arXiv subjects

G. Modanese

Publications and source records attributed to G. Modanese.

At least 37 records · Page 2Linked to original sources

arXiv2023

Numerical Simulations Unveil Superradiant Coherence in a Lattice of Charged Quantum Oscillators

A system of ${N_{osc}}$ charged oscillators interacting with the electromagnetic field, spatially confined in a 3D lattice of sub-wavelength dimension, can condense into a superradiant coherent state if appropriate density and frequency conditions are met. In this state, the common frequency $ω$ of the oscillators and the plasma frequency $ω_p$ of the charges are combined into a frequency $ω'=\sqrt{ω^2+ω_p^2}$ that is off-shell with respect to the wavelength of the photon modes involved, preventing them from propagating outside the material. Unlike other atomic cavity systems, the frequency $ω$ in this case is not determined by the cavity itself but is defined by the periodic electrostatic potential that confines the charged particles in the lattice. Additionally, the electromagnetic modes involved have wave vectors distributed in all spatial directions, resulting in a significant increase in coupling. The analytical study of this system can be carried out in the limit of large ${N_{osc}}$ by searching for an approximation of the ground state via suitable coherent trial states. Alternatively, numerical simulations can be employed for smaller ${N_{osc}}$. In the numerical approach, it is possible to go beyond the Rotating Wave Approximation (RWA) and introduce a dissipation term for the photon modes. This dissipation term can account for the ohmic quench in a metal and also consider photon losses at the boundary of the material. By utilizing numerical solutions and Monte Carlo simulations, the presence of condensation has been confirmed, and an energy gap of a few electron volts (eV) per particle has been observed in typical metal crystals with protons bound to tetrahedral or octahedral sites.

physics.gen-ph↗

arXiv2023

Aharonov-Bohm electrodynamics in material media: a scalar e.m. field cannot cause dissipation in a medium

In the extension of Maxwell equations based on the Aharonov-Bohm Lagrangian the e.m. field has an additional degree of freedom, namely a scalar field generated by charge and currents that are not locally conserved. We analyze the propagation of this scalar field through two different media (a pure dielectric and an ohmic conductor) in a range of frequencies such that the properties of the media are independent from the frequency. We find that an e.m. scalar wave cannot propagate in a material medium. If a scalar wave in vacuum impinges on a material medium it is reflected, at most exciting in the medium a pure "potential" wave (which we also call a "gauge" wave) propagating at $c$, the speed of light in vacuum, with a vector potential whose Fourier amplitude is related to that of the scalar potential by $ω\mathbf{A}_{0}=\mathbf{k}ϕ_{0}$, where $ω^{2}=c^{2}\left\vert \mathbf{k}\right\vert^{2}$.

physics.class-ph↗

arXiv2022

Coherent Plasma in a Lattice

We present a fully second-quantized calculation showing the emergence of spontaneous coherent configurations of the electromagnetic field in interaction with charged bosons in a regular lattice. The bosons tend to oscillate at their plasma frequency, but are also subjected to electrostatic forces which keep them confined close to lattice sites and cause a frequency shift in the oscillation. Under certain conditions on these frequencies, we find that a suitably defined set of coherent states (coherent both in the field and matter degrees of freedom) exhibit a negative energy gap with respect to the perturbative ground state. This is true in the RWA approximation and for position-independent fields, both to first and second order in the interaction Hamiltonian. We compare this result with other recent findings from cavity QED and notice that: (1) consideration of full 3D wavefunctions and a careful definition of the coherent states are essential for obtaining the energy gap; (2) although our calculation is referred to bosons, it may also apply to protons bound in a crystal matrix, if their density is very low compared to the density of available states.

physics.gen-ph↗

arXiv2021

Diagonal degree correlations vs. epidemic threshold in scale-free networks

We prove that the presence of a diagonal assortative degree correlation, even if small, has the effect of dramatically lowering the epidemic threshold of large scale-free networks. The correlation matrix considered is $P(h|k)=(1-r)P^U_{hk}+rδ_{hk}$, where $P^U$ is uncorrelated and $r$ (the Newman assortativity coefficient) can be very small. The effect is uniform in the scale exponent $γ$, if the network size is measured by the largest degree $n$. We also prove that it is possible to construct, via the Porto-Weber method, correlation matrices which have the same $k_{nn}$ as the $P(h|k)$ above, but very different elements and spectrum, and thus lead to different epidemic diffusion and threshold. Moreover, we study a subset of the admissible transformations of the form $P(h|k) \to P(h|k)+Φ(h,k)$ with $Φ(h,k)$ depending on a parameter which leave $k_{nn}$ invariant. Such transformations affect in general the epidemic threshold. We find however that this does not happen when they act between networks with constant $k_{nn}$, i.e. networks in which the average neighbor degree is independent from the degree itself (a wider class than that of strictly uncorrelated networks).

physics.soc-ph↗

arXiv2021

Quantum uncertainty and energy flux in extended electrodynamics

In quantum theory, for a system with macroscopic wavefunction, the charge density and current density are represented by non-commuting operators. It follows that the anomaly $I=\partial_t ρ+ \nabla \cdot \mathbf{j}$, being essentially a linear combination of these two operators in the frequency-momentum domain, does not admit eigenstates and has a minimum uncertainty fixed by the Heisenberg relation $ΔN Δϕ\simeq 1$ which involves the occupation number and the phase of the wavefunction. We give an estimate of the minimum uncertainty in the case of a tunnel Josephson junction made of Nb. Due to this violation of the local conservation of charge, for the evaluation of the e.m. field generated by the system it is necessary to use the extended Aharonov-Bohm electrodynamics. After recalling its field equations, we compute in general form the energy-momentum tensor and the radiation power flux generated by a localized oscillating source. The physical requirements that the total flux be positive, negative or zero yield some conditions on the dipole moment of the anomaly $I$.

physics.gen-ph↗

arXiv2021

Quantum metrics with very low action in $R+R^2$ gravity

We have run numerical simulations of Euclidean lattice quantum gravity for metrics which are time-independent and spherically symmetric. The radial variable is discretized as $r=hL_{Planck}$, with $h=0,1,...,N$ and $N$ up to $10^5$. The Lagrangian is of the form $\sqrt{g}(R+αR^2)$ (in units $c=\hbar=G=1$) and the action is positive-definite, allowing the use of a standard Metropolis algorithm with update probability $\exp(-βΔS)$. By minimizing the $R+R^2$ action with respect to conformal modes, Bonanno and Reuter have recently found analytical evidence of a non-trivial "rippled" ground state resembling a kinetic condensate of QCD. Our simulations at low but finite temperature ($T=β^{-1}$) also display strong localized oscillations of the metric, whose total action $S$ remains $\ll \hbar$ thanks to the indefinite sign of $R$. The average metric $\langle g_{rr} \rangle$ is significantly different from flat space. The scaling properties of $S$ and $\langle g_{rr} \rangle$ are investigated in dependence on $N$ and $β$.

physics.gen-ph↗

arXiv2021

Are current discontinuities in molecular devices experimentally observable?

An ongoing debate in the first-principles description of conduction in molecular devices concerns the correct definition of current in the presence of non-local potentials. If the physical current density ${\bf j}=(-ie\hbar/2m)(Ψ^* \nabla Ψ- Ψ\nabla Ψ^*)$ is not locally conserved but can be re-adjusted by a non-local term, which current should be regarded as real? We prove that the extended Maxwell equations by Aharonov-Bohm give the e.m.\ field generated by such currents without any ambiguity. For an oscillating dipole we show that the radiated electrical field has a longitudinal component proportional to $ ω\hat{P}$, where $\hat{P}$ is the anomalous moment $\int \hat{I}(\mathbf{x})\mathbf{x} d^3x$ and $\hat{I}$ is the space-dependent part of the anomaly $I=\partial_t ρ+\nabla \cdot \mathbf{j}$. In the case of a stationary current in a molecular device, a failure of local current conservation causes a "missing field" effect that can be experimentally observable, especially if its entity depends on the total current.

physics.gen-ph↗

arXiv2020

Quantum-only metrics in spherically symmetric gravity

The Einstein action for the gravitational field has some properties which make of it, after quantization, a rare prototype of systems with quantum configurations that do not have a classical analogue. Assuming spherical symmetry in order to reduce the effective dimensionality, we have performed a Monte Carlo simulation of the path integral with transition probability $e^{-β|S|}$. Although this choice does not allow to reproduce the full dynamics, it does lead us to find a large ensemble of metric configurations having action $|S|\ll \hbar$ by several magnitude orders. These vacuum fluctuations are strong deformations of the flat space metric (for which $S=0$ exactly). They exhibit a periodic polarization in the scalar curvature $R$. In the simulation we fix a length scale $L$ and divide it into $N$ sub-intervals. The continuum limit is investigated by increasing $N$ up to $\sim 10^6$; the average squared action $\langle S^2 \rangle$ is found to scale as $1/N^2$ and thermalization of the algorithm occurs at a very low temperature (classical limit). This is in qualitative agreement with analytical results previously obtained for theories with stabilized conformal factor in the asymptotic safety scenario.

gr-qc↗

arXiv2020

Network rewiring in the $r$-$K$ plane

We generate correlated scale-free networks in the configuration model through a new rewiring algorithm which allows to tune the Newman assortativity coefficient $r$ and the average degree of the nearest neighbors $K$ (in the range $-1\le r \le 1$, $K\ge \langle k \rangle$). At each attempted rewiring step, local variations $Δr$ and $ΔK$ are computed and then the step is accepted according to a standard Metropolis probability $ \exp(\pmΔr/T)$, where $T$ is a variable temperature. We prove a general relation between $Δr$ and $ΔK$, thus finding a connection between two variables which have very different definitions and topological meaning. We describe rewiring trajectories in the $r$-$K$ plane and explore the limits of maximally assortative and disassortative networks, including the case of small minimum degree ($k_{min} \ge 1$) which has previously not been considered. The size of the giant component and the entropy of the network are monitored in the rewiring. The average number of second neighbours in the branching approximation $\bar{z}_{2,B}$ is proven to be constant in the rewiring, and independent from the correlations for Markovian networks. As a function of the degree, however, the number of second neighbors gives useful information on the network connectivity and is also monitored.

physics.soc-ph↗

arXiv2020

Metrics with zero and almost-zero Einstein action in quantum gravity

We generate numerically on a lattice an ensemble of stationary metrics, with spherical symmetry, which have Einstein action $S_E \ll \hbar$. This is obtained through a Metropolis algorithm with weight $\exp(-β^2 S^2_E)$ and $β\gg \hbar^{-1}$. The squared action in the exponential allows to circumvent the problem of the non-positivity of $S_E$. The discretized metrics obtained exhibit a spontaneous polarization in regions of positive and negative scalar curvature. We compare this ensemble with a class of continuous metrics previously found, which satisfy the condition $S_E=0$ exactly, or in certain cases even the stronger condition $R({\bf x})=0$ for any ${\bf x}$. All these gravitational field configurations are of considerable interest in quantum gravity, because they represent possible vacuum fluctuations and are markedly different from Wheeler's "spacetime foam".

gr-qc↗

arXiv2019

The configuration model for Barabasi-Albert networks

We develop and test a rewiring method (originally proposed by Newman) which allows to build random networks having pre-assigned degree distribution and two-point correlations. For the case of scale-free degree distributions, we discretize the tail of the distribution according to the general prescription by Dorogovtsev and Mendes. The application of this method to Barabasi-Albert (BA) networks is possible thanks to recent analytical results on their correlations, and allows to compare the ensemble of random networks generated in the configuration model with that of "real" networks obtained from preferential attachment. For $β\ge 2$ ($β$ is the number of parent nodes in the preferential attachment scheme) the networks obtained with the configuration model are completely connected (giant component equal to 100%). In both generation schemes a clear disassortativity of the small degree nodes is demonstrated from the computation of the function $k_{nn}$. We also develop an efficient rewiring method which produces tunable variations of the assortativity coefficient $r$, and we use it to obtain maximally disassortative networks having the same degree distribution of BA networks with given $β$. Possible applications of this method concern assortative social networks.

physics.soc-ph↗

arXiv2019

High-frequency electromagnetic emission from non-local wavefunctions

In systems with non-local potentials or other kinds of non-locality, the Landauer-Büttiker formula of quantum transport leads to replace the usual gauge-invariant current density $\textbf{J}$ with a current $\textbf{J}^{ext}$ which has a non-local part and coincides with the current of the extended Aharonov-Bohm electrodynamics. It follows that the electromagnetic field generated by this current can have some peculiar properties, and in particular the electric field of an oscillating dipole can have a long-range longitudinal component. The calculation is complex because it requires the evaluation of double-retarded integrals. We report the outcome of some numerical integrations with specific parameters for the source: dipole length $\sim 10^{-7}$ cm, frequency 10 GHz. The resulting longitudinal field $E_L$ turns out to be of the order of $10^2$ to $10^3$ times larger than the transverse component (only for the non-local part of the current). Possible applications concern the radiation field generated by Josephson tunnelling in thick SNS junctions in YBCO and by current flow in molecular nano-devices.

physics.class-ph↗

arXiv2019

Design of a test for the electromagnetic coupling of non-local wavefunctions

It has recently been proven that certain effective wavefunctions in fractional quantum mechanics and condensed matter do not have a locally conserved current; as a consequence, their coupling to the electromagnetic field leads to extended Maxwell equations, featuring non-local, formally simple additional source terms. Solving these equations in general form or finding analytical approximations is a formidable task, but numerical solutions can be obtained by performing some bulky double-retarded integrals. We focus on concrete experimental situations which may allow to detect an anomalous quasi-static magnetic field generated by these (collective) wavefunctions in cuprate superconductors. We compute the spatial dependence of the field and its amplitude as a function of microscopic parameters including the fraction $η$ of supercurrent that is not locally conserved in Josephson junctions between grains, the thickness $a$ of the junctions and the size $\varepsilon$ of their current sinks and sources. The results show that the anomalous field is actually detectable at the macroscopic level with sensitive experiments, and can be important at the microscopic level because of virtual charge effects typical of the extended Maxwell equations.

physics.gen-ph↗

arXiv2018

Time in quantum mechanics and the local non-conservation of the probability current

In relativistic quantum field theory with local interactions, charge is locally conserved. This implies local conservation of probability for the Dirac and Klein-Gordon wavefunctions, as special cases; and then in turn for non-relativistic quantum field theory and for the Schroedinger and Ginzburg-Landau equations, regarded as low energy limits. Quantum mechanics, however, is wider than quantum field theory, as an effective model of reality. For instance, fractional quantum mechanics and Schroedinger equations with non-local terms have been successfully employed in several applications. The non-locality of these formalisms is strictly related to the problem of time in quantum mechanics. We compute explicitly for continuum wave packets the terms of the fractional Schroedinger equation and of the non-local Schroedinger equation by Lenzi et al. which break the local current conservation, and discuss their physical significance. The results are especially relevant for the electromagnetic coupling of these wavefunctions. A connection with the non-local Gorkov equation for superconductors and their proximity effect is also outlined.

physics.gen-ph↗

arXiv2018

The Bass diffusion model on finite Barabasi-Albert networks

Using a mean-field network formulation of the Bass innovation diffusion model and exact results by Fotouhi and Rabbat on the degree correlations of Barabasi-Albert networks, we compute the times of the diffusion peak and compare them with those on scale-free networks which have the same scale-free exponent but different assortativity properties. We compare our results with those obtained by Caldarelli et al. for the SIS epidemic model with the spectral method applied to adjacency matrices. It turns out that diffusion times on finite Barabasi-Albert networks are at a minimum. This may be due to a little-known property of these networks: although the value of the assortativity coefficient is close to zero, they look disassortative if one considers only a bounded range of degrees, including the smallest ones, and slightly assortative on the range of the higher degrees. We also find that if the trickle-down character of the diffusion process is enhanced by a larger initial stimulus on the hubs (via a inhomogeneous linear term in the Bass model), the relative difference between the diffusion times for BA networks and uncorrelated networks is even larger, reaching for instance the 34% in a typical case on a network with $10^4$ nodes.

physics.soc-ph↗

arXiv2017

Covariant formulation of Aharonov-Bohm electrodynamics and its application to coherent tunnelling

The extended electrodynamic theory introduced by Aharonov and Bohm (after an earlier attempt by Ohmura) and recently developed by Van Vlaenderen and Waser, Hively and Giakos, can be re-written and solved in a simple and effective way in the standard covariant 4D formalism. This displays more clearly some of its features. The theory allows a very interesting consistent generalization of the Maxwell equations. In particular, the generalized field equations are compatible with sources (classical, or more likely of quantum nature) for which the continuity/conservation equation $\partial_μj^μ=0$ is not valid everywhere, or is valid only as an average above a certain scale. And yet, remarkably, in the end the observable $F^{μν}$ field is still generated by a conserved effective source which we denote as $(j^ν+i^ν)$, being $i^ν$ a suitable non-local function of $j^ν$. This implies that any microscopic violation of the charge continuity condition is "censored" at the macroscopic level, although it has real consequences, because it generates a non-Maxwellian component of the field. We consider possible applications of this formalism to condensed-matter systems with macroscopic quantum tunneling. The extended electrodynamics can also be coupled to fractional quantum systems.

physics.gen-ph↗

arXiv2017

Electromagnetic coupling of strongly non-local quantum mechanics

Although standard quantum mechanics has some non-local features, the probability current of the Schrödinger equation is locally conserved, and this allows minimal electromagnetic coupling. For some important extensions of the Schrödinger equation, however, the probability current is not locally conserved. We show that in these cases the correct electromagnetic coupling requires a relatively simple extension of Maxwell theory which has been known for some time and recently improved by covariant integration of a scalar degree of freedom. We discuss some general properties of the solutions and examine in particular the case of an oscillating dipolar source. Remarkable mathematical and physical differences emerge with respect to Maxwell theory, as a consequence of additional current terms present in the equations for $\nabla \cdot \textbf{E}$ and $\nabla \times \textbf{B}$. Several possible applications are mentioned.

physics.gen-ph↗

arXiv2017

Oscillating dipole with fractional quantum source in Aharonov-Bohm electrodynamics

We show, in the case of a special dipolar source, that electromagnetic fields in fractional quantum mechanics have an unexpected space dependence: propagating fields may have non-transverse components, and the distinction between near-field zone and wave zone is blurred. We employ an extension of Maxwell theory, Aharonov-Bohm electrodynamics, which is compatible with currents $j^ν$ conserved globally but not locally, we have derived in another work the field equation $\partial_μF^{μν}=j^ν+i^ν$, where $i^ν$ is a non-local function of $j^ν$, called "secondary current". Y.\ Wei has recently proved that the probability current in fractional quantum mechanics is in general not locally conserved. We compute this current for a Gaussian wave packet with fractional parameter $a=3/2$ and find that in a suitable limit it can be approximated by our simplified dipolar source. Currents which are not locally conserved may be present also in other quantum systems whose wave functions satisfy non-local equations. The combined electromagnetic effects of such sources and their secondary currents are very interesting both theoretically and for potential applications.

physics.gen-ph↗