arXiv subjects

G. Modanese

Publications and source records attributed to G. Modanese.

At least 55 records · Page 3Linked to original sources

arXiv2016

Ultra-light and strong: the massless harmonic oscillator and its singular path integral

In classical mechanics, a light particle bound by a strong elastic force just oscillates at high frequency in the region allowed by its initial position and velocity. In quantum mechanics, instead, the ground state of the particle becomes completely de-localized in the limit $m \to 0$. The harmonic oscillator thus ceases to be a useful microscopic physical model in the limit $m \to 0$, but its Feynman path integral has interesting singularities which make it a prototype of other systems exhibiting a "quantum runaway" from the classical configurations near the minimum of the action. The probability density of the coherent runaway modes can be obtained as the solution of a Fokker-Planck equation associated to the condition $S=S_{min}$. This technique can be applied also to other systems, notably to a dimensional reduction of the Einstein-Hilbert action.

physics.gen-ph↗

arXiv2016

Mathematical models describing the effects of different tax evasion behaviors

Microscopic models describing a whole of economic interactions in a closed society are considered. The presence of a tax system combined with a redistribution process is taken into account, as well as the occurrence of tax evasion. In particular, the existence is postulated, in relation to the level of evasion, of different individual taxpayer behaviors. The effects of the mentioned different behaviors on shape and features of the emerging income distribution profile are investigated qualitatively and quantitatively. Numerical solutions show that the Gini inequality index of the total population increases when the evasion level is higher, but does not depend significantly on the evasion spread. For fixed spread, the relative difference between the average incomes of the worst evaders and honest taxpayers increases approximately as a quadratic function of the evasion level.

q-fin.GN↗

arXiv2016

Stochastic Effects in a Discretized Kinetic Model of Economic Exchange

Linear stochastic models and discretized kinetic theory are two complementary analytical techniques used for the investigation of complex systems of economic interactions. The former employ Langevin equations, with an emphasis on stock trade; the latter is based on systems of ordinary differential equations and is better suited for the description of binary interactions, taxation and welfare redistribution. We propose a new framework which establishes a connection between the two approaches by introducing stochastic effects into the kinetic model based on Langevin and Fokker-Planck formalisms. Numerical simulations of the resulting model indicate positive correlations between the Gini index and the total wealth, that suggests a growing inequality with increasing income. Further analysis shows a simultaneous decrease in inequality as social mobility increases in presence of a conserved total wealth, in conformity with economic data.

q-fin.GN↗

arXiv2016

Generalized Maxwell equations and charge conservation censorship

The Aharonov-Bohm electrodynamics is a generalization of Maxwell theory with reduced gauge invariance. It allows to couple the electromagnetic field to a charge which is not locally conserved, and has an additional degree of freedom, the scalar field $S=\partial_αA^α$, usually interpreted as a longitudinal wave component. By re-formulating the theory in a compact Lagrangian formalism, we are able to eliminate $S$ explicitly from the dynamics and we obtain generalized Maxwell equation with interesting properties: they give $\partial_μF^{μν}$ as the (conserved) sum of the (possibly non-conserved) physical current density $j^ν$, and a "secondary" current density $i^ν$ which is a non-local function of $j^ν$. This implies that any non-conservation of $j^ν$ is effectively "censored" by the observable field $F^{μν}$, and yet it may have real physical consequences. We give examples of stationary solutions which display these properties. Possible applications are to systems where local charge conservation is violated due to anomalies of the ABJ kind or to macroscopic quantum tunnelling with currents which do not satisfy a local continuity equation.

physics.gen-ph↗

arXiv2016

Innovation diffusion equations on correlated scale-free networks

We introduce a heterogeneous network structure into the Bass diffusion model, in order to study the diffusion times of innovation or information in networks with a scale-free structure, typical of regions where diffusion is sensitive to geographic and logistic influences (like for instance Alpine regions). We consider both the diffusion peak times of the total population and of the link classes. In the familiar trickle-down processes the adoption curve of the hubs is found to anticipate the total adoption in a predictable way. In a major departure from the standard model, we model a trickle-up process by introducing heterogeneous publicity coefficients (which can also be negative for the hubs, thus turning them into stiflers) and a stochastic term which represents the erratic generation of innovation at the periphery of the network. The results confirm the robustness of the Bass model and expand considerably its range of applicability.

physics.soc-ph↗

arXiv2016

The Bass diffusion model on networks with correlations and inhomogeneous advertising

The Bass model, which is an effective forecasting tool for innovation diffusion based on large collections of empirical data, assumes an homogeneous diffusion process. We introduce a network structure into this model and we investigate numerically the dynamics in the case of networks with link density $P(k)=c/k^γ$, where $k=1, \ldots , N$. The resulting curve of the total adoptions in time is qualitatively similar to the homogeneous Bass curve corresponding to a case with the same average number of connections. The peak of the adoptions, however, tends to occur earlier, particularly when $γ$ and $N$ are large (i.e., when there are few hubs with a large maximum number of connections). Most interestingly, the adoption curve of the hubs anticipates the total adoption curve in a predictable way, with peak times which can be, for instance when $N=100$, between 10% and 60% of the total adoptions peak. This may allow to monitor the hubs for forecasting purposes. We also consider the case of networks with assortative and disassortative correlations and a case of inhomogeneous advertising where the publicity terms are "targeted" on the hubs while maintaining their total cost constant.

physics.soc-ph↗

arXiv2016

Microscopic models for the study of taxpayer audit effects

A microscopic dynamic model is here constructed and analyzed, describing the evolution of the income distribution in the presence of taxation and redistribution in a society in which also tax evasion and auditing processes occur. The focus is on effects of enforcement regimes, characterized by different choices of the audited taxpayer fraction and of the penalties imposed to noncompliant individuals. A complex systems perspective is adopted: society is considered as a system composed by a large number of heterogeneous individuals. These are divided into income classes and may as well have different tax evasion behaviors. The variation in time of the number of individuals in each class is described by a system of nonlinear differential equations of the kinetic discretized Boltzmann type involving transition probabilities.

q-fin.GN↗

arXiv2015

Common Origin of Power-law Tails in Income Distributions and Relativistic Gases

Power-law tails are ubiquitous in income distributions and in the energy distributions of diluted relativistic gases. We analyze the conceptual link between these two cases. In economic interactions fat tails arise because the richest individuals enact some protection mechanisms ("saving propensity") which allow them to put at stake, in their interactions, only a small part of their wealth. In high-energy particle collisions something similar happens, in the sense that when particles with very large energy collide with slow particles, then as a sole consequence of relativistic kinematics (mass dilation), they tend to exchange only a small part of their energy; processes like the frontal collision of two identical particles, where the exchanged energy is 100%, are very improbable, at least in a diluted gas. We thus show how in two completely different systems, one of socio-economic nature and one of physical nature, a certain feature of the binary microscopic interactions leads to the same consequence in the macroscopic distribution for the income or respectively for the energy.

physics.gen-ph↗

arXiv2015

Gravitational radiation of a vibrating physical string as a model for the gravitational emission of an astrophysical plasma

The vibrating string is a source of gravitational waves which requires novel computational techniques, based on the explicit construction of a conserved and renormalized (in a classical sense) energy-momentum tensor. The renormalization is necessary to take into account the effect of external constraints, which affect the emission considerably. Vibrating media offer in general a testing ground for reconciling conflicts between General Relativity and other branches of physics; however, constraints are absent in sources like the Weber bar, for which the standard covariant formalism for elastic bodies can also be applied. Our solution method is based on the linearized Einstein equations, but relaxes other usual assumptions like far-field approximation, spherical or plane wave symmetry, TT gauge and source without internal interference. The string solution is then adapted to give the radiation field of a transversal Alfven wave in a rarefied plasma, where the tension is produced by an external static magnetic field. Like for the string, the field strength turns out to be independent from the frequency. We give a preliminary example of a numerical solution based on parameters referred to Alfven waves in the solar corona. Further astrophysical applications require an extension of the solution procedure to second order in the amplitude, and consideration of border effects. Future work will also address numerical and analytical near-field solutions.

physics.gen-ph↗

arXiv2014

Functional integral transition elements of a massless oscillator

The massless harmonic oscillator is a rare example of a system whose Feynman path integral can be explicitly computed and receives its main contributions from regions of the functional space that are far from the classical and semiclassical configurations near the stationary point of the action. The functional average $\langle q_m^2 \rangle$ of the square of the coordinate at a time $t_m$ which is intermediate between the initial and final time gives a measure of the amplitude of quantum fluctuations with respect to the classical path. This average, or "transition element", is divergent in the massless limit, signaling a quantum runaway. We show that the divergence is not due to the continuum limit and formulate the conjecture that the divergent contributions come from regions where the action $S$ is constant and therefore the interference factor $e^{-iS/\hbar}$ does not oscillate. For most systems these regions have zero functional measure and thus give a null contribution to the path integral, but this is not the case for the massless oscillator. We study the simplest functional subspace with constant action, namely the one with $S=0$, which is connected to the classical solutions but extends to infinity, like an hyperplane through the origin; this subspace turns out to be infinite-dimensional. Some possible applications and developments are mentioned.

physics.gen-ph↗

arXiv2013

Comparison of metrics from retarded integrals and transverse traceless subgauge

The time-varying gravitational field produced by a Weber bar is used to explore mathematical features of the linearized Einstein equation. We present a self-contained formal framework for the treatment of the linear field, which is applicable to several situations where the standard quadrupolar formulas are not adequate. The expressions for retarded integrals reveal a singularity associated with boundary conditions. Results from the transverse traceless subgauge are compared with the radiation calculated from retarded integrals. Lienard-Wiechert potentials are used in a treatment of the Weber bar as a collection of point particles and further possible applications are outlined. The Riemann tensor clarifies the transition from near-field geodesic forces to tidal forces in the far field.

gr-qc↗

arXiv2011

Evolution of the IGG concept at IGF from 2004 to 2007

IGG is the acronym for Impulse Gravity Generator, a device developed by E. Podkletnov in 1997-2003 for generating high-voltage discharges through YBCO electrodes. According to Podkletnov, an anomalous force beam is generated at the discharge, which acts on distant material target of any composition with a small repulsive force proportional to the target mass. An independent replication of this device was started in 2004 at IGF, Germany (Institut fuer Gravitationsforschung, Goede Foundation). The author was involved as theoretical consultant and his first assignment was to study a possible scaled-down version of the device. This required a thorough analysis of the physical working principles of the apparatus, which was documented in several internal reports from 2004 to 2009. The whole content of those from 2004 to 2007 is given here. Several parts are outdated, but useful for an understanding of the phenomenon. In particular, the discharge mechanism was eventually found to be different, namely a vacuum spark discharge instead of a low pressure discharge with cascade gas ionization. Also outdated is the theoretical model developed in Ch. 1 on the "acceleration of Cooper pairs through the superconductor" as a possible basis for the anomalous emission. This naive representation, however, is useful to show that such an acceleration does not make sense in a superconductor like YBCO and that the correct picture is that of (low-voltage) tunnelling of pairs through intrinsic Josephson junctions. The present paper should therefore be regarded as an "historical summary", mainly valuable as a reference for further developments.

physics.gen-ph↗

arXiv2009

Conditions for stimulated emission in anomalous gravity-superconductors interactions

Several authors have studied the generation of gravitational fields by condensed-matter systems in non-extreme density conditions. General Relativity and lowest-order perturbative Quantum Gravity predict in this case an extremely small emission rate, so these phenomena can become relevant only if some strong quantum effect occurs. Quantum aspects of gravity are still poorly understood. It is believed that they could play a role in systems which exhibit macroscopic quantum coherence, like superconductors and superfluids, leading to an "anomalous" coupling between matter and field. We mention here recent work in this field by Woods, Chiao, Becker, Agop et al., Ummarino, Kiefer and Weber. New results are presented concerning anomalous stimulated gravitational emission in a layered superconductor like YBCO. We model the superconductor as an array of intrinsic Josephson junctions. The superconducting parameters are defined by our preliminary measurements with melt-textured samples. We write explicitly and solve numerically the Josephson equations which give the normal and super components of the total current in the superconductor, and derive from this the total available power P=IV. Then, assuming that the coefficients A and B for spontaneous and stimulated gravitational emission are known, we apply to this case the Frantz-Nodvik equation for a laser amplifier. The equation is suitably modified in order to allow for a "continuous pumping" given by an oscillating transport current. The conclusions are relevant for the evaluation of gravitational emission from superconductors. We find that even if the A and B coefficients are anomalously large (possibly because of the Quantum Gravity effects mentioned above), the conditions for stimulated emission are quite strict and the emission rate strongly limited by the IV value.

physics.gen-ph↗

arXiv2003

Local contribution of a quantum condensate to the vacuum energy density

We evaluate the local contribution g_[mu nu]L of coherent matter with lagrangian density L to the vacuum energy density. Focusing on the case of superconductors obeying the Ginzburg-Landau equation, we express the relativistic invariant density L in terms of low-energy quantities containing the pairs density. We discuss under which physical conditions the sign of the local contribution of the collective wave function to the vacuum energy density is positive or negative. Effects of this kind can play an important role in bringing about local changes in the amplitude of gravitational vacuum fluctuations - a phenomenon reminiscent of the Casimir effect in QED.

gr-qc↗

arXiv2002

Possible quantum gravity effects in a charged Bose condensate under variable e.m. field

In the weak field approximation to quantum gravity, a "local" positive cosmological term mu^2(x) corresponds to a local negative squared mass term in the Lagrangian and may thus induce instability and local pinning of the gravitational field. Such a term can be produced by the coupling to an external Bose condensate. In the functional integral, the local pinning acts as a constraint on the field configurations. We discuss this model in detail and apply it to a phenomenological analysis of recent experimental results.

gr-qc↗

arXiv2000

Zero-point field induced mass vs. QED mass renormalization

Haisch and Rueda have recently proposed a model in which the inertia of charged particles is a consequence of their interaction with the electromagnetic zero-point field. This model is based on the observation that in an accelerated frame the momentum distribution of vacuum fluctuations is not isotropic. We analyze this issue through standard techniques of relativistic field theory, first by regarding the field A_mu as a classical random field, and then by making reference to the mass renormalization procedure in Quantum Electrodynamics and scalar-QED.

hep-th↗

arXiv2000

The dipolar zero-modes of Einstein action: An informal summary with some new issues

We recall the main features of metric vacuum fluctuations which have the global property int d^4x sqrt{g(x)} R(x) = 0, even though R(x) does not vanish locally. We stress that these fluctuations could mediate an anomalous coupling between the gravitational field and coherent matter. Some new issues are discussed: (1) these fluctuations still imply that =0; (2) they are not extrema of the action; (3) for finite duration, their volume in phase space is not zero; (4) vacuum fluctuations of this kind are not allowed in QED; (5) their null-action property is a nonperturbative feature; (6) any -real- pure e.m. field generates zero-modes of this kind, too, up to terms of order G^2.

gr-qc↗

arXiv2000

Large "Dipolar" Vacuum Fluctuations in Quantum Gravity

We study a novel set of gravitational field configurations, called "dipolar zero modes", which give an exactly null contribution to the Einstein action and are thus candidates to become large fluctuations in the quantized theory. They are generated by static unphysical sources satisfying (up to terms of order G^2) the simple condition Int d^3x T_00(x) = 0. We give two explicit examples of virtual sources: (i) a "mass dipole" consisting of two separated mass distributions with different signs; (ii) two concentric "+/- shells". The field fluctuations can be large even at macroscopic scale. There are some, for instance, which last ~ 1 s or more and correspond to the field generated by a virtual source with size ~ 1 cm and mass ~ 10^6 g. This appears paradoxical, for several reasons, both theoretical and phenomenological. We also give an estimate of possible suppression effects following the addition to the pure Einstein action of cosmological or R^2 terms.

gr-qc↗