Generalized hydrodynamics in complete box-ball system for  $U_q(\widehat{sl}_n)$

Kuniba, Atsuo; Misguich, Grégoire; Pasquier, Vincent

doi:10.21468/scipostphys.10.4.095

Cited by 3 publications

(5 citation statements)

References 47 publications

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“…We mention some possible extensions of Proposition 2.2 and Theorem 2.2. In literature, various extensions of the BBS have been defined and studied [HHIKTT, HKT, IKT, KMP2, KOY, T, TTM]. One such generalization is given by the multicolor BBS with finite/infinite carrier capacity, and it is known that such model can also be linearized by the KKR bijection.…”

Section: Resultsmentioning

confidence: 99%

Relationships between two linearizations of the box-ball system: Kerov–Kirillov–Reschetikhin bijection and slot configuration

Mucciconi,

Sasada,

Sasamoto

et al. 2024

Forum of Mathematics, Sigma

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The box-ball system (BBS), which was introduced by Takahashi and Satsuma in 1990, is a soliton cellular automaton. Its dynamics can be linearized by a few methods, among which the best known is the Kerov–Kirillov–Reschetikhin (KKR) bijection using rigged partitions. Recently, a new linearization method in terms of ‘slot configurations’ was introduced by Ferrari–Nguyen–Rolla–Wang, but its relations to existing ones have not been clarified. In this paper, we investigate this issue and clarify the relation between the two linearizations. For this, we introduce a novel way of describing the BBS dynamics using a carrier with seat numbers. We show that the seat number configuration also linearizes the BBS and reveals explicit relations between the KKR bijection and the slot configuration. In addition, by using these explicit relations, we also show that even in case of finite carrier capacity the BBS can be linearized via the slot configuration.

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Section: Resultsmentioning

confidence: 99%

Relationships between two linearizations of the box-ball system: Kerov–Kirillov–Reschetikhin bijection and slot configuration

Mucciconi,

Sasada,

Sasamoto

et al. 2024

Forum of Mathematics, Sigma

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show abstract

“…It has been applied successfully to many integrable quantum and classical systems. On the classical side, we can mention for instance the application of GHD to the hard-rods model [17,18], to the Toda model [19], to the sinh-Gordon model [20], to the BBS [10,12] and to the (higher rank) complete BBS [21].…”

Section: Introductionmentioning

confidence: 99%

“…In the context of BBS, the evolution triggered by an initial domain-wall state with two different ball densities in the left half and the right half has been studied in details using GHD [12,21]. In such a setup the BBS develops a series of plateaux in the variable ζ = x/t (space coordinate divided by time).…”

Section: Introductionmentioning

confidence: 99%

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Current correlations, Drude weights and large deviations in a box–ball system

Kuniba

Misguich

Pasquier

2022

J. Phys. A: Math. Theor.

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We explore several aspects of the current fluctuations and correlations in the box-ball system (BBS), an integrable cellular automaton in one space dimension. The state we consider is an ensemble of microscopic configurations where the box occupancies are independent random variables (i.i.d. state), with a given mean ball density. We compute several quantities exactly in such homogeneous stationary state: the mean value and the variance of the number of ballst crossing the origin during time t, and the scaled cumulants generating function associated to Nt. We also compute two spatially integrated current-current correlations. The first one, involving the long-time limit of the current-current correlations, is the so-called Drude weight and is obtained with thermodynamic Bethe Ansatz (TBA). The second one, involving equal time current-current correlations is calculated using a transfer matrix approach. A family of generalized currents, associated to the conserved charges and to the different time evolutions of the models are constructed. The long-time limits of their correlations generalize the Drude weight and the second cumulant of t and are found to obey nontrivial symmetry relations. They are computed using TBA and the results are found to be in good agreement with microscopic simulations of the model. TBA is also used to compute explicitly the whole family of flux Jacobian matrices. Finally, some of these results are extended to a (non-i.i.d.) two-temperatures generalized Gibbs state (with one parameter coupled to the total number of balls, and another one coupled to the total number of solitons).

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“…Integrable systems have been in the spotlight lately [13][14][15][16][16][17][18][19][20][21][22], largely due to their inherent non-ergodic features [23][24][25][26] and anomalous transport properties [5,[27][28][29][30][31][32][33][34][35][36][37] as recently covered in a compilation of review articles [38][39][40][41][42][43]. The study of nonequilibrium properties in classical integrable dynamical systems of interacting particles or fields has received comparatively less attention [44][45][46][47][48][49][50][51].…”

Section: Introductionmentioning

confidence: 99%

Anisotropic Landau-Lifshitz model in discrete space-time

et al. 2021

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We construct an integrable lattice model of classical interacting spins in discrete space-time, representing a discrete-time analogue of the lattice Landau-Lifshitz ferromagnet with uniaxial anisotropy. As an application we use this explicit discrete symplectic integration scheme to compute the spin Drude weight and diffusion constant as functions of anisotropy and chemical potential. We demonstrate qualitatively different behavior in the easy-axis and the easy-plane regimes in the non-magnetized sector. Upon approaching the isotropic point we also find an algebraic divergence of the diffusion constant, signaling a crossover to spin superdiffusion.

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Generalized hydrodynamics in complete box-ball system for $U_q(\widehat{sl}_n)$

Cited by 3 publications

References 47 publications

Relationships between two linearizations of the box-ball system: Kerov–Kirillov–Reschetikhin bijection and slot configuration

Relationships between two linearizations of the box-ball system: Kerov–Kirillov–Reschetikhin bijection and slot configuration

Current correlations, Drude weights and large deviations in a box–ball system

Anisotropic Landau-Lifshitz model in discrete space-time

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