Brownian non-Gaussian polymer diffusion and queing theory in the mean-field limit

We link the Brownian non-Gaussian diffusion of a polymer center of mass to a microscopic cause: the polymerization/depolymerization phenomenon occurring when the polymer is in contact with a monomer chemostat. The anomalous behavior is triggered by the polymer critical point, separating the dilute and the dense phase in the grand canonical ensemble. In the mean-field limit we establish contact with queuing theory and show that the kurtosis of the polymer center of mass diverges alike a response function when the system becomes critical, a result which holds for general polymer dynamics (Zimm, Rouse, reptation). Both the equilibrium and nonequilibrium behaviors are solved exactly as a reference study for novel stochastic modeling and experimental setup.

Large N external-field quantum electrodynamics

We advocate the study of external-field quantum electrodynamics with N charged particle flavors. Our main focus is on the Heisenberg-Euler effective action for this theory in the large N limit which receives contributions from all loop orders. The contributions beyond one loop stem from one-particle reducible diagrams. We show that specifically in constant electromagnetic fields the latter are generated by the one-loop Heisenberg-Euler effective Lagrangian. Hence, in this case the large N Heisenberg-Euler effective action can be determined explicitly at any desired loop order. We demonstrate that further analytical insights are possible for electric-and magnetic-like field configurations characterized by the vanishing of one of the secular invariants of the electromagnetic field and work out the all-orders strong field limit of the theory.

Nontrivial Isometric Embeddings for Flat Spaces

Nontrivial isometric embeddings for flat metrics (i.e., those which are not just planes in the ambient space) can serve as useful tools in the description of gravity in the embedding gravity approach. Such embeddings can additionally be required to have the same symmetry as the metric. On the other hand, it is possible to require the embedding to be unfolded so that the surface in the ambient space would occupy the subspace of the maximum possible dimension. In the weak gravitational field limit, such a requirement together with a large enough dimension of the ambient space makes embedding gravity equivalent to general relativity, while at lower dimensions it guarantees the linearizability of the equations of motion. We discuss symmetric embeddings for the metrics of flat Euclidean three-dimensional space and Minkowski space. We propose the method of sequential surface deformations for the construction of unfolded embeddings. We use it to construct such embeddings of flat Euclidean three-dimensional space and Minkowski space, which can be used to analyze the equations of motion of embedding gravity.

A mean-field approach to self-interacting networks, convergence and regularity

The propagation of chaos property for a system of interacting particles, describing the spatial evolution of a network of interacting filaments is studied. The creation of a network of mycelium is analyzed as representative case, and the generality of the modeling choices are discussed. Convergence of the empirical density for the particle system to its mean-field limit is proved, and a result of regularity for the solution is presented.

Effect of the Magnetic Charge on Weak Deflection Angle and Greybody Bound of the Black Hole in Einstein-Gauss-Bonnet Gravity

The objective of this paper is to analyze the weak deflection angle of Einstein-Gauss-Bonnet gravity in the presence of plasma medium. To attain our results, we implement the Gibbons and Werner approach and use the Gauss-Bonnet theorem to Einstein gravity to acquire the resulting deflection angle of photon's ray in the weak field limit. Moreover, we illustrate the behavior of plasma medium and non-plasma mediums on the deflection of photon's ray in the framework of Einstein-Gauss-Bonnet gravity. Similarly, we observe the graphical influences of deflection angle on Einstein-Gauss-Bonnet gravity with the consideration of both plasma and non-plasma mediums. Later, we observe the rigorous bounds phenomenon of the greybody factor in contact with Einstein-Gauss-Bonnet gravity and calculate the outcomes, analyze graphically for specific values of parameters.

From Nucleation to Percolation: The Effect of System Size when Disorder and Stress Localization Compete

A phase diagram for a one-dimensional fiber bundle model is constructed with a continuous variation in two parameters guiding the dynamics of the model: strength of disorder and range of stress relaxation. When the range of stress relaxation is very low, the stress concentration plays a prominent role and the failure process is nucleating where a single crack propagates from a particular nucleus with a very high spatial correlation unless the disorder strength is high. On the other hand, a high range of stress relaxation represents the mean-field limit of the model where the failure events are random in space. At an intermediate disorder strength and stress release range, when these two parameters compete, the failure process shows avalanches and precursor activities. As the size of the bundle is increased, it favors a nucleating failure. In the thermodynamic limit, we only observe a nucleating failure unless either the disorder strength is extremely high or the stress release range is high enough so that the model is in the mean-field limit. A complex phase diagram on the plane of disorder strength, stress release range, and system size is presented showing different failure modes - 1) nucleation 2) avalanche, and 3) percolation, depending on the spatial correlation observed during the failure process.

Gravitational Effects on Neutrino Decoherence in the Lense–Thirring Metric

We analyze the effects of gravity on neutrino wave packet decoherence. As a specific example, we consider the gravitational field of a spinning spherical body described by the Lense–Thirring metric. By working in the weak-field limit and employing Gaussian wave packets, we show that the characteristic coherence length of neutrino oscillation processes is nontrivially affected, with the corrections being dependent on the mass and angular velocity of the gravity source. Possible experimental implications are finally discussed.

Time delay in the strong field limit for null and timelike signals and its simple interpretation

Gravitational lensing can happen not only for null signals but also timelike signals such as neutrinos and massive gravitational waves in some theories beyond GR. In this work we study the time delay between different relativistic images formed by signals with arbitrary asymptotic velocity v in general static and spherically symmetric spacetimes. A perturbative method is used to calculate the total travel time in the strong field limit, which is found to be a quasi-power series of the small parameter $$a=1-b_c/b$$ a = 1 - b c / b where b is the impact parameter and $$b_c$$ b c is its critical value. The coefficients of the series are completely fixed by the behaviour of the metric functions near the particle sphere $$r_c$$ r c and only the first term of the series contains a weak logarithmic divergence. The time delay $$\Delta t_{n,m}$$ Δ t n , m to the leading non-trivial order was shown to equal the particle sphere circumference divided by the local signal velocity and multiplied by the winding number and the redshift factor. By assuming the Sgr A* supermassive black hole is a Hayward one, we were able to validate the quasi-series form of the total time, and reveal the effects of the spacetime parameter l, the signal velocity v and the source/detector coordinate difference $$\Delta \phi _{sd}$$ Δ ϕ sd on the time delay. It is found that as l increases from 0 to its critical value $$l_c$$ l c , both $$r_c$$ r c and $$\Delta t_{n,m}$$ Δ t n , m decrease. The variation of $$\Delta t_{n+1,n}$$ Δ t n + 1 , n for l from 0 to $$l_c$$ l c can be as large as $$7.2\times 10^1$$ 7.2 × 10 1 [s], whose measurement then can be used to constrain the value of l. While for ultra-relativistic neutrino or gravitational wave, the variation of $$\Delta t_{n,m}$$ Δ t n , m is too small to be resolved. The dependence of $$\Delta t_{n,-n}$$ Δ t n , - n on $$\Delta \phi _{sd}$$ Δ ϕ sd shows that to temporally resolve the two sequences of images from opposite sides of the lens, $$|\Delta \phi _{sd}-\pi |$$ | Δ ϕ sd - π | has to be larger than a certain value, or equivalently if $$|\Delta \phi _{sd}-\pi |$$ | Δ ϕ sd - π | is small, the time resolution of the observatories has to be good.

Mean Field Derivation of DNLS from the Bose–Hubbard Model

We prove that the flow of the discrete nonlinear Schrödinger equation (DNLS) is the mean field limit of the quantum dynamics of the Bose–Hubbard model for N interacting particles. In particular, we show that the Wick symbol of the annihilation operators evolved in the Heisenberg picture converges, as N becomes large, to the solution of the DNLS. A quantitative $$L^p$$ L p -estimate, for any $$p \ge 1$$ p ≥ 1 , is obtained with a linear dependence on time due to a Gaussian measure on initial data coherent states.