Impurity states in the quantum spin Hall phase in graphene

Two-dimensional insulators with time-reversal symmetry can have two topologically different phases, the quantum spin Hall and the normal phase. The former is revealed by the existence of conducting edge states that are topologically protected. Here we show that the reaction to impurity, in bulk, is radically different in the two phases and can be used as a marker for the topological phase. Within the context of the Kane-Mele model for graphene, we find that strictly normalizable in-gap impurity states only occur in the quantum spin Hall phase and carry a dissipationless current whose chirality is determined by the spin and pseudospin of the residing electron.

Outer crust of a cold non-accreting magnetar

The outer-crust structure and composition of a cold, non-accreting magnetar are studied. We model the outer crust to be made of fully equilibrated matter where ionized nuclei form a Coulomb crystal embedded in an electron gas. The main effects of the strong magnetic field are those of quantizing the electron motion in Landau levels and of modifying the nuclear single-particle levels producing, on average, an increased binding of nucleons in nuclei present in the Coulomb lattice. The effect of a homogeneous and constant magnetic field on nuclear masses has been predicted by using a covariant density functional in which induced currents and axial deformation due to the presence of a magnetic field that breaks time-reversal symmetry have been included self-consistently in the nucleon and meson equations of motion. Although not yet observed, for Ba 1016 G both effects contribute to produce different compositions - odd-mass nuclei are frequently predicted - and to increase the neutron-drip pressure as compared to a typical neutron star. Specifically, in such a regime, the magnetic-field effects on nuclei favor the appearance of heavier nuclei at low pressures. As B increases, such heavier nuclei are also preferred up to larger pressures. For the most extreme magnetic field considered, B=1018 G, and for the models studied, almost the whole outer crust is made of 4092Zr52.

Computation of relativistic symmetry orbitals for finite double point groups

A program is presented for the construction of relativistic symmetry-adapted molecular basis functions. It is applicable to 36 finite double point groups. The algorithm, based on the projection operator method, automatically generates linearly independent basis sets. Time reversal invariance is included in the program, leading to additional selection rules in the non-relativistic limit.

Generalising unitary time evolution

In this third Quantum Interaction (QI) meeting it is time to examine our failures. One of the weakest elements of QI as a field, arises in its continuing lack of models displaying proper evolutionary dynamics. This paper presents an overview of the modern generalised approach to the derivation of time evolution equations in physics, showing how the notion of symmetry is essential to the extraction of operators in quantum theory. The form that symmetry might take in non-physical models is explored, with a number of viable avenues identified.

Transport across a junction of topological insulators and a superconductor

We study transport across a line junction lying between two orthogonal topological insulator surfaces and a superconductor which can have either s-wave (spin-singlet) or p-wave (spin-triplet) pairing symmetry. The junction can have three time-reversal invariant barriers on three sides. We compute the charge and the spin conductance across such a junction and study their behaviors as a function of the bias voltage applied across the junction and the three parameters used to characterize the barrier. We find that the presence of topological insulators and a superconductor leads to both Dirac- and Schrodinger-like features in charge and spin conductances. We discuss the effect of bound states on the superconducting side of the barrier on the conductance; in particular, we show that for triplet p-wave superconductors, such a junction may be used to determine the spin state of its Cooper pairs. Our study reveals that there is a nonzero spin conductance for some particular spin states of the triplet Cooper pairs; this is an effect of the topological insulators which break the spin rotation symmetry. Finally, we find an unusual satellite peak (in addition to the usual zero bias peak) in the spin conductance for p-wave symmetry of the superconductor order parameter.

Deep tissue fluorescence imaging with time-reversed light

Advances in optical techniques have enabled many breakthroughs in biology and medicine. However, light scattering by biological tissues remains a great obstacle, restricting the use of optical methods to thin ex vivo sections or superficial layers in vivo. In this thesis, we present two related methods that overcome the optical depth limit—digital time reversal of ultrasound encoded light (digital TRUE) and time reversal of variance-encoded light (TROVE). These two techniques share the same principle of using acousto-optic beacons for time reversal optical focusing within highly scattering media, like biological tissues. Ultrasound, unlike light, is not significantly scattered in soft biological tissues, allowing for ultrasound focusing. In addition, a fraction of the scattered optical wavefront that passes through the ultrasound focus gets frequency-shifted via the acousto-optic effect, essentially creating a virtual source of frequency-shifted light within the tissue. The scattered ultrasound-tagged wavefront can be selectively measured outside the tissue and time-reversed to converge at the location of the ultrasound focus, enabling optical focusing within deep tissues. In digital TRUE, we time reverse ultrasound-tagged light with an optoelectronic time reversal device (the digital optical phase conjugate mirror, DOPC). The use of the DOPC enables high optical gain, allowing for high intensity optical focusing and focal fluorescence imaging in thick tissues at a lateral resolution of 36 µm by 52 µm. The resolution of the TRUE approach is fundamentally limited to that of the wavelength of ultrasound. The ultrasound focus (~ tens of microns wide) usually contains hundreds to thousands of optical modes, such that the scattered wavefront measured is a linear combination of the contributions of all these optical modes. In TROVE, we make use of our ability to digitally record, analyze and manipulate the scattered wavefront to demix the contributions of these spatial modes using variance encoding. In essence, we encode each spatial mode inside the scattering sample with a unique variance, allowing us to computationally derive the time reversal wavefront that corresponds to a single optical mode. In doing so, we uncouple the system resolution from the size of the ultrasound focus, demonstrating optical focusing and imaging between highly diffusing samples at an unprecedented, speckle-scale lateral resolution of ~ 5 µm. Our methods open up the possibility of fully exploiting the prowess and versatility of biomedical optics in deep tissues.

Formulação supersimétrica de processos estocásticos com ruído multiplicativo

Os processos estocásticos com ruído branco multiplicativo são objeto de atenção constante em uma grande área da pesquisa científica. A variedade de prescrições possíveis para definir matematicamente estes processos oferece um obstáculo ao desenvolvimento de ferramentas gerais para seu tratamento. Na presente tese, estudamos propriedades de equilíbrio de processos markovianos com ruído branco multiplicativo. Para conseguirmos isto, definimos uma transformação de reversão temporal de tais processos levando em conta que a distribuição estacionária de probabilidade depende da prescrição. Deduzimos um formalismo funcional visando obter o funcional gerador das funções de correlação e resposta de um processo estocástico multiplicativo representado por uma equação de Langevin. Ao representar o processo estocástico neste formalismo (de Grassmann) funcional eludimos a necessidade de fixar uma prescrição particular. Neste contexto, analisamos as propriedades de equilíbrio e estudamos as simetrias ocultas do processo. Mostramos que, usando uma definição apropriada da distribuição de equilíbrio e considerando a transformação de reversão temporal adequada, as propriedades usuais de equilíbrio são satisfeitas para qualquer prescrição. Finalmente, apresentamos uma dedução detalhada da formulação supersimétrica covariante de um processo markoviano com ruído branco multiplicativo e estudamos algumas das relações impostas pelas funções de correlação através das identidades de Ward-Takahashi.

Duality with time-changed Lévy processes

In this paper we study the pricing problem of derivatives written in terms of a two dimensional time{changed L¶evy processes. Then, we examine an existing relation between prices of put and call options, of both the European and the American type. This relation is called put{call duality. It includes as a particular case, the relation known as put{call symmetry. Necessary and su±cient conditions for put{call symmetry to hold are shown, in terms of the triplet of local charac- teristic of the Time{changed L¶evy process. In this way we extend the results obtained in Fajardo and Mordecki (2004) to the case of time{changed Lévy processes.

Soluções analíticas da equação de Duffin-Kemmer-Petiau

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Geometric and Combinatorial Aspects of NonEquilibrium Statistical Mechanics

Non-Equilibrium Statistical Mechanics is a broad subject. Grossly speaking, it deals with systems which have not yet relaxed to an equilibrium state, or else with systems which are in a steady non-equilibrium state, or with more general situations. They are characterized by external forcing and internal fluxes, resulting in a net production of entropy which quantifies dissipation and the extent by which, by the Second Law of Thermodynamics, time-reversal invariance is broken. In this thesis we discuss some of the mathematical structures involved with generic discrete-state-space non-equilibrium systems, that we depict with networks in all analogous to electrical networks. We define suitable observables and derive their linear regime relationships, we discuss a duality between external and internal observables that reverses the role of the system and of the environment, we show that network observables serve as constraints for a derivation of the minimum entropy production principle. We dwell on deep combinatorial aspects regarding linear response determinants, which are related to spanning tree polynomials in graph theory, and we give a geometrical interpretation of observables in terms of Wilson loops of a connection and gauge degrees of freedom. We specialize the formalism to continuous-time Markov chains, we give a physical interpretation for observables in terms of locally detailed balanced rates, we prove many variants of the fluctuation theorem, and show that a well-known expression for the entropy production due to Schnakenberg descends from considerations of gauge invariance, where the gauge symmetry is related to the freedom in the choice of a prior probability distribution. As an additional topic of geometrical flavor related to continuous-time Markov chains, we discuss the Fisher-Rao geometry of nonequilibrium decay modes, showing that the Fisher matrix contains information about many aspects of non-equilibrium behavior, including non-equilibrium phase transitions and superposition of modes. We establish a sort of statistical equivalence principle and discuss the behavior of the Fisher matrix under time-reversal. To conclude, we propose that geometry and combinatorics might greatly increase our understanding of nonequilibrium phenomena.

The search for the neutron electric dipole moment

A permanent electric dipole moment of the neutron violates time reversal as well as parity symmetry. Thus it also violates the combination of charge conjugation and parity symmetry if the combination of all three symmetries is a symmetry of nature. The violation of these symmetries could help to explain the observed baryon content of the Universe. The prediction of the Standard Model of particle physics for the neutron electric dipole moment is only about 10e−32 ecm. At the same time the combined violation of charge conjugation and parity symmetry in the Standard Model is insufficient to explain the observed baryon asymmetry of the Universe. Several extensions to the Standard Model can explain the observed baryon asymmetry and also predict values for the neutron electric dipole moment just below the current best experimental limit of d n < 2.9e−26 ecm, (90% C.L.) that has been obtained by the Sussex-RAL-ILL collaboration in 2006. The very same experiment that set the current best limit on the electric dipole moment has been upgraded and moved to the Paul Scherrer Institute. Now an international collaboration is aiming at increasing the sensitivity for an electric dipole moment by more than an order of magnitude. This thesis took place in the frame of this experiment and went along with the commissioning of the experiment until first data taking. After a short layout of the theoretical background in chapter 1, the experiment with all subsystems and their performance are described in detail in chapter 2. To reach the goal sensitivity the control of systematic errors is as important as an increase in statistical sensitivity. Known systematic efects are described and evaluated in chapter 3. During about ten days in 2012, a first set of data was measured with the experiment at the Paul Scherrer Institute. An analysis of this data is presented in chapter 4, together with general tools developed for future analysis eforts. The result for the upper limit of an electric dipole moment of the neutron is |dn| ≤ 6.4e−25 ecm (95%C.L.). Chapter 5 presents investigations for a next generation experiment, to build electrodes made partly from insulating material. Among other advantages, such electrodes would reduce magnetic noise, generated by the thermal movement of charge carriers. The last Chapter summarizes this work and gives an outlook.

On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schrödinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations and similar operators in detail. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive a non-local self-adjoint operator similar to the Schrödinger operator and also find the associated “charge conjugation” operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.

Time Reversed Electromagnetic Wave Propagation as a Novel Method of Wireless Power Transfer

We investigate the application of time-reversed electromagnetic wave propagation to transmit energy in a wireless power transmission system. “Time reversal” is a signal focusing method that exploits the time reversal invariance of the lossless wave equation to direct signals onto a single point inside a complex scattering environment. In this work, we explore the properties of time reversed microwave pulses in a low-loss ray-chaotic chamber. We measure the spatial profile of the collapsing wavefront around the target antenna, and demonstrate that time reversal can be used to transfer energy to a receiver in motion. We demonstrate how nonlinear elements can be controlled to selectively focus on one target out of a group. Finally, we discuss the design of a rectenna for use in a time reversal system. We explore the implication of these results, and how they may be applied in future technologies.

Information theory and one-dimensional disordered conductors

A novel method is proposed to treat the problem of the random resistance of a strictly one-dimensional conductor with static disorder. It is suggested, for the probability distribution of the transfer matrix of the conductor, the distribution of maximum information-entropy, constrained by the following physical requirements: 1) flux conservation, 2) time-reversal invariance and 3) scaling, with the length of the conductor, of the two lowest cumulants of ζ, where = sh2ζ. The preliminary results discussed in the text are in qualitative agreement with those obtained by sophisticated microscopic theories.

Information theory and resistance fluctuations in one-dimensional disordered conductors

A novel method is proposed to treat the problem of the random resistance of a strictly one-dimensional conductor with static disorder. For the probability distribution of the transfer matrix R of the conductor we propose a distribution of maximum information entropy, constrained by the following physical requirements: (1) flux conservation, (2) time-reversal invariance, and (3) scaling with the length of the conductor of the two lowest cumulants of ω, where R=exp(iω→⋅Jbhat). The preliminary results discussed in the text are in qualitative agreement with those obtained by sophisticated microscopic theories.