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E. T. Akhmedov

Publications and source records attributed to E. T. Akhmedov.

At least 19 recordsLinked to original sources
arXiv2026

Surprises of Klein paradox

We consider second quantized $1+1$ dimensional Dirac fermions with mass $m$ in background electric fields. This theory mimics the following situations. We consider two parallel capacitors with opposite directions of the electric field $E$ in them. The potential energy difference in one of them is equal to $V_0 > 2m$ and in the other to $V+V_0$, with $0 2m$. We also consider the same theory in the presence of the infinite wall and a deep well $V_0>2m$. We show that in such a potential the limiting expectation value of the current is zero in the Gaussian approximation. We discuss the relation of these observations to the Schwinger effet and to the decay of supercritical nuclei.

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arXiv2026

On radiation from hyperbolic motion, behavior of electromagnetic fields, and coordinate transformations at infinity

We show explicitly that radiation from a uniformly accelerating charge escapes outside Rindler wedge, while within Rindler wedge there is no flux through infinity, neither in the Minkowski frame nor in the Rindler frame. This remains true despite the fact that the coordinate transformation between the Rindler and Minkowski frames is not trivial at infinity.

physics.class-ph↗
arXiv2026

Sine-Gordon solitons in AdS, dS and other hyperbolic spaces

We find infinitely many soliton-like solutions in a deformation of the sine-Gordon theory in $(d+1)$-dimensional $AdS_{d+1}$ (anti-de Sitter) spacetime for $d \geq 2$, as well as single solitonic solutions in $dS_{d+1}$ (de Sitter) and $\mathrm{H}{d+1}$ (Lobachevsky) spaces for $d \geq 1$ and in $AdS_2$. We also find a deformation of the kink solution in scalar field theory with a polynomial potential in $AdS_2$. The deformation of the sine-Gordon theory strikingly resembles the bosonic part of the flat-space supersymmetric sine-Gordon theory. In the infinite radius limit, single soliton solutions reduce to solitons in flat space. Meanwhile, the multisoliton solution of $AdS{d+1}$, $d\geq 2$ for certain values of the parameters reduces in the same limit to a single soliton solution boosted in the normal direction. However, there are also multisoliton solutions in $AdS_{d+1}$, $d \geq 2$ that do not have a flat space limit.

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arXiv2025

Lessons from the Klein paradox

We re-examine the Klein paradox from a many-particle perspective in quantum field theory. Specifically, we compute the expectation value of the particle current induced by a sufficiently strong step-like electric potential in 1+1 dimensions. First, for a constant (eternal) potential, we calculate the current for different Fock space ground states corresponding to distinct mode bases. While one basis yields a zero current, another produces the standard nonzero value. We then consider a potential that is rapidly switched on, recovering the standard current in the asymptotic future. This result is generalized to potentials that interpolate between different constant values at spatial infinity. Finally, we analyze a potential acting for a finite duration and again reproduce the standard current. A physical interpretation of these results is provided.

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arXiv2025

Once more about radiation from uniformly accelerating charge

We consider an electric charge uniformly accelerating along $x$ direction and moving with constant velocity along $y$ direction. We show that in the co-accelerating along $x$ direction Rinder's frame this charge creates non-zero Poynting vector, which, however, does not lead to a non-vanishing flux through an infinitely distant surface. Furthermore, we show that in the laboratory Minkowski frame such a charge creates a stress energy flux that does not vanish at infinity. We interpret these observations as that while the Rindler's frame corresponds to the static zone around the charge, the Minkowski frame does contain the wave zone. We give detailed calculations and explanations concluding that uniformly accelerating charge does radiate

physics.class-ph↗
arXiv2024

On (dis)agreement between different methods of calculation of the imaginary part of the effective action in expanding space-times

We consider two approaches to calculate imaginary parts of effective actions in expanding space-times. While the first approach uses Bogolyubov coefficients, the second one uses the functional integral or the Feynman propagator. In eternally expanding space-times these two approaches give different answers for the imaginary parts. The origin of the difference can be traced to the presence if the wave-functionals for the initial and final states in the functional integral. We show this explicitly on the example of the expanding Poincare patch of the de Sitter space-time.

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arXiv2024

On two approaches to quantization in strong background fields

There are two ways to quantize free (gaussian) theory in strong background fields. In one of them, which we refer to as the Heisenberg approach, the mode functions are defined once and for entire space-time. In this approach there is no any apparent presence of an initial Cauchy surface. Another method, which we refer to as the Schrodinger approach, assumes the presence of the initial Cauchy surface on which one defines a spatial basis of modes and only then considers the evolution of the creation and annihilation operators in time with the use of the (free) Hamiltonian. The first method usually used to respect the symmetries of the problem (e.g. isometry of the de Sitter space-time), while in the second method the isometry is apparently broken by the presence of the initial Cauchy surface. In this paper we compare the two methods of quantization and find conditions under which they give the same result.

hep-th↗
arXiv2024

Light fields in various patches of de Sitter space-time

We start with the consideration of the loop effects for light fields with non-zero mass in the expanding Poincaré patch of de Sitter space-time. We derive the Dyson-Schwinger equation, which sums up the leading infrared (growing with time) loop corrections in certain limit for small initial perturbations above the Bunch-Davies state. The solution of this equation shows the destiny of the initial state at the future infinity. Then we discuss the case of the contracting Poincaré patch and global de Sitter space-time and briefly the case of different initial conditions in the expanding Poincaré patch.

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arXiv2024

Higher loop corrections to the current of created pairs in the lengthy electric pulse

The Schwinger's current appearing due to the breakdown of the vacuum in the strong constant electric pulse background is well known and calculated in many places. It appears due to the amplification of the zero-point fluctuations. However, we find that in higher loop corrections there are hidden redistributions of the level populations of charged particles and photons. These redistributions lead to the corrections to the current, which become large for the lengthy enough pulse and change the Schwinger's expression for the current.

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arXiv2024

Nontrivial self-consistent backreaction of quantum fields in 2D dilaton gravity

We consider $(1+1)$-dimensional dilatonic black hole with two horizons, canonical temperatures of which do not coincide. We show that the presence of quantum fields in such a background leads to a substantial backreaction on the metric: 2D dilatonic analog of the semiclassical Einstein equations are solved self-consistently, and we demonstrate that taking into account of backreaction leads to a geometry with two horizons with coinciding temperatures.

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arXiv2024

On the relevance of quantum corrections to the matter stress-energy tensor in eternally expanding universes

We study a toy-model of continuous infinite expansion of space-time with the flat start. We use as the gravitational background a conformaly flat metric with an exponentially growing factor in conformal time. We aim to clarify some properties of quantum fields in such a gravitational background. In particular, we calculate one-loop corrections to the Keldysh propagator to verify the fact of secular growth of the occupation number and anomalous quantum average in the massless scalar field theory with selfinteractions. We perform the calculation in arbitrary dimensions with the use of the Schwinger-Keldysh technique. We get a secular growth which is not of a kinetic type. We provide some results for the case of generic interaction $\fracλ{b!}ϕ^b$.

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arXiv2023

Isometry invariance of exact correlation functions in various charts of Minkowski and de Sitter spaces

We consider quantum field theory with selfinteractions in various patches of Minkowski and de Sitter space-times. Namely, in Minkowski space-time we consider separately right (left) Rindler wedge, past wedge and future wedge. In de Sitter space-time we consider expanding Poincare patch, static patch, contracting Poincare patch and global de Sitter itself. In all cases we restrict our considerations to the isometry invariant states leading to maximally analytic propagators. We prove that loop corrections in right (left) Rindler wedge, in the past wedge (of Minkowski space-time), in the static patch and in the expanding Poincare patch (of de Sitter space-time) respect the corresponding isometries of the corresponding symmetric space-times. All these facts are related to the causality and analyticity properties of the propagators for the states that we consider. At the same time in the future wedge, in the contracting Poincare patch and in global de Sitter space-time infrared effects violate the isometries.

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arXiv2023

Loop corrections to the current of created pairs in the lengthy electric pulse

We discuss loop-corrections to the electric current produced by strong and lengthy electric pulse. Namely we calculate one loop contribution to the electric current, distinguishing terms which depend on the pulse duration. We show that one loop correction does not lead to a strong modification of the tree-level current, which linearly grows with the pulse duration. Meanwhile, the correction to the photon propagator does contain the additional secular growth with the pulse duration. Based on the latter observation we argue that higher loop corrections will strongly modify the tree-level current, but that will demand a longer duration of the pulse than if the growth was at the first loop level.

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arXiv2023

On the backreaction issue for the black hole in de Sitter space-time

We consider quantum real massive scalar field in the de Sitter-Schwarzschild space-time backround. To have an analytic head way we study in detail the two-dimensional case, assuming that the situation in four dimensions will not be much different conceptually. It is assumed, that quantum field is in a thermal state i.e. described by the planckian distribution for the exact modes in the geometry under consideration. We calculate approximately the expectation value of stress-energy tensor near the cosmological and black hole horizons. It is shown that for a generic temperature backreaction from quantum fields on the geometry cannot be neglected. Thus, de Sitter-Schwarzschild space-time geometry inevitably is strongly modified by the quantum fluctuations of the matter fields.

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arXiv2022

Loop corrections to a cosmological particle creation

We consider dynamics of the massive minimally coupled scalar field theory in an expanding Friedmann-Lemaitre-Robertson-Walker universe. We consider the standard toy model of the conformally flat space-time where the conformal factor becomes constant at the distant past and the distant future. Employing Schwinger-Keldysh diagrammatic technique, we compute infrared loop corrections to the occupation number and anomalous quantum average of the scalar field and show that these corrections are growing with time. Using these observations, we demonstrate that the regularized stress-energy tensor at the distant future acquires substantial quantum corrections which exceed the long known tree-level contributions to the particle flux.

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arXiv2022

Free energy and entropy in Rindler and de Sitter space-times

We investigate the free energy and entropy of the Gaussian massive scalar field theory in the static de Sitter space-time for arbitrary temperature. For the inverse temperatures of the form $β=2 π2^k, \ \ k\in \mathbf{Z}$, in curvature units, we find the explicit form of the free energy and its derivatives with respect to the temperature. There are two types of contributions to the free energy: one is of the "area type" and can be attributed to the horizon, while the other is of the "volume type" and is associated with the interior of the space-time. The latter contribution in the odd-dimensional case in the limit of the week field (large mass or small Hubble constant) significantly depends on the temperature. Namely, for $ β<2π$, the free energy behaves as $ F^{bulk}_β \sim e^{- β\, m} $, while for $β>2π$ it behaves as $ F^{bulk}_β \sim e^{- 2 \, π\, m}$. We also show that even the leading UV contributions to the free energy significantly depend on the state of the theory, which is very unusual. We explain the origin and physical meaning of these observations. As the model example we consider the situation in the Rindler wedge of the flat space-time.

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