Narrow Results

To the best of our knowledge, for the first time, the quantum Hall effect (QHE) is considered in thermal non-equilibrium conditions (TNEC) via $q$-algebra. The $q$-algebra is a topological tool that provides a controlling $q$-parameter to approximate theoretical results to the laboratory ones. We obtain the QHE spectrum and $q$-deformed Hall potential (or Hall potential in TNEC) via the density probability current. Because of the Pauli Exclusion Principle, we model the QHE using relativistic Fermi electron gas and the $q$-deformed Fermi–Dirac distribution. We find the dependence of deformed Hall potential to temperature and magnetic field for different geometric $q$-regions. Further, we geometrically prove that the magnitude of the Hall potentials depends on the $q$-regions (i.e. $\left|V_H^{(q>1)}\right|>\left|V_H^{(q=1)}\right|>\left|V_H^{(q<1)}\right|$). We find that for some $q$-amounts, the Landau energy gap on graphene-based materials can be explained in the room-temperature quantum Hall effect (RTQHE). Our method may be applied to analyze new electronic devices based on graphene in TNEQ.

The q-deformed Fermi–Dirac distribution derived from the q-fermion algebra is used to study the thermostatistical properties of a q-deformed Fermi gas trapped in a generic power-law potential, and the effects of q-deformation on the properties of the system are discussed. It is shown that q-deformation leads to some novel characteristics compared with those of an original Fermi system. It is found that the effects of q-deformation display different characteristics in the cases of different kinematic characteristics of particles and different shapes of external potentials. The results obtained here present a unified description for the thermostatistical properties of a class of q-deformed as well as original Fermi systems, so that many important conclusions in the literature are included in this paper.

In this work, the thermal properties, such as total energy, pressure and free energy of an interacting electron gas system have been investigated. The Thomas–Fermi equation was numerically solved for a harmonically confined, two-dimensional gas system at finite temperatures. Numerical results were compared with analytical ones provided by the literature for a non-interacting case at finite temperatures and for a interacting case at T = 0 K. Excellent agreement was achieved for both cases. The results indicate that interactions affect the density of particles and hence, the density-dependent thermal functions significantly.

The Thomas–Fermi (TF) equation is solved numerically for an electron gas system that interacts via the Coulomb potential. An emphasis is placed on how certain physical properties, such as the chemical potential and the total energy, change with the shape of the confinement at finite temperatures. By comparing these results with the results calculated for the noninteracting case, we are able to analyze how the inter-particle forces affect the thermodynamic properties of electrons. It is shown that the total energy and other properties of an electron gas is very sensitive to the particle interactions and the shape of the confining potential, even at high temperatures. The results are also applicable to nanostructures like two-dimensional quantum dot systems, wires.

The question whether an imbalanced Fermi gas can accommodate polarized superfluidity has been the subject of intense study. One prominent candidate for a polarized superfluid state is the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state. In a one-dimensional (1D) Fermi gas, indirect evidence for this state has recently been found, but in the three-dimensional (3D) case, this exotic state has hitherto remained elusive. In this brief review, we study the influence of a 1D periodic potential on the FFLO state in an imbalanced 3D Fermi gas. We present a path-integral derivation of the free energy of the system, where the possibility of the FFLO state is included through the saddle-point approximation. Using the free energy, the phase diagram of the system, both at fixed chemical potentials and at fixed densities, is constructed, showing that the stability region of the FFLO state is significantly enlarged by the 1D potential. Subsequently, the influence of the potential on the FFLO pairing mechanism is investigated, leading to a qualitative understanding of the shape of the FFLO region in the different phase diagrams. We conclude by investigating the possibility of an FFLO state with a wave vector that lies skewed with respect to the direction along which the periodic potential varies. Our results provide an additional way to facilitate the experimental observation of the FFLO state in a 3D Fermi gas.

The scissors mode plays a crucial role in the study of the unitary Fermi gas. In this paper, we simulate the scissors mode by solving the hydrodynamic equations with appropriate initial conditions, and then extract the flow field of the gas. The flow fields in different regimes are found to be essentially different. The characteristic differences in the flow patterns between the superfluid and the normal viscous fluid are presented. Irrotational flow signals superfluidity, while rotational one indicates normal hydrodynamical behavior. These different characteristics can be visualized by the velocity portraits of the flow, which provide an intuitive way to discriminate the states of the Fermi gas.

The properties of cold interacting Fermi gases in terms of scattering length are investigated. The scattering length is calculated by exact solution of Schrödinger equation. A Cosine hyperbolic potential with variable strength is employed in this study. The different interaction regimes are provided by choosing different strength of potential, which are characterized by an inverse of S-wave scattering length and Fermi wave number. The energy per particle for ³He system is calculated within the lowest order constrained variational (LOCV) method. It is found that the bound bosonic pairs as well as bound molecules are formed at positive scattering length, only by considering two-body interactions.

The role of Pauli potentials in the semiclassical simulation of Fermi gases at low temperatures is investigated. An alternative Pauli potential to the usual bivariate Gaussian form by Dorso et al⁵ is proposed. This new Pauli potential allows for a simultaneous good reproduction of not only the kinetic energy per particle but also the momentum distribution and the two-body correlation function. The reproduction of the binding energies in finite nuclei in the low and medium mass range is also analyzed. What is found is that given a reasonable short-range atractive nuclear interaction one can include correlation effects in a suitable chosen density dependent Pauli potential.

Fermi gases with magnetically tunable interactions provide a clean and controllable laboratory system for modelling interparticle interactions between fermions. Near a Feshbach resonance, the s-wave scattering length diverges and Fermi gases are strongly interacting, enabling tests of nonperturbative many-body theories in a variety of disciplines, from high temperature superconductors to neutron matter and quark-gluon plasmas. We measure the entropy and energy of this model system, enabling model-independent comparison with thermodynamic predictions. Our experiments on the expansion dynamics of rotating strongly interacting Fermi gases reveal extremely low viscosity hydrodynamics. Combining the thermodynamic and hydrodynamic measurements enables an estimate of the ratio of the shear viscosity to the entropy density. A strongly interacting Fermi gas in the normal fluid regime is found to be a nearly perfect fluid, where the ratio of the viscosity to the entropy density is close to a universal minimum that has been conjectured by string theory methods. In the weakly interacting regime near a zero crossing in the s-wave scattering length, we observe coherently prepared Fermi gases that slowly evolve into long-lived spin-segregated states that are far from equilibrium and weakly damped.