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George Ruppeiner - One of the best experts on this subject based on the ideXlab platform.
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riemannian geometry in thermodynamic Fluctuation Theory
Reviews of Modern Physics, 1995Co-Authors: George RuppeinerAbstract:Although thermodynamic Fluctuation Theory originated from statistical mechanics, it may be put on a completely thermodynamic basis, in no essential need of any microscopic foundation. This review views the Theory from the macroscopic perspective, emphasizing, in particular, notions of covariance and consistency, expressed naturally using the language of Riemannian geometry. Coupled with these concepts is an extension of the basic structure of thermodynamic Fluctuation Theory beyond the classical one of a subsystem in contact with an infinite uniform reservoir. Used here is a hierarchy of concentric subsystems, each of which samples only the thermodynamic state of the subsystem immediately larger than it. The result is a covariant thermodynamic Fluctuation Theory which is plausible beyond the standard second-order entropy expansion. It includes the conservation laws and is mathematically consistent when applied to Fluctuations inside subsystems. Tests on known models show improvements. Perhaps most significantly, the covariant Theory offers a qualitatively new tool for the study of Fluctuation phenomena: the Riemannian thermodynamic curvature. The thermodynamic curvature gives, for any given thermodynamic state, a lower bound for the length scale where the classical thermodynamic Fluctuation Theory based on a uniform environment could conceivably hold. Straightforward computation near the critical point reveals that themore » curvature equals the correlation volume, a physically appealing finding. The combination of the interpretation of curvature with a well-known proportionality between the free energy and the inverse of the correlation volume yields a purely thermodynamic Theory of the critical point. The scaled equation of state follows from the values of the critical exponents. The thermodynamic Riemannian metric may be put into the broader context of information Theory.« less
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riemannian geometry in thermodynamic Fluctuation Theory
Reviews of Modern Physics, 1995Co-Authors: George RuppeinerAbstract:Although thermodynamic Fluctuation Theory originated from statistical mechanics, it may be put on a completely thermodynamic basis, in no essential need of any microscopic foundation. This review views the Theory from the macroscopic perspective, emphasizing, in particular, notions of covariance and consistency, expressed naturally using the language of Riemannian geometry. Coupled with these concepts is an extension of the basic structure of thermodynamic Fluctuation Theory beyond the classical one of a subsystem in contact with an infinite uniform reservoir. Used here is a hierarchy of concentric subsystems, each of which samples only the thermodynamic state of the subsystem immediately larger than it. The result is a covariant thermodynamic Fluctuation Theory which is plausible beyond the standard second-order entropy expansion. It includes the conservation laws and is mathematically consistent when applied to Fluctuations inside subsystems. Tests on known models show improvements. Perhaps most significantly, the covariant Theory offers a qualitatively new tool for the study of Fluctuation phenomena: the Riemannian thermodynamic curvature. The thermodynamic curvature gives, for any given thermodynamic state, a lower bound for the length scale where the classical thermodynamic Fluctuation Theory based on a uniform environment could conceivably hold. Straightforward computation near the critical point reveals that the curvature equals the correlation volume, a physically appealing finding. The combination of the interpretation of curvature with a well-known proportionality between the free energy and the inverse of the correlation volume yields a purely thermodynamic Theory of the critical point. The scaled equation of state follows from the values of the critical exponents. The thermodynamic Riemannian metric may be put into the broader context of information Theory.
Herbert Spohn - One of the best experts on this subject based on the ideXlab platform.
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numerical test of hydrodynamic Fluctuation Theory in the fermi pasta ulam chain
Physical Review E, 2014Co-Authors: Suman G Das, Abhishek Dhar, Keiji Saito, Christian B Mendl, Herbert SpohnAbstract:Recent work has developed a nonlinear hydrodynamic Fluctuation Theory for a chain of coupled anharmonic oscillators governing the conserved fields, namely, stretch, momentum, and energy. The linear Theory yields two propagating sound modes and one diffusing heat mode, all three with diffusive broadening. In contrast, the nonlinear Theory predicts that, at long times, the sound mode correlations satisfy Kardar-Parisi-Zhang scaling, while the heat mode correlations have L\'evy-walk scaling. In the present contribution we report on molecular dynamics simulations of Fermi-Pasta-Ulam chains to compute various spatiotemporal correlation functions and compare them with the predictions of the Theory. We obtain very good agreement in many cases, but also some deviations.
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numerical test of hydrodynamic Fluctuation Theory in the fermi pasta ulam chain
Physical Review E, 2014Co-Authors: Abhishek Dhar, Keiji Saito, Christian B Mendl, Herbert SpohnAbstract:Institute for Advanced Study, Einstein Drive, Princeton NJ 08540, USA(Dated: August 1, 2014)Recent work has developed a nonlinear hydrodynamic fluctuation Theory for a chain of coupled anharmonicoscillators governing the conserved fields, namely stretch, momentum, and energy. The linear Theory yields twopropagating sound modes and one diffusing heat mode. In contrast, the nonlinear Theory predicts that, at longtimes, the sound mode correlations satisfy Kardar-Parisi-Zhang (KPZ) scaling, while the heat mode correla-tions satisfies L´evy-walk scaling. In the present contribution we report on molecular dynamics simulations ofFermi-Pasta-Ulam chains to compute various spatiotemporal correlation functions and compare them with thepredictions of the Theory. We find very good agreement in many cases, but also some deviations.I. INTRODUCTION
C Landim - One of the best experts on this subject based on the ideXlab platform.
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macroscopic Fluctuation Theory
Reviews of Modern Physics, 2015Co-Authors: Lorenzo Bertini, Alberto De Sole, Davide Gabrielli, Giovanni Jonalasinio, C LandimAbstract:The statistical mechanics of systems out of equilibrium provides a formidable challenge. This review describes an approach to a subset of such problems, viz., stationary nonequilibrium states. The review includes what is known as the macroscopic Fluctuation Theory, which allows for the definition of nonequilibrium analogs of thermodynamics potentials, and is applied to various illustrative models.
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Macroscopic Fluctuation Theory for Stationary Non-Equilibrium States
Journal of Statistical Physics, 2002Co-Authors: Lorenzo Bertini, Alberto De Sole, Davide Gabrielli, G. Jona-lasinio, C LandimAbstract:We formulate a dynamical Fluctuation Theory for stationary non-equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our Theory a crucial role is played by the time reversed dynamics. Within this Theory we derive the following results: the modification of the Onsager–Machlup Theory in the SNS; a general Hamilton–Jacobi equation for the macroscopic entropy; a non-equilibrium, nonlinear Fluctuation dissipation relation valid for a wide class of systems; an H theorem for the entropy. We discuss in detail two models of stochastic boundary driven lattice gases: the zero range and the simple exclusion processes. In the first model the invariant measure is explicitly known and we verify the predictions of the general Theory. For the one dimensional simple exclusion process, as recently shown by Derrida, Lebowitz, and Speer, it is possible to express the macroscopic entropy in terms of the solution of a nonlinear ordinary differential equation; by using the Hamilton–Jacobi equation, we obtain a logically independent derivation of this result.
Etsuji Yamamoto - One of the best experts on this subject based on the ideXlab platform.
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phenomenological approach to study the degree of the itinerancy of the 5f electrons in actinide ferromagnets with spin Fluctuation Theory
arXiv: Strongly Correlated Electrons, 2018Co-Authors: Naoyuki Tateiwa, Yoshinori Haga, Hironori Sakai, Tatsuma D Matsuda, J Pospisil, Etsuji YamamotoAbstract:Actinide compounds with 5f electrons have been attracting much attention because of their interesting magnetic and electronic properties such as heavy fermion state, unconventional superconductivity, co-existence of the superconductivity and magnetism. Recently, we have reported a phenomenological analysis on 80 actinide ferromagnets with the spin Fluctuation Theory originally developed to explain the ferromagnetic properties of itinerant ferromagnets in the 3d transition metals and their intermetallics (N. Tateiwa et al., Phys. Rev. B 96, 035125 (2017)). Our study suggests the itinerancy of the $5f$ electrons in most of the actinide ferromagnets and the applicability of the spin Fluctuation Theory to actinide 5f system. In this paper, we present a new analysis for the spin Fluctuation parameter obtained with a different theoretical formula not used in the reference. We also discuss the results of the analysis from different points of views.
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itinerant ferromagnetism in actinide 5 f electron systems phenomenological analysis with spin Fluctuation Theory
Physical Review B, 2017Co-Authors: Naoyuki Tateiwa, Jiři Pospisil, Yoshinori Haga, Hironori Sakai, Tatsuma D Matsuda, Etsuji YamamotoAbstract:We have carried out an analysis of magnetic data in 69 uranium, 7 neptunium, and 4 plutonium ferromagnets with the spin Fluctuation Theory developed by Takahashi [Y. Takahashi, J. Phys. Soc. Jpn. 55, 3553 (1986)]. The basic and spin Fluctuation parameters of the actinide ferromagnets are determined and the applicability of the spin Fluctuation Theory to actinide $5f$ system has been discussed. Itinerant ferromagnets of the $3d$ transition metals and their intermetallics follow a generalized Rhodes-Wohlfarth relation between ${p}_{\mathrm{eff}}/{p}_{\mathrm{s}}$ and ${T}_{\mathrm{C}}/{T}_{0}$, viz., ${p}_{\mathrm{eff}}/{p}_{\mathrm{s}}\phantom{\rule{0.16em}{0ex}}\ensuremath{\propto}\phantom{\rule{0.16em}{0ex}}{({T}_{\mathrm{C}}/{T}_{0})}^{\ensuremath{-}3/2}$. Here, ${p}_{\mathrm{s}}$, ${p}_{\mathrm{eff}}$, ${T}_{\mathrm{C}}$, and ${T}_{0}$ are the spontaneous and effective magnetic moments, the Curie temperature, and the width of spin Fluctuation spectrum in energy space, respectively. The same relation is satisfied for ${T}_{\mathrm{C}}/{T}_{0}l1.0$ in the actinide ferromagnets. However, the relation is not satisfied in a few ferromagnets with ${T}_{\mathrm{C}}/{T}_{0}\phantom{\rule{0.16em}{0ex}}\ensuremath{\sim}\phantom{\rule{0.16em}{0ex}}1.0$ that corresponds to local moment system in the spin Fluctuation Theory. The deviation from the theoretical relation may be due to several other effects not included in the spin Fluctuation Theory such as the crystalline electric field effect on the $5f$ electrons from ligand atoms. The value of the spontaneous magnetic moment ${p}_{\mathrm{s}}$ increases linearly as a function of ${T}_{\mathrm{C}}/{T}_{0}$ in the uranium and neptunium ferromagnets below ${({T}_{\mathrm{C}}/{T}_{0})}_{\mathrm{kink}}\phantom{\rule{0.16em}{0ex}}=\phantom{\rule{0.16em}{0ex}}0.32\phantom{\rule{0.16em}{0ex}}\ifmmode\pm\else\textpm\fi{}\phantom{\rule{0.16em}{0ex}}0.02$, where a kink structure appears in relation between the two quantities. ${p}_{\mathrm{s}}$ increases more weakly above ${({T}_{\mathrm{C}}/{T}_{0})}_{\mathrm{kink}}$. A possible interpretation with the ${T}_{\mathrm{C}}/{T}_{0}$ dependence of ${p}_{\mathrm{s}}$ is given.
Hiroshi Kontani - One of the best experts on this subject based on the ideXlab platform.
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Multipole Fluctuation Theory for heavy fermion systems: Application to multipole orders in CeB 6
Physical Review B, 2019Co-Authors: Rina Tazai, Hiroshi KontaniAbstract:In heavy fermion systems, the emergence of rich phenomena, such as hidden orders and superconductivities, is made possible by multipole degrees of freedom. However, many of them remain unsolved since the origin of the higher-rank multipole interaction is not well understood. Among these issues, we focus on the quadrupole order in ${\mathrm{CeB}}_{6}$, which is a famous multipolar heavy fermion system that has been actively studied for decades. We analyze the multiorbital periodic Anderson model for ${\mathrm{CeB}}_{6}$, and find that magnetic, quadrupole, and octupole Fluctuations all develop cooperatively due to the strong intermultipole coupling given by higher-order many-body effects, called vertex corrections. It is found that the antiferroquadrupole order in ${\mathrm{CeB}}_{6}$ is driven by the interference between magnetic-multipole Fluctuations. The discovered intermultipole coupling mechanism is a potential origin of numerous hidden orders in various heavy fermion systems.
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orbital Fluctuation Theory in iron based superconductors s wave superconductivity structure transition and impurity induced nematic order
Solid State Communications, 2012Co-Authors: Hiroshi Kontani, Yoshio Inoue, Tetsuro Saito, Youichi Yamakawa, Seiichiro OnariAbstract:Abstract The main features in iron-based superconductors would be (i) the orthorhombic transition accompanied by remarkable softening of shear modulus, (ii) high- T c superconductivity close to the orthorhombic phase, and (iii) nematic transition in the tetragonal phase. In this paper, we present a unified explanation for them, based on the orbital Fluctuation Theory, considering both the e -ph and the Coulomb interaction. It is found that a small e -phonon coupling constant ( λ ∼ 0.2 ) is enough to produce large orbital ( = charge quadrupole O x z / y z ) Fluctuations, which causes the s -wave superconductivity without sign reversal ( s + + -wave state). The derived orbital Fluctuations also cause the instability toward the structure transition due to the bound state formation of two orbitons with opposite momenta, which is called the “two-orbiton process”. Moreover, impurity-induced non-local orbital order with C 2 -symmetry is obtained when the orbital Fluctuations are strong. This “impurity-induced nematic state” explains the in-plane anisotropy of resistivity in detwinned samples. We stress that (i)–(iii) are reproducible only when orbital Fluctuations with respect to O x z and O y z charge quadrupoles are the most divergent. This fact ensures the reliability of the present model Hamiltonian and calculation.