Related papers: Locating phase transitions in computationally hard…
From a dynamical viewpoint, basic phase transitions of statistical mechanics can be regarded as a breaking of ergodicity. While many random models exhibiting such transitions at the thermodynamics limit exist, finite-dimensional examples…
In complex systems, external parameters often determine the phase in which the system operates, i.e., its macroscopic behavior. For nearly a century, statistical physics has extensively studied systems' transitions across phases,…
Inverse problems arise in situations where data is available, but the underlying model is not. It can therefore be necessary to infer the parameters of the latter starting from the former. Statistical mechanics offers a toolbox of…
The dynamical organization in the presence of noise of a Boolean neural network with random connections is analyzed. For low levels of noise, the system reaches a stationary state in which the majority of its elements acquire the same…
Machine learning algorithms provide a new perspective on the study of physical phenomena. In this paper, we explore the nature of quantum phase transitions using multi-color convolutional neural-network (CNN) in combination with quantum…
Real-world non-autonomous systems are open, out-of-equilibrium systems that evolve in and are driven by temporally varying environments. Such systems can show multiple timescale and transient dynamics together with transitions to very…
The statistical mechanical interpretation of algorithmic information theory (AIT, for short) was introduced and developed in our former work [K. Tadaki, Local Proceedings of CiE 2008, pp.425-434, 2008], where we introduced the notion of…
A number of tools have been developed to detect topological phase transitions in strongly correlated quantum systems. They apply under different conditions, but do not cover the full range of many-body models. It is hence desirable to…
The transition between distinct phases of matter is characterized by the nature of fluctuations near the critical point. We demonstrate that noise spectroscopy can not only diagnose the presence of a phase transition, but can also determine…
The application of state-of-the-art machine learning techniques to statistical physic problems has seen a surge of interest for their ability to discriminate phases of matter by extracting essential features in the many-body wavefunction or…
Computers are deterministic dynamical systems (CHAOS 19:033124, 2009). Among other things, that implies that one should be able to use deterministic forecast rules to predict their behavior. That statement is sometimes-but not always-true.…
In nearly every discipline, scientific computations are limited by the cost and speed of computation. For example, the best-known exact algorithms for the canonical Traveling Salesman Problem would take centuries to run on an instance of…
This paper introduces a problem in which the state of a system needs to be determined through costly tests of its components by a limited number of testing units and before a given deadline. We also consider a closely related search problem…
This is a status report on a companion subject to extremal combinatorics, obtained by replacing extremality properties with emergent structure, `phases'. We discuss phases, and phase transitions, in large graphs and large permutations,…
Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the…
In the study of phase transitions a very few models are accessible to exact solution. In the most cases analytical simplifications have to be done or some numerical technique has to be used to get insight about their critical properties.…
The detection of change points is a pivotal task in statistical analysis. In the quantum realm, it is a new primitive where one aims at identifying the point where a source that supposedly prepares a sequence of particles in identical…
Advanced inference techniques allow one to reconstruct the pattern of interaction from high dimensional data sets. We focus here on the statistical properties of inferred models and argue that inference procedures are likely to yield models…
We find a series of topological phase transitions of increasing order, beyond the more standard second-order phase transition in a one-dimensional topological superconductor. The jumps in the order of the transitions depend on the range of…
We investigate the computational power of creating steady-states of quantum dissipative systems whose evolution is governed by time-independent and local couplings to a memoryless environment. We show that such a model allows for efficient…