In this paper we discuss a family of models of particle and energy diffusion on a one-dimensional lattice, related to those studied previously in Sasamoto and Wadati (Phys Rev E 58:4181–4190, 1998), Barraquand and Corwin (Probab Theory Relat Fields 167(3–4):1057–1116, 2017) and Povolotsky (J Phys A 46(46):465205, 2013) in the context of KPZ universality class. We show that they may be mapped onto an integrable (2) Heisenberg spin chain whose Hamiltonian density in the bulk has been already studied in the AdS/CFT and the integrable system literature. Using the quantum inverse scattering method, we study various new aspects, in particular we identify boundary terms, modeling reservoirs in non-equilibrium statistical mechanics models, for which the spin chain (and thus also the stochastic process) continues to be integrable. We also show how the construction of a “dual model” of probability theory is possible and useful. The fluctuating hydrodynamics of our stochastic model corresponds to the semiclassical evolution of a string that derives from correlation functions of local gauge invariant operators of =4 super Yang–Mills theory (SYM), in imaginary-time. As any stochastic system, it has a supersymmetric completion that encodes for the thermal equilibrium theorems: we show that in this case it is equivalent to the (2|1) superstring that has been derived directly from =4 SYM.

Non-compact quantum spin chains as integrable stochastic particle processes / Frassek, R.; Giardinà, C; Kurchan, J. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - 180:1-6(2020), pp. 135-171. [10.1007/s10955-019-02375-4]

Non-compact quantum spin chains as integrable stochastic particle processes

Frassek, R.;Giardinà, C;Kurchan, J
2020

Abstract

In this paper we discuss a family of models of particle and energy diffusion on a one-dimensional lattice, related to those studied previously in Sasamoto and Wadati (Phys Rev E 58:4181–4190, 1998), Barraquand and Corwin (Probab Theory Relat Fields 167(3–4):1057–1116, 2017) and Povolotsky (J Phys A 46(46):465205, 2013) in the context of KPZ universality class. We show that they may be mapped onto an integrable (2) Heisenberg spin chain whose Hamiltonian density in the bulk has been already studied in the AdS/CFT and the integrable system literature. Using the quantum inverse scattering method, we study various new aspects, in particular we identify boundary terms, modeling reservoirs in non-equilibrium statistical mechanics models, for which the spin chain (and thus also the stochastic process) continues to be integrable. We also show how the construction of a “dual model” of probability theory is possible and useful. The fluctuating hydrodynamics of our stochastic model corresponds to the semiclassical evolution of a string that derives from correlation functions of local gauge invariant operators of =4 super Yang–Mills theory (SYM), in imaginary-time. As any stochastic system, it has a supersymmetric completion that encodes for the thermal equilibrium theorems: we show that in this case it is equivalent to the (2|1) superstring that has been derived directly from =4 SYM.
2020
29-ago-2019
180
1-6
135
171
Non-compact quantum spin chains as integrable stochastic particle processes / Frassek, R.; Giardinà, C; Kurchan, J. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - 180:1-6(2020), pp. 135-171. [10.1007/s10955-019-02375-4]
Frassek, R.; Giardinà, C; Kurchan, J
File in questo prodotto:
File Dimensione Formato  
1904.01048(1).pdf

Open access

Tipologia: Versione originale dell'autore proposta per la pubblicazione
Dimensione 777.14 kB
Formato Adobe PDF
777.14 kB Adobe PDF Visualizza/Apri
VOR_Non-compactQuantumSpinChainsAs.pdf

Accesso riservato

Tipologia: Versione pubblicata dall'editore
Dimensione 622.3 kB
Formato Adobe PDF
622.3 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Pubblicazioni consigliate

Licenza Creative Commons
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1188587
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 17
  • ???jsp.display-item.citation.isi??? 16
social impact