In renormalized field theories there are in general one or few fixed points which are accessible by the renormalization-group flow. They can be identified from the fixed-point equations. Exceptionally, an infinite family of fixed points exists, parameterized by a scaling exponent $ζ$, itself function of a non-renormalizing parameter. Here we report a different scenario with an infinite family of fixed points of which seemingly only one is chosen by the renormalization-group flow. This dynamical selection takes place in systems with an attractive interaction ${\cal V}(ϕ)$, as in standard $ϕ^4$ theory, but where the potential $\cal V$ at large $ϕ$ goes to zero, as e.g. the attraction by a defect.
A Markovian lattice model for photoreceptor cells is introduced to describe the growth of mosaic patterns on fish retina. The radial stripe pattern observed in wild-type zebrafish is shown to be selected naturally during the retina growth, against the geometrically equivalent, circular stripe pattern. The mechanism of such dynamical pattern selection is clarified on the basis of both numerical simulations and theoretical analyses, which find that the successive emergence of local defects plays a critical role in the realization of the wild-type pattern.
I discuss the relationship between edge exponents in the statistics of work done, dynamical phase transitions, and the role of different kinds of excitations appearing when a non-equilibrium protocol is performed on a closed, gapped, one-dimensional system. I show that the edge exponent in the probability density function of the work is insensitive to the presence of interactions and can take only one of three values: +1/2, -1/2 and -3/2. It also turns out that there is an interesting interplay between spontaneous symmetry breaking or the presence of bound states and the exponents. For instant…
We have developed a unified finite-size scaling method for quantum phase transitions that requires no prior knowledge of the dynamical exponent $z$. During a quantum Monte Carlo simulation, the temperature is automatically tuned by the Robbins-Monro stochastic approximation method, being proportional to the lowest gap of the finite-size system. The dynamical exponent is estimated in a straightforward way from the system-size dependence of the temperature. As a demonstration of our novel method, the two-dimensional $S=1/2$ quantum $XY$ model in uniform and staggered magnetic fields is investiga…
We describe a new universality class of dynamical quantum phase transitions of the Loschmidt amplitude of quantum spin chains off equilibrium criticality. We demonstrate that in many cases it is possible to change the conventional linear singularity of the Loschmidt rate function into a smooth peak by tuning one parameter of the quench protocol. Exactly at the point when this change-over occurs, the singularity of the Loschmidt rate function persists, with a critical exponent equal to $\frac{1}{2}$ . The non-equilibrium renormalization group fixed-point controlling this universality class is d…
Nonequilibrium relaxation behaviors in the Ising model on a square lattice based on the Wolff algorithm are totally different from those based on local-update algorithms. In particular, the critical relaxation is described by the stretched-exponential decay. We propose a novel scaling procedure to connect nonequilibrium and equilibrium behaviors continuously, and find that the stretched-exponential scaling region in the Wolff algorithm is as wide as the power-law scaling region in local-update algorithms. We also find that relaxation to the spontaneous magnetization in the ordered phase is cha…
The dynamics of the system is investigated when one part of the system initially behaves in a regular manner and the other in a chaotic one. The propagation of the chaos is considered as the motion of a region with the maximal Lyapunov exponent greater than zero. The time dependencies of the chaos propagation parameters were calculated for the classical and non-local models of non-stationary heat transfer. The system responses were considered to disturbances in the form of the Dirac delta function and the Heaviside step function.
Emergent universal statistics in nonequilibrium systems with dynamical scale selection
Massachusetts Institute of Technology（麻省理工学院）；University of Helsinki（赫尔辛基大学）；University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校）；ETH Zurich（苏黎世联邦理工学院）
We obtained the exact solution of a probabilistic cellular automaton related to the diagonal-to-diagonal transfer matrix of the six-vertex model on a square lattice. The model describes the flow of ants (or particles), traveling on a one-dimensional lattice whose sites are small craters containing sleeping or awake ants (two kinds of particles). We found the Bethe ansatz equations and the spectral gap for the time-evolution operator of the cellular automaton. From the spectral gap we show that in the asymmetric case it belongs to the Kardar-Parisi-Zhang (KPZ) universality class, exhibiting a d…
Dynamical quantum phase transitions (DQPTs) feature singular temporal behavior in transient quantum states during nonequilibrium real-time evolution. In this work we show that DQPTs in random Ising chains exhibit critical behavior with nontrivial exponents that are not integer valued and not of mean-field type. By means of an exact renormalization group transformation we estimate the exponents with high accuracy eliminating largely any finite-size effects. We further discuss how the considered dynamical phenomena can be made accessible in current Rydberg atom platforms. In this context we expl…
