arXiv subjects

Levent Akant

Publications and source records attributed to Levent Akant.

12 recordsLinked to original sources

arXiv2021

Estimation of attenuation of gravitational waves by Bose-Einstein condensate dark matter halos using Bogoliubov-de Gennes theory

We consider a gravitational plane wave passing through a galactic dark matter halo composed of weakly self-interacting, self-gravitating, Bose-Einstein condensate of ultralight particles. Treating the gravitational wave as a time dependent perturbation, we study energy transfer between the gravitational wave and the Bose-Einstein condensate by applying linear response theory to a non-uniform condensate described by the Bogoliubov-de Gennes theory, and compute the fractional loss in gravitational wave energy. We apply our results to investigate the extent to which this loss effects the estimation of the distance between the gravitational wave source and the earth. We show that the effect is negligible.

gr-qc↗

arXiv2021

The Higgs Field and the Jordan Brans Dicke Cosmology

We investigate a field theoretical approach to the Jordan-Brans- Dicke (JBD) theory extended with a particular potential term on a cosmological background by starting with the motivation that the Higgs field and the scale factor of the universe are related. Based on this relation, it is possible to come up with mathematically equivalent but two different interpretations. From one point of view while the universe is static, the masses of the elementary particles change with time. The other one, which we stick with throughout the manuscript, is that while the universe is expanding, particle masses are constant. Thus, a coupled Lagrangian density of the JBD field and the scale factor (the Higgs field), which exhibit a massive particle and a linearly expanding space in zeroth order respectively, is obtained. By performing a coordinate transformation in the field space for the reduced JBD action whose kinetic part is nonlinear sigma model, the Lagrangian of two scalar fields can be written as uncoupled for the Higgs mechanism. After this transformation, as a result of spontaneous symmetry breaking, the time dependent vacuum expectation value (vev) of the Higgs field and the Higgs bosons which are the particles corresponding to quantized oscillation modes about the vacuum, are found.

gr-qc↗

arXiv2018

Non-relativistic Limit of Thermodynamics of Bose Field in a Static Space-time and Bose-Einstein Condensation

We consider the grand canonical thermodynamics of a noninteracting scalar field in a static spacetime. We take the nonrelativistic limit of thermodynamic quantities in a way that leaves the curved structure of the background geometry intact. Using Mellin transform and heat kernel techniques we obtain asymptotic expansions of thermodynamic quantities appropriate for the analysis of Bose-Einstein condensation. We apply our results to investigate gravitational effects on the Bose-Einstein condensation for a scalar field in a finite volume. We also analyze the boundary effects on the depletion coefficient of the scalar field.

gr-qc↗

arXiv2016

On the Thermodynamic Limit of Bogoluibov's Theory of Bose Gas

Assuming that Bogoliubov's theory of weakly interacting dilute Bose gas defines a self-consistent model Hamiltonian, we investigate its thermodynamic limit as we take the volume to infinity. The infinite volume is taken via a sequence of scaled convex regions with piecewise smooth boundary and the volumes staying proportional to the cube of the diameter of the region. To get a strict bound on the behavior of the thermodynamic limit, we use the recent formulation of Bogoliubov's theory of condensation in terms of heat kernels for a given domain as well as an estimate of the difference of traces between the heat kernel with Neumann boundary conditions on this domain and the infinite space result. We cannot control the limiting process by the area term; however, we can come arbitrarily close to it.

math-ph↗

arXiv2015

Boundary Effects on the Thermodynamics of Quantum Fields Near a Static Black Hole

We investigate thermodynamics of a non-interacting quantum field in a static black hole background. The horizon divergences are regulated by the brick wall method, which consists of subjecting the quantum field to Dirichlet boundary conditions on a surface (the brick wall) just outside the horizon. Using heat kernel and Mellin transform methods, we derive high-temperature expansions for the free energy and entropy and study the boundary and higher-order geometric effects on the horizon divergences induced by the brick wall. We consider real scalar, complex scalar, and Dirac fields in Schwarzschild, Reissner-Nordstr\"{o}m and dilatonic black hole backgrounds, as well as in their near-horizon geometries. By evaluating the high-temperature expansion of the entropy (up to a certain order) at the Hawking temperature, we show that, for a given field type, the leading horizon divergence is the same for all the metrics considered. Moreover, we show that the different orders in the high-temperature expansion become comparable at the Hawking temperature and compare our findings with existing results in the literature. We derive an explicit formula for the sub-leading horizon divergence expressed in terms of the field mass, surface gravity, horizon area, and dilaton parameter, which is applicable to all the exact metrics considered. We also consider the possibility of using Neumann boundary conditions to regularize the horizon divergences.

hep-th↗

arXiv2014

Bose-Einstein Condensation on a Manifold with Nonnegative Ricci Curvature

The Bose-Einstein condensation for an ideal Bose gas and for a dilute weakly interacting Bose gas in a manifold with nonnegative Ricci curvature is investigated using the heat kernel and eigenvalue estimates of the Laplace operator. The main focus is on the nonrelativistic gas. However, special relativistic ideal gas is also discussed. The thermodynamic limit of the heat kernel and eigenvalue estimates is taken and the results are used to derive bounds for the depletion coefficient. In the case of a weakly interacting gas Bogoliubov approximation is employed. The ground state is analyzed using heat kernel methods and finite size effects on the ground state energy are proposed. The justification of the c-number substitution on a manifold is given.

math-ph↗

arXiv2008

Equivariant Symplectic Geometry of Gauge Fixing in Yang-Mills Theory

The Faddeev-Popov gauge fixing in Yang-Mills theory is interpreted as equivariant localization. It is shown that the Faddeev-Popov procedure amounts to a construction of a symplectic manifold with a Hamiltonian group action. The BRST cohomology is shown to be equivalent to the equivariant cohomology based on this symplectic manifold with Hamiltonian group action. The ghost operator is interpreted as a (pre)symplectic form and the gauge condition as the moment map corresponding to the Hamiltonian group action. This results in the identification of the gauge fixing action as a closed equivariant form, the sum of an equivariant symplectic form and a certain closed equivariant 4-form which ensures convergence. An almost complex structure compatible with the symplectic form is constructed. The equivariant localization principle is used to localize the path integrals onto the gauge slice. The Gribov problem is also discussed in the context of equivariant localization principle. As a simple illustration of the methods developed in the paper, the partition function of N=2 supersymmetric quantum mechanics is calculated by equivariant localization

hep-th↗

arXiv2008

Equivariant Localization in Stochastic Quantization and Quenched Matrix Models

It is shown that Parisi-Sourlas supersymmetry of stochastic quantization is a Cartan model of equivariant cohomology. Equivariant cohomological structure of stochastic quantization of linear and non-linear sigma models are discussed. Witten's nonabelian localization principle is applied to the stochastic quantization of matrix models. As a result the equivalence between the original matrix model and the corresponding quenched Eguchi-Kawai model is established.

hep-th↗

arXiv2008

Non-anomalous `Ward' identities to supplement large-N multi-matrix loop equations for correlations

This work concerns single-trace correlations of Euclidean multi-matrix models. In the large-N limit we show that Schwinger-Dyson equations imply loop equations and non-anomalous Ward identities. Loop equations are associated to generic infinitesimal changes of matrix variables (vector fields). Ward identities correspond to vector fields preserving measure and action. The former are analogous to Makeenko-Migdal equations and the latter to Slavnov-Taylor identities. Loop equations correspond to leading large-N Schwinger-Dyson equations. Ward identities correspond to 1/N^2 suppressed Schwinger-Dyson equations. But they become leading equations since loop equations for non-anomalous vector fields are vacuous. We show that symmetries at infinite N persist at finite N, preventing mixing with multi-trace correlations. For one matrix, there are no non-anomalous infinitesimal symmetries. For two or more matrices, measure preserving vector fields form an infinite dimensional graded Lie algebra, and non-anomalous action preserving ones a subalgebra. For Gaussian, Chern-Simons and Yang-Mills models we identify up to cubic non-anomalous vector fields, though they can be arbitrarily non-linear. Ward identities are homogeneous linear equations. We use them with the loop equations to determine some correlations of these models. Ward identities alleviate the underdeterminacy of loop equations. Non-anomalous symmetries give a naturalness-type explanation for why several linear combinations of correlations in these models vanish.

hep-th↗

arXiv2007

Deformation Quantization of Odd Dimensional anti-de Sitter Spaces as Contact Manifolds

We quantize odd dimensional anti-de Sitter spaces by applying the method of deforming contact manifolds proposed by Rajeev. The construction in the present paper consists of the identification of the odd dimensional anti-de Sitter space as a hypersurface of contact type and the subsequent use of 'symplectization' principle. We also show that this construction generalizes to any odd dimensional hypersurface which can be represented as a nonzero level set of a homogenous function.

hep-th↗

arXiv2006

Nonabelian Localization for Statistical Mechanics of Matrix Models at High Temperatures

We show that in the high temperature limit the partition function of a matrix model is localized on certain shells in the phase space where on each shell the classically conjugate matrix variables obey the canonical commutation relations. The result is obtained by applying the nonabelian equivariant localization principle to the partition function of a matrix model driven by a specific random external source coupled to a conserved charge of the system.

hep-th↗

arXiv2005

Equivariant Localization for Supersymmetric Quantum Mechanics

We apply equivariant localization to supersymmetric quantum mechanics and show that the partition function localizes on the instantons of the theory. Our construction of equivariant cohomology for SUSY quantum mechanics is different than the ones that already exist in the literature. A hidden bosonic symmetry is made explicit and the supersymmetry is extended. New bosonic symmetry is the square of the new fermionic symmetry. The D term is now the parameter of the bosonic symmetry. This construction provides us with an equivariant complex together with a Cartan differential and makes the use of localization principle possible.

hep-th↗