The energy market is facing a major transition, in which natural gas and renewable gasses will play an important role. However, changing gas sources and compositions will force the gas transporters, gas engine manufacturers, and gas grid operators to monitor the gas quality in a more intensive way. This leads to the need for lower cost, smaller, and easy to install gas quality sensors. A new approach is proposed in this study that is based on the chemical interactions of the various gas components and responsive layers applied to an array of capacitive interdigitated electrodes. For Liquid Natural Gas (LNG), containing a relative high concentration of higher hydrocarbons, an array of ten capacitive chips is proposed, that is sufficient to calculate the full composition, and can be used to calculate energy parameters, such as Wobbe Index, Calorific Value, and Methane Number. A first prototype was realized that was small enough to be inserted in low and medium pressure gas pipes and LNG engine fuel lines. Adding the pressure and temperature data to the chip readings enables the determination of the concentrations of the various alkanes, hydrogen, nitrogen, and carbon dioxide, including small fluctuations in water vapor pressure. The sensitivity and selectivity of the new sensor is compared to a compact analyzer employing tunable filter infrared spectrometry.

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Lett. 101, 135301 (2008)]. A key feature in the experiment was the use of a Feshbach resonance, which made large values of the scattering length accessible. Due to the large values of the scattering length, existing models such as the Beliaev model could not be used to explain the observations, and therefore the experiment was a particularly interesting one to analyze. In our first approach, we constructed ad hoc potentials that fitted the observed excitation spectrum, and later we improved our approach by using T-matrix formalism to describe the Feshbach resonant system. All in all, the phenomenological model we developed fits the observed excitation spectrum and yields correct molecular Feshbach resonance state energies in certain cases.The second part of this thesis studies fermionic quantum gases. We focus on studying a gas of spin-1/2 particles confined to a spin-dependent optical lattice. The lattice geometry is such that the up-spin component is loaded in a honeycomb lattice, and the down-spin component is confined to the underlying triangular lattice. We considered attractive on-site and nearestneighbor interactions, and formulated the nearest-neighbor interaction term in such a way that it takes into account the possibility of spontaneous time-reversal symmetry breaking. Furthermore, we took into account the possibility of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase, which breaks spatial symmetry. Within a mean-field approximation, we showed that the FFLO state is the ground state of the system in many instances. In addition, we found out that the system spontaneously breaks time-reversal symmetry if the nearest-neighbor interaction strength is large. Due to the time-reversal symmetry breaking, the system has topologically non-trivial phases characterized by nonzero Chern numbers. Finally, there were also cases where the time-reversal symmetry was broken in the FFLO phase, and thus we found a phase where spatial and time-reversal symmetries are simultaneously broken. Tiivistelmä Tässä väitöskirjassa käsitellään bosonisia ja fermionisia kvanttikaasuja. Työn ensimmäisessä osassa mallinnetaan eräässä Bose-kaasussa tehdyn Braggin sirontakokeen tulokset variaatiolaskentaan perustuvan monen kappaleen teorian avulla. Kokeessa sirontapituus pystyttiin säätämään suureksi Feshbach-resonanssin avulla ja tämän takia olemassa olevia malleja ei voitu käyttää tulosten selittämiseen. Tämä teki kokeesta erityisen kiinnostavan tutkimuskohteen. Ensin kehitimme joukon ad hoc -potentiaaleja, joilla sovitimme havaitun eksitaatiospektrin. Myöhemmin hyödynsimme T-matriisiformalismia Feshbach-resonanssin kuvaamisessa ja tällöin pystyimme mallintamaan myös sidottujen tilojen energioita. Yhteenvetona mallista voidaan todeta, että se mallintaa havaitun eksitaatiospektrin ja antaa oikean sidotun tilan energian joissain tapauksissa.Tämän työn toisessa osassa tutkitaan fermionisia kvanttikaasuja. Erityisesti tutkimme spinriippuvaan optiseen hilaan vangittuja spin-1/2 hiukkasia. Hilageometriassa ylös-spin komponentti liikkuu hunaja...

We study the dynamic structure function of ultracold alkali-metal gases for large scattering lengths and momenta where corrections to the mean field approximation become important. We compare our result with the Bragg-scattering measurements in 85 Rb by Papp et al. (Phys. Rev. Lett. 101:135301, 2008) and show that these experiments set very strict limits to the shape of the effective two-particle interaction ruling out the contact and hard spheres potentials. Using the Feshbach resonance approximation we derive the effective interaction, which turns out to be very similar to the soft spheres potential in momentum space. At large scattering lengths the interaction becomes universal and could be directly measured by Bragg scattering. We also discuss the experimental conditions needed for the appearance of the maxonroton structure in the excitation spectrum and finally show that when the scattering length becomes larger than 2000 Bohr radii the uniform gas phase undergoes a phase transition into the density wave state.

We study fermions in a lattice, with on-site and nearest neighbor attractive interactions between two spin species. We consider two geometries: (1) both spins in a triangular lattice and (2) a mixed geometry with up spins in honeycomb and down spins in triangular lattices. We focus on the interplay between spin-population imbalance, on-site and valence bond pairing, and order parameter symmetry. The mixed geometry leads to a rich phase diagram of topologically nontrivial phases. In both geometries, we predict order parameters with simultaneous time-reversal and translational symmetry breaking.