Mykola Semenyakin
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View article: Classifying fermionic states via many-body correlation measures
Classifying fermionic states via many-body correlation measures Open
Understanding the structure of quantum correlations in a many-body system is key to its computational treatment. For fermionic systems, correlations can be defined as deviations from Slater determinant states. The link between fermionic co…
View article: Cluster Reductions, Mutations, and $q$-Painlevé Equations
Cluster Reductions, Mutations, and $q$-Painlevé Equations Open
We propose an extension of the Goncharov-Kenyon class of cluster integrable systems by their Hamiltonian reductions. This extension allows us to fill in the gap in cluster construction of the $q$-difference Painlevé equations, showing that…
View article: Classifying fermionic states via many-body correlation measures
Classifying fermionic states via many-body correlation measures Open
Understanding the structure of quantum correlations in a many-body system is key to its computational treatment. For fermionic systems, correlations can be defined as deviations from Slater determinant states. The link between fermionic co…
View article: Topological string amplitudes and Seiberg-Witten prepotentials from the counting of dimers in transverse flux
Topological string amplitudes and Seiberg-Witten prepotentials from the counting of dimers in transverse flux Open
View article: Topological string amplitudes and Seiberg-Witten prepotentials from the counting of dimers in transverse flux
Topological string amplitudes and Seiberg-Witten prepotentials from the counting of dimers in transverse flux Open
Important illustration to the principle ``partition functions in string theory are $τ$-functions of integrable equations'' is the fact that the (dual) partition functions of $4d$ $\mathcal{N}=2$ gauge theories solve Painlevé equations. In …
View article: A brief introduction to quantum groups
A brief introduction to quantum groups Open
These are lecture notes of a mini-course given by the first author in Moscow in July 2019, taken by the second author and then edited and expanded by the first author. They were also a basis of the lectures given by the first author at the…
View article: Cluster integrable systems and spin chains
Cluster integrable systems and spin chains Open
A bstract We discuss relation between the cluster integrable systems and spin chains in the context of their correspondence with 5d supersymmetric gauge theories. It is shown that $$ {\mathfrak{gl}}_N $$ XXZ-type spin chain on M sites …
View article: Alternating currents and shear waves in viscous electronics
Alternating currents and shear waves in viscous electronics Open
Strong interaction among charge carriers can make them move like viscous\nfluid. Here we explore alternating current (AC) effects in viscous electronics.\nIn the Ohmic case, incompressible current distribution in a sample adjusts fast\nto …
View article: Comment on 'Linking Spatial Distributions of Potential and Current in Viscous Electronics'
Comment on 'Linking Spatial Distributions of Potential and Current in Viscous Electronics' Open
In recent paper of Falkovich and Levitov it was shown, that geometry of separatrixes for viscous electronic flow in graphene is sensitive to boundary conditions. Here we discover theis relation in details. Also we propose, how boundary con…