Article
Materials Science, Multidisciplinary
Angelo Russomanno, Michele Fava, Markus Heyl
Summary: In this study, large-scale exact diagonalization was used to investigate the quantum Ising chain with long-range power-law interactions. The level-spacing statistics indicate a Wigner-Dyson distribution and quantum chaos for all alpha > 0. However, the microcanonical entropy is nonconvex for alpha < 1 due to energetically separated multiplets in the spectrum.
Article
Mechanics
Tong Wu, Tomos David, Wouter J. T. Bos
Summary: In turbulent systems with inverse cascades, energy will accumulate at large scales if there is no large-scale sink. We observed condensation in forced-dissipative three-dimensional turbulence without vortex-stretching, which is associated with an inverse cascade of helicity. The large-scale structure of this condensate is characterized by a hyperbolic sine relation between vorticity and velocity, similar to the relationship observed in freely decaying 2D turbulence in periodic domains.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2023)
Article
Mathematics
Mircea Balaj, Dan Florin Serac
Summary: This paper studies the existence of solutions for generalized equilibrium problems and equilibrium problems. In addition to the given bifunction f, another bifunction is introduced, which are linked by a certain compatibility condition. The uniqueness of the equilibrium theorems in the last section is the absence of the classic equilibrium condition (f(x, x) = 0, for all x in X). The applications given in the paper relate to the Minty variational inequality problem and quasi-equilibrium problems.
Article
Physics, Fluids & Plasmas
Yuanting Chen, Benno Rumpf
Summary: The study reveals that there are two opposing dynamics when solitary waves interact with random Rayleigh-Jeans distributed waves, depending on the dynamical property of the solitary wave and the statistical property of the thermal waves. The transition between the two dynamics results in an increase in wave entropy.
Article
Physics, Fluids & Plasmas
Jae Dong Noh
Summary: We investigate the eigenstate thermalization properties of the spin-1/2 XXZ model in two-dimensional rectangular lattices. The numerical analysis supports that the model follows the eigenstate thermalization hypothesis, and this hypothesis is still valid within each subspace where the total spin is a good quantum number.
Article
Physics, Fluids & Plasmas
Felix Fritzsch, Tomaz Prosen
Summary: The study investigates the distribution of matrix elements for a class of operators in dual-unitary quantum circuits, providing an exact asymptotic expression for the spectral function and confirming excellent agreement with results obtained by exact diagonalization. Furthermore, fluctuations at finite system size are explicitly related to dynamical correlations at intermediate times, while numerical computation of higher moments of the matrix elements confirms the expected Gaussian distribution.
Article
Materials Science, Multidisciplinary
Xiang Gao
Summary: This study reveals that the generalized Boltzmann distribution is mathematically consistent with thermodynamics and challenges the fundamental assumptions of statistical mechanics. It provides a new approach to derive the Boltzmann distribution and could have implications for non-Boltzmann-Gibbs statistical mechanics and philosophical studies on its foundations.
RESULTS IN PHYSICS
(2022)
Article
Optics
Leela Ganesh Chandra Lakkaraju, Srijon Ghosh, Debasis Sadhukhan, Aditi Sen(De)
Summary: The quantum long-range extended Ising model exhibits distinct features that are not observed in the corresponding short-range model. It has been discovered that the entanglement pattern between any two arbitrary sites of the long-range model can be mimicked by a model with finite-range interactions when the interaction strength is moderate. However, when the interactions are strong, the entanglement distribution in the long-range model does not match that of a model with only a few interactions. Furthermore, the monogamy score of entanglement is in good agreement with the behavior of pairwise entanglement.
Article
Mechanics
Derek Frydel
Summary: The study investigates extensions of the run-and-tumble particle model in 1D, finding that expanding the model to three drifts leads to complexity. Therefore, the researchers modified their goal and considered a version of the model with an arbitrary distribution of states, analyzing the system through self-consistent relations and Laplace transform techniques.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2021)
Article
Chemistry, Physical
Giacomo Gradenigo, Stefano Iubini, Roberto Livi, Satya N. Majumdar
Summary: The study explicitly solves the thermodynamics of the discrete nonlinear Schrodinger equation near infinite temperature in the microcanonical ensemble through large deviation techniques, revealing a first-order phase transition between a thermalized phase and a condensed phase along the infinite-temperature line. In the condensed phase, inequivalence between statistical ensembles is observed, highlighting the inability of the grand-canonical representation. Control over finite-size corrections of the microcanonical partition function allows for the design of an experimental test of delocalized negative-temperature states in lattices of cold atoms.
EUROPEAN PHYSICAL JOURNAL E
(2021)
Editorial Material
Multidisciplinary Sciences
Victor A. Kovtunenko, Hiromichi Itou, Alexander M. Khludnev, Evgeny M. Rudoy
Summary: Mathematical methods based on the variational approach have successfully been used in many applications, particularly in the field of partial differential equations. This article focuses on singular and unilaterally constrained problems in mechanics and physics, which are governed by complex systems of generalized variational equations and inequalities. The article highlights the need for non-standard well-posedness analysis and numerical methods to address these problems.
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2022)
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
Physics, Multidisciplinary
K. Baudin, J. Garnier, A. Fusaro, N. Berti, C. Michel, K. Krupa, G. Millot, A. Picozzi
Summary: This paper reports the observation of Rayleigh-Jeans thermalization of light waves to negative-temperature equilibrium states. The optical wave relaxes to the equilibrium state through its propagation in a multimode optical fiber, where high energy levels are more populated than low energy levels. Experimental results show that negative-temperature speckle beams have a nonmonotonic radial intensity profile.
PHYSICAL REVIEW LETTERS
(2023)
Article
Chemistry, Physical
Javier Varillas, Giovanni Ciccotti, Jorge Alcala, Lamberto Rondoni
Summary: Mathematical relations concerning particle systems require applicability conditions. The Jarzynski equality, a mechanical theory, shows surprising generality in determining free-energy variations for non-equilibrium processes. However, it can be process-dependent and its verification may be challenging.
JOURNAL OF CHEMICAL PHYSICS
(2022)
Article
Optics
Mark T. Mitchison, Archak Purkayastha, Marlon Brenes, Alessandro Silva, John Goold
Summary: This study proposes a scheme to measure the temperature of pure states through quantum interference, showing that even individual pure quantum states can have temperatures in completely isolated quantum systems.
Article
Mathematics, Applied
Melanie Kobras, Valerio Lucarini, Maarten H. P. Ambaum
Summary: In this study, a minimal dynamical system derived from the classical Phillips two-level model is introduced to investigate the interaction between eddies and mean flow. The study finds that the horizontal shape of the eddies can lead to three distinct dynamical regimes, and these regimes undergo transitions depending on the intensity of external baroclinic forcing. Additionally, the study provides insights into the continuous or discontinuous transitions of atmospheric properties between different regimes.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Shu-hong Xue, Yun-yun Yang, Biao Feng, Hai-long Yu, Li Wang
Summary: This research focuses on the robustness of multiplex networks and proposes a new index to measure their stability under malicious attacks. The effectiveness of this method is verified in real multiplex networks.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Julien Nespoulous, Guillaume Perrin, Christine Funfschilling, Christian Soize
Summary: This paper focuses on optimizing driver commands to limit energy consumption of trains under punctuality and security constraints. A four-step approach is proposed, involving simplified modeling, parameter identification, reformulation of the optimization problem, and using evolutionary algorithms. The challenge lies in integrating uncertainties into the optimization problem.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Alain Bourdier, Jean-Claude Diels, Hassen Ghalila, Olivier Delage
Summary: In this article, the influence of a turbulent atmosphere on the growth of modulational instability, which is the cause of multiple filamentation, is studied. It is found that considering the stochastic behavior of the refractive index leads to a decrease in the growth rate of this instability. Good qualitative agreement between analytical and numerical results is obtained.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Ling An, Liming Ling, Xiaoen Zhang
Summary: In this paper, an integrable fractional derivative nonlinear Schrodinger equation is proposed and a reconstruction formula of the solution is obtained by constructing an appropriate Riemann-Hilbert problem. The explicit fractional N-soliton solution and the rigorous verification of the fractional one-soliton solution are presented.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Marzia Bisi, Nadia Loy
Summary: This paper proposes and investigates general kinetic models with transition probabilities that can describe the simultaneous change of multiple microscopic states of the interacting agents. The mathematical properties of the kinetic model are proved, and the quasi-invariant asymptotic regime is studied and compared with other models. Numerical tests are performed to demonstrate the time evolution of distribution functions and macroscopic fields.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Carlos A. Pires, David Docquier, Stephane Vannitsem
Summary: This study presents a general theory for computing information transfers in nonlinear stochastic systems driven by deterministic forcings and additive and/or multiplicative noises. It extends the Liang-Kleeman framework of causality inference to nonlinear cases based on information transfer across system variables. The study introduces an effective method called the 'Causal Sensitivity Method' (CSM) for computing the rates of Shannon entropy transfer between selected causal and consequential variables. The CSM method is robust, cheaper, and less data-demanding than traditional methods, and it opens new perspectives on real-world applications.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Feiting Fan, Minzhi Wei
Summary: This paper focuses on the existence of periodic and solitary waves for a quintic Benjamin-Bona-Mahony (BBM) equation with distributed delay and diffused perturbation. By transforming the corresponding traveling wave equation into a three-dimensional dynamical system and applying geometric singular perturbation theory, the existence of periodic and solitary waves are established. The uniqueness of periodic waves and the monotonicity of wave speed are also analyzed.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Wangbo Luo, Yanxiang Zhao
Summary: We propose a generalized Ohta-Kawasaki model to study the nonlocal effect on pattern formation in binary systems with long-range interactions. In the 1D case, the model displays similar bubble patterns as the standard model, but Fourier analysis reveals that the optimal number of bubbles for the generalized model may have an upper bound.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Corentin Correia, Ana Cristina Moreira Freitas, Jorge Milhazes Freitas
Summary: The emergence of clustering of rare events is due to periodicity, where fast returns to target sets lead to a bulk of high observations. In this research, we explore the potential of a new mechanism to create clustering of rare events by linking observable functions to a finite number of points belonging to the same orbit. We show that with the right choice of system and observable, any given cluster size distribution can be obtained.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Enyu Fan, Changpin Li
Summary: This paper numerically studies the Allen-Cahn equations with different kinds of time fractional derivatives and investigates the influences of time derivatives on the solutions of the considered models.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Yuhang Zhu, Yinghao Zhao, Chaolin Song, Zeyu Wang
Summary: In this study, a novel approach called Time-Variant Reliability Updating (TVRU) is proposed, which integrates Kriging-based time-dependent reliability with parallel learning. This method enhances risk assessment in complex systems, showcasing exceptional efficiency and accuracy.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Chiara Cecilia Maiocchi, Valerio Lucarini, Andrey Gritsun, Yuzuru Sato
Summary: The predictability of weather and climate is influenced by the state-dependent nature of atmospheric systems. The presence of special atmospheric states, such as blockings, is associated with anomalous instability. Chaotic systems, like the attractor of the Lorenz '96 model, exhibit heterogeneity in their dynamical properties, including the number of unstable dimensions. The variability of unstable dimensions is linked to the presence of finite-time Lyapunov exponents that fluctuate around zero. These findings have implications for understanding the structural stability and behavior modeling of high-dimensional chaotic systems.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Christian Klein, Goksu Oruc
Summary: A numerical study on the fractional Camassa-Holm equations is conducted to construct smooth solitary waves and investigate their stability. The long-time behavior of solutions for general localized initial data from the Schwartz class of rapidly decreasing functions is also studied. Additionally, the appearance of dispersive shock waves is explored.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Mathematics, Applied
Vasily E. Tarasov
Summary: This paper extends the standard action principle and the first Noether theorem to consider the general form of nonlocality in time and describes dissipative and non-Lagrangian nonlinear systems. The general fractional calculus is used to handle a wide class of nonlocalities in time compared to the usual fractional calculus. The nonlocality is described by a pair of operator kernels belonging to the Luchko set. The non-holonomic variation equations of the Sedov type are used to describe the motion equations of a wide class of dissipative and non-Lagrangian systems. Additionally, the equations of motion are considered not only with general fractional derivatives but also with general fractional integrals. An application example is presented.
PHYSICA D-NONLINEAR PHENOMENA
(2024)