Related papers: Stochastic $\phi^4-$Theory in the Strong Coupling …
Entanglement entropy in the vacuum state of local field theories exhibits an area law. However, nonlocal theories at large N and strong coupling violate this area law. In these theories, the leading divergence in the entanglement entropy is…
In this work we use the lattice regularization method to study the behavior of the six point renormalized coupling constant defined at zero momentum for the three-dimensional $\phi^4 $ theory in the intermediate and strong coupling domain.…
Random perturbations applied in tandem to an ensemble of oscillating objects can synchronize their motion. We study multiple copies of an arbitrary dynamical system in a stable limit cycle, described via a standard phase reduction picture.…
This paper describes the application of finite-size scaling concepts to domain growth in systems with a non-conserved order parameter. A finite-size scaling ansatz for the time-dependent order parameter distribution function is proposed,…
We investigate the dynamics of two interacting diffusing particles in an infinite effectively one dimensional system; the particles interact through a step-like potential of width b and height phi_0 and are allowed to pass one another. By…
We present a perturbative calculation of finite-size effects near $T_c$ of the $\phi^4$ lattice model in a $d$-dimensional cubic geometry of size $L$ with periodic boundary conditions for $d > 4$. The structural differences between the…
The four dimensional Gaussian random field Ising magnet is investigated numerically at zero temperature, using samples up to size $64^4$, to test scaling theories and to investigate the nature of domain walls and the thermodynamic limit. As…
A statistical theory is developed for the stochastic Burgers equation in the inviscid limit. Master equations for the probability density functions of velocity, velocity difference and velocity gradient are derived. No closure assumptions…
A self-consistent theory of the frequency dependent diffusion coefficient for the Anderson localization problem is presented within the tight-binding model of non-interacting electrons on a lattice with randomly distributed on-site energy…
Assuming the space dimension is not constant but decreases during the expansion of the Universe, we study chaotic inflation with the potential $m^2 \phi^2/2$. We write down field equations in the slow-roll approximation and define slow…
We study cutoff and lattice effects in the O(n) symmetric $\phi^4$ theory for a $d$-dimensional cubic geometry of size $L$ with periodic boundary conditions. In the large-N limit above $T_c$, we show that $\phi^4$ field theory at finite…
Stochastic resetting is a rapidly developing topic in the field of stochastic processes and their applications. It denotes the occasional reset of a diffusing particle to its starting point and effects, inter alia, optimal first-passage…
Recently it was shown that the scaling dimension of the operator $\phi^n$ in $\lambda(\phi^*\phi)^2$ theory may be computed semi-classically at the Wilson-Fisher fixed point in $d=4-\epsilon$, for generic values of $\lambda n$ and this was…
This paper derives a somewhat surprising but interesting enough result on the stabilizability of discrete-time parameterized uncertain systems. Contrary to an intuition, it shows that the growth rate of a discrete-time stabilizable system…
The probability density function (PDF) of the roughness, i.e., of the temporal variance, of 1/f^alpha noise signals is studied. Our starting point is the generalization of the model of Gaussian, time-periodic, 1/f noise, discussed in our…
Perturbation Theory (PT) applied to a cosmological density field with Gaussian initial fluctuations suggests a specific hierarchy for the correlation functions when the variance is small. In particular quantitative predictions have been…
An algorithm is proposed for determining asymptotics of the sum of a perturbative series in the strong coupling limit using given values of the expansion coefficients. Operation of the algorithm is illustrated by test examples, method for…
Coupled double well (phi4) one-dimensional potentials abound in both condensed matter physics and field theory. Here we provide an exhaustive set of exact periodic solutions of a coupled $\phi^4$ model in an external field in terms of…
Numerical stochastic perturbation theory is a powerful tool for estimating high-order perturbative expansions in lattice field theory. The standard algorithms based on the Langevin equation, however, suffer from several limitations which in…
Let $F$ be a distribution function on the line in the domain of attraction of a stable law with exponent $\alpha\in(0,1/2]$. We establish the strong renewal theorem for a random walk $S_1,S_2,\ldots$ with step distribution $F$, by extending…