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Causal Dynamical Triangulations (CDT) are a concrete attempt to define a nonperturbative path integral for quantum gravity. We present strong evidence that the lattice theory has a second-order phase transition line, which can potentially…
We study the transition time distribution for a particle moving between two wells of a multidimensional potential in the low-noise limit of overdamped Langevin dynamics. Possible transition paths are restricted to a thin tube surrounding…
The aim of this paper is to develop tractable large deviation approximations for the empirical measure of a small noise diffusion. The starting point is the Freidlin-Wentzell theory, which shows how to approximate via a large deviation…
This paper introduces a comprehensive extension of the path integral formalism to model stochastic processes with arbitrary multiplicative noise. To do so, It\^o diffusive process is generalized by incorporating a multiplicative noise term…
Large deviations in chaotic dynamics have potentially significant and dramatic consequences. We study large deviations of series of finite lengths $N$ generated by chaotic maps. The distributions generally display an exponential decay with…
Starting from the chemical master equation, we employ field theoretic techniques to derive Langevin-type equations that exactly describe the stochastic dynamics of the Frank chiral amplification model with spatial diffusion. The intrinsic…
Transition phenomena between thermal noise state and turbulent state observed in a submarginal turbulent plasma are analyzed with statistical theory. Time-development of turbulent fluctuation is obtained by numerical simulations of Langevin…
The reduction of quantum scattering leads to the suppression of shot noise. In the present paper, we analyze the crossover from the quantum transport regime with universal shot noise, to the classical regime where noise vanishes. By making…
We prove the small-noise large deviation principle (LDP) for stochastic evolution equations in an $L^2$-setting. As the coefficients are allowed to be non-coercive, our framework encompasses a much broader scope than variational settings.…
We consider potential type dynamical systems in finite dimensions with two meta-stable states. They are subject to two sources of perturbation: a slow external periodic perturbation of period $T$ and a small Gaussian random perturbation of…
We propose a new mechanism for the achievment of homochirality in life without any autocatalytic production process. Our model consists of a spontaneous production together with a recycling cross inhibition in a closed system. It is shown…
't Hooft's derivation of quantum from classical physics is analyzed by means of the classical path integral of Gozzi et al.. It is shown how the key element of this procedure - the loss of information constraint - can be implemented by…
We consider a stochastic Cahn-Hilliard partial differential equation driven by a space-time white noise. We prove the Large Deviations Principle (LDP) for the law of the solutions in the H\"older norm. We use the weak convergence approach…
Previously, we have shown that the transition probability of the Landau-Zener problem in periodic lattice systems becomes large by taking into account the nonlinearity of the energy spectra, compared with the probability by the conventional…
We often rely on probabilistic measures -- e.g. event probability or expected time -- to characterize systems' safety. However, determining these quantities for extremely low-probability events is generally challenging, as standard safety…
One intriguing property of non-Hermitian systems is the breakdown of adiabatic theorem and chiral state conversion as the system dynamically encircles exceptional points. However, the subtle dependence of the chiral dynamics on the loop…
We refine an earlier introduced 5-dimensional gravity solution capable of holographically capturing several qualitative aspects of (lattice) QCD in a strong magnetic background such as the anisotropic behaviour of the string tension,…
Path integral techniques are used to understand the behaviour of a particle moving in a bistable potential well and acted upon by quasi-monochromatic external noise. In the limit of small diffusion coefficient, a steepest descent evaluation…
We study the localization transition in periodically driven one-dimensional non-Hermitian lattices where the piece-wise two-step drive is constituted by uniform coherent tunneling and incommensurate onsite gain and loss. We find that the…
Using a rough path formulation, we investigate existence, uniqueness and regularity for the stochastic Landau-Lifshitz-Gilbert equation with Stratonovich noise on the one dimensional torus. As a main result we show the continuity of the…