Diffusion and Superdiffusion from Hydrodynamic Projections

Hydrodynamic projections, the projection onto conserved charges representing ballistic propagation of fluid waves, give exact transport results in many-body systems, such as the exact Drude weights. Focussing one one-dimensional systems, I show that this principle can be extended beyond the Euler scale, in particular to the diffusive and superdiffusive scales. By hydrodynamic reduction, Hilbert spaces of observables are constructed that generalise the standard space of conserved densities and describe the finer scales of hydrodynamics. The Green–Kubo formula for the Onsager matrix has a natural expression within the diffusive space. This space is associated with quadratically extensive charges, and projections onto any such charge give generic lower bounds for diffusion. In particular, bilinear expressions in linearly extensive charges lead to explicit diffusion lower bounds calculable from the thermodynamics, and applicable for instance to generic momentum-conserving one-dimensional systems. Bilinear charges are interpreted as covariant derivatives on the manifold of maximal entropy states, and represent the contribution to diffusion from scattering of ballistic waves. An analysis of fractionally extensive charges, combined with clustering properties from the superdiffusion phenomenology, gives lower bounds for superdiffusion exponents. These bounds reproduce the predictions of nonlinear fluctuating hydrodynamics, including the Kardar–Parisi–Zhang exponent 2/3 for sound-like modes, the Levy-distribution exponent 3/5 for heat-like modes, and the full Fibonacci sequence.

Hole probability for non-interacting fermions in a d-dimensional trap

The hole probability, i.e., the probability that a region is void of particles, is a benchmark of correlations in many body systems. We compute analytically this probability P (R) for a sphere of radius R in the case of N noninteracting fermions in their ground state in a d-dimensional trapping potential. Using a connection to the Laguerre-Wishart ensembles of random matrices, we show that, for large N and in the bulk of the Fermi gas, P (R) is described by a universal scaling function of kF R, for which we obtain an exact formula (kF being the local Fermi wave-vector). It exhibits a super exponential tail P (R) / e-κd(kF R)d+1 where κdis a universal amplitude, in good agreement with existing numerical simulations. When R is of the order of the radius of the Fermi gas, the hole probability is described by a large deviation form which is not universal and which we compute exactly for the harmonic potential. Similar results also hold in momentum space.

Automatic differentiation applied to excitations with projected entangled pair states

The excitation ansatz for tensor networks is a powerful tool for simulating the low-lying quasiparticle excitations above ground states of strongly correlated quantum many-body systems. Recently, the two-dimensional tensor network class of infinite projected entangled-pair states gained new ground state optimization methods based on automatic differentiation, which are at the same time highly accurate and simple to implement. Naturally, the question arises whether these new ideas can also be used to optimize the excitation ansatz, which has recently been implemented in two dimensions as well. In this paper, we describe a straightforward way to reimplement the framework for excitations using automatic differentiation, and demonstrate its performance for the Hubbard model at half filling.

Correlation functions and transport coefficients in generalised hydrodynamics

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 exact methods to extract large scale behaviours. Finally, we overview various applications in integrable spin chains and field theories.

PANCREATIC PATHOMORPHOLOGY IN SUPERINVASIVE OPISTHORCHIASIS

Superinvasive opisthorchiasis involves many body systems in the pathological process. The parasite, due to its unique characteristics, changes numerous genes, and contributes to proliferative processes. Stem cells are initiated and subsequently differentiated along various cell lineages. The liver and pancreas are econiches, where parasites vegetate for a long time. However, there is no available information on the dynamics of proliferative pancreatic changes and various histogenetic pathways. The aim of the paper is to reveal the proliferative activity of pancreatic stem cells in superinvasive opisthorchiasis and their differentiation. Materials and Methods. Fragments of pancreatic tissue were selected and analyzed in departments of morbid anatomy of medical institutions located on the territory of the hyperendemic focus (Tyumen region, Omsk region, Khanty-Mansiysk Autonomous Okrug). The following groups were formed: Group 1 – patients with a history of superinvasive opisthorchiasis with a more than 10-year invasion (n=70); Group 2 – patients without invasion with all-cause mortality (n=10). The material was subjected to routine histological examination. The authors used histochemical and immunohistochemical staining methods and performed statistical analysis. Results. The authors observed marked proliferative reactions in the epithelial layer of the duct system, the secretory section of the pancreas, as well as changes in the endocrine apparatus. The histological types of pancreatic endocrine formations were revealed, namely, normal, hyperplastic and newly formed islets of Langerhans. The difference between the newly formed islets and the preexisting forms was in a disorderly arrangement, an indefinite shape, significantly larger sizes, and in the absence or presence of a forming capsule. The newly formed islets contained cells similar to preexisting endocrinocytes. Conclusion. Under the influence of the Opisthorchis felineus secretome, there occurs initiation and differentiation of pancreatic stem cells. Newly formed clusters of endocrine cells are formed, but they have the characteristics of the preexisting endocrine apparatus and secretory cells with exocrine properties. Key words: pancreas, opisthorchiasis, secretion, superinvasion, stem cells, differentiation. Суперинвазионный описторхоз – заболевание, при котором в патологический процесс вовлекаются многие системы организма. Паразит вследствие своих уникальных свойств изменяет многочисленные гены, дает начало пролиферативным процессам. Происходит инициация стволовых клеток с последующей дифференцировкой их по линиям различных дифферонов. Печень и поджелудочная железа являются эконишами, где длительное время вегетируют паразиты, однако сведений о динамике пролиферативных изменений в железе с рассмотрением различных гистогенетических путей в литературе не представлено. Цель работы. Выявить пролиферативную активность стволовых клеток поджелудочной железы при суперинвазионном описторхозе и их дифференцировку. Материалы и методы. Фрагменты ткани поджелудочной железы были отобраны для изучения в патологоанатомических отделениях медицинских учреждений, расположенных на территории гиперэндемического очага (Тюменская, Омская области, Ханты-Мансийский автономный округ). Сформированы следующие группы: 1 группа – лица, в анамнезе которых имелся суперинвазионный описторхоз с длительностью инвазии более 10 лет (n=70); 2 группа – лица без инвазии, умершие от случайных причин (n=10). Материал подвергался рутинному гистологическому исследованию, использовались гистохимические и иммуногистохимические методы окрашивания, проводился статистический анализ. Результаты. Обнаружены выраженные пролиферативные реакции в эпителиальном пласте протоковой системы, секреторном отделе поджелудочной железы и изменения структуры эндокринного аппарата. Выявлены гистологические типы эндокринных образований поджелудочной железы: островки Лангерганса обычного строения, гиперплазированные и новообразованные островки. Отличие последних от предсуществующих форм состояло в беспорядочном расположении, неопределенной форме, существенно более крупных размерах, отсутствии или наличии формирующейся капсулы. Новообразованные островки содержали аналогичные клетки, обладающие идентичными свойствами предсуществующих эндокриноцитов. Выводы. При воздействии секретома Opisthorchis felineus происходит инициация и дифференцировка стволовых клеток поджелудочной железы с формированием новообразованных скоплений эндокринных клеток со свойствами предсуществующего эндокринного аппарата и секреторных клеток с экзокринными свойствами. Ключевые слова: поджелудочная железа, описторхоз, секретом, суперинвазия, стволовые клетки, дифференцировка.