arXiv subjects

Emine Ertugrul

Publications and source records attributed to Emine Ertugrul.

5 recordsLinked to original sources

arXiv2026

BCS Gap Equation on Riemannian Manifolds: A Heat Kernel Analysis

In this paper, we investigate the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity formulated on a three dimensional Riemannian manifold. We derive the gap equation in the path integral picture by employing a Hubbard-Stratonovich transformation followed by a saddle point approximation. Under the assumption that the length scale set by the metric is much larger than the healing length, we solve the gap equation to find a slowly varying gap function that exhibits the effects of curvature. To rigorously address the ultraviolet divergences inherent in the gap equation, we utilize heat kernel expansion techniques, which provide a systematic and mathematically transparent renormalization scheme. We explicitly evaluate the renormalized gap equation at both zero and finite temperatures, computing the relevant integrals asymptotically in the weak-coupling limit ($Δ\ll μ$). Furthermore, we establish a universal, regularization-independent relation connecting the finite-temperature gap to the zero-temperature gap and the temperature itself. Based on this fundamental relation, we analytically prove the monotonic decrease of the energy gap with increasing temperature ($\partial Δ/ \partial T < 0$), successfully recovering the standard universal BCS behavior near the critical temperature within a curved space framework.

hep-th↗

arXiv2026

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↗

arXiv2025

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-Nordström 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↗

arXiv2023

Perturbative solution of the Einstein Constraints with Spin and Momentum Far Away From a Binary Source in the Bowen-York formalism

We study the momentum and Hamiltonian constraints of vacuum Einstein equations, within the Bowen-York formalism, for two interacting black holes in close separation, with anti-parallel spins and anti-parallel linear momenta. We give an analytical solution using perturbation theory. We also compute the location and the shape of the apparent horizon which generically depend on all the parameters, angles and the separation between the black holes. Our solution only works for distances far away from the black holes. To gain more insight close to the black holes, one has to go to the higher orders in perturbation theory, which is a rather cumbersome process. But the solution presented here can be of some use for numerical computations as the latter should match our result for the described problem.

gr-qc↗

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↗