Related papers: Heat kernel approach for confined quantum gas
A diagramatic heat kernel expansion technique is presented. The method is especially well suited to the small-derivative expansion of the heat kernel, but it can also be used to reproduce the results obtained by the approach known as…
The heat kernel method is extended to the case of finite temperature. Special emphasis is given to the study of gauge theories. Due to the compactness of space in the Euclidean time direction (inverse temperature) the field strength cannot…
We propose a phenomenological approach for the equation of state of a unitary Fermi gas. The universal equation of state is parametrised in terms of Fermi-Dirac integrals. This reproduces the experimental data over the accessible range of…
We consider a Fermi gas with short-range attractive interactions that is confined along one direction by a tight harmonic potential. For this quasi-two-dimensional (quasi-2D) Fermi gas, we compute the pressure equation of state, radio…
Thermodynamic functions of the ideal Fermi gas at arbitrary temperatures are calculated using the standard Fermi-Stoner functions. The properties of the Fermi-Stoner functions are analyzed. The limiting cases of low-temperature and…
In this letter we present a unified derivation of the pressure equation of states, thermodynamics and scaling functions for the one-dimensional (1D) strongly attractive Fermi gases with $SU(w)$ symmetry. These physical quantities provide a…
Heat capacities of model systems with finite numbers of effective degrees of freedom are evaluated using canonical and microcanonical thermodynamics. Discrepancies between both approaches, which are observed even in the infinite-size limit,…
Quantum measurements are the means by which we recover messages encoded into quantum states. They are at the forefront of quantum hypothesis testing, wherein the goal is to perform an optimal measurement for arriving at a correct…
For an understanding of a heat engine working in the microscopic scale, it is often necessary to estimate the amount of reversible work extracted by isothermal expansion of the quantum gas used as its working substance. We consider an…
The Carnot statement of the second law of thermodynamics poses an upper limit on the efficiency of all heat engines. Recently, it has been studied whether generic quantum features such as coherence and quantum entanglement could allow for…
Differential geometry offers a powerful framework for optimising and characterising finite-time thermodynamic processes, both classical and quantum. Here, we start by a pedagogical introduction to the notion of thermodynamic length. We…
A procedure to find optimal regimes for quantum thermal engines (QTMs) is described and demonstrated. The QTMs are modelled as the periodically-driven non-equilibrium steady states of open quantum systems, whose dynamics is approximated in…
The calculation of heat-kernel coefficients with the classical DeWitt algorithm has been discussed. We present the explicit form of the coefficients up to $h_5$ in the general case and up to $h_7^{min}$ for the minimal parts. The results…
We report on the measurement of the heat capacity for an optically-trapped, strongly-interacting Fermi gas of atoms. In the experiments, a precise input of energy to the gas is followed by single-parameter thermometry. The thermometry…
One of the principal objectives of quantum thermodynamics is to explore quantum effects and their potential beneficial role in thermodynamic tasks like work extraction or refrigeration. So far, even though several papers have already shown…
A new method is proposed for a treatment of ideal quantum gases in the microcanonical ensemble near the thermodynamic limit. The method allows rigorous asymptotic calculations of the average number of particles and particle number…
For an ideal D-dimensional Fermi gas under generic external confinement we derive the correcting coefficient $(D-2)/3D$ of the von Weizsacker term in the kinetic energy density. To obtain this coefficient we use the Kirzhnits semiclassical…
Thermodynamics imposes restrictions on what state transformations are possible. In the macroscopic limit of asymptotically many independent copies of a state---as for instance in the case of an ideal gas---the possible transformations…
The results on the heat kernel expansion for the electromagnetic field in the background of dielectric media are briefly reviewed. The common approaches to the calculation of the heat kernel coefficients are discussed from the viewpoint of…
A unified description for the Bose and Fermi gases trapped in an external generic power law potential $U=\sum_{i=1} ^d c_i |\frac{x_i}{a_i}|^{n_i}$ is presented using the grandpotential of the system in $d$ dimensional space. The…