separate free, parallel bulk dielectric parameter, ε_D∞. The crucial error of the OMF approach is its identification of a high-frequency-limiting dielectric constant intrinsic to K1 response and associated entirely with conductive effects, with the full high-frequency-limiting dielectric constant of the material, ε_∞, one that must include the non-ionic, primarily dipolar quantity ε_D∞. Comparison here of OMF fitting results with those of the CMF CK1 model for both an experimental data set and an exact one derived from it demonstrate the incorrectness of the OMF and the virtues of the CK1 alternative. The OMF fitting approach, but not the CMF one, leads to crucial inconsistency between the estimates of its β shape parameter for fits of the data expressed at all immittance levels except those of σ′ and ε″, where it yields the same results as the CK1. Its incorrect β estimates, extensively used in the Ngai coupling model and interpreted as being associated with ion–ion correlations, also lead to erroneous “excess wing” effects in plots of the imaginary part of the data and fit at the modulus level. Further, OMF modulus-level fits yield non-physical estimated values of the characteristic relaxation time of the K1 model. Finally, some possible alternatives to the CK1 model are discussed for situations involving dielectric-system dispersion.     

Orientational dynamics of superfluid 3He: A “two-fluid” model. II. Orbital dynamics

We present a phenomenological theory of the homogeneous orbital dynamics of the class of “separable” anisotropic superfluid phases which includes the ABM state generally identified with ³He-A. The theory is developed by analogy with the spin dynamics described in the first paper of this series; the basic variables are the orientation of the Cooper-pair wavefunction (in the ABM phase, the l-vector) and a quantity K which we visualize as the “pseudo-angular momentum” of the Cooper pairs but which must be distinguished, in general, from the total orbital angular momentum of the system. In the ABM case l is the analog of d in the spin dynamics and K of the “superfluid spin” S_p. Important points of difference from the spin case which are taken into account include the fact that a rotation of l without a simultaneous rotation of the normal-component distribution strongly increases the energy of the system (“normal locking”), and that the equilibrium value of K is zero even for finite total angular momentum. The theory does not claim to handle correctly effects associated with any intrinsic angular momentum arising from particle-hole asymmetry, but it is shown that the magnitude of this quantity can be estimated directly from experimental data and is extremely small; also, the Landau damping does not emerge automatically from the theory, but can be put in in an ad hoc way. With these provisos the theory should be valid for all frequencies $\text{ω ?}\text{Δ(T)}\text{h}\text{?}$ irrespective of the value of ωτ. (Δ = gap parameter, τ = quasi-particle relaxation time.) It disagrees with all existing phenomenological theories of comparable generality, although the disagreement with that of Volovik and Mineev is confined to the “gapless” region very close to T_c.The phenomenological equations of motion, which are similar in general form to those of the spin dynamics with damping, involve an “orbital susceptibility of the Cooper pairs” χ_orb(T). We give a possible microscopic definition of the variable K and use it to calculate χ_orb(T) for a general phase of the “separable” type. The theory is checked by inserting the resulting formula in the phenomenological equations for ωτ ? 1 and comparing with the results of a fully microscopic calculation based on the collisionless kinetic equation; precise agreement is obtained for both the ABM and the (real) polar phase, showing that the complex nature of the ABM phase and the associated “pair angular momentum” is largely irrelevant to its orbital dynamics. We note also that the phenomenological theory gives a good qualitative picture even when ω ～ Δ(T), e.g., for the flapping mode near T_c. Our theory permits a simple and unified calculation of (1) the Cross-Anderson viscous torque in the overdamped regime, (2) the flapping-mode frequency near zero temperature, (3) orbital effects on the NMR, both at low temperatures and near T_c, (4) the orbit wave spectrum at zero temperature (this requires a generalization to inhomogeneous situations which is possible at T = 0 but probably not elsewhere). We also discuss the possibility of experiments of the Einstein-de Haas type. Generally speaking, our results for any one particular application can be also obtained from some alternative theory, but in the case of orbital and spin relaxation very close to T_c (within the “gapless” region) our predictions, while somewhat tentative and qualitative, appear to disagree with those of all existing theories. We discuss briefly how our approach could be extended to apply to more general phases.