Recently a new outlook on dealing with dipolar ultracold fermions based on density functional methods has received attention. A Thomas-Fermi treatment coupled with a variational approach has been developed for a collection of fermions trapped in a harmonic potential interacting via dipole-dipole forces. In this thesis, firstly our alternative formalism for Thomas-Fermi method by performing some calculations based on the Kohn-Sham formalism which is one of the main idea of density functional theory is investigated. Furthermore, density distributions are obtained dependent to the parameters / rescaled interaction strength, dipole-dipole energy and the trap parameter which determine the trap geometry based on this theory. The thesis starts with a brief outline of the density functional theory and theory of our system, continues with calculations based on this theory, which are free of any variational assumptions for the density profile. Moreover, results of density graphics for harmonic trap will be followed by discussion of comparison and contrast with Thomas-Fermi method based on the paper of Goral et al.. These discussions are mainly about the shape of the density distribution, variation of the cloud parameters and energy behaviours according to the rescaled interaction strength. The thesis concludes with an analysis of contribution of density functional theory to this fermionic system.

Thèse doctorat : Physique Théorique : Strasbourg 1 : 2006. / Titre provenant de l'écran-titre. Bibliogr. 10 p.

We study scalar-fermion models with Yukawa interaction on a space-time lat- tice. Such models can describe the Higgs sector of the Standard Model in the case when the Higgs particle is very heavy (few hundred GeV) and there are very heavy fermions whose masses are due to their Yukawa interactions with the Higgs field. We study a realistic model with four component scalar field as well as simplified models with one and two component scalar fields. We use a mean field approximation to calculate equations for critical lines in the large d (dimension of space-time) limit. These lines are in very good agreement with available Monte Carlo data for the models at d = 4. We calculate fermion correlation functions in the mean field and large d approximations to study properties of different phases in the lattice models. We find two distinct phases with vanishing expectation values of the scalar field. One (at small Yukawa coupling Y) contains massless fermions, while in the other (at large F) the fermions have masses larger than the scale given by the inverse lattice spacing. We find that in the latter phase fermions can form bosonic bound states. These states show up as poles in a four-fermion correlator. We discuss pos- sible continuum limits in the lattice scalar-fermion models. In particular, we show that a theory defined near the critical line separating the disordered phase from the phase with antiferromagnetic order is not unitary.

Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 2003. / "July 2003" Bibliography: leaves 101-107.

Thesis (Ph. D.)--Carleton University, 1992. / Also available in electronic format on the Internet.

Th.--Sci. phys.--Paris 6, 1979.

Made available in DSpace on 2014-12-02T11:16:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2014-02-26Bitstream added on 2014-12-02T11:20:54Z : No. of bitstreams: 1 000796467.pdf: 1758200 bytes, checksum: bfd4db6cb4fdc5f43c50532672283497 (MD5) / De acordo com o Phys. Rev. B 84, 201308(R) (2011), um estado de Majorana isolado na borda de uma longa cadeia de Kitaev em sua fase topológica e conectado a um ponto quântico, resulta em uma transmitância robusta de 1/2 no valor zero da voltagem. Neste trabalho, nós mostramos que a remoção de tal marca pode ser alcançada utilizando uma superfície metálica hospedando dois átomos adsorvidos em um cenário onde ocorre uma quebra de simetria no efeito Fano de tal sistema, que é realizável acoplando-se a cadeia de Kitaev a um desses átomos adsorvidos. Assim, a fim de detectar essa característica experimentalmente, deve-se aplicar o seguinte procedimento de dois estágios: (i) primeiro, em relação aos átomos adsorvidos, é necessário fixar pontas de AFM em valores opostos de voltagem (separação simétrica dos níveis ) e medir, através de uma ponta de STM, a condutância para baixas voltagens; (ii) depois disso, a medida de condutância deve ser repetida com as voltagens invertidas. Para | | longe do nível de energia de Fermi e para o caso de acoplamento forte entre a ponta de STM e o hospedeiro, esta estrutura revela na transmitância, uma anti-ressonância persistente localizada na voltagem zero e imune sob a permutação citada anteriormente, mas caracterizada por uma amplitude que flutua levemente ao redor de 1/2. Entretanto, no caso da ponta de STM atuando como uma sonda, o átomo adsorvido desacoplado da cadeia de Kitaev se torna completamente inerte e nenhuma flutuação é observada. Por consequência, a ponta de STM deve ser considerada no mesmo pé de igualdade com o sistema hospedeiro+átomos adsorvidos. Como resultado, nós verificamos que apesar da pequena diferença entre essas duas anti-ressonâncias de Majorana, a transmitância de baixas voltagens como função da separação simétrica produz dois comportamentos distintos, na qual um deles não é predito segundo a ... / According to the Phys. Rev. B 84, 201308(R) (2011), an isolated Majorana state bound to one edge of a long enough Kitaev chain in the topological phase and connected to a quantum dot, results in a robust transmittance of 1/2 at zero-bias. In this work, we show that the removal of such a hallmark can be achieved by using a metallic surface hosting two adatoms in a scenario where there is a lack of symmetry in the Fano effect, which is feasible by coupling the Kitaev chain to one of these adatoms. Thus in order to detect this feature experimentally, one should apply the following two-stage procedure: (i) first, attached to the adatoms, one has to lock AFM tips in opposite gate voltages (symmetric detuning of the levels ) and measure by an STM tip, the zero-bias conductance; (ii) thereafter, the measurement of the conductance is repeated with the gates swapped. For | | away from the Fermi energy and in the case of strong coupling tip-host, this approach reveals in the transmittance, a persistent dip placed at zero-bias and immune to the aforementioned permutation, but characterized by an amplitude that fluctuates slightly around 1/2. However, in the case of a tip acting as a probe, the adatom decoupled from the Kitaev chain becomes completely inert and no fluctuation is observed. Therefore, the STM tip must be considered in the same footing as the “host+adatoms” system. As a result, we have found that despite the small difference between these two Majorana dips, the zero-bias transmittance as a function of the symmetric detuning yields two distinct behaviors, in which one of them is unpredictable by the standard Fano’s theory. Therefore, to access such a non trivial pattern of Fano interference, the hypothesis of the STM tip acting as a probe should be discarded

Ultracold atomic systems have provided an ideal platform to study the physics of strongly interacting many body systems in an unprecedentedly controlled and clean environment. And, since fermions are the building blocks of visible matter, being naturally motivated we focus on the physics of ultracold fermionic systems in this thesis. There have been many recent experimental developments in these systems such as the creation of synthetic gauge fields, realization of dimensional crossover and realization of systems with synthetic dimensions. These developments pose many open theoretical questions, some of which we address in this thesis. We start the discussion by studying the spectral function of an ideal spin-12 Fermi gas in a harmonic trap in any dimensions. We discuss the performance of the local density approximation (LDA) in calculating the spectral function of the system by comparing it to exact numerical results. We show that the LDA gives better results for larger number of particles and in higher dimensions. Fermionic systems with quasi two dimensional geometry are of great importance because of their connections to the high-Tc superconducting cuprate materials. Keeping this in mind, we consider a spin-12 fermionic system in three dimensions interacting with a contact interaction and confined by a one dimensional optical potential in one direction. Using the Bogoliubov-de Gennes formalism, we show that with increasing the depth of the optical potential the three dimensional superfluid evolves into a two dimensional one by looking at the shifts in the radio-frequency spectrum of the system and the change in the binding energy of the pairs that are formed. The next topic of interest is studying the effect of synthetic gauge fields on the ultracold fermionic systems. We show that a synthetic non-Abelian Rashba type gauge field has experimentally observable signatures on the size and shape of a cloud of a system of non-interacting spin-12 Fermi system in a harmonic trap. Also, the synthetic gauge field in conjunction with the harmonic potential gives rise to ample possibilities of generating novel quantum Hamiltonians like the spherical geometry quantum Hall, magnetic monopoles etc. We then address the physics of fermions in “synthetic dimensions”. The hyperfine states of atoms loaded in a one dimensional optical lattice can be used as an extra dimension, called the synthetic dimension (SD), by using Raman coupling. This way a finite strip Hofstadter model is realized with a tunable flux per plaquette. The experimental realization of the SD system is most naturally possible in systems which also have SU(M) symmetric interactions between the fermions. The SU(M) symmetric interactions manifest as long-ranged along the synthetic dimension and is the root cause of all the novel physics in these systems. This rich physics is revealed by a mapping of the Hamiltonian of the system to a system of particles interacting via an SU(M) symmetric interaction under the influence of an SU(M) Zeeman field and a non-Abelian SU(M) gauge field. For example, this equivalence brings out the possibility of generating a non-local interaction between the particles at different sites; while the gauge filed mitigates the baryon (SU(M) singlet M-body bound states) breaking effect of the Zeeman field. As a result, the site localized SU(M) singlet baryon gets deformed and forms a “squished baryon”. Also, finite momentum dimers and resonance like states are formed in the system. Many body physics in the SD system is then studied using both analytical and numerical (Density Matrix Renormalization Group) techniques. This study reveals fascinating possibilities such as the formation of Fulde-Ferrell-Larkin-Ovchinnikov states even without any “imbalance” and the possibility to evolve a “ferromagnet” to a “superfluid” by the application of a magnetic field. Other novel fermionic phases with quasi-condensates of squished baryons are also demonstrated. In summary, the topics addressed in this thesis demonstrate the possibilities and versatilities of the ultracold fermionic systems used in conjunction with synthetic gauge fields and dimensions

In this thesis we investigate numerically SU(2) theories with Dirac—or Majorana—fermions in the adjoint representation. Majorana fermions have historically proven difficult to treat numerically; here, a change of basis is introduced that allows two Majorana fermions to be expressed in terms of one Dirac fermion. This also provides greater insight into the analysis of the properties of theories with Dirac fermions. Attention is focused on the SU(2) theory with a single Dirac flavour (or equivalently two Majorana flavours). Its lattice phase diagram, spectrum, and the anomalous dimension of the chiral condensate are investigated. We observe a long region of constant mass ratios and an anomalous dimension 0.9 ≲ γ∗ ≲ 0.95. The behaviour of the pion mass and the presence of a light scalar in particular point to behaviour that is not traditionally confining; instead the theory appears to lie in or near the conformal window. The topological susceptibility and instanton size distribution are also investigated, for the one-Dirac-flavour theory and additionally the pure-gauge and two-Dirac-flavour (Minimal Walking Technicolor) theories. The properties are found to not depend on number of flavours, indicating a quenching of the fermions in the topology, also consistent with (near-)conformal behaviour (as has previously been reported in studies of other observables for Minimal Walking Technicolor). The code used is described, and a high-performance computing benchmark developed from it is detailed. While the benchmark was originally developed to investigate the performance of different supercomputer architectures for the class of problems we are interested in. Due to the nature of the code on which it is based, it has an unusual flexibility in the demands it may place on machine’s performance characteristics, which may allow it to be applicable to problems outside of lattice physics. The benchmark is used to characterise a number of machines’ relative performance.

Dans cette thèse, nous avons étudié les propriétés électroniques de WS2 et WSe2 par µ-PL, spectroscopie Raman, absorption optique inter bande et µ-PL résolue en temps combinées avec des champs magnétiques intenses. Nous montrons que l'émission de l'exciton par rapport au trion dans les monocouches de WS2 et WSe2 est fonction de la puissance du laser utilisé pour l'excitation de la µ-PL. De plus, nous montrons que l'intensité de l'émission du trion peut être contrôlée indépendamment en utilisant une énergie d'excitation plus basse que la bande interdite. Il s'agit d'une preuve du contrôle de la densité de porteurs dans ces systèmes 2D. Nous avons également étudié la diffusion Raman en résonance dans une monocouche de WS2. Nous observons un mode acoustique (2LA), seulement 4cm-1 en-dessous du mode E12g. Nous montrons qu'en fonction du rapport des intensité et la largeur de ligne de chacun de ces deux pics, toute analyse qui néglige la présence de la mode 2LA peut conduire à une estimation incorrecte du nombre de couche. Les propriétés électroniques de chaque vallée d'une monocouche de WSe2 ont été sondées par µ-PL via l'étude de l'émission et de la polarisation des excitons neutres et chargés. Nous montrons que le temps de diffusion de l'exciton entre les vallées de K+ et K- est de l'ordre de plusieurs ps. Enfin, grâce à la magnéto-spectroscopie, nous mettons en évidence différents types de porteurs de charges entre la monocouche et le cristal massif. Nous montrons que dans la monocouche, les porteurs de charge se comportent comme des fermions massifs Dirac, tandis que dans le monocristal de WSe2 nous observons un comportement excitonique, décrit par le modèle de l'atome d'hydrogène / In this thesis, we have studied tungsten dichalcogenides (WS2 and WSe2) by means of steady-state µ-photoluminescence (µ-PL) and Raman spectroscopy, optical interband absorption and time-resolved µ-PL techniques in the visible spectral range combined with high magnetic fields. We demonstrate that the ratio between the trion and exciton emission can be tuned by varying the power of the laser used for excitation of the µ-PL in ungated monolayer WS2 and WSe2 samples. Moreover, the intensity of the trion emission can be independently tuned using additional sub band gap illumination. This is a direct evidence that we can control the density of carriers in a 2D system. We have investigated the resonant Raman scattering in a WS2 monolayer. We observe a second order longitudinal acoustic mode (2LA) at only 4cm-1 below the first order E12g mode. We demonstrate, that depending on the intensity ratio and the respective line widths of these two peaks, any analysis which neglects the presence of the 2LA mode can lead to a potentially incorrect assignment for the number of layers. The valley dynamics in monolayer WSe2 has been probed by monitoring the emission and polarization dynamics of neutral and charged excitons in µ-PL. We demonstrate that the exciton inter valley scattering between the K+ and K- valleys is in the order of several picoseconds. Finally, using magneto-spectroscopy studies, we reveal the very different nature of carriers in monolayer and bulk dichalcogenides. We demonstrate that in monolayer WSe2, the carriers behave as massive Dirac fermions, while in bulk WSe2 we observe a distinctly excitonic behavior which is best described within the hydrogen model