arXiv subjects

Alexander A. Andrianov

Publications and source records attributed to Alexander A. Andrianov.

At least 19 recordsLinked to original sources

arXiv2023

The spectrum of states of Ba~nados-Teitelboim-Zanelli black hole formed by a collapsing dust shell

We perform canonical analysis of an action in which 2+1-dimensional gravity with negative cosmological constant is coupled to cylindrically symmetric dust shell. The resulting phase space is finite dimensional having geometry of SO(2; 2) group manifold. Representing the Poisson brackets by commutators results in the algebra of observables which is a quantum double D(SL(2)q). Deformation parameter q is real when the total energy of the system is below the threshold of a black hole formation, and a root of unity when it is above. Inside the black hole the spectra of the shell radius and time operator are discrete and take on a finite set of values. The Hilbert space of the black hole is thus finite-dimensional.

hep-th↗

arXiv2022

The Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) Equation for Two-Dimensional Systems

Open quantum systems are, in general, described by a density matrix that is evolving under transformations belonging to a dynamical semigroup. They can obey the Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation. We exhaustively study the case of a Hilbert space of dimension $2$. First, we find final fixed states (called pointers) of an evolution of an open system, and we then obtain a general solution to the FGKLS equation and confirm that it converges to a pointer. After this, we check that the solution has physical meaning, i.e., it is Hermitian, positive and has trace equal to $1$, and find a moment of time starting from which the FGKLS equation can be used - the range of applicability of the semigroup symmetry. Next, we study the behavior of a solution for a weak interaction with an environment and make a distinction between interacting and non-interacting cases. Finally, we prove that there cannot exist oscillating solutions to the FGKLS equation, which would resemble the behavior of a closed quantum system.

quant-ph↗

arXiv2020

Quantum Analysis of BTZ Black Hole Formation Due to the Collapse of a Dust Shell

We perform Hamiltonian reduction of a model in which 2+1 dimensional gravity with negative cosmological constant is coupled to a cylindrically symmetric dust shell. The resulting action contains only a finite number of degrees of freedom. The phase space consists of two copies of $ADS^2$ -- both coordinate and momentum space are curved. Different regions in the Penrose diagram can be identified with different patches of $ADS^2$ momentum space. Quantization in the momentum representation becomes particularly simple in the vicinity of the horizon, where one can neglect momentum non-commutativity. In this region, we calculate the spectrum of the shell radius. This spectrum turns out to be continuous outside the horizon and becomes discrete inside the horizon with eigenvalue spacing proportional to the square root of the black hole mass. We also calculate numerically quantum transition amplitudes between different regions of the Penrose diagram in the vicinity of the horizon. This calculation shows a possibility of quantum tunneling of the shell into classically forbidden regions of the Penrose diagram, although with an exponentially damped rate away from the horizon.

gr-qc↗

arXiv2020

Cylindrically symmetric 2+1 gravity in terms of global variables:quantum dynamics

We perform quantization of a model in which gravity is coupled to a circular dust shell in 2+1 spacetime dimensions. Canonical analysis shows that momentum space of this model is ADS^2-space, and the global chart for it is provided by the Euler angles. In quantum kinematics, this results in non-commutativity in coordinate space and discreteness of the shell radius in timelike region, which includes the collapse point. At the level of quantum dynamics, we find transition amplitudes between zero and non-zero eigenvalues of the shell radius, which describe the rate of gravitational collapse (bounce). Their values are everywhere finite, which could be interpreted as resolution of the central singularity.

gr-qc↗

arXiv2018

Integrable Minisuperspace Models with Liouville Field: Energy Density Self-Adjointness and Semiclassical Wave Packets

The homogeneous cosmological models with a Liouville scalar field are investigated in classical and quantum context of Wheeler-DeWitt geometrodynamics. In the quantum case of quintessence field with potential unbounded from below and phantom field, the energy density operators are not essentially self-adjoint and self-adjoint extensions contain ambiguities. Therefore the same classical actions correspond to a family of distinct quantum models. For the phantom field the energy spectrum happens to be discrete. The probability conservation and appropriate classical limit can be achieved with a certain restriction of the functional class. The appropriately localized wave packets are studied numerically using the Schrodinger's norm and a conserved Mostafazadeh's norm introduced from techniques of pseudo-Hermitian quantum mechanics. These norms give a similar packet evolution that is confronted with analytical classical solutions.

hep-th↗

arXiv2015

Quantum cosmology of the multi-field scalar matter: some exact solutions

We consider the gravity interacting with matter scalar fields and quantized in the minisuperspace approach in which the wave functional is described by the Wheeler-DeWitt equations (WdW). Assuming the domination of the homogeneous and isotropic geometry the leading contributions to the wave functional in the approximation of the minisuperspace with Friedmann-Robertson-Walker metric (FRW) and spatially uniform scalar fields are considered. The model of several scalar fields with exponential potentials and kinetic terms admitting such a special mixing that ultimately it is possible to separate the variables in the WdW equation and to find its exact solution in terms of the special functions is proposed. The semiclassical approximation is thoroughly investigated and the boundary conditions permitting the physical solution selection for classical cosmologies are chosen.

hep-th↗

arXiv2014

Minimal Realizations of Supersymmetry for Matrix Hamiltonians

The notions of weak and strong minimizability of a matrix intertwining operator are introduced. Criterion of strong minimizability of a matrix intertwining operator is revealed. Criterion and sufficient condition of existence of a constant symmetry matrix for a matrix Hamiltonian are presented. A method of constructing of a matrix Hamiltonian with a given constant symmetry matrix in terms of a set of arbitrary scalar functions and eigen- and associated vectors of this matrix is offered. Examples of constructing of $2\times2$ matrix Hamiltonians with given symmetry matrices for the cases of different structure of Jordan form of these matrices are elucidated.

math-ph↗

arXiv2014

Analysis of dilepton angular distributions in a parity breaking medium

We investigate how local parity breaking (LPB) due to large topological fluctuations may affect hadron physics. A distorted dispersion relation is derived for the lightest vector mesons $ρ$ and $ω$. They are characterised by a mass splitting depending on their polarization. We present a detailed analysis of the angular distribution associated to the lepton pairs created from these mesons searching for polarization dependencies. Two angular variables are found to carry the main information related to the parity breaking effect. Possible signatures for experimental detection of local parity breaking that could potentially be seen by the PHENIX and STAR collaborations are discussed.

hep-ph↗

arXiv2013

Chemical potentials and parity breaking: the Nambu-Jona-Lasinio model

We consider the "two flavour" Nambu--Jona-Lasinio model in the presence of a vector and an axial external chemical potentials and study the phase structure of the model at zero temperature. The Nambu--Jona-Lasinio model is often used as a toy replica of QCD and it is therefore interesting to explore the consequences of adding external vector and axial chemical potentials in this model, mostly motivated by claims that such external drivers could trigger a phase where parity could be broken in QCD. We are also motivated by some lattice analysis that attempt to understand the nature of the so-called Aoki phase using this simplified model. Analogies and differences with the expected behaviour in QCD are discussed and the limitations of the model are pointed out.

hep-ph↗

arXiv2013

Gravity effects on thick brane formation from scalar field dynamics

The formation of a thick brane in five-dimen\-sional space-time is investigated when warp geometries of $AdS_5$ type are induced by scalar matter dynamics and triggered by a thin-brane defect. The scalar matter is taken to consist of two fields with $O(2)$ symmetric self interaction and with manifest $O(2)$ symmetry breaking by terms quadratic in fields. One of them serves as a thick brane formation mode around a kink background and another one is of a Higgs-field type which may develop a classical background as well. Scalar matter interacts with gravity in the minimal form and gravity effects on (quasi)localized scalar fluctuations are calculated with usage of gauge invariant variables suitable for perturbation expansion. The calculations are performed in the vicinity of the critical point of spontaneous breaking of the combined parity symmetry where a non-trivial v.e.v. of the Higgs-type scalar field is generated. The nonperturbative discontinuous gravitational effects in the mass spectrum of light localized scalar states are studied in the presence of a thin-brane defect. The thin brane with negative tension happens to be the most curious case when the singular barriers form a potential well with two infinitely tall walls and the discrete spectrum of localized states arises completely isolated from the bulk.

hep-th↗

arXiv2013

Implications of local parity breaking in heavy ion collisions

Recent data on dilepton production in heavy ion collisions revealed an abnormal excess in the region of invariant masses below 1 GeV. Our proposal is the creation of a slowly varying time-dependent pseudoscalar condensate within the hot nuclear fireball that comes from the very collision. The local parity breaking effect that immediately arises substantially modifies the vector meson properties leading to an excess of lepton pairs that could be a part of the explanation for the observed abnormal dilepton yield.

hep-ph↗

arXiv2013

An effective theory for QCD with an axial chemical potential

We consider the low energy realization of QCD in terms of meson fields when an axial chemical potential is present; a situation that may be relevant in heavy ion collisions. We shall demonstrate that the presence of an axial charge constitutes an explicit source of parity breaking. The eigenstates of strong interactions do not have a definite parity and interactions that would otherwise be forbidden compete with the familiar ones. In this work, we first focus on scalars and pseudoscalars that are described by a generalized linear sigma model; and next, we give some hints on how the Vector Meson Dominance model describes the vector sector.

hep-ph↗

arXiv2013

Localization of scalar fields on self-gravitating thick branes

The model of a domain wall ("thick" brane) in noncompact five-dimensional space-time is considered with geometries of $AdS_5$ type generated by self-interacting scalar matter. The scalar matter is composed of two fields with O(2) symmetric self interaction. One of them is mixed with gravity scalar modes and plays role of the brane formation mode (due to a kink background) and another one is of a Higgs-field type. The interplay between soft breaking of O(2) symmetry and gravity influence is thoroughly investigated around the critical point of spontaneous $τ$ symmetry breaking when the v.e.v. of the Higgs-type scalar field occurs. The possibility of (quasi)localization of scalar modes on such thick branes is examined.

hep-th↗

arXiv2013

CP violation in the models of fermion localization on a domain wall (brane)

A brief survey of fermion localization mechanism on a domain wall ("thick brane") generated by a topologically nontrivial vacuum configuration of scalar fields is given. The extension of scalar fields interaction with fermions which supplies fermions with an axial mass is proposed. For several flavors and generations of fermions this extension can entail the Cabibbo-Kobayashi-Maskawa matrix of the Standard Model. As well the model with two scalar doublets which provide a supplementary CP violation mechanism is considered.

hep-th↗

arXiv2012

An effective QCD Lagrangian in the presence of an axial chemical potential

We consider the low energy realization of QCD in terms of mesons when an axial chemical potential is present; a situation that may be relevant in heavy ion collisions. We shall demonstrate that the presence of an axial charge has profound consequences on meson physics. The most notorious effect is the appearance of an explicit source of parity breaking. The eigenstates of strong interactions do not have a definite parity and interactions that would otherwise be forbidden compete with the familiar ones. In this work we focus on scalars and pseudoscalars that are described by a generalized linear sigma model. We comment briefly on the screening role of axial vectors in formation of effective axial charge and on the possible experimental relevance of our results, whose consequences may have been already seen at RHIC.

hep-ph↗

arXiv2011

Resolutions of Identity for Some Non-Hermitian Hamiltonians. I. Exceptional Point in Continuous Spectrum

Resolutions of identity for certain non-Hermitian Hamiltonians constructed from biorthogonal sets of their eigen- and associated functions are given for the spectral problem defined on entire axis. Non-Hermitian Hamiltonians under consideration possess the continuous spectrum and the following peculiarities are investigated: (1) the case when there is an exceptional point of arbitrary multiplicity situated on a boundary of continuous spectrum; (2) the case when there is an exceptional point situated inside of continuous spectrum. The reductions of the derived resolutions of identity under narrowing of the classes of employed test functions are revealed. It is shown that in the case (1) some of associated functions included into the resolution of identity are normalizable and some of them may be not and in the case (2) the bounded associated function corresponding to the exceptional point does not belong to the physical state space. Spectral properties of a SUSY partner Hamiltonian for the Hamiltonian with an exceptional point are examined.

math-ph↗

arXiv2009

Anomalous positron excess from Lorentz-violating QED

We entertain the idea that a suitable background of cold (very low momentum) pseudoscalar particles or condensate, may trigger a background that effectively generates Lorentz-invariance violation. This aether-like background induces a Chern-Simons modification of QED. Physics is different in different frames and, in the rest frame of the pseudoscalar background, high momentum photons can decay into pairs. The threshold for such decay depends quadratically on the rest mass of the particles. This mechanism could explain in a natural way why antiprotons are absent in recent cosmic ray measurements. A similar signal could be used as a probe of pseudoscalar condensation in heavy ion collisions.

hep-ph↗

arXiv2009

Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics

When several inequivalent supercharges form a closed superalgebra in Quantum Mechanics it entails the appearance of hidden symmetries of a Super-Hamiltonian. We examine this problem in one-dimensional QM for the case of periodic potentials and potentials with finite number of bound states. After the survey of the results existing in the subject the algebraic and analytic properties of hidden-symmetry differential operators are rigorously elaborated in the Theorems and illuminated by several examples.

hep-th↗