Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/9710287

Metastability and spinodal points for a random walker on a triangle

Peter F. Arndt·Thomas Heinzel
View original source ↗Read source document ↗Export metadata ↓

Abstract

We investigate time-dependent properties of a single particle model in which a random walker moves on a triangle and is subjected to non-local boundary conditions. This model exhibits spontaneous breaking of a Z_2 symmetry. The reduced size of the configuration space (compared to related many-particle models that also show spontaneous symmetry breaking) allows us to study the spectrum of the time-evolution operator. We break the symmetry explicitly and find a stable phase, and a meta-stable phase which vanishes at a spinodal point. At this point, the spectrum of the time evolution operator has a gapless and universal band of excitations with a dynamical critical exponent z=1. Surprisingly, the imaginary parts of the eigenvalues E_j(L) are equally spaced, following the rule Im E_j(L)\propto j/L. Away from the spinodal point, we find two time scales in the spectrum. These results are related to scaling functions for the mean path of the random walker and to first passage times. For the spinodal point, we find universal scaling behavior. A simplified version of the model which can be handled analytically is also presented.

Explore related subjects

cond-mat.stat-mech

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Peter F. Arndt, Thomas Heinzel. 1997-10-27. Metastability and spinodal points for a random walker on a triangle. https://doi.org/10.1023/a%3A1023036408873

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Competition for Survival and the Law of Maximum Entropy Production

The law of maximum entropy production (LMEP) is a selection principle stating that a non-equilibrium system will select the path or assembly of paths out of available paths that minimizes the potential or maximizes the entropy at the fastest rate given the constraints. Precise quantitative experimental tests are desirable for LMEP verification. Here we report electrical-circuit experiments on suspensions of silver particles which self-organize under electric field, form conducting paths and thus generate entropy by Joule heating. Our experiments on parallel-connected pairs of samples demonstrate a competitive relationship, thereby supporting the selection of the most efficient path. We find: (1) With sufficient voltage, a conducting bundle of silver particles forms, which acts as a self-organized dissipative structure (SODS). (2) With two samples in parallel, usually only one can develop SODS, due to the competition effect. As one sample approaches the maximum EPR, the others EPR is near zero. This confirms the path selection principle: only the highest EPR path survives. (3) At the end of the evolution, the sum of the sample EPR and the power supply circuit EPR approaches the calculated maximum. The deviation from the maximum is slightly lower when there are two competing samples. We identify the selection mechanism enabling natural selection and LMEP: A SODS gains a form of physical "fitness" when it establishes a pathway that efficiently suppresses the driving thermodynamic potential. As it develops and approaches the maximum EPR, the SODS modifies its nonequilibrium environment by consuming available free energy and eliminating the gradients that could support alternative pathways. We also examine the global implications of LMEP and propose that it serves as a driving mechanism propelling the hypothetical ascent of civilizations along the Kardashev scale.

cond-mat.stat-mech↗
arXiv2026

Measurement-induced spatially nonuniform fluctuations of the local particle number and their crossover in a quasiperiodic free-fermion chain

We study continuously monitored dynamics of a quasiperiodic free-fermion chain defined on a Fibonacci lattice. We focus on fluctuations of the local particle number, which do not exhibit quasiperiodic spatial modulation in the unitary limit. Remarkably, we demonstrate that they exhibit a nonuniform spatial pattern originating from the quasiperiodic long-range order under continuous measurement. Furthermore, employing both physicaland perpendicular-space analyses, we elucidate that a measurement-induced crossover emerges in fluctuations due to the interplay between the incommensurate modulation and the continuous measurement. While weak measurement yields a distribution reflecting the long-range spatial structure of the quasiperiodic system, an increase in measurement strength alters the distribution into one dominated by the local environment of each site. A structure-factor analysis further reveals that the weak-measurement regime is characterized by two dominant Bragg peaks corresponding to the golden-mean modulation, whereas the strong-measurement regime exhibits the characteristic Bragg-peak hierarchy of the Fibonacci pattern. We also elucidate that the measurement-induced crossover emerges in other physical quantities such as connected correlation functions. These findings offer insights into nonequilibrium quasiperiodic phenomena emerging in continuously monitored dynamics.

cond-mat.stat-mech↗
arXiv2026

Entanglement Asymmetry in Random Quantum Automata

We investigate the subsystem entanglement asymmetry in random quantum automaton ensembles, which are generated by permuting the basis states in the Hilbert space and applying global phase shifts. We compute the ensemble average of the $U(1)$ subsystem asymmetry in different connectivity geometries, showing that the late-time limit of the ensemble associated to a 2-local circuit geometry coincides with the all-to-all ensemble average. By focusing on different subsystem sizes, we demonstrate that, similarly to Haar-random circuits, the system locally symmetrizes. However, in sharp contrast to the Haar-random setting, the scale at which symmetrization happens depends on the initial state, a phenomenon we associate with the interplay of conservation of the participation entropy and the uniform exploration of charge sectors. Additionally, we connect the growth of the subsystem asymmetry to the subsystem coherence and show that their growth is characterized by the same symmetrization scale.

cond-mat.stat-mech↗