arXiv subjects

Nikita Kolganov

Publications and source records attributed to Nikita Kolganov.

9 recordsLinked to original sources

arXiv2026

One-loop QED effective action at finite temperature and density beyond HTL limit

We develop a framework for computing the nonlocal one-loop effective action in scalar and spinor QED at finite temperature and chemical potential in arbitrary even spacetime dimensions. Based on the heat kernel expansion to quadratic order in background fields, the framework reduces the effective action form factors to a common fundamental kernel. By resumming the external-momentum expansion, we obtain explicit closed-form expressions for the massless form factors in terms of polylogarithms and their derivatives with respect to the order. The same method determines the coefficients of the small-mass expansion to arbitrary order. The resulting expressions retain the full dependence on external Euclidean momentum, temperature, and chemical potential, without invoking the soft-momentum approximation. We also derive the corresponding photon polarization operators and evaluate their static limits, obtaining the Debye screening masses and electromagnetic susceptibilities.

hep-th↗

arXiv2026

Non-vacuum gravitational effective action

Curvature expansion for the heat kernel trace and the one-loop effective action is built for the wave operator of the theory in the quasi-thermal setup of a nonvacuum quantum state. This setup implies a non-static and non-stationary Euclidean gravitational background with periodic boundary conditions of the period $β=1/T$, where $T$ plays the role of effective global temperature to be locally rescaled by the metric gravitational potential. The results are obtained in the approximation quadratic in metric perturbations on top of flat Euclidean space and covariantized in terms of spacetime curvature. Covariantization includes a special vector field $ξ^μ(x)$ which generalizes the Killing vector of static geometries with time translation isometry to the case of a generic arbitrarily inhomogeneous metric subject to timelike periodicity condition. This vector field is obtained as a covariant metric functional to quadratic order in metric perturbations and gives rise to the local function $T/\sqrt{ξ^2(x)}$, $ξ^2(x)=g_{μν}(x)ξ^μ(x)ξ^ν(x)$, reducing to Tolman temperature $T/\sqrt{g_{00}(\boldsymbol{x})}$ on stationary manifolds with Killing symmetry. High ``temperature'' asymptotic behavior of the nonlocal form factors---operator coefficients of the curvature tensor structures in the heat kernel and effective action---are obtained and possible cosmological applications of these results are discussed.

hep-th↗

arXiv2025

Streamlined Krylov construction and classification of ergodic Floquet systems

We generalize Krylov construction to periodically driven (Floquet) quantum systems using the theory of orthogonal polynomials on the unit circle. Compared to other approaches, our method works faster and maps any quantum dynamics to a one-dimensional tight-binding Krylov chain, which is efficiently simulated on both classical and quantum computers. We also suggest a classification of chaotic and integrable Floquet systems based on the asymptotic behavior of Krylov chain hopping parameters (Verblunsky coefficients). We illustrate this classification with random matrix ensembles, kicked top, and kicked Ising chain.

quant-ph↗

arXiv2024

Unperturbation theory: reconstructing Lagrangians from instanton fluctuations

Instantons present a deep insight into non-perturbative effects both in physics and mathematics. While leading instanton effects can be calculated simply as an exponent of the instanton action, the calculation of subleading contributions usually requires the spectrum of fluctuation operator on the instanton background and its Green's function, explicit knowledge of which is rare and a great success. Thus, we propose an inverse problem, namely, the reconstruction of the nonlinear action of the theory admitting instantons from the given fluctuation operator with a known Green's function. We constructively build the solution for this problem and apply it to a wide class of exactly solvable Schrödinger operators, called shape-invariant operators, and its simpler subclass, namely reflectionless Pöschl-Teller operators. In the latter case, we found that for the most values of parameters the reconstructed potentials are naturally defined not on the real line, but on some special multisheet covering of the complex plane, and discuss its physical interpretation. For the wider but less simple class of shape-invariant operators, we derive the set of parameters leading to the new infinite families of analytic potentials.

hep-th↗

arXiv2023

Nonequilibrium Schwinger-Keldysh formalism for density matrix states: analytic properties and implications in cosmology

Motivated by cosmological Hartle-Hawking and microcanonical density matrix prescriptions for the quantum state of the Universe we develop Schwinger-Keldysh in-in formalism for generic nonequilibrium dynamical systems with the initial density matrix. We build the generating functional of in-in Green's functions and expectation values for a generic density matrix of the Gaussian type and show that the requirement of particle interpretation selects a distinguished set of positive/negative frequency basis functions of the wave operator of the theory, which is determined by the density matrix parameters. Then we consider a special case of the density matrix determined by the Euclidean path integral of the theory, which in the cosmological context can be considered as a generalization of the no-boundary pure state to the case of the microcanonical ensemble, and show that in view of a special reflection symmetry its Wightman Green's functions satisfy Kubo-Martin-Schwinger periodicity conditions which hold despite the nonequilibrium nature of the physical setup. Rich analyticity structure in the complex plane of the time variable reveals the combined Euclidean-Lorentzian evolution of the theory, which depending on the properties of the initial density matrix can be interpreted as a decay of a classically forbidden quantum state.

hep-th↗

arXiv2022

Real-time diagram technique for instantonic systems

The Schwinger-Keldysh diagram technique is usually involved in the calculation of real-time in-in correlation functions. In the case of a thermal state, one can analytically continue imaginary-time Matsubara correlation functions to real times. Nevertheless, not all real-time correlation functions usually can be obtained by such procedure. Moreover, numerical analytic continuation is an ill-posed problem. Thus, even in the case of a thermal state one may need for the Schwinger-Keldysh formalism. If the potential of a system admits degenerate minima, instantonic effects enter the game, so one should also integrate over the instantonic moduli space, including the one, corresponding to the imaginary time translational invariance. However, the Schwinger-Keldysh closed time contour explicitly breaks such invariance. We argue, that this invariance must be recovered, and show, how it can be done. After that, we construct an extension of the Schwinger-Keldysh diagram technique to instantonic systems and demonstrate it on the example of the first few-point correlation functions.

hep-th↗

arXiv2022

Classical and quantum butterfly effect in nonlinear vector mechanics

We establish the correspondence between the classical and quantum butterfly effects in nonlinear vector mechanics with the broken $O(N)$ symmetry. On one hand, we analytically calculate the out-of-time ordered correlation functions and the quantum Lyapunov exponent using the augmented Schwinger-Keldysh technique in the large-$N$ limit. On the other hand, we numerically estimate the classical Lyapunov exponent in the high-temperature limit, where the classical chaotic behavior emerges. In both cases, Lyapunov exponents approximately coincide and scale as $κ\approx 1.3 \sqrt[4]{λT}/N$ with temperature $T$, number of degrees of freedom $N$, and coupling constant $λ$.

hep-th↗

arXiv2022

Large $k$ topological quantum computer

Chern-Simons topological quantum computer is a device that can be effectively described by the Chern-Simons topological quantum field theory and used for quantum computations. Quantum qudit gates of this quantum computer are represented by sequences of quantum $\mathcal{R}$-matrices. Its dimension and explicit form depend on the parameters of the Chern-Simons theory -- level $k$, gauge group $SU(N)$, and representation, which is chosen to be symmetric representation $[r]$. In this paper, we examine the universality of such a quantum computer. We prove that for sufficiently large $k$ it is universal, and the minimum allowed value of $k$ depends on the remaining parameters $r$ and $N$.

hep-th↗

arXiv2020

Quantum $\mathcal{R}$-matrices as universal qubit gates

We study the Chern-Simons approach to the topological quantum computing. We use quantum $\mathcal{R}$-matrices as universal quantum gates and study the approximations of some one-qubit operations. We make some modifications to the known Solovay-Kitaev algorithm suitable for our particular problem.

hep-th↗