Sergey M. Sergeev

Sergey M. Sergeev
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Mathematical Physics (17)
 
Mathematics - Mathematical Physics (17)
 
High Energy Physics - Theory (13)
 
Physics - Statistical Mechanics (9)
 
Nonlinear Sciences - Exactly Solvable and Integrable Systems (8)
 
Mathematics - Quantum Algebra (5)
 
Astrophysics (4)
 
High Energy Astrophysical Phenomena (2)
 
Mathematics - Differential Geometry (1)
 
Cosmology and Nongalactic Astrophysics (1)
 
Mathematics - Spectral Theory (1)
 
Solar and Stellar Astrophysics (1)

Publications Authored By Sergey M. Sergeev

Motivated by applications for non-perturbative topological strings in toric Calabi--Yau manifolds, we discuss the spectral problem for a pair of commuting modular conjugate (in the sense of Faddeev) Harper type operators, corresponding to a special case of the quantized mirror curve of local $\mathbb{P}^1\times\mathbb{P}^1$ and complex values of Planck's constant. We illustrate our analytical results by numerical calculations. Read More

In this paper we give an overview of exactly solved edge-interaction models, where the spins are placed on sites of a planar lattice and interact through edges connecting the sites. We only consider the case of a single spin degree of freedom at each site of the lattice. The Yang-Baxter equation for such models takes a particular simple form called the star-triangle relation. Read More

The occurrence of low-amplitude flux variations in blazars on hourly timescales, commonly known as microvariability, is still a widely debated subject in high-energy astrophysics. Several competing scenarios have been proposed to explain such occurrences, including various jet plasma instabilities leading to the formation of shocks, magnetic reconnection sites, and turbulence. In this letter we present the results of our detailed investigation of a prominent, five-hour-long optical microflare detected during recent WEBT campaign in 2014, March 2-6 targeting the blazar 0716+714. Read More

We construct $2^n$-families of solutions of the Yang-Baxter equation from $n$-products of three-dimensional $R$ and $L$ operators satisfying the tetrahedron equation. They are identified with the quantum $R$ matrices for the Hopf algebras known as generalized quantum groups. Depending on the number of $R$'s and $L$'s involved in the product, the trace construction interpolates the symmetric tensor representations of $U_q(A^{(1)}_{n-1})$ and the anti-symmetric tensor representations of $U_{-q^{-1}}(A^{(1)}_{n-1})$, whereas a boundary vector construction interpolates the $q$-oscillator representation of $U_q(D^{(2)}_{n+1})$ and the spin representation of $U_{-q^{-1}}(D^{(2)}_{n+1})$. Read More

For every quantized Lie algebra there exists a map from the tensor square of the algebra to itself, which by construction satisfies the set-theoretic Yang-Baxter equation. This map allows one to define an integrable discrete quantum evolution system on quadrilateral lattices, where local degrees of freedom (dynamical variables) take values in a tensor power of the quantized Lie algebra. The corresponding equations of motion admit the zero curvature representation. Read More

We introduce a homomorphism from the quantum affine algebras $U_q(D^{(2)}_{n+1}), U_q(A^{(2)}_{2n}), U_q(C^{(1)}_{n})$ to the $n$-fold tensor product of the $q$-oscillator algebra ${\mathcal A}_q$. Their action commute with the solutions of the Yang-Baxter equation obtained by reducing the solutions of the tetrahedron equation associated with the modular and the Fock representations of ${\mathcal A}_q$. In the former case, the commutativity is enhanced to the modular double of these quantum affine algebras. Read More

In this paper we construct a three-dimensional (3D) solvable lattice model with non-negative Boltzmann weights. The spin variables in the model are assigned to edges of the 3D cubic lattice and run over an infinite number of discrete states. The Boltzmann weights satisfy the tetrahedron equation, which is a 3D generalisation of the Yang-Baxter equation. Read More

We prove a recently conjectured star-star relation, which plays the role of an integrability condition for a class of 2D Ising-type models with multicomponent continuous spin variables. Namely, we reduce this relation to an identity for elliptic gamma functions, previously obtained by Rains. Read More

The Zamolodchikov model describes an exact relativistic factorized scattering theory of straight strings in (2+1)-dimensional space-time. It also defines an integrable 3D lattice model of statistical mechanics and quantum field theory. The three-string S-matrix satisfies the tetrahedron equation which is a 3D analog of the Yang-Baxter equation. Read More

We present new photometric observations of Supernova (SN) 2003ie starting one month before discovery, obtained serendipitously while observing its host galaxy. With only a weak upper limit derived on the mass of its progenitor (<25 M_sun) from pre-explosion studies, this event could be a potential exception to the "red supergiant (RSG) problem" (the lack of high mass RSGs exploding as Type IIP supernovae). However, this is true only if SN2003ie was a Type IP event, something which has never been determined. Read More

It is known that a solution of the tetrahedron equation generates infinitely many solutions of the Yang-Baxter equation via suitable reductions. In this paper this scheme is applied to an oscillator solution of the tetrahedron equation involving bosons and fermions by using special 3d boundary conditions. The resulting solutions of the Yang-Baxter equation are identified with the quantum R matrices for the spin representations of B^{(1)}_n, D^{(1)}_n and D^{(2)}_{n+1}. Read More

We define a map S: D^2 x D^2 --> D^2 x D^2, where D is an arbitrary division ring (skew field), associated with the Veblen configuration, and we show that such a map provides solutions to the functional dynamical pentagon equation. We explain that fact in elementary geometric terms using the symmetry of the Veblen and Desargues configurations. We introduce also another map of a geometric origin with the pentagon property. Read More

We present a generalization of the master solution to the quantum Yang-Baxter equation (obtained recently in arXiv:1006.0651) to the case of multi-component continuous spin variables taking values on a circle. The Boltzmann weights are expressed in terms of the elliptic gamma-function. Read More

We obtain a new solution of the star-triangle relation with positive Boltzmann weights which contains as special cases all continuous and discrete spin solutions of this relation, that were previously known. This new master solution defines an exactly solvable 2D lattice model of statistical mechanics, which involves continuous spin variables, living on a circle, and contains two temperature-like parameters. If one of the these parameters approaches a root of unity (corresponds to zero temperature), the spin variables freezes into discrete positions, equidistantly spaced on the circle. Read More

We study geometric consistency relations between angles of 3-dimensional (3D) circular quadrilateral lattices -- lattices whose faces are planar quadrilaterals inscribable into a circle. We show that these relations generate canonical transformations of a remarkable "ultra-local" Poisson bracket algebra defined on discrete 2D surfaces consisting of circular quadrilaterals. Quantization of this structure allowed us to obtain new solutions of the tetrahedron equation (the 3D analog of the Yang-Baxter equation) as well as reproduce all those that were previously known. Read More

We study "circular net" (discrete orthogonal net) equations for angular data generalized by external spectral parameters. A criterion defining physical regimes of these Hamiltonian equations is the reality of Lagrangian density. There are four distinct regimes for fields and spectral parameters classified by four types of spherical or hyperbolic triangles. Read More

In this paper we consider three-dimensional quantum q-oscillator field theory without spectral parameters. We construct an essentially big set of eigenstates of evolution with unity eigenvalue of discrete time evolution operator. All these eigenstates belong to a subspace of total Hilbert space where an action of evolution operator can be identified with quantized discrete BKP equations (synonym Miwa equations). Read More

Discrete Darboux-Manakov-Zakharov systems possess two distinct Hamiltonian forms. In the framework of discrete-differential geometry one Hamiltonian form appears in a geometry of circular net. In this paper a geometry of second form is identified. Read More

We study geometric consistency relations between angles on 3-dimensional (3D) circular quadrilateral lattices -- lattices whose faces are planar quadrilaterals inscribable into a circle. We show that these relations generate canonical transformations of a remarkable ``ultra-local'' Poisson bracket algebra defined on discrete 2D surfaces consisting of circular quadrilaterals. Quantization of this structure leads to new solutions of the tetrahedron equation (the 3D analog of the Yang-Baxter equation). Read More

We present a stellar dynamical estimate of the black hole (BH) mass in the Seyfert 1 galaxy, NGC 4151. We analyze ground-based spectroscopy as well as imaging data from the ground and space, and we construct 3-integral axisymmetric models in order to constrain the BH mass and mass-to-light ratio. The dynamical models depend on the assumed inclination of the kinematic symmetry axis of the stellar bulge. Read More

The Faddeev-Volkov model is an Ising-type lattice model with positive Boltzmann weights where the spin variables take continuous values on the real line. It serves as a lattice analog of the sinh-Gordon and Liouville models and intimately connected with the modular double of the quantum group U_q(sl_2). The free energy of the model is exactly calculated in the thermodynamic limit. Read More

The Faddeev-Volkov solution of the star-triangle relation is connected with the modular double of the quantum group U_q(sl_2). It defines an Ising-type lattice model with positive Boltzmann weights where the spin variables take continuous values on the real line. The free energy of the model is exactly calculated in the thermodynamic limit. Read More

We describe results from a new ground-based monitoring campaign on NGC 5548, the best studied reverberation-mapped AGN. We find that it was in the lowest luminosity state yet recorded during a monitoring program, namely L(5100) = 4.7 x 10^42 ergs s^-1. Read More

We present new observations leading to an improved black hole mass estimate for the Seyfert 1 galaxy NGC 4593 as part of a reverberation-mapping campaign conducted at the MDM Observatory. Cross-correlation analysis of the H_beta emission-line light curve with the optical continuum light curve reveals an emission-line time delay of 3.73 (+-0. Read More

We have undertaken a new ground-based monitoring campaign to improve the estimates of the mass of the central black hole in NGC 4151. We measure the lag time of the broad H beta line response compared to the optical continuum at 5100 A and find a lag of 6.6 (+1. Read More

We investigate the exact solution of the q-deformed one-dimensional Bose gas to derive all integrals of motion and their corresponding eigenvalues. As an application, the thermodynamics is given and compared to an effective field theory at low temperatures. Read More

The tetrahedron equation is a three-dimensional generalization of the Yang-Baxter equation. Its solutions define integrable three-dimensional lattice models of statistical mechanics and quantum field theory. Their integrability is not related to the size of the lattice, therefore the same solution of the tetrahedron equation defines different integrable models for different finite periodic cubic lattices. Read More