Kubo formula for frequency dispersion of dielectric permittivity and static conductivity of the Coulomb system

It is proved that the Kubo formula for the conductivity σ(ω) is valid at real frequencies ω. On this basis, an exact relation is derived for the static conductivity σst of the Coulomb system. It is shown that the static conductivity is determined by the time correlation function in the limit t→∞. It is proved that the permittivity ε(ω) satisfies the Kramers-Kronig relations which take into account a singularity associated with static conductivity.     

An evolutionary framework for cultural change: Selectionism versus communal exchange

Dawkins? replicator-based conception of evolution has led to widespread mis-application of selectionism across the social sciences because it does not address the paradox that necessitated the theory of natural selection in the first place: how do organisms accumulate change when traits acquired over their lifetime are obliterated? This is addressed by von Neumann?s concept of a self-replicating automaton (SRA). A SRA consists of a self-assembly code that is used in two distinct ways: (1) actively deciphered during development to construct a self-similar replicant, and (2) passively copied to the replicant to ensure that it can reproduce. Information that is acquired over a lifetime is not transmitted to offspring, whereas information that is inherited during copying is transmitted. In cultural evolution there is no mechanism for discarding acquired change. Acquired change can accumulate orders of magnitude faster than, and quickly overwhelm, inherited change due to differential replication of variants in response to selection. This prohibits a selectionist but not an evolutionary framework for culture and the creative processes that fuel it. The importance non-Darwinian processes in biological evolution is increasingly recognized. Recent work on the origin of life suggests that early life evolved through a non-Darwinian process referred to as communal exchange that does not involve a self-assembly code, and that natural selection emerged from this more haphazard, ancestral evolutionary process. It is proposed that communal exchange provides an evolutionary framework for culture that enables specification of cognitive features necessary for a (real or artificial) societies to evolve culture. This is supported by a computational model of cultural evolution and a conceptual network based program for documenting material cultural history, and it is consistent with high levels of human cooperation.     

Compressible effect algebras

We define a special type of additive map J on an effect algebra E called a compression. We call J(1) the focus of J and if p is the focus of a compression then p is called a projection. The set of projections in E is denoted by P(E). A compression J is direct if J(a) ≤ a for all a ε E. We show that direct compressions are equivalent to projections onto components of cartesian products. An effect algebra E is said to be compressible if every compression on E is uniquely determined by its focus and every compression on E has a supplement. We define and characterize the commutant C(p) of a projection p and show that a compression with focus p is direct if and only if C(p) = E. We show that P(E) is an orthomodular poset. It is proved that the cartesian product of effect algebras is compressible if and only if each component is compressible. We then consider compressible sequential effect algebras, Lüders maps and conditional probabilities.     

Central charges and Lorentz and internal symmetries in massive supersymmetric quantum field theory

The properties of central charges in the framework of the massive supersymmetric quantum field theory related to internal symmetries, Lorentz covariance and locality of the fields are investigated. It is shown that in the presence of z central charges the largest semisimple part of the internal symmetry algebra is a direct sum of z compact symplectic group algebras and possibly an additional term representing the unimodular unitary group algebra. Next it is shown that 4j ? N + K, where j is the highest spin value of the underlying fields, N is the number of spinorial charges and K the number of these spinorial charges which are not linked to other spinorial charges by a central charge. It is further demonstrated that, in general, the central charge can not be redefined in such a way that it is at the same time real and preserves the locality principle. The discussion of the obtained results concludes the paper.     

Momentum distributions in the nucleus

The nuclear form factor F(q) and one particle momentum distribution p(q) can be shown to have a power law decrease for large momenta. For the form factor F(q) we show that it is q/A that must be large for this asymptotic behavior to be important. For only q large the form factor, in a simple model, is shown to decrease exponentially in q. A similar behavior for p(q) is proposed.     

The Monge Problem for Distance Cost in Geodesic Spaces

We address the Monge problem in metric spaces with a geodesic distance: (X, d) is a Polish space and d _L is a geodesic Borel distance which makes (X, d _L ) a non branching geodesic space. We show that under the assumption that geodesics are d-continuous and locally compact, we can reduce the transport problem to 1-dimensional transport problems along geodesics. We introduce two assumptions on the transport problem π which imply that the conditional probabilities of the first marginal on each geodesic are continuous or absolutely continuous w.r.t. the 1-dimensional Hausdorff distance induced by d _L . It is known that this regularity is sufficient for the construction of a transport map. We study also the dynamics of transport along the geodesic, the stability of our conditions and show that in this setting d _L -cyclical monotonicity is not sufficient for optimality.     

Killing vector fields and the Einstein-Maxwell field equations with perfect fluid source

This paper is concerned with space-times that satisfy the Einstein-Maxwell field equations in the presence of a perfect fluid, which may be charged. We consider the following question. Suppose that the space-time admits a group of motions (isometries), i.e., that the metric is invariant under a group of transformations. Does it follow that the quantities that describe the source, i.e., the electromagnetic field tensorF _ij, the charge densityε, and the four-velocityu ⁱ, energy densityμ, and pressurep of the fluid, are invariant under the group? It is found that the behavior of these quantities under the group is strongly restricted. In particular in the case of the three-dimensional special orthogonal groupSO(3), which arises in the case of spherically symmetric space-times, it is found that the source quantities are invariant. On the other hand, it is established that there exist groups under whichF _ij is not necessarily invariant. The above question is also considered for the case of homothetic motions.     

On the ground state of an impurity in a dilute fermi gas

The system under consideration is a large collection of identical fermions (B), forming a background, into which is inserted a relatively small number of distinct impurity (I) particles. The background is considered to be dilute in the sense that R ? a, where R is the average separation of the B particles, and a is the range of their interaction potential; and the I particles are so dilute with respect to the B particles that I-I interactions can be ignored. The I particles are then all essentially at rest in their ground state. The BB and BI interaction potentials are chosen to be hard cores of the same range a. A series expansion is developed for the ground-state energy of the I particles, and the first four terms are calculated explicitly using two distinct methods, employing Feynman and Goldstone diagrams respectively. It is shown that each method has distinct advantages over the other, and that a judicious combination of both can be used to considerable benefit.     

Isochronous Systems, the Arrow of Time, and the Definition of Deterministic Chaos

It is shown how, given an arbitrary dynamical system, other systems can be manufactured which are isochronous (periodic in all their degrees of freedom with an arbitrarily assigned fixed period T) and whose dynamics coincides exactly with that of the original system over a fraction 1 ? ?? of that period where ?? is a number that can be arbitrarily assigned in the range 0 < ?? < 1. The treatment is in the context of autonomous dynamical systems whose equations of motion feature infinitely differentiable functions of the dependent variables. It is argued that this possibility suggests that it would be useful to devise measures of the degree of complexity of a dynamical system which are associated with finite portions of its time evolution??hence going beyond the standard characterizations of the chaotic behavior of a dynamical system (via its Lyapunov coefficients or its ergodic properties), requiring its observation over infinite time.     

Spectral changes of partially coherent flat topped beam in turbulent atmosphere

Spectral characteristics of partially coherent flat-topped (PCFT) beams propagated in a turbulent atmosphere are investigated and an analytical formula for the spectrum S(ω) is derived. It is shown that, if the scaling law is valid, the normalized spectrum S(ω) of PCFT beams propagating through turbulent atmosphere is the same as the normalized source spectrum S⁽⁰⁾(ω), this similarity is valid for any arbitrary order of the circular flat-topped “N”. It is proved that if the scaling law is not valid, S(ω) of PCFT is different from S⁽⁰⁾(ω). Also spectral behavior of PCFT beams in free space and turbulence media is investigated in detail.     

Index of authors and papers

It is shown that a hydrodynamic matrix describing the coupling between n variables that are even under time reversal and m variables that are odd has in the dissipation-free limit 2n or 2m (whichever is smaller) purely imaginary roots and ∣n ? m∣ roots that are zero.     

Effect of diffusion on gain saturation in gas lasers

A theoretical model is developed to account for the effect of diffusion on gain saturation in gas lasers. It is shown that the effect can be characterized by the functionK(k ₂ a, k ₂ b), which depends on pressure, temperature, radius of the beama, and the radius of the cylindrical cavityb. It is concluded that diffusion can be very effective whenk ₂ a is small andb is several times larger thana.     

Mass shift of σ-meson in nuclear matter

The propagation of σ-meson in nuclear matter is studied in the Walecka model, by assuming that the sigma couples to a pair of nucleon–antinucleon states and to particle–hole states. The in-medium effect of σ–ω mixing is also studied. For completeness, the coupling of sigma to two virtual pions was also considered. It is found that the σ-meson mass decreases with respect to its value in vacuum and that the contribution of the σ–ω mixing effect on the mass shift is relatively small.     

On holomorphic extrapolations of the scattering amplitude into the complex plane

Dispersion-relation extrapolations of the scatering amplitude compatible with error affected data are discussed. It is shown that if the complex argument z is chosen so that the analyticity domain D of the amplitude is the interior of the unit circle the Cauchy kernel 1/(z'-z) gives the best holomorphic extrapolation linear in the data input in the sense that its error bounds cannot be improved simultaneously for all points of D.     

Objectivity vs. Locality in Quantum Physics

An Objectivity Principle (O) and a Locality Principle (L) are considered with respect to two simple, but fundamental Gedanken experiments, namely a “Welcher-Weg” Gedanken experiment and an Einstein-Podolsky-Rosen (EPR) Gedanken experiment. It is shown that, if both principles (O) and (L) are assumed to be valid, a contradiction, in the EPR case Bell’s inequality, can be derived implying that at least one of the two principles (O) and (L) has to be denied. It is shown that, if (O) is denied, (L) is preserved in the EPR-Gedanken experiment. For a more adequate discussion, in particular of (L), the two experiments are described in Minkowskian space-time of special relativity.     

Movement of gas-filled cavities in alkalihalide crystals produced by external force fields

The migration of gas-filled cavities in KBr, NaCl, LiF single-crystals is investigated experimentally in an electric field and a temperature gradient.It is shown, that migration in an electric field is strongly dependent on the surface purity, due to its influence on matter transport along cavity surface. It is found that the velocity of cavity (v), having a ‘dirty’ surface follows a V～1/R dependence. (R—cavity size). In case of a ‘pure’ cavity surface. V is independent of R. Different types of V-vs-R dependence result in intermediate regions.Migration in a temperature gradient is also sensitive to surface purity. When the state of surface purity is determined, an appropriate critical size (R^*) exists such that if R is smaller than R^*, V～R and if R is larger than R^*, V is independent of R.Some constants of investigated process are determined from obtained experimental data.     

Light-front quark model and analysis of the spectrum of photons from inclusive B → X s γ decays

The electroweak-decay width Γ(B → X _s γ) is investigated in a light-front (LF) constituent quark model. A new partonlike formula is derived that establishes a simple relation between Γ(B → X _s γ) and the b → sγ decay width. A treatment of the b quark as an on-mass-shell particle and the inclusion of effects that arise from the transverse motion of the b quark in the B meson are basic features of this approach. Adopting different b-quark LF distribution functions, both phenomenological ones and those that are derived from constituent quark models, and neglecting perturbative corrections, we compute the photon energy spectra and the moments of the shape function. It is shown that the LF approach can be matched completely with a heavy-quark expansion (HQE), provided that the constituent b-quark mass is redefined in a way similar to that used in HQE to define the pole mass of the b quark. In this way, the correction to first order in 1/m _b can be eliminated from the total width in agreement with the general statement of HQE. We also show that the photon energy spectra calculated in the LF approach agree well with those obtained in the model of Altarelli et al., provided that the same distribution function is used as an input in both cases. Despite the simplicity of the model, our results are in fairly good agreement both with HQE predictions and with available experimental data.     

Optically pumped quantum magnetometer with combined advantages of M X and M Z devices

A scheme of the magnetometer that simultaneously employs M _X and M _R magnetic resonance signals with the latter signal related to the radial component of the rotating atomic magnetic moment is proposed and tested. With respect to the shape, dynamic characteristics, and metrological parameters, the M _R signal is similar to the M _X signal that is widely used in magnetometry but the former signal can be detected simultaneously with the M _X signal using a common radio optical scheme. The proposed device represents a fast M _X magnetometer with the phase in the feedback loop that is controlled by a slow precise M _R magnetometer implemented using the same atoms. The device that can be based on a conventional M _X sensor simultaneously exhibits a relatively short response time (τ ≤ 0.1 s) and the accuracy that is approximately equal to the resolution of the quantum M _X discriminator at times of 10–100 s. The scheme is experimentally tested, and the statistic estimate of reproducibility is (1.2 ± 1.1) pT.     

Structure of Shocks in Burgers Turbulence with Lévy Noise Initial Data

We study the structure of the shocks for the inviscid Burgers equation in dimension 1 when the initial velocity is given by Lévy noise, or equivalently when the initial potential is a two-sided Lévy process ψ ₀. When ψ ₀ is abrupt in the sense of Vigon or has bounded variation with lim?sup_|h|↓0 h ^?2 ψ ₀(h)=∞, we prove that the set of points with zero velocity is regenerative, and that in the latter case this set is equal to the set of Lagrangian regular points, which is non-empty. When ψ ₀ is abrupt we show that the shock structure is discrete. When ψ ₀ is eroded we show that there are no rarefaction intervals.     

Hot electron streaming and population inversion for polar and deformation scattering

Comparison of hot electron phenomena under polar (n-GaAs) and deformation (p-Ge) inelastic optical phonon scattering is made on the basis of analytical calculation and numerical simulation by the Monte-Carlo method. The difference in the character of drift velocity saturation in these materials is demonstrated. It is shown that population inversion of hot carriers in crossed E ⊥ B fields provides negative magnetoresistance and may give rise (in p-Ge) even to NDC. It is shown that in p-Ge in crossed fields overpopulation of the light hole band arises which can strongly affect J-E characteristics and can result in amplification of FIR radiation.