記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1103/physrevlett.133.117102

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掲載種別：研究論文（学術雑誌）  

<jats:title>Abstract</jats:title>
<jats:p>We give a short overview of recent developments in exact solutions for macroscopic fluctuation theory by using connections to classical integrable systems. A calculation of the cumulant generating function for a tagged particle is also given, agreeing with a previous result obtained from a microscopic analysis.</jats:p>

DOI： 10.1088/1742-5468/ad485e

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掲載種別：研究論文（学術雑誌）  

<jats:p>The Cauchy identities play an important role in the theory of symmetric functions. It is known that Cauchy sums for the $q$-Whittaker and the skew Schur polynomials produce the same factorized expressions modulo a $q$-Pochhammer symbol. We consider the sums with restrictions on the length of the first rows for labels of both polynomials and prove an identity which relates them. The proof is based on techniques from integrable probability: we rewrite the identity in terms of two probability measures: the $q$-Whittaker measure and the periodic Schur measure. The relation follows by comparing their Fredholm determinant formulas.</jats:p>

DOI： 10.3842/sigma.2024.064

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1103/physrevlett.132.087101

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

<jats:title>Abstract</jats:title>
<jats:p>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.</jats:p>

DOI： 10.1017/fms.2024.39

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1038/s41567-023-02306-x

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掲載種別：研究論文（学術雑誌）  

<jats:p>We introduce a new universal framework describing fluctuations and correlations in quantum and classical many-body systems, at the Euler hydrodynamic scale of space and time. The framework adapts the ideas of the conventional macroscopic fluctuation theory (MFT) to systems that support ballistic transport. The resulting “ballistic MFT” (BMFT) is solely based on the Euler hydrodynamics data of the many-body system. Within this framework, mesoscopic observables are classical random variables depending only on the fluctuating conserved densities, and Euler-scale fluctuations are obtained by deterministically transporting thermodynamic fluctuations via the Euler hydrodynamics. Using the BMFT, we show that long-range correlations in space generically develop over time from long-wavelength inhomogeneous initial states in interacting models. This result, which we verify by numerical calculations, challenges the long-held paradigm that at the Euler scale, fluid cells may be considered uncorrelated. We also show that the Gallavotti-Cohen fluctuation theorem for non-equilibrium ballistic transport follows purely from time-reversal invariance of the Euler hydrodynamics. We check the validity of the BMFT by applying it to integrable systems, and in particular the hard-rod gas, with extensive simulations that confirm our analytical results.</jats:p>

DOI： 10.21468/scipostphys.15.4.136

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

<jats:p>We give a short account of our new approach to study models in the Kardar–Parisi–Zhang universality class by connecting them to free fermions at positive temperature. Our ideas and methods are explained mainly for the semi-discrete directed polymer model due to O’Connell and Yor.</jats:p>

DOI： 10.1063/5.0089778

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1103/physrevlett.131.027101

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掲載種別：研究論文（学術雑誌）  

<jats:p>
We obtain exact formulas for the time-dependence of a few physical observables for the open XX spin chain with Lindbladian dynamics. Our analysis is based on the fact that the Lindblad equation for an arbitrary open quadratic system of
<jats:inline-formula>
<jats:alternatives>
<jats:tex-math>N</jats:tex-math>
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline">
<mml:mi>N</mml:mi>
</mml:math>
</jats:alternatives>
</jats:inline-formula>
fermions is explicitly solved in terms of diagonalization of a
<jats:inline-formula>
<jats:alternatives>
<jats:tex-math>4N\times4N</jats:tex-math>
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline">
<mml:mrow>
<mml:mn>4</mml:mn>
<mml:mi>N</mml:mi>
<mml:mo>×</mml:mo>
<mml:mn>4</mml:mn>
<mml:mi>N</mml:mi>
</mml:mrow>
</mml:math>
</jats:alternatives>
</jats:inline-formula>
matrix called structure matrix by following the scheme of the third quantization. We mainly focus on the time-dependence of magnetization and spin current. As a short-time behavior at a given site, we observe the plateau regime except near the center of the chain. Basic features of this are explained by the light-cone structure created by propagations of boundary effects from the initial time, but we can explain their more detailed properties analytically using our exact formulas. On the other hand, after the plateau regime, the magnetization and spin current exhibit a slow decay to the steady state values described by the Liouvillian gap. We analytically establish its
<jats:inline-formula>
<jats:alternatives>
<jats:tex-math>O(N^{-3})</jats:tex-math>
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline">
<mml:mrow>
<mml:mi>O</mml:mi>
<mml:mrow>
<mml:mo stretchy="true" form="prefix">(</mml:mo>
<mml:msup>
<mml:mi>N</mml:mi>
<mml:mrow>
<mml:mo>−</mml:mo>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mo stretchy="true" form="postfix">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</jats:alternatives>
</jats:inline-formula>
scaling and also determine its coefficient.
</jats:p>

DOI： 10.21468/scipostphys.14.5.112

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1103/physreva.107.l010201

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

<jats:title>Abstract</jats:title><jats:p>Iterating the skew RSK correspondence discovered by Sagan and Stanley in the late 1980s, we define deterministic dynamics on the space of pairs of skew Young tableaux<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S2050508623000239_inline1.png" /><jats:tex-math>$(P,Q)$</jats:tex-math></jats:alternatives></jats:inline-formula>. We find that these skew RSK dynamics display conservation laws which, in the picture of Viennot’s shadow line construction, identify generalizations of Greene invariants. The introduction of a novel realization of<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S2050508623000239_inline2.png" /><jats:tex-math>$0$</jats:tex-math></jats:alternatives></jats:inline-formula>-th Kashiwara operators reveals that the skew RSK dynamics possess symmetries induced by an affine bicrystal structure, which, combined with connectedness properties of Demazure crystals, leads to the linearization of the time evolution. Studying asymptotic evolution of the dynamics started from a pair of skew tableaux<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S2050508623000239_inline3.png" /><jats:tex-math>$(P,Q)$</jats:tex-math></jats:alternatives></jats:inline-formula>, we discover a new bijection<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S2050508623000239_inline4.png" /><jats:tex-math>$\Upsilon : (P,Q) \mapsto (V,W; \kappa , \nu )$</jats:tex-math></jats:alternatives></jats:inline-formula>. Here,<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S2050508623000239_inline5.png" /><jats:tex-math>$(V,W)$</jats:tex-math></jats:alternatives></jats:inline-formula>is a pair of vertically strict tableaux, that is, column strict fillings of Young diagrams with no condition on rows, with the shape prescribed by the Greene invariant,<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S2050508623000239_inline6.png" /><jats:tex-math>$\kappa $</jats:tex-math></jats:alternatives></jats:inline-formula>is an array of nonnegative weights and<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S2050508623000239_inline7.png" /><jats:tex-math>$\nu $</jats:tex-math></jats:alternatives></jats:inline-formula>is a partition. An application of this construction is the first bijective proof of Cauchy and Littlewood identities involving<jats:italic>q</jats:italic>-Whittaker polynomials. New identities relating sums of<jats:italic>q</jats:italic>-Whittaker and Schur polynomials are also presented.</jats:p>

DOI： 10.1017/fmp.2023.23

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1007/s00220-022-04408-8

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1103/physrevlett.129.040601

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1103/physreva.105.022219

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1007/s00220-021-03954-x

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1007/s00440-020-00966-x

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掲載種別：研究論文（学術雑誌）  

DOI： 10.1088/1742-5468/ab1dd6

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1007/s00440-018-0868-3

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1103/physrevlett.120.240601

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.7566/jpsj.87.054006

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掲載種別：研究論文（学術雑誌）  

DOI： 10.1088/1751-8121/aa6e17

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1103/physrevlett.118.160601

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

<jats:title>Abstract</jats:title><jats:p>We study a new process, which we call ASEP(<jats:italic>q</jats:italic>, <jats:italic>j</jats:italic>), where particles move asymmetrically on a one-dimensional integer lattice with a bias determined by <jats:inline-formula><jats:alternatives><jats:tex-math>$$q\in (0,1)$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mi>q</mml:mi>
<mml:mo>∈</mml:mo>
<mml:mo>(</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:math></jats:alternatives></jats:inline-formula> and where at most <jats:inline-formula><jats:alternatives><jats:tex-math>$$2j\in \mathbb {N}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi>j</mml:mi>
<mml:mo>∈</mml:mo>
<mml:mi>N</mml:mi>
</mml:mrow>
</mml:math></jats:alternatives></jats:inline-formula> particles per site are allowed. The process is constructed from a <jats:inline-formula><jats:alternatives><jats:tex-math>$$(2j+1)$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:mn>2</mml:mn>
<mml:mi>j</mml:mi>
<mml:mo>+</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:math></jats:alternatives></jats:inline-formula>-dimensional representation of a quantum Hamiltonian with <jats:inline-formula><jats:alternatives><jats:tex-math>$$U_q(\mathfrak {sl}_2)$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:msub>
<mml:mi>U</mml:mi>
<mml:mi>q</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mo>(</mml:mo>
<mml:msub>
<mml:mi>sl</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo>)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math></jats:alternatives></jats:inline-formula> invariance by applying a suitable ground-state transformation. After showing basic properties of the process ASEP(<jats:italic>q</jats:italic>, <jats:italic>j</jats:italic>), we prove self-duality with several self-duality functions constructed from the symmetries of the quantum Hamiltonian. By making use of the self-duality property we compute the first <jats:italic>q</jats:italic>-exponential moment of the current for step initial conditions (both a shock or a rarefaction fan) as well as when the process is started from a homogeneous product measure.</jats:p>

DOI： 10.1007/s00440-015-0674-0

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1007/s10955-016-1492-1

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1007/s10955-016-1473-4

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

<jats:title>Abstract</jats:title>
<jats:p>The Kardar–Parisi–Zhang (KPZ) equation, which was introduced in 1986 as a model equation to describe the dynamics of an interface motion, has been attracting renewed interest in recent years. In particular, the height distribution of its 1D version was determined exactly for a few special initial conditions. Its relevance in experiments was demonstrated and our understanding of the mathematical structures behind its tractability has deepened considerably. There are also new developments in the applicability of the KPZ universality in wider contexts. This paper is a short introductory review on the basics of the equation and on a few recent topics.</jats:p>

DOI： 10.1093/ptep/ptw002

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1007/s00220-015-2424-7

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掲載種別：研究論文（学術雑誌）  

DOI： 10.1214/ejp.v20-3926

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掲載種別：研究論文（学術雑誌）  

DOI： 10.1214/13-aop868

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.4310/joc.2014.v5.n4.a1

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1007/s10955-013-0842-5

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1007/s10955-013-0710-3

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1103/physrevlett.108.190603

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掲載種別：研究論文（学術雑誌）  

DOI： 10.1088/1751-8113/44/38/385001

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1038/srep00034

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1007/s10955-011-0149-3

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記述言語：英語   掲載種別：研究論文（学術雑誌）  

DOI： 10.1103/physrevlett.104.230602

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掲載種別：研究論文（学術雑誌）  

DOI： 10.1088/0305-4470/38/33/l01

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掲載種別：研究論文（学術雑誌）  

DOI： 10.1088/0305-4470/37/18/006

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掲載種別：研究論文（学術雑誌）  

DOI： 10.1088/0305-4470/32/41/306

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