Related papers: Energy-pressure relation for low-dimensional gases
In this thesis, we explore various aspects of equilibrium and nonequilibrium thermodynamics for ultracold atomic gases, with a focus on the experimentally realisable one-dimensional (1D) Bose gas. This is a paradigmatic example of an…
The local balance equations for the density, momentum, and energy of a dilute gas of elastic or inelastic hard spheres, strongly confined between two parallel hard plates are obtained. The starting point is a Boltzmann-like kinetic…
We study the interplay of quantum statistics, strong interactions and finite temperatures in the two-component (spinor) Bose gas with repulsive delta-function interactions in one dimension. Using the Thermodynamic Bethe Ansatz, we obtain…
Photon Bose-Einstein condensates are characterised by a quite weak interaction, so they behave nearly as an ideal Bose gas. Moreover, since the current experiments are conducted in a microcavity, the longitudinal motion is frozen out and…
We derive the fundamental thermodynamic equation for Fermi-Dirac and Bose-Einstein quantum gases, which contains the first order contribution due to the quantum nature of the gas particles. Then, we analyze the fundamental equation in the…
We consider the d-dimensional imperfect (mean-field) Bose gas confined in a slit-like geometry and subject to periodic boundary conditions. Within an exact analytical treatment we first extract the bulk critical properties of the system at…
The ideal Bose gas has two major shortcomings: at zero temperature, all the particles 'condense' at zero energy or momentum, thus violating the Heisenberg principle; the second is that the pressure below the critical point is independent of…
Spatial profiles of the pressure have been measured in atomic Fermi gases with primarily 2D kinematics. The in-plane motion of the particles is confined by a gaussian-shape potential. The two-component deeply-degenerate Fermi gases are…
Thermodynamics of power means applies to an ideal quantum gas which may be nonextensive. Transition to an ideal classical gas occurs when the empirical temperature exponents of the internal energy and absolute temperature coalesce. Limiting…
In typical one-dimensional models the Mermin-Wagner theorem forbids long range order, thus preventing finite-temperature phase transitions. We find a finite-temperature phase transition for a homogeneous system of attractive bosons in one…
The 'absolute stiff' matter ($P=E$) can be a Fermi or Bose gas of particles with the energy spectrum $\epsilon_p \sim p^q$ in $q$-dimensional space, particularly $\epsilon_p =p^3/m^2$ in 3-dimensional space. We obtain its pressure, particle…
The interacting quantum Bose gas is a random ensemble of many Brownian bridges (cycles) of various lengths with interactions between any pair of legs of the cycles. It is one of the standard mathematical models in which a proof for the…
We address the problem of computing the thermodynamic properties of the repulsive one-dimensional two-component Fermi gas with contact interaction, also known as the Gaudin-Yang model. Using a specific lattice embedding and the quantum…
We study the thermodynamical properties of an ideal gas of non-Abelian Chern-Simons particles and we compute the second virial coefficient, considering the effect of general soft-core boundary conditions for the two-body wavefunction at…
Bose-Einstein condensation happens as a gas of bosons is cooled below its transition temperature, and the ground state becomes macroscopically occupied. The phase transition occurs in the thermodynamic limit of many particles. However,…
We report the effects on the thermodynamic properties of a 3D Bose gas caused by a temperature dependent energy gap between the ground state and the first excited state of the energy spectrum of the particles constituting the Bose gas which…
Dark energy, the enigmatic force driving the accelerated cosmic expansion of the universe, is conventionally described as a cosmological constant in the standard $\Lambda$CDM model. However, measurements from the Dark Energy Spectroscopic…
We show that the free relativistic wave equation which describes the particle without or with rest mass has more than one part of energy spectrum. One part of energy spectrum is beginning with rest energy and it is not limited by above.…
We consider the Bose gas on a $d$-dimensional anisotropic lattice employing the imperfect (mean-field) gas as a prototype example. We study the dimensional crossover arising as a result of varying the dispersion relation at finite…
Classic and recent results for the critical behaviour of ideal Bose gas at constant volume and constant pressure and for various spatial dimensionalities d>0 are reviewed. New results about the critical properties in a close vicinity of the…