Review
Physics, Multidisciplinary
David P. Feldman, James P. Crutchfield
Summary: This article compares and contrasts three different, but complementary views of structure and pattern in spatial processes. It applies these approaches to one-dimensional Ising spin systems and demonstrates that the measures of pattern from information theory and computational mechanics differ from known thermodynamic and statistical mechanical functions. It argues that these analyses capture the intrinsic computational capabilities embedded in spin systems and how they produce spatial structure.
Article
Physics, Multidisciplinary
Asmi Haldar, Krishnanand Mallayya, Markus Heyl, Frank Pollmann, Marcos Rigol, Arnab Das
Summary: Quantum phase transitions are important for understanding the distinct properties exhibited by matter at very low temperatures upon small changes in microscopic parameters. Locating these transitions accurately is challenging, but a new method involving sudden quenches to force systems out of equilibrium shows promise. The transitions leave distinctive features in intermediate-time dynamics and equilibrated local observables, with effective temperature showing minima near quantum critical points. Further research will focus on testing these results in experiments with Rydberg atoms and exploring nonequilibrium signatures of quantum critical points in models with topological transitions.
Article
Physics, Multidisciplinary
Xiaoming Cai, Hongting Yang, Hai-Long Shi, Chaohong Lee, Natan Andrei, Xi-Wen Guan
Summary: Recent research has rigorously studied the QWs of three indistinguishable bosons and fermions in one-dimensional lattices, demonstrating that strong correlations can lead to statistics- and interaction-dependent ballistic transports.
PHYSICAL REVIEW LETTERS
(2021)
Article
Physics, Fluids & Plasmas
L. F. Souza, T. M. Rocha Filho
Summary: This study shows that homogeneous and nonhomogeneous states of the one-dimensional self-gravitating sheets models have different ergodic properties. The former are nonergodic, and the collision term of the one-particle distribution function becomes zero under proper limit of the periodic boundary conditions. Therefore, homogeneous states of the sheets model are nonergodic and do not relax to the equilibrium state, while nonhomogeneous states are ergodic within a time window of the order of the relaxation time to equilibrium, similar to other systems with long-range interaction.
Article
Physics, Fluids & Plasmas
Mathieu Roule, Jean-Baptiste Fouvry, Christophe Pichon, Pierre-Henri Chavanis
Summary: In this study, we investigate the long-term relaxation of one-dimensional self-gravitating systems using both kinetic theory and N-body simulations. Our findings show that all combinations of thermal and Plummer equilibria, with or without collective effects, are consistent with the predictions of Balescu-Lenard and Landau for diffusion coefficients. Interestingly, collective effects reduce diffusion by a factor of about 10. The predicted flux for Plummer equilibrium matches the measured one, providing a remarkable validation of kinetic theory. We also observe a case of quasikinetic blocking for the same equilibrium.
Article
Biochemical Research Methods
Srilakshmi Pattabiraman, Tandy Warnow
Summary: Profile Hidden Markov Models (HMMs) are graphical models that generate finite length sequences from a distribution, widely used in bioinformatics. The construction of profile HMMs is a statistical estimation problem, and it is unknown whether they are statistically identifiable.
IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS
(2021)
Article
Materials Science, Multidisciplinary
Patrycja Lydzba, Janez Bonca
Summary: The study investigates the unitary time evolution of a symmetry-broken state in a finite system of interacting hard-core bosons, which can be mapped onto the XXZ Heisenberg chain. A spatially homogeneous and time-dependent vector potential is introduced to mimic a short laser pulse, allowing control over the onset of charge density wave order. Nonthermal long-lived states with nonzero charge density wave order, translated by one lattice site, are found to have lifetimes significantly longer than typical times given by the system parameters, although they are suppressed by integrability-breaking perturbations. The existence of these long-lived nonthermal states in the thermodynamic limit is speculated based on the findings.
Article
Mathematics, Interdisciplinary Applications
Abdessatar Souissi, El Gheteb Soueidi
Summary: This paper aims to expand on previous research on quantum hidden Markov processes by introducing the concept of entangled hidden Markov processes. These are hidden Markov processes in which the hidden processes themselves are entangled Markov processes. The paper provides an explicit expression for the joint expectation of these processes and demonstrates that the approach also applies to the classical case.
CHAOS SOLITONS & FRACTALS
(2023)
Review
Physics, Multidisciplinary
B. Bertini, F. Heidrich-Meisner, C. Karrasch, T. Prosen, R. Steinigeweg, M. Znidaric
Summary: Significant progress has been made in the theoretical understanding of transport properties in one-dimensional quantum lattice systems in the past decade, with Bethe-ansatz integrable models and novel simulation methods playing important roles. The discovery of quasilocal conserved quantities provides insight into the origins of finite-temperature transport behavior, while state-of-the-art theoretical methods, including matrix-product-state-based simulation and generalized hydrodynamics, are discussed. The close connection between theoretical models and recent experiments, particularly in the context of quantum magnets and ultracold quantum gases in optical lattices, is also highlighted.
REVIEWS OF MODERN PHYSICS
(2021)
Article
Automation & Control Systems
Feng Li, Zhenghao Ni, Lei Su, Jianwei Xia, Hao Shen
Summary: This paper addresses the problem of finite-region passive control for 2-D Markov jump Roesser systems, considering the partial statistical information issues on Markov parameters and transition probabilities. A 2-D hidden Markov model with partial statistical information is established to model this situation. The goal is to design a controller based on the 2-D hidden Markov model that ensures finite-time boundedness of both horizontal and vertical states of the 2-D Markov jump Roesser systems, while meeting a passive performance criterion. By employing the Lyapunov function method, criteria for the finite-region boundedness of 2-D Markov jump Roesser systems are developed, and a design method for the asynchronous controller based on the 2-D hidden Markov model is presented. The effectiveness of the proposed design method is validated through an illustrative example.
NONLINEAR ANALYSIS-HYBRID SYSTEMS
(2024)
Article
Optics
Lin -Lin Su, Jun Ren, Z. Wang, Yan-Kui Bai
Summary: Here we study the properties of multipartite quantum correlation (MQC) in a one-dimensional spin-1/2 XY chain, focusing on the three-spin reduced states and using four introduced MQC measures based on entanglement negativity and entanglement of formation. We find that even in the Ising case, the three-spin subsystems exhibit long-range MQC, and the tripartite quantum correlations beyond the nearest-neighbor three spins can detect quantum phase transition and follow finite-size scaling around the critical point. Furthermore, in the XY model, we show that the selected MQTT can exactly indicate the factorization point of the ground state for the anisotropic model in both thermodynamic and finite-size cases. Moreover, the spatial distribution of MQC based on entanglement negativity can extend to a larger range by tuning the anisotropic parameter, and the newly defined MQC based on entanglement of formation can detect bound entanglement in the three-spin subsystems when entanglement negativity becomes ineffective.
Article
Physics, Fluids & Plasmas
Yash Chugh, Kusum Dhochak, Uma Divakaran, Prithvi Narayan, Amit Kumar Pal
Summary: In this paper, we generalize one-dimensional quantum XY and Ising-like models using 2-dimensional gamma matrices as degrees of freedom. The resulting models have quadratic Fermionic Hamiltonians with Jordan-Wigner-like transformations. We illustrate these techniques using a specific case of 4-dimensional gamma matrices and explore the quantum phase transitions present in the model.
Article
Physics, Fluids & Plasmas
M. Onorato, G. Dematteis, D. Proment, A. Pezzi, M. Ballarin, L. Rondoni
Summary: In this study, we predict the presence of negative temperature states in the discrete nonlinear Schodinger (DNLS) equation and provide exact solutions using the associated wave kinetic equation. We define an entropy within the wave kinetic approach that monotonically increases in time and reaches a stationary state in accordance with classical equilibrium statistical mechanics. Our analysis shows that fluctuations of actions at fixed wave numbers relax to their equilibrium behavior faster than the spectrum reaches equilibrium. Numerical simulations of the DNLS equation confirm our theoretical results. The boundedness of the dispersion relation is found to be critical for observing negative temperatures in lattices characterized by two invariants.
Article
Statistics & Probability
Masahito Hayashi
Summary: This paper proposes a method for estimating the transition matrix of a hidden Markovian process using information geometry and only the histogram of k-memory data. The method focuses on a partial observation model and introduces an efficient estimator with asymptotic estimation error given in terms of the inverse of projective Fisher information of transition matrices. The estimator is then applied to estimate the transition matrix of the hidden Markovian process, with careful discussion on the equivalence problem for hidden Markovian process on the tangent space.
Article
Materials Science, Multidisciplinary
Jin-Lou Ma, Qing Li, Lei Tan
Summary: The study reveals a transition from ergodic to nonergodic regimes with increasing atom-photon detuning, and the nonergodic phases should exist in the thermodynamic limit while violating the eigenstate thermalization hypothesis.
Article
Biochemical Research Methods
Charles K. Fisher, Pankaj Mehta
Article
Physics, Mathematical
Pankaj Mehta, Alex H. Lang, David J. Schwab
JOURNAL OF STATISTICAL PHYSICS
(2016)
Article
Physics, Multidisciplinary
Ching-Hao Wang, Pankaj Mehta, Michael Elbaum
PHYSICAL REVIEW LETTERS
(2017)
Review
Physics, Multidisciplinary
Michael Kolodrubetz, Dries Sels, Pankaj Mehta, Anatoli Polkovnikov
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS
(2017)
Article
Cell & Tissue Engineering
Keri Dame, Steven Cincotta, Alex H. Lang, Reeti M. Sanghrajka, Liye Zhang, Jinyoung Choi, Letty Kwok, Talitha Wilson, Maciej M. Kandula, Stefano Monti, Anthony N. Hollenberg, Pankaj Mehta, Darrell N. Kotton, Laertis Ikonomou
Article
Multidisciplinary Sciences
Joshua E. Goldford, Nanxi Lu, Djordje Bajic, Sylvie Estrela, Mikhail Tikhonov, Alicia Sanchez-Gorostiaga, Daniel Segre, Pankaj Mehta, Alvaro Sanchez
Article
Multidisciplinary Sciences
Robert Marsland, Wenping Cui, Pankaj Mehta
SCIENTIFIC REPORTS
(2020)
Article
Physics, Multidisciplinary
Wenping Cui, Robert Marsland, Pankaj Mehta
PHYSICAL REVIEW LETTERS
(2020)
Article
Multidisciplinary Sciences
Robert Marsland, Owen Howell, Andreas Mayer, Pankaj Mehta
Summary: The study presents a biophysically realistic model of Treg-mediated self-tolerance, demonstrating the importance of Treg diversity in maintaining stability against fluctuations in self-antigen concentrations and the potential risk of autoimmune response with decreased Treg diversity.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2021)
Article
Biochemical Research Methods
James Anibal, Alexandre G. Day, Erol Bahadiroglu, Liam O'Neil, Long Phan, Alec Peltekian, Amir Erez, Mariana Kaplan, Gregoire Altan-Bonnet, Pankaj Mehta
Summary: Data clustering plays a significant role in biomedical sciences, especially in the analysis of single-cell data. The new hierarchical density clustering algorithm (HAL-x) introduced in this report improves computational efficiency and achieves high accuracy in single cell classification. This algorithm is scalable, tunable, and rapid, providing a valuable tool for analyzing vast biological datasets.
PLOS COMPUTATIONAL BIOLOGY
(2022)
Article
Developmental Biology
Maria Yampolskaya, Michael J. Herriges, Laertis Ikonomou, Darrell N. Kotton, Pankaj Mehta
Summary: Advances in single-cell RNA sequencing have provided a new way to understand cellular identity. The scTOP method, a statistical and physics-inspired approach, accurately classifies cells, visualizes developmental trajectories, and evaluates engineered cells without feature selection or dimensional reduction. Its application on human and mouse datasets has demonstrated its power in characterizing cellular populations and differentiation.
Article
Physics, Fluids & Plasmas
Jason W. Rocks, Pankaj Mehta
Summary: The bias-variance trade-off is a concept in classical statistics that describes how the complexity of a model affects its ability to make accurate predictions. This understanding needs to be revisited for overparameterized models, which have shown incredible predictive performance even with a large number of fit parameters. In this study, the authors analyze a simple overparameterized model and derive analytic expressions for various error metrics. They discover three phase transitions in the model and explain them using random matrix theory.
Article
Physics, Multidisciplinary
Jason W. Rocks, Pankaj Mehta
Summary: The bias-variance trade-off is a central concept in supervised learning. Modern deep learning methods challenge the traditional belief by achieving state-of-the-art performance with overparameterized models. Statistical physics methods help to understand the bias and variance in these models.
PHYSICAL REVIEW RESEARCH
(2022)
Article
Biochemistry & Molecular Biology
Sai Teja Pusuluri, Alex H. Lang, Pankaj Mehta, Horacio E. Castillo
Article
Physics, Fluids & Plasmas
Benjamin Dickens, Charles K. Fisher, Pankaj Mehta
