Related papers: A deformation formula for the heat kernel
Deformation quantization conventionally is described in terms of multidifferential operators. Jet manifold technique is well-known provide the adequate formulation of theory of differential operators. We extended this formulation to the…
By making use of the potentials of the heat conduction equation the integral equations are derived which determine the heat kernel for the Laplace operator $-a^2\Delta$ in the case of compound media. In each of the media the parameter $a^2$…
Based on the Mehler heat kernel of the Schroedinger operator for a free electron in a constant magnetic field an estimate for the kernel of E_A is derived, where E_A represents the kinetic energy of a Dirac electron within the…
Among the available perturbative approaches in quantum field theory, heat kernel techniques provide a powerful and geometrically transparent framework for computing effective actions in nontrivial backgrounds. In this work, resummation…
In this thesis we describe a type of metric space called an Euclidean polyhedral complex. We define a Dirichlet form on it; this is used to give a corresponding heat kernel. We provide a uniform small time Poincare inequality for complexes…
This paper investigates the eigenvalue problem of integral operators whose kernels can be expressed as a finite sum of pairwise products of single-variable functions, making them separable. By consdiering the matrix form of the separable…
We point out that using the heat kernel on a cone to compute the first quantum correction to the entropy of Rindler space does not yield the correct temperature dependence. In order to obtain the physics at arbitrary temperature one must…
In this work, we propose an efficient and robust multigrid method for solving the time-fractional heat equation. Due to the nonlocal property of fractional differential operators, numerical methods usually generate systems of equations for…
We consider the heat-kernel expansion of the massive Laplace operator on the three dimensional ball with Dirichlet boundary conditions. Using this example, we illustrate a very effective scheme for the calculation of an (in principle)…
We use the heat kernel (on differential forms) on a compact Riemannian manifold to assign a real number to a k-tuple of cycles on the manifold satisfying certain conditions. If k is 2, this number is the ordinary topological linking number,…
The quantization of gauge fields and gravitation on manifolds with boundary makes it necessary to study boundary conditions which involve both normal and tangential derivatives of the quantized field. The resulting one-loop divergences can…
We derive a microscopic expression for the instantaneous diagonal elements of the density matrix $\rho_{nn}(t)$ in the adiabatic basis for an arbitrary time dependent process in a closed Hamiltonian system. If the initial density matrix is…
We provide a general condition on the kernel of an integro-differential operator so that its associated quadratic form satisfies a coercivity estimate with respect to the $H^s$-seminorm.
We suggest a new technique of the asymptotic heat kernel expansion for minimal higher derivative operators of a generic $2M$-th order, $F(\nabla)=(-\Box)^M+\cdots$, in the background field formalism of gauge theories and quantum gravity.…
In modern science, the thermo mechanics motion can be traced back to quantum motion in micro viewpoint. On the other hand, the thermo mechanics is definitely related with geometrical configuration motion (phase) in macro viewpoint. On this…
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…
A simple model is used to estimate the Q factor in numerical simulations of differential phase shift keying (DPSK) with optical delay demodulation and balanced detection. It is found that an alternative definition of Q is needed for DPSK in…
This paper is divided into three parts. The first part focuses on periodic layer heat potentials, demonstrating their smooth dependence on regular perturbations of the support of integration. In the second part, we present an application of…
A master equation for the deformed quantum harmonic oscillator interacting with a dissipative environment, in particular with a thermal bath, is derived in the microscopic model by using perturbation theory. The coefficients of the master…
The first heat kernel coefficients are calculated for a dispersive ball whose permittivity at high frequency differs from unity by inverse powers of the frequency. The corresponding divergent part of the vacuum energy of the electromagnetic…