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Journal articles on the topic 'Hydrodynamic integrable systems'

Author: Grafiati

Published: 14 March 2023

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1

Kupershmidt, Boris A. "Noncommutative Integrable Systems of Hydrodynamic Type." Acta Applicandae Mathematicae 92, no. 3 (2006): 269–92. http://dx.doi.org/10.1007/s10440-006-9054-1.

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2

Fava, Michele, Sounak Biswas, Sarang Gopalakrishnan, Romain Vasseur, and S. A. Parameswaran. "Hydrodynamic nonlinear response of interacting integrable systems." Proceedings of the National Academy of Sciences 118, no. 37 (2021): e2106945118. http://dx.doi.org/10.1073/pnas.2106945118.

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We develop a formalism for computing the nonlinear response of interacting integrable systems. Our results are asymptotically exact in the hydrodynamic limit where perturbing fields vary sufficiently slowly in space and time. We show that spatially resolved nonlinear response distinguishes interacting integrable systems from noninteracting ones, exemplifying this for the Lieb–Liniger gas. We give a prescription for computing finite-temperature Drude weights of arbitrary order, which is in excellent agreement with numerical evaluation of the third-order response of the XXZ spin chain. We identi

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3

Prykarpatskyy, Yarema. "On the Integrable Chaplygin Type Hydrodynamic Systems and Their Geometric Structure." Symmetry 12, no. 5 (2020): 697. http://dx.doi.org/10.3390/sym12050697.

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A class of spatially one-dimensional completely integrable Chaplygin hydrodynamic systems was studied within framework of Lie-algebraic approach. The Chaplygin hydrodynamic systems were considered as differential systems on the torus. It has been shown that the geometric structure of the systems under analysis has strong relationship with diffeomorphism group orbits on them. It has allowed to find a new infinite hierarchy of integrable Chaplygin like hydrodynamic systems.

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4

Mokhov, O. I. "Integrable bi-Hamiltonian systems of hydrodynamic type." Russian Mathematical Surveys 57, no. 1 (2002): 153–54. http://dx.doi.org/10.1070/rm2002v057n01abeh000483.

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5

Ferapontov, E. V., and A. P. Fordy. "Separable Hamiltonians and integrable systems of hydrodynamic type." Journal of Geometry and Physics 21, no. 2 (1997): 169–82. http://dx.doi.org/10.1016/s0393-0440(96)00013-7.

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6

Odesskii, A. V., and V. V. Sokolov. "Integrable (2+1)-dimensional systems of hydrodynamic type." Theoretical and Mathematical Physics 163, no. 2 (2010): 549–86. http://dx.doi.org/10.1007/s11232-010-0043-1.

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7

Kodama, Y., and B. G. Konopelchenko. "Confluence of hypergeometric functions and integrable hydrodynamic-type systems." Theoretical and Mathematical Physics 188, no. 3 (2016): 1334–57. http://dx.doi.org/10.1134/s0040577916090051.

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8

Dubrovin, B. A. "Differential geometry of strongly integrable systems of hydrodynamic type." Functional Analysis and Its Applications 24, no. 4 (1991): 280–85. http://dx.doi.org/10.1007/bf01077332.

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9

El, Gennady A. "Soliton gas in integrable dispersive hydrodynamics." Journal of Statistical Mechanics: Theory and Experiment 2021, no. 11 (2021): 114001. http://dx.doi.org/10.1088/1742-5468/ac0f6d.

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Abstract We review the spectral theory of soliton gases in integrable dispersive hydrodynamic systems. We first present a phenomenological approach based on the consideration of phase shifts in pairwise soliton collisions and leading to the kinetic equation for a non-equilibrium soliton gas. Then, a more detailed theory is presented in which soliton gas dynamics are modelled by a thermodynamic type limit of modulated finite-gap spectral solutions of the Korteweg–de Vries and the focusing nonlinear Schrödinger (NLS) equations. For the focusing NLS equation the notions of soliton condensate and

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10

De Nardis, Jacopo, Benjamin Doyon, Marko Medenjak, and Miłosz Panfil. "Correlation functions and transport coefficients in generalised hydrodynamics." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 1 (2022): 014002. http://dx.doi.org/10.1088/1742-5468/ac3658.

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Abstract We review the recent advances on exact results for dynamical correlation functions at large scales and related transport coefficients in interacting integrable models. We discuss Drude weights, conductivity and diffusion constants, as well as linear and nonlinear response on top of equilibrium and non-equilibrium states. We consider the problems from the complementary perspectives of the general hydrodynamic theory of many-body systems, including hydrodynamic projections, and form-factor expansions in integrable models, and show how they provide a comprehensive and consistent set of e

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11

Bonnemain, Thibault, Benjamin Doyon, and Gennady El. "Generalized hydrodynamics of the KdV soliton gas." Journal of Physics A: Mathematical and Theoretical 55, no. 37 (2022): 374004. http://dx.doi.org/10.1088/1751-8121/ac8253.

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Abstract We establish the explicit correspondence between the theory of soliton gases in classical integrable dispersive hydrodynamics, and generalized hydrodynamics (GHD), the hydrodynamic theory for many-body quantum and classical integrable systems. This is done by constructing the GHD description of the soliton gas for the Korteweg–de Vries equation. We further predict the exact form of the free energy density and flux, and of the static correlation matrices of conserved charges and currents, for the soliton gas. For this purpose, we identify the solitons’ statistics with that of classical

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12

Kokotov, A., and D. Korotkin. "A new hierarchy of integrable systems associated to Hurwitz spaces." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 366, no. 1867 (2007): 1055–88. http://dx.doi.org/10.1098/rsta.2007.2061.

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In this paper, we introduce a new class of integrable systems, naturally associated to Hurwitz spaces (spaces of meromorphic functions over Riemann surfaces). The critical values of the meromorphic functions play the role of ‘times’. Our systems give a natural generalization of the Ernst equation; in genus zero, they realize the scheme of deformation of integrable systems proposed by Burtsev, Mikhailov and Zakharov. We show that any solution of these systems in rank 1 defines a flat diagonal metric (Darboux–Egoroff metric) together with a class of corresponding systems of hydrodynamic type and

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13

Artemovych, Orest D., Denis Blackmore, and Anatolij K. Prykarpatski. "Poisson brackets, Novikov-Leibniz structures and integrable Riemann hydrodynamic systems." Journal of Nonlinear Mathematical Physics 24, no. 1 (2016): 41–72. http://dx.doi.org/10.1080/14029251.2016.1274114.

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14

Manno, Gianni, and Maxim V. Pavlov. "Hydrodynamic-type systems describing 2-dimensional polynomially integrable geodesic flows." Journal of Geometry and Physics 113 (March 2017): 197–205. http://dx.doi.org/10.1016/j.geomphys.2016.10.023.

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15

Bogdanov, L. V., and B. G. Konopelchenko. "Symmetry constraints for dispersionless integrable equations and systems of hydrodynamic type." Physics Letters A 330, no. 6 (2004): 448–59. http://dx.doi.org/10.1016/j.physleta.2004.08.024.

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16

Błaszak, Maciej, and Wen-Xiu Ma. "Separable Hamiltonian equations on Riemann manifolds and related integrable hydrodynamic systems." Journal of Geometry and Physics 47, no. 1 (2003): 21–42. http://dx.doi.org/10.1016/s0393-0440(02)00173-0.

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17

Pavlov, Maxim V. "Algebro-Geometric Approach in the Theory of Integrable Hydrodynamic Type Systems." Communications in Mathematical Physics 272, no. 2 (2007): 469–505. http://dx.doi.org/10.1007/s00220-007-0235-1.

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18

Ferapontov, E. V. "Isoparametric hypersurfaces in spheres, integrable nondiagonalizable systems of hydrodynamic type, and N-wave systems." Differential Geometry and its Applications 5, no. 4 (1995): 335–69. http://dx.doi.org/10.1016/0926-2245(95)00022-4.

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19

Konopelchenko, B. G., and W. K. Schief. "Integrable discretization of hodograph-type systems, hyperelliptic integrals and Whitham equations." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2172 (2014): 20140514. http://dx.doi.org/10.1098/rspa.2014.0514.

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Based on the well-established theory of discrete conjugate nets in discrete differential geometry, we propose and examine discrete analogues of important objects and notions in the theory of semi-Hamiltonian systems of hydrodynamic type. In particular, we present discrete counterparts of (generalized) hodograph equations, hyperelliptic integrals and associated cycles, characteristic speeds of Whitham-type and (implicitly) the corresponding Whitham equations. By construction, the intimate relationship with integrable system theory is maintained in the discrete setting.

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20

Ferapontov, E. V., and A. Moro. "Dispersive deformations of hydrodynamic reductions of (2 + 1)D dispersionless integrable systems." Journal of Physics A: Mathematical and Theoretical 42, no. 3 (2008): 035211. http://dx.doi.org/10.1088/1751-8113/42/3/035211.

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21

Doyon, Benjamin, and Jason Myers. "Fluctuations in Ballistic Transport from Euler Hydrodynamics." Annales Henri Poincaré 21, no. 1 (2019): 255–302. http://dx.doi.org/10.1007/s00023-019-00860-w.

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AbstractWe propose a general formalism, within large-deviation theory, giving access to the exact statistics of fluctuations of ballistically transported conserved quantities in homogeneous, stationary states. The formalism is expected to apply to any system with an Euler hydrodynamic description, classical or quantum, integrable or not, in or out of equilibrium. We express the exact scaled cumulant generating function (or full counting statistics) for any (quasi-)local conserved quantity in terms of the flux Jacobian. We show that the “extended fluctuation relations” of Bernard and Doyon foll

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22

Ferapontov, E. V., and K. R. Khusnutdinova. "The characterization of two-component (2+1)-dimensional integrable systems of hydrodynamic type." Journal of Physics A: Mathematical and General 37, no. 8 (2004): 2949–63. http://dx.doi.org/10.1088/0305-4470/37/8/007.

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23

Umurzhakhova, Zh B., M. D. Koshanova, Zh Pashen, and K. R. Yesmakhanova. "QUASICLASSICAL LIMIT OF THE SCHRÖDINGER-MAXWELL- BLOCH EQUATIONS." PHYSICO-MATHEMATICAL SERIES 2, no. 336 (2021): 179–84. http://dx.doi.org/10.32014/2021.2518-1726.39.

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The study of integrable equations is one of the most important aspects of modern mathematical and theoretical physics. Currently, there are a large number of nonlinear integrable equations that have a physical application. The concept of nonlinear integrable equations is closely related to solitons. An object being in a nonlinear medium that maintains its shape at moving, as well as when interacting with its own kind, is called a soliton or a solitary wave. In many physical processes, nonlinearity is closely related to the concept of dispersion. Soliton solutions have dispersionless properties

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24

Durnin, Joseph, Andrea De Luca, Jacopo De Nardis, and Benjamin Doyon. "Diffusive hydrodynamics of inhomogenous Hamiltonians." Journal of Physics A: Mathematical and Theoretical 54, no. 49 (2021): 494001. http://dx.doi.org/10.1088/1751-8121/ac2c57.

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Abstract We derive a large-scale hydrodynamic equation, including diffusive and dissipative effects, for systems with generic static position-dependent driving forces coupling to local conserved quantities. We show that this equation predicts entropy increase and thermal states as the only stationary states. The equation applies to any hydrodynamic system with any number of local, parity and time-symmetric conserved quantities, in arbitrary dimension. It is fully expressed in terms of elements of an extended Onsager matrix. In integrable systems, this matrix admits an expansion in the density

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25

Ferapontov, E. V., A. V. Odesskii, and N. M. Stoilov. "Classification of integrable two-component Hamiltonian systems of hydrodynamic type in 2 + 1 dimensions." Journal of Mathematical Physics 52, no. 7 (2011): 073505. http://dx.doi.org/10.1063/1.3602081.

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26

Makridin, Z. V. "An Effective Algorithm for Finding Multidimensional Conservation Laws for Integrable Systems of Hydrodynamic Type." Theoretical and Mathematical Physics 194, no. 2 (2018): 274–83. http://dx.doi.org/10.1134/s0040577918020071.

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27

Spohn, Herbert. "Hydrodynamic equations for the Ablowitz–Ladik discretization of the nonlinear Schrödinger equation." Journal of Mathematical Physics 63, no. 3 (2022): 033305. http://dx.doi.org/10.1063/5.0075670.

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Ablowitz and Ladik discovered a discretization that preserves the integrability of the nonlinear Schrödinger equation in one dimension. We compute the generalized free energy of this model and determine the generalized Gibbs ensemble averaged fields and their currents. They are linked to the mean-field circular unitary matrix ensemble. The resulting hydrodynamic equations follow the pattern already known from other integrable many-body systems. The discretized modified Korteweg–de-Vries equation is also studied, which turns out to be related to the beta Jacobi log gas.

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28

Alba, Vincenzo, Bruno Bertini, Maurizio Fagotti, Lorenzo Piroli, and Paola Ruggiero. "Generalized-hydrodynamic approach to inhomogeneous quenches: correlations, entanglement and quantum effects." Journal of Statistical Mechanics: Theory and Experiment 2021, no. 11 (2021): 114004. http://dx.doi.org/10.1088/1742-5468/ac257d.

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Abstract We give a pedagogical introduction to the generalized hydrodynamic approach to inhomogeneous quenches in integrable many-body quantum systems. We review recent applications of the theory, focusing in particular on two classes of problems: bipartitioning protocols and trap quenches, which represent two prototypical examples of broken translational symmetry in either the system initial state or post-quench Hamiltonian. We report on exact results that have been obtained for generic time-dependent correlation functions and entanglement evolution, and discuss in detail the range of applica

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29

Prykarpatski, Anatolij K. "Quantum Current Algebra in Action: Linearization, Integrability of Classical and Factorization of Quantum Nonlinear Dynamical Systems." Universe 8, no. 5 (2022): 288. http://dx.doi.org/10.3390/universe8050288.

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This review is devoted to the universal algebraic and geometric properties of the non-relativistic quantum current algebra symmetry and to their representations subject to applications in describing geometrical and analytical properties of quantum and classical integrable Hamiltonian systems of theoretical and mathematical physics. The Fock space, the non-relativistic quantum current algebra symmetry and its cyclic representations on separable Hilbert spaces are reviewed and described in detail. The unitary current algebra family of operators and generating functional equations are described.

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30

Ferapontov, E. V. "Dupin hypersurfaces and integrable hamiltonian systems of hydrodynamic type, which do not possess Riemann invariants." Differential Geometry and its Applications 5, no. 2 (1995): 121–52. http://dx.doi.org/10.1016/0926-2245(95)00011-r.

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31

Procopio, Giuseppe, and Massimiliano Giona. "Stochastic Modeling of Particle Transport in Confined Geometries: Problems and Peculiarities." Fluids 7, no. 3 (2022): 105. http://dx.doi.org/10.3390/fluids7030105.

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The equivalence between parabolic transport equations for solute concentrations and stochastic dynamics for solute particle motion represents one of the most fertile correspondences in statistical physics originating from the work by Einstein on Brownian motion. In this article, we analyze the problems and the peculiarities of the stochastic equations of motion in microfluidic confined systems. The presence of solid boundaries leads to tensorial hydrodynamic coefficients (hydrodynamic resistance matrix) that depend also on the particle position. Singularity issues, originating from the non-int

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32

BUROVSKIY, P. A., E. V. FERAPONTOV, and S. P. TSAREV. "SECOND-ORDER QUASILINEAR PDEs AND CONFORMAL STRUCTURES IN PROJECTIVE SPACE." International Journal of Mathematics 21, no. 06 (2010): 799–841. http://dx.doi.org/10.1142/s0129167x10006215.

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We investigate second-order quasilinear equations of the form fijuxixj = 0, where u is a function of n independent variables x1, …, xn, and the coefficients fij depend on the first-order derivatives p1 = ux1, …, pn = uxn only. We demonstrate that the natural equivalence group of the problem is isomorphic to SL(n + 1, R), which acts by projective transformations on the space Pn with coordinates p1, …, pn. The coefficient matrix fij defines on Pn a conformal structure fij(p)dpidpj. The necessary and sufficient conditions for the integrability of such equations by the method of hydrodynamic reduc

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33

Zakharov, Vladimir E. "Description of the $n$ -orthogonal curvilinear coordinate systems and Hamiltonian integrable systems of hydrodynamic type, I: Integration of the Lamé equations." Duke Mathematical Journal 94, no. 1 (1998): 103–39. http://dx.doi.org/10.1215/s0012-7094-98-09406-6.

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34

Błaszak, Maciej, and Artur Sergyeyev. "A coordinate-free construction of conservation laws and reciprocal transformations for a class of integrable hydrodynamic-type systems." Reports on Mathematical Physics 64, no. 1-2 (2009): 341–54. http://dx.doi.org/10.1016/s0034-4877(09)90038-6.

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35

Ferapontov, E. V., and O. I. Mokhov. "The associativity equations in the two-dimensional topological field theory as integrable Hamiltonian nondiagonalizable systems of hydrodynamic type." Functional Analysis and Its Applications 30, no. 3 (1996): 195–203. http://dx.doi.org/10.1007/bf02509506.

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36

Ferapontov, E. V. "On the matrix Hopf equation and integrable Hamiltonian systems of hydrodynamic type, which do not possess Riemann invariants." Physics Letters A 179, no. 6 (1993): 391–97. http://dx.doi.org/10.1016/0375-9601(93)90096-i.

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37

Moore, Joel E. "A perspective on quantum integrability in many-body-localized and Yang–Baxter systems." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 375, no. 2108 (2017): 20160429. http://dx.doi.org/10.1098/rsta.2016.0429.

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Two of the most active areas in quantum many-particle dynamics involve systems with an unusually large number of conservation laws. Many-body-localized systems generalize ideas of Anderson localization by disorder to interacting systems. While localization still exists with interactions and inhibits thermalization, the interactions between conserved quantities lead to some dramatic differences from the Anderson case. Quantum integrable models such as the XXZ spin chain or Bose gas with delta-function interactions also have infinite sets of conservation laws, again leading to modifications of c

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38

Ferapontov, E. V. "Several conjectures and results in the theory of integrable Hamiltonian systems of hydrodynamic type, which do not possess Riemann invariants." Theoretical and Mathematical Physics 99, no. 2 (1994): 567–70. http://dx.doi.org/10.1007/bf01016140.

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39

Kambe, Tsutomu. "Geometrical Aspects in Hydrodynamics and Integrable Systems." Theoretical and Computational Fluid Dynamics 10, no. 1-4 (1998): 249–61. http://dx.doi.org/10.1007/s001620050062.

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40

MARSHAKOV, A. "EXACT SOLUTIONS TO QUANTUM FIELD THEORIES AND INTEGRABLE EQUATIONS." Modern Physics Letters A 11, no. 14 (1996): 1169–83. http://dx.doi.org/10.1142/s021773239600120x.

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The exact solutions to quantum string and gauge field theories are discussed and their formulation in the framework of integrable systems is presented. In particular we consider in detail several examples of the appearance of solutions to the first-order integrable equations of hydrodynamical type and stress that all known examples can be treated as partial solutions to the same problem in the theory of integrable systems.

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41

Cubero, Axel Cortés, Takato Yoshimura, and Herbert Spohn. "Form factors and generalized hydrodynamics for integrable systems." Journal of Statistical Mechanics: Theory and Experiment 2021, no. 11 (2021): 114002. http://dx.doi.org/10.1088/1742-5468/ac2eda.

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42

Bulchandani, Vir B. "On classical integrability of the hydrodynamics of quantum integrable systems." Journal of Physics A: Mathematical and Theoretical 50, no. 43 (2017): 435203. http://dx.doi.org/10.1088/1751-8121/aa8c62.

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43

Bastianello, Alvise, Bruno Bertini, Benjamin Doyon, and Romain Vasseur. "Introduction to the Special Issue on Emergent Hydrodynamics in Integrable Many-Body Systems." Journal of Statistical Mechanics: Theory and Experiment 2022, no. 1 (2022): 014001. http://dx.doi.org/10.1088/1742-5468/ac3e6a.

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44

Prykarpatsky, Yarema A., Ilona Urbaniak, Radosław A. Kycia, and Anatolij K. Prykarpatski. "Dark Type Dynamical Systems: The Integrability Algorithm and Applications." Algorithms 15, no. 8 (2022): 266. http://dx.doi.org/10.3390/a15080266.

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Based on a devised gradient-holonomic integrability testing algorithm, we analyze a class of dark type nonlinear dynamical systems on spatially one-dimensional functional manifolds possessing hidden symmetry properties and allowing their linearization on the associated cotangent spaces. We described main spectral properties of nonlinear Lax type integrable dynamical systems on periodic functional manifolds particular within the classical Floquet theory, as well as we presented the determining functional relationships between the conserved quantities and related geometric Poisson and recursion

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45

De Nardis, Jacopo, Denis Bernard, and Benjamin Doyon. "Hydrodynamic Diffusion in Integrable Systems." Physical Review Letters 121, no. 16 (2018). http://dx.doi.org/10.1103/physrevlett.121.160603.

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46

Doyon, Benjamin. "Lecture notes on Generalised Hydrodynamics." SciPost Physics Lecture Notes, August 28, 2020. http://dx.doi.org/10.21468/scipostphyslectnotes.18.

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These are lecture notes for a series of lectures given at the Les Houches Summer School on Integrability in Atomic and Condensed Matter Physics, 30 July to 24 August 2018. The same series of lectures has also been given at the Tokyo Institute of Technology, October 2019. I overview in a pedagogical fashion the main aspects of the theory of generalised hydrodynamics, a hydrodynamic theory for quantum and classical many-body integrable systems. Only very basic knowledge of hydrodynamics and integrable systems is assumed.

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47

Perfetto, Gabriele, and Benjamin Doyon. "Euler-scale dynamical fluctuations in non-equilibrium interacting integrable systems." SciPost Physics 10, no. 5 (2021). http://dx.doi.org/10.21468/scipostphys.10.5.116.

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We derive an exact formula for the scaled cumulant generating function of the time-integrated current associated to an arbitrary ballistically transported conserved charge. Our results rely on the Euler-scale description of interacting, many-body, integrable models out of equilibrium given by the generalized hydrodynamics, and on the large deviation theory. Crucially, our findings extend previous studies by accounting for inhomogeneous and dynamical initial states in interacting systems. We present exact expressions for the first three cumulants of the time-integrated current. Considering the

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48

VU, Dinh-Long, and Takato Yoshimura. "Equations of state in generalized hydrodynamics." SciPost Physics 6, no. 2 (2019). http://dx.doi.org/10.21468/scipostphys.6.2.023.

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We, for the first time, report a first-principle proof of the equations of state used in the hydrodynamic theory for integrable systems, termed generalized hydrodynamics (GHD). The proof makes full use of the graph theoretic approach to Thermodynamic Bethe ansatz (TBA) that was proposed recently. This approach is purely combinatorial and relies only on common structures shared among Bethe solvable models, suggesting universal applicability of the method. To illustrate the idea of the proof, we focus on relativistic integrable quantum field theories with diagonal scatterings and without bound s

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49

Ferapontov, E. V., and M. V. Pavlov. "Kinetic Equation for Soliton Gas: Integrable Reductions." Journal of Nonlinear Science 32, no. 2 (2022). http://dx.doi.org/10.1007/s00332-022-09782-0.

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AbstractMacroscopic dynamics of soliton gases can be analytically described by the thermodynamic limit of the Whitham equations, yielding an integro-differential kinetic equation for the density of states. Under a delta-functional ansatz, the kinetic equation for soliton gas reduces to a non-diagonalisable system of hydrodynamic type whose matrix consists of several $$2\times 2$$ 2 × 2 Jordan blocks. Here we demonstrate the integrability of this system by showing that it possesses a hierarchy of commuting hydrodynamic flows and can be solved by an extension of the generalised hodograph method.

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50

Fagotti, Maurizio. "Locally quasi-stationary states in noninteracting spin chains." SciPost Physics 8, no. 3 (2020). http://dx.doi.org/10.21468/scipostphys.8.3.048.

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Locally quasi-stationary states (LQSS) were introduced as inhomogeneous generalisations of stationary states in integrable systems. Roughly speaking, LQSSs look like stationary states, but only locally. Despite their key role in hydrodynamic descriptions, an unambiguous definition of LQSSs was not given. By solving the dynamics in inhomogeneous noninteracting spin chains, we identify the set of LQSSs as a subspace that is invariant under time evolution, and we explicitly construct the latter in a generalised XY model. As a by-product, we exhibit an exact generalised hydrodynamic theory (includ

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