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We generalize the phase transition model studied in [R. Colombo. Hyperbolic phase transition in traffic flow.\ SIAM J.\ Appl.\ Math., 63(2):708-721, 2002], that describes the evolution of vehicular traffic along a one-lane road. Two…
We propose a family of renormalization group transformations characterized by free parameters that may be tuned in order to reduce the truncation effects. As a check we test them in the three dimensional XY model. The Schwinger--Dyson…
We investigate the probable delocalization-localization transition in open quantum systems with disorder. The disorder can induce localization in isolated quantum systems and it is generally recognized that localization is fragile under the…
We develop a systematic multi-local expansion of the Polchinski-Wilson exact renormalization group (ERG) equation. Integrating out explicitly the non local interactions, we reduce the ERG equation obeyed by the full interaction functional…
In the group field theory approach to quantum gravity, continuous spacetime geometry is expected to emerge via phase transition. However, understanding the phase diagram and finding fixed points under the renormalization group flow remains…
Discrete wavelet-based methods promise to emerge as an excellent framework for the non-perturbative analysis of quantum field theories. In this work, we investigate aspects of renormalization in theories analyzed using wavelet-based…
We study the delocalisation transition which takes places in one-dimensional disordered systems when the random potential exhibits specific long-range correlations. We consider the case of weak disorder; using a systematic perturbative…
We propose a new Neural Galerkin Normalizing Flow framework to approximate the transition probability density function of a diffusion process by solving the corresponding Fokker-Planck equation with an atomic initial distribution,…
We study the long-time asymptotics of a certain class of nonlinear diffusion equations with time-dependent diffusion coefficients which arise, for instance, in the study of transport by randomly fluctuating velocity fields. Our primary goal…
Whenever an It\^o-Wentsel type of formula holds for composition of flows of a certain differential dynamics, there exists locally a decomposition of the corresponding flow according to complementary distributions (or foliations, in the case…
We use two renormalization techniques, Effective Field Theory and the Similarity Renormalization Group, to solve simple Schr{\"o}dinger equations with delta-function potentials in one and two dimensions. The familiar one-dimensional…
First we give an introduction to the method of diagonalizing or block-diagonalizing continuously a Hamiltonian and explain how this procedure can be used to analyze the two-dimensional Hubbard model. Then we give a short survey on…
We investigate the localization properties of a quasi-one-dimensional two-channel system with symmetric and asymmetric onsite energies using the Aubry-Andr\'{e} model. By analyzing the Lyapunov exponent and localization length, we…
The one-dimensional Hubbard model with different on-site interactions is investigated by renormalization group technique. In the case of a 1/4-filled band the dynamical nonequivalence of sites leads to the appearance of Umklapp processes in…
U(1) lattice gauge theory with $\theta$-term is investigated by real space renormalization group approach. Flows of renormalized coupling constants are analyzed. For each $\theta$, renormalization flows converge to a single trajectory…
We use the method of the exact renormalization group to study the renormalization group flows of an O(N) invariant Yukawa model in three dimensional Euclidean space consisting of one real scalar and N real spinor fields. We obtain a phase…
We use the renormalization group method to study model E of critical dynamics in the presence of velocity fluctuations arising in accordance with the stochastic Navier-Stokes equation. Using Martin-Siggia-Rose theorem, we obtain a field-…
We discuss here in detail a new analytical random walk approach to calculating the phase-diagram for spatially extended systems with multiplicative noise. We use the Anderson localization problem as an example. The transition from…
We develop a formalism to describe the formation of bound states in quantum field theory using an exact renormalization group flow equation. As a concrete example we investigate a nonrelativistic field theory with instantaneous interaction…
Fluctuating hydrodynamics provides a model for fluids at mesoscopic scales where thermal fluctuations can have a significant impact on the behavior of the system. Here we investigate a model for fluctuating hydrodynamics of a single…