Related papers: Nonperturbative late time asymptotics for heat ker…
Inspired by the entropy-area relation of black hole thermodynamics, we study the thermodynamics of cosmological apparent horizon in a spatially flat Friedmann-Robertson-Walker (FRW) universe in the framework of an Extended Uncertainty…
In this paper, we study the asymptotic behavior of the heat kernel with respect to the Witten Laplacian. We introduce the localization and the scaling technique in semi-classical analysis, and study the semi-classical asymptotic behavior of…
The unification of relativity and thermodynamics has been a subject of considerable debate over the last 100 years. The reasons for this are twofold: (i) Thermodynamic variables are nonlocal quantities and, thus, single out a preferred…
A common belief is that further quantum corrections near the singularity of a large black hole should not substantially modify the semiclassical picture of black hole evaporation; in particular, the outgoing spectrum of radiation should be…
We study a technical problem arising from the spectral geometry of noncommutative tori: the small time heat trace asymptotic associated to a general second order elliptic operator. We extend the rearrangement operators in the conformal case…
A new representation is found for the action of the recently suggested ghost-free nonlocal gravity models generating de Sitter or Anti-de Sitter background with an arbitrary value of the effective cosmological constant. This representation…
The regularized trace of the heat kernel of a one-dimensional Schr\"odinger operator with a singular two-particle contact interaction being of Lieb-Liniger type is considered. We derive a complete small-time asymptotic expansion in…
In this paper we study the small time asymptotics for the heat kernel on a sub-Riemannian manifold, using a perturbative approach. We then explicitly compute, in the case of a 3D contact structure, the first two coefficients of the small…
Assuming the existence of a cosmological constant depending on time, we study the evolution of this field in a local region of spacetime. Solving the standard equations of Einstein Relativity in the weak field approximation we find two…
We relate Gruet formula for the heat kernel on real hyperbolic spaces to the commonly used one derived from Millson induction. The bridge between both formulas is settled by Yor result on the joint distribution of a Brownian motion and of…
Nonlocality is a defining feature of quantum mechanics and has long served as a key indicator of quantum resources since the formulation of Bell's inequalities. Identifying the contribution of nonlocality to extractable work remains a…
We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are H\"older continuous locally in space and time. This is done via local…
We introduce an ergotropy-based formulation of quantum thermodynamics, which provides a strong connection between average heat and von Neumann entropy. By adopting this formulation, we can reinterpret the infinitesimal average heat in terms…
I take non-locality to be the Michaelson Morley experiment of the 21st Century, assume its universal validity, and try to derive its consequences. Spacetime, with its locality, cannot be fundamental, but emergent from entangled coherent…
We consider the heat kernel (and the zeta function) associated with Laplace type operators acting on a general irreducible rank 1 locally symmetric space X. The set of Minakshisundaram- Pleijel coefficients {A_k(X)}_{k=0}^{\infty} in the…
Generalizing to relativistic exponential scaling and using the theory of noise from quantum fluctuations, it has been shown that one vacuum (Rindler, Hartle-Hawking, or Gibbons-Hawking for the cases of the uniformly accelerated detector,…
We consider a scenario of large-scale modification of gravity that does not invoke extra degrees of freedom but includes coupling between baryonic matter and dark matter in the Einstein frame. The total matter energy density follows the…
The instability of (quasi) de Sitter spacetime from quantum gravitational effects has been discussed in many works. Especially, the gravitational backreaction from quantum energy momentum tensor is crucial for understanding the low-energy…
In this thesis we are interested in the problem of dark energy in cosmology. In particular, we consider the possibility that this effect is due to an infrared non-local modification of the theory of General Relativity. Inspired by massive…
The subject of this thesis is the coupling of quantum fields to a classical gravitational background in a semiclassical fashion. It contains a thorough introduction into quantum field theory on curved spacetime with a focus on the…