Oleg Evnin
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A Set of Master Variables for the Two-Star Random Graph Open
The two-star random graph is the simplest exponential random graph model with nontrivial interactions between the graph edges. We propose a set of auxiliary variables that control the thermodynamic limit where the number of vertices N tend…
Ensemble inequivalence and phase transitions in unlabeled networks Open
We discover a first-order phase transition in the canonical ensemble of random unlabeled networks with a prescribed average number of links. The transition is caused by the nonconcavity of microcanonical entropy. Above the critical point c…
Statistical field theory of random graphs with prescribed degrees Open
Statistical field theory methods have been very successful with a number of random graph and random matrix problems, but it is challenging to apply these methods to graphs with prescribed degree sequences due to the extensive number of con…
Hammerstein equations for sparse random matrices Open
Finding eigenvalue distributions for a number of sparse random matrix ensembles can be reduced to solving nonlinear integral equations of the Hammerstein type. While a systematic mathematical theory of such equations exists, it has not bee…
Multiseed Krylov complexity Open
Krylov complexity is an attractive measure for the rate at which quantum operators spread in the space of all possible operators under dynamical evolution. One expects that its late-time plateau would distinguish between integrable and cha…
First return times on sparse random graphs Open
We consider random walks in the form of nearest-neighbor hopping on Erdos-Renyi random graphs of finite fixed mean degree c as the number of vertices N tends to infinity. In this regime, using statistical field theory methods, we develop a…
MATLAB code for 'Phase-space localization at the lowest Landau level' Open
We provide the MATLAB code and data to reproduce the numerical results presented in the paper "Phase-space localization at the lowest Landau level".
A Gaussian integral that counts regular graphs Open
In a recent article J. Phys. Compl. 4 (2023) 035005, Kawamoto evoked statistical physics methods for the problem of counting graphs with a prescribed degree sequence. This treatment involved truncating a particular Taylor expansion at the …
Democratic Lagrangians from topological bulk Open
Chiral form fields in d dimensions can be effectively described as edge modes of topological Chern-Simons theories in d+1 dimensions. At the same time, manifestly Lorentz-invariant Lagrangian description of such fields directly in terms of…
Integrability and complexity in quantum spin chains Open
There is a widespread perception that dynamical evolution of integrable systems should be simpler in a quantifiable sense than the evolution of generic systems, though demonstrating this relation between integrability and reduced complexit…
Nonlinear instability and solitons in a self-gravitating fluid Open
We study a spherical, self-gravitating fluid model, which finds applications in cosmic structure formation. We argue that since the system features nonlinearity and gravity-induced dispersion, the emergence of solitons becomes possible. We…
A relation between Krylov and Nielsen complexity Open
Krylov complexity and Nielsen complexity are successful approaches to quantifying quantum evolution complexity that have been actively pursued without much contact between the two lines of research. The two quantities are motivated by quan…
Report on scipost_202307_00036v1 Open
There is a widespread perception that dynamical evolution of integrable systems should be simpler in a quantifiable sense than the evolution of generic systems, though demonstrating this relation between integrability and reduced complexit…
Report on scipost_202307_00036v1 Open
There is a widespread perception that dynamical evolution of integrable systems should be simpler in a quantifiable sense than the evolution of generic systems, though demonstrating this relation between integrability and reduced complexit…
Democracy from topology Open
Chiral form fields in $d$ dimensions can be effectively described as edge modes of topological Chern-Simons theories in $d+1$ dimensions. At the same time, manifestly Lorentz-invariant Lagrangian description of such fields directly in term…
Obstruction to ergodicity in nonlinear Schrödinger equations with resonant potentials Open
We identify a class of trapping potentials in cubic nonlinear Schrödinger equations (NLSEs) that make them nonintegrable, but prevent the emergence of power spectra associated with ergodicity. The potentials are characterized by equidistan…
Random matrices with row constraints and eigenvalue distributions of graph Laplacians Open
Symmetric matrices with zero row sums occur in many theoretical settings and in real-life applications. When the offdiagonal elements of such matrices are i.i.d. random variables and the matrices are large, the eigenvalue distributions con…
Three approaches to chiral form interactions Open
We briefly review and critically compare three approaches to constructing Lagrangian theories of self-interacting Abelian chiral form fields with manifest Lorentz invariance. The first approach relies on the original ideas of Pasti, Soroki…
Code for `Integrability and complexity in quantum spin chains' Open
We provide the code and data to reproduce the numerical results presented in the paper https://arxiv.org/abs/2305.00037.
Obstruction to ergodicity in nonlinear Schrödinger equations with resonant potentials Open
We identify a class of trapping potentials in cubic nonlinear Schrödinger equations (NLSEs) that make them non-integrable, but prevent the emergence of power spectra associated with ergodicity. The potentials are characterized by equidista…
de Sitter Bubbles from Anti–de Sitter Fluctuations Open
Cosmological acceleration is difficult to accommodate in theories of fundamental interactions involving supergravity and superstrings. An alternative is that the acceleration is not universal but happens in a large localized region, which …
Random matrices with row constraints and eigenvalue distributions of graph Laplacians Open
Symmetric matrices with zero row sums occur in many theoretical settings and in real-life applications. When the offdiagonal elements of such matrices are i.i.d. random variables and the matrices are large, the eigenvalue distributions con…
Bounds on quantum evolution complexity via lattice cryptography Open
We address the difference between integrable and chaotic motion in quantum theory as manifested by the complexity of the corresponding evolution operators. Complexity is understood here as the shortest geodesic distance between the time-de…
De Sitter bubbles from anti-de Sitter fluctuations Open
Cosmological acceleration is difficult to accommodate in theories of fundamental interactions involving supergravity and superstrings. An alternative is that the acceleration is not universal but happens in a large localized region, which …
Three approaches to chiral form interactions Open
We briefly review and critically compare three approaches to constructing Lagrangian theories of self-interacting Abelian chiral form fields with manifest Lorentz invariance. The first approach relies on the original ideas of Pasti, Soroki…
Report on scipost_202204_00030v1 Open
We address the difference between integrable and chaotic motion in quantum theory as manifested by the complexity of the corresponding evolution operators.Complexity is understood here as the shortest geodesic distance between the time-dep…
Turbulent cascades in a truncation of the cubicSzegő equation and related systems Open
The cubic Szego equation has been studied as an integrable model for deterministic turbulence, starting with the foundational work of Gerard and Grellier. We introduce a truncated version of this equation, wherein a majority of the Fourier…
MATLAB code for 'Bounds on quantum evolution complexity via lattice cryptography' Open
We provide the MATLAB code and data to reproduce the numerical results presented in the paper https://arxiv.org/abs/2202.13924.
Resistance distance distribution in large sparse random graphs Open
We consider an Erdős–Rényi random graph consisting of N vertices connected by randomly and independently drawing an edge between every pair of them with probability c / N so that at N → ∞ one obtains a graph of finite mean degree c . In th…