Related papers: Heat kernel approach for confined quantum gas
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…
From sand piles to electrons in metals, one of the greatest challenges in modern physics is to understand the behavior of an ensemble of strongly interacting particles. A class of quantum many-body systems such as neutron matter and cold…
The thermodynamics of ideal gas on the noncommutative geometry in the coherent state formalism is investigated. We first evaluate the statistical interparticle potential and see that there are residual "attraction (repulsion) potential"…
The thermodynamic properties of ideal quantum gases are derived solely from dimensional arguments, the Pauli principle and thermodynamic relations, without resorting to statistical mechanics.
We study the properties of a thermodynamic system having the symmetry of a quantum group and interacting with a harmonic potential. We calculate the dependence of the chemical potential, heat capacity and spatial distribution of the gas on…
We obtain an analytical equation of state for one-dimensional strongly attractive Fermi gas for all parameter regime in current experiments. From the equation of state we derive universal scaling functions that control whole thermodynamical…
It is shown that the heat kernel operator for the Laplace operator on any covariantly constant curved background, i.e. in symmetric spaces, may be presented in form of an averaging over the Lie group of isometries with some nontrivial…
Heat kernel coefficients encode the short distance behavior of propagators in the presence of background fields, and are thus useful in quantum field theory. We present a Mathematica program for computing these coefficients and their…
The behavior of a decoupled ideal Fermi gas in a homogeneously expanding three-dimensional volume is investigated, starting from an equilibrium spectrum. In case the gas is massless and/or completely degenerate, the spectrum of the gas can…
For the Fermi gas filling the space inside a cubic cavity of a fixed volume, at arbitrary temperatures and number of particles, the thermodynamic characteristics are calculated, namely: entropy, thermodynamic potential, energy, pressure,…
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…
Using our recently proposed covariant algebraic approach the heat kernel for a Laplace-like differential operator in low-energy approximation is studied. Neglecting all the covariant derivatives of the gauge field strength (Yang-Mills…
Covariant perturbation expansion is an important method in quantum field theory. In this paper an expansion up to arbitrary order for off-diagonal heat kernels in flat space based on the covariant perturbation expansion is given. In…
Many-particle systems pose commonly known computational challenges in quantum theory. The obstacles arise from the difficulty in finding sets of eigenvalues and eigenvectors of the underlying Hamiltonian while enforcing fermion or boson…
We present a formalism for computing arbitrary multi-loop Feynman graphs in curved spacetime using the heat kernel approach. To this end, we compute the off-diagonal components of the heat kernel in Riemann normal coordinates up to second…
We discuss the application of techniques of quantum estimation theory and quantum metrology to thermometry. The ultimate limit to the precision at which the temperature of a system at thermal equilibrium can be determined is related to the…
This paper is an overview on our recent results in the calculation of the heat kernel in quantum field theory and quantum gravity. We introduce a deformation of the background fields (including the metric of a curved spacetime manifold) and…
An approach for solving scattering problems, based on two quantum field theory methods, the heat kernel method and the scattering spectral method, is constructed. This approach converts a method of calculating heat kernels into a method of…
We propose an analytical model for the accurate calculation of size and density dependent quantum oscillations in thermodynamic and transport properties of confined and degenerate non-interacting Fermi gases. We provide a universal,…
We investigate the thermodynamics of a Fermi gas whose single-particle energy levels are given by the complex zeros of the Riemann zeta function. This is a model for a gas, and in particular for an atomic nucleus, with an underlying fully…