1,721,154 research outputs found
Hydrodynamics of Bose gases with internal degrees of freedom
No full textJust a couple decades ago bosonic low-temperature physics was synonymous with one particular liquid at a temperature of several degrees Kelvin. This liquid, helium-4, and its famous Helium-II phase, has revealed remarkable quantum properties such as quantized vortices and second sound. Yet, despite many things learned by investigating helium, its study has certain limitations. On the one hand, helium is a strongly interacting liquid, which makes first-principles theoretical research challenging. To name one example, establishing a connection between the non-interacting condensate state described by Bose and Einstein, and the helium properties observed in the lab took decades. Furthermore, helium is a specific chemical element, and hence there is no surprise that its physical properties are fixed by nature. However, every particular chemical element has particular physical properties, so for a long time it seemed that it was as good as it gets. The picture has changed drastically when the first Bose-Einstein condensate (BEC) was observed in an ultracold atomic gas. “Low temperature” has become synonymous with “ultracold”, and the latter implies temperatures on the order of nanokelvins. Most strikingly, the relationship between what is fixed by nature and what is experimentally changeable has evolved. In particular, systems of different particle statistics, spin, and interactions have been engineered using ultracold vapours of various alkali atoms. This versatile manipulation not only makes emulating various condensed-matter physics models in a controlled system without impurities possible, but also opens a path towards novel phenomena that are at present not achievable in any other manner. In this thesis, we have explored some of the novel phenomena that arise in systems of bosonic particles with internal degrees of freedom, such as (pseudo)spin and electric dipole moment. In the introduction, we describe a ferromagnetically coupled spin-1/2 Bose gas with contact interactions in the mean- field approximation. In particular, we compute and discuss the phase diagram of this gas, since it is a simple system which nevertheless has two order parameters. In the chapters that follow, the ideas touched upon in the introduction are developed in more detail. In Chapter 2 we develop a hydrodynamic description of the ferromagnetic spin-1/2 Bose gas at arbitrary temperatures. We study magnetization relaxation and geometric forces. In particular, we consider the topological Hall effect due to the presence of a skyrmion. In Chapter 3 we investigate the miscible (non-ferromagnetic) spin-1/2 Bose gas at arbitrary temperatures, construct its hydrodynamic description, calculate the thermodynamic properties, and study the collective modes of this system. In Chapter 4 we discuss the influence of the off-diagonal Berry curvature on the Bose-Einstein condensation temperature. Finally, in Chapter 5 we study a Bose-Einstein condensate of dipolar molecules in a weak electric field and find it to be described by a quantum rotor model. Moreover, we show that the molecular Bose-Einstein condensate is a ferroelectric material that is fully disordered by quantum fluctuations
Essays on how social network structure affects asymmetric coordination and trust
No full textNetwork structure has been put forward as a possible solution to
cooperation problems and social dilemmas. In the first part of this
dissertation, the effect of network structure is studied for a social
dilemma situation involving asymmetric coordination. The effects
of network properties on these coordination problems are studied
by means of agent-based models, models of statistical physics,
and a laboratory experiment. In the second part, we study the
question on how general trust can be established in societies that
are becoming more individualistic. The theory known as organic
solidarity argues that division of labor is one of the key foundations
of trust and solidarity between people. This proposition is studied
by quantifying aspects of the division of labor. We show that these
aspects are strongly related to general trust
Initial stages of Bose-Einstein condensation
No full textWe present the quantum theory for the nucleation of Bose-Einstein condensation in a dilute atomic Bose gas. This quantum theory confirms the results of the semiclassical treatment, but has the important advantage that both the kinetic and coherent stages of the nucleation process can now be described in a unified way by a single Fokker-Planck equation
Formation of the condensate in a dilute Bose gas
No full textWe examine the time evolution of a weakly interacting Bose gas in the course of the Bose-Einstein phase transition and show that, in contrast with previous claims in the literature, the relevant time scale for the appearance of the condensate is finite and, under the conditions we consider, of O(ħ/kBTc), which is very small compared to the characteristic lifetime of the system due to inelastic collisions in the gas
Field theory for trapped atomic gases
No full textIn this course we give a selfcontained introduction to the quantum field theory for trapped atomic gases, using functional methods throughout. We consider both equilibrium and nonequilibrium phenomena. In the equilibrium case, we first derive the appropriate Hartree—Fock theory for the properties of the gas in the normal phase. We then turn our attention to the properties of the gas in the superfluid phase, and present a microscopic derivation of the Bogoliubov and Popov theories of Bose-Einstein condensation and the Bardeen-Cooper-Schrieffer theory of superconductivity. The former are applicable to trapped bosonic gases such as rubidium, lithium, sodium and hydrogen, and the latter in particular to the fermionic isotope of atomic lithium. In the nonequilibrium case, we discuss various topics for which a field-theoretical approach is especially suited, because they involve physics that is not contained in the Gross-Pitaevskii equation. Examples are quantum kinetic theory, the growth and collapse of a Bose condensate, the phase dynamics of bosonic and fermionic superfluids, and the collisionless collective modes of a Bose gas below the critical temperature
Electric and heat transport in two-channel Kondo systems
No full textIn this thesis we theoretically study a certain class of materials, namely solids that have a crystal structure on the atomic scale, such as most metals, diamond and table salt. For such materials, quantum mechanics tells us that the electrons cannot simply do whatever they want, but can instead only be in very specific states. If there are many easily accessible states, the electrons can freely move around between the atoms that make up the material, such that the material supports electrical currents and is therefore a conductor; if this is not the case, the material is an insulator. However, materials or devices in which the electrons are strongly interacting often have much more complicated properties. The goal of this thesis is to advance our understanding of such exotic materials by studying the electric and thermal transport properties of a specific strongly interacting nanoelectronic quantum dot device. In practice, whether or not a material can have unconventional properties is often determined by measuring the electrical conductance and the heat conductance and calculating their ratio. One of the most important results of this thesis is that this common method does actually not always work: we provide an explicit example of a device with proven exotic behaviour, which does nevertheless not show any signs of such behaviour in the ratio of the electrical conductance and the heat conductance. This is an important step in the quest to properly understand strongly interacting materials, which can potentially have useful applications in future technology
Berry Curvature and Topology in Low-Dimensional Crystals
No full textThis thesis relies on two crucial concepts that for the past decades have been the subject of intense research in condensed matter physics: the electronic Berry curvature effects that appear in crystals and topological insulators. These concepts are deeply connected, making their first combined appearance in the description of the integer quantum Hall effect. Since then, a new way of classifying phases of matter based on band topology has emerged and a vast class of Berry curvature induced effects have been observed in condensed matter systems. In the first part of the thesis we investigate how the Berry curvature causes transverse currents, also known as Hall currents, to appear in two-dimensional crystals such as graphene. These exotic effects are responsible for the production of rectified currents which can potentially have numerous technological applications spanning from wireless communication to wireless charging. The last part of the research is about topological insulators, a special kind of insulating materials which have metallic edges. We study the transport properties of the quantum spin-Hall insulator and how these systems behave under strain gradients such as bending
Coherent versus incoherent dynamics during Bose-Einstein condensation in atomic gases
No full textWe review and extend the theory of the dynamics of Bose-Einstein condensation in weakly interacting atomic gases. We present in a unified way both the semiclassical theory as wel as the full quantum theory. This is achieved by deriving a Fokker-Planck equation that incorporates both the coherent and incoherent effects of the interactions in a dilute Bose gas. In first instance we focus our attention on the nonequilibrium dynamics of a homogeneous Bose gas with a positive interatomic scattering length. After that we discuss how our results can be generalized to the inhomogeneous situation that exists in the present experiments with magnetically trapped alkali gases, and how we can deal with a negative interatomic scattering length in that case as well. We also show how to arrive at a discription of the collective modes of the gas that obeys the Kohn theorem at all temperatures. The theory is based on the many-body T-matrix approximation throughout, since this aproximation has the coherent physical behaviour near the critical temperature and also treats the coherent and incoherent process taking place in the gas on an equal footing
Over quantumvloeistoffen en de koudste atomen ter wereld
No full textDe geschiedenis van de quantumvloeistoffen begint in 1924 met een artikel van Albert Einstein. Het wonderbaarlijke van dit artikel is dat Einstein hierin, nog voor de ontdekking van de quantummechanica en nog voordat er een serieus begin is gemaakt met de bestudering van faseovergangen, alleen op grond van statistische argumenten een juiste beschrijving geeft van een ideale quantumvloeistof en van de daarin bij extreem lage temperaturen optredende faseovergang, die nu bekent staat als Einsteincondensatie. Deze naam is bijzonder toepasselijk vanwege de grote analogie met het, zeker in Nederland, alom bekende verschijnsel van waterdamp die condenseert op een koud oppervlak
Macroscopic quantum tunneling of a Bose condensate
No full textWe study, by means of a variational method, the stability of a condensate in a megnetically trapped Bose gas with a negative scattering length and find that the condensate is unstable in general. However, for temperatures sufficiently close to the citical temperature the condensate turns out to be metastable. For that case we determine in the usual WKB approximation the decay rate of the condensate due to macroscopic quantum fluctuations. When appropiate, we also calculate the decay rate due to thermal fluctuations. An important feature of our approach is that (nonsingular) phase fluctuations of the condensate are taken into account exactly
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