Related papers: Conformal Invariance in Percolation, Self-Avoiding…
We review the critical behavior of nonequilibrium systems, such as directed percolation (DP) and branching-annihilating random walks (BARW), which possess phase transitions into absorbing states. After reviewing the bulk scaling behavior of…
The coupling of branching-annihilating random walks to a static field with a local conservation law is shown to change the scaling properties of their phase transitions to absorbing states. In particular, we find that DP-class transitions…
We explain how the axioms of Conformal Field Theory are used to make predictions about critical exponents of continuous phase transitions in three dimensions, via a procedure called the conformal bootstrap. The method assumes conformal…
Quantum Stochastic Walks (QSW) allow for a generalization of both quantum and classical random walks by describing the dynamic evolution of an open quantum system on a network, with nodes corresponding to quantum states of a fixed basis. We…
A solution to the long-standing problem of identifying the conformal field theory governing the transition between quantized Hall plateaus of a disordered noninteracting 2d electron gas, is proposed. The theory is a nonlinear sigma model…
We study the two-dimensional domain morphology of twisted nematic liquid crystals during their phase-ordering kinetics [R. A. L. Almeida, Phys. Rev. Lett. 131 (2023) 268101], which is a physical candidate to self-generate critical clusters…
We describe infinite clusters which arise in nearest-neighbour percolation for so-called cocycle measures on the square lattice. These measures arise naturally in the study of random transformations. We show that infinite clusters have a…
The effect of rotational constraint on the properties of lattice models like the self-avoiding walk, lattice animals and percolation is discussed. The results obtained so far, using a variety of exact and approximate techniques, are…
This work deals with both instantaneous uniform mixing property and temporal standard deviation for continuous-time quantum random walks on circles in order to study their fluctuations comparing with discrete-time quantum random walks, and…
We review briefly a stream of ideas concerning the role of quantum groups as hidden symmetries in conformal field theories, paying particular attention to the field theoretical representations of quantum groups based on Coulomb gas methods.…
Statistics of classical Hamiltonian random walk of particle colliding with atoms of ideal gas is considered from viewpoint of earlier suggested exact pseudo-quantum path integral representation of the problem, and qualitative agreement is…
This article proposes a new way of deriving mean-field exponents for the weakly self-avoiding walk model in dimensions $d>4$. Among other results, we obtain up-to-constant estimates for the full-space and half-space two-point functions in…
We point out that the (pseudo-)conformal Universe scenario may be realized as decay of conformally invariant, metastable vacuum, which proceeds via spontaneous nucleation and subsequent growth of a bubble of a putative new phase. We study…
L\'evy walks (LWs) are spatiotemporally coupled random-walk processes describing superdiffusive heat conduction in solids, propagation of light in disordered optical materials, motion of molecular motors in living cells, or motion of…
We discuss the partition function point of view for chordal Schramm-Loewner evolutions and their relationship with correlation functions in conformal field theory. Both are closely related to crossing probabilities and interfaces in…
In [Can et al. 2016], quantum Hall states on singular surfaces were shown to possess an emergent conformal symmetry. In this paper, we develop this idea further and flesh out details on the emergent conformal symmetry in holomorphic…
Recent progress on the understanding of the Random Conductance Model is reviewed. A particular emphasis is on homogenization results such as functional central limit theorems, local limit theorems and heat kernel estimates for almost every…
Quantum walks in atomic systems, owing to their continuous nature, are especially well-suited for the simulation of many-body physics and can potentially offer an exponential speedup in solving certain black box problems. Photonics offers…
Considering a "random walk in a random environment" in a topologically closed circuit, we explore the implications of the percolation and sliding transitions for its relaxation modes. A complementary question regarding the "delocalization"…
We study the behavior of the random walk in a continuum independent long-range percolation model, in which two given vertices $x$ and $y$ are connected with probability that asymptotically behaves like $|x-y|^{-\alpha}$ with $\alpha>d$,…