Quantum trajectories are investigated within the complex quantum Hamilton-Jacobi formalism. A unified description is presented for complex quantum trajectories for one-dimensional time-dependent and time-independent problems. Complex quantum trajectories are examined for the free Gaussian wave packet, the coherent state in the harmonic potential, and the the barrier scattering problems. We analyze the variations of the complex-valued kinetic energy, the classical potential, and the quantum potential along the complex quantum trajectories. For one-dimensional time-independent scattering problems, we demonstrate general properties and similar structures of the complex quantum trajectories and the quantum potentials. In addition, it is shown that a quantum vortex forms around a node in the wave function in complex space, and the quantized circulation integral originates from the discontinuity in the real part of the complex action. Although the quantum momentum field displays hyperbolic flow around a node, the corresponding Polya vector field displays circular flow. Moreover, local topologies of the quantum momentum function and the Polya vector field are thoroughly analyzed near a stagnation point or a pole (including circular, hyperbolic, and attractive or repulsive structures). The local structure of the quantum momentum function and the Polya vector field around a stagnation point are related to the first derivative of the quantum momentum function. However, the magnitude of the asymptotic structures for these two fields near a pole depends only on the order of the node in the wave function. Finally, quantum interference is investigated and it leads to the formation of the topological structure of quantum caves in space-time Argand plots. These caves consist of the vortical and stagnation tubes originating from the isosurfaces of the amplitude of the wave function and its first derivative. Complex quantum trajectories display helical wrapping around the stagnation tubes and hyperbolic deflection near the vortical tubes. Moreover, the wrapping time for a specific trajectory is determined by the divergence and vorticity of the quantum momentum field. The lifetime for interference features is determined by the rotational dynamics of the nodal line in the complex plane. Therefore, these results demonstrate that the complex quantum trajectory method provides a novel perspective for analysis and interpretation of quantum phenomena. / text

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The algebra of SU(2) is ubiquitous in physics, applicable both to the atomic spin states and the polarisation states of light. The method developed by Majorana and Schwinger to represent pure, symmetric spin-states of arbitrary value as a product of spin-1/2 states is a powerful tool that allows for a great conceptual and practical simplification. Foremost, it allows the representation of a qudit on the same geometry as a qubit, i.e., the Bloch sphere. An experimental implementation of the Majorana representation in the realm of quantum optics is presented. The technique allows the projection of arbitrary quantum states from a coherent state input. It is also shown that the method can be used to synthesise arbitrary interference patterns with unit visibility, and without resorting to quantum resources. In this context, it is argued that neither the shape nor the visibility of the interference pattern is a good measure of quantumness. It is only the measurement scheme that allows for the perceived quantum behaviour. The Majorana representation also proves useful in delineating uncertainty limits of states with a particular spin value. Issues with traditional uncertainty relations involving the SU(2) operators, such as trivial bounds for certain states and non-invariance, are thereby resolved with the presented pictorial solution. / <p>QC 20170428</p>

Bakgrund: Målet med de flesta investeringar är att nå en hög avkastning till låg risk. Tidigare forskning har identifierat möjligheter till att överträffa marknaden vilket motsäger hypotesen om den effektiva marknaden. Investeringar i småbolag har blivit alltmer attraktivt de senaste åren vilket lyfter frågan angående hur en investering i dessa aktier kan genomföras på ett framgångsrikt sätt. Småbolagsaktier, och framförallt de allra minsta aktierna sett till marknadsvärde, förknippas ofta med högre risk. Detta medför att det är av relevans att undersöka huruvida en riskjusterad överavkastning är möjlig vid en applicering av dessa med befintliga investeringsstrategier. Syfte: Syftet med denna uppsats är att analysera huruvida det existerar en småbolagseffekt på den svenska aktiemarknaden mellan 2007-2019. Studien syftar även till att undersöka om det går att generera riskjusterad överavkastning vid investeringar i småbolagsaktier genom att kombinera dessa med alternativa investeringsstrategier som momentumeffekten samt relativvärdering i form av bolag med låga EV/EBITDA- multiplar. Metod: Studien har genomförts med en kvantitativ metod och en deduktiv ansats. Nio portföljer har konstruerats utefter olika bolagsstorlekar samt olika investeringsstrategier under tidsperioden 2007-2019 på den svenska aktiemarknaden. Dessa portföljer har sedan utvärderats sett till både avkastning samt riskjusterad avkastning för att slutligen testas statistiskt genom parata t-test. Slutsats: En småbolagseffekt kunde inte observeras på den svenska aktiemarknaden under den studerade tidsperioden. De portföljer som baserades på bolagen med lägst marknadsvärde presterade en signifikant lägre avkastning än jämförelseindexet. Vid en applicering av momentumeffekten samt låga EV/EBITDA- multiplar på småbolag kunde däremot fyra av fyra portföljer observeras generera en riskjusterad överavkastning relativt jämförelseindexet. Denna överavkastning kunde dock inte säkerställas statistiskt och skulle därmed kunna vara slumpmässig. / Background: The goal of most investments is to achieve a high return at a low risk. Previous research has identified opportunities to exceed the market, which contradicts the efficient-market hypothesis. Investments in small enterprises have become increasingly popular in recent years, which raises the question of how an investment on these markets can be done successfully. Small company shares, and especially the smallest shares in terms of market value, are often associated with higher risk. This means that a study that investigates whether a risk-adjusted excess return is possible with the application of existing investment strategies is of relevance. Purpose: The aim of this study is to analyze whether there exists a small firm effect on the Swedish stock market between the years 2007-2019. The study also aims to investigate whether it is possible to generate risk-adjusted excess returns when investing in small companies and combine these investments with alternative strategies such as the momentum effect and relative valuation in terms of companies with low EV / EBITDA multiples. Methodology: The study was conducted with a quantitative methodology and a deductive design. Nine portfolios were designed with different company sizes and based on different investment strategies during the period 2007-2019 on the Swedish stock market. These portfolios have then been evaluated in terms of both returns and risk-adjusted returns and the results were then finally statistically tested through the implement of parwise t-tests. Conclusion: A small firm effect could not be observed on the Swedish stock market during the examined time period. The portfolios based on the companies with the lowest market value generated a significantly lower return than the benchmark index. Meanwhile, when applying the momentum effect and the strategy of low EV/EBITDA multiples on small companies, four out of four portfolios were found to generate a risk-adjusted excess return relative to the benchmark index. However, this excess return could not be statistically proven and could thus be the result of randomness.

The study examines how the investment strategy Magic Formula (Greenblatt, 2006) has performed on the Swedish stock market. It is also investigated how the performance is affected when the strategy is combined with momentum. Since the expected pension for future generations is expected to decline it is important to have private savings with as high return as possible. Therefore, it is relevant to investigate if simple investment strategies can be used to achieve higher return. The purpose with this study is to find out if the investment strategies Magic Formula and Magic Formula combined with momentum has had a higher risk-adjusted return than the benchmark index OMX30. The results show that both Magic Formula and Magic Formula combined with momentum yielded a higher risk-adjusted return than the benchmark index. The results also showed that Magic Formula yielded an even better risk-adjusted return when it was combined with momentum. We wish that the result that was found in this study will give inspiration to private investors in order to achieve a higher return in their savings and a more satisfactory pension in the future

Consideramos aqui a obtenção da parte inferior do espectro de energia-momento para modelos de Cromodinâmica Quântica (QCD) na rede, na formulação usando integral funcional com tempo imaginário e no regime de acoplamento forte, isto é, com o parâmetro de \"hopping\'\' &#954; > 0 satisfazendo 1 >> &#954; >> &#946; > 0, onde &#946; &#8801; g-20 é o parâmetro de acoplamento da interação dos campos de calibre entre si, aqui definidos na álgebra de Lie $SU(3)$. Consideramos modelos de QCD com campos fermiônicos de quarks com um ou dois sabores (isospin) e em $2+1$ e $3+1$ dimensões, com diferentes dimensionalidades para matrizes de spin. Analisamos o setor mesônico: o espectro de uma e duas partículas. Detectamos estados de um méson e obtivemos suas aberturas de massa. Detectamos também, dependendo do modelo tratado, estados ligados de dois mésons. A existência de estados ligados de um méson e um bárion foi também analisada / We consider the energy-momentum spectrum of lattice quantum chromodynamics (QCD) models, using the functional integral formulation, with imaginary time and in the strong coupling regime. This regime corresponds to taking the hopping parameter $\\kappa>0$ satisfying $1>>\\kappa>>\\beta>0$, where $\\beta\\equiv g_0^$ is the coupling parameter among the gauge fields, here defined in the $SU(3)$ Lie algebra. We consider QCD models with fermionic quark fields with one and two flavors (isospin) and in $2+1$ and $3+1$ dimensions, and different types of spin matrices. We analyzed the mesonic sector: one and two-particle spectra. We detected one-meson states and obtained their mass splittings. Depending on the model, two-meson states were also obtained. The existence of bound states of one baryon and one meson was also analyzed

O trabalho tem como objetivo identificar a existência do efeito momento, de comprar ações com alto desempenho relativo no passado e vender as de baixo desempenho relativo no passado, e do efeito contrário, de comprar ações com baixo desempenho relativo no passado e vender as de alto desempenho relativo no passado. A análise considerou 662 ações negociadas na BM&FBOVESPA entre julho de 1994 e junho de 2015, considerando quatro períodos de formação (3, 6, 9 e 12 meses) e seis de manutenção (3, 6, 9 e 12, 18 e 24 meses) das carteiras. A metodologia adotada para o efeito momento utiliza a abordagem de Jegadeesh e Titman (1993) e, para o efeito contrário, optou-se por De Bondt e Thaler (1985). A partir da identificação das carteiras vencedoras e perdedoras, passou-se a calcular as diferenças dos retornos acumulados mensais com uma janela móvel para expurgar o viés de seleção. Das 24 estratégias analisadas, verificou-se que apenas uma não apresentou significância para o efeito momento e rejeitou-se a hipótese de existência do efeito contrário. Constatou-se o efeito momento em 23 estratégias, sendo que duas apresentaram desempenho médio mensal superior ao Ibovespa no mesmo período, nas carteiras \"12x3\" e \"9x6\", respectivamente, de 1,60% e 1,48%. As principais contribuições do trabalho foram a adoção de uma carteira móvel para a avaliação do desempenho das carteiras, o amplo período utilizado na análise e o grande número de ativos, o que proporciona maior robustez aos resultados encontrados. / The work aims to find momentum effect, that buys stocks with relative high return in the past and sells stocks with relative poor return in the past, and the contrarian effect, that buys stocks with relative poor return in the past and sells stocks with relative high performance in the past. The analysis included 662 stocks traded on BM&FBOVESPA between July 1994 and June 2015, considering four formation periods (3, 6, 9 and 12 months) and six holding periods (3, 6, 9 and 12, 18 and 24 months) for the portfolios. The methodology adopted for momentum effect uses the theory of Jegadeesh and Titman (1993) and the contrarian effect uses De Bondt and Thaler (1985) theory. From the identification of winners\' portfolios and losers\' portfolios, it was calculated the differences in monthly cumulative returns with a rolling window to purge the selection bias. Of the 24 strategies analyzed, it was found that only one has no significance for momentum effect, and the hypothesis of contrarian effect was rejected. Momentum effect was found in 23 strategies, and two had average monthly performance superior to Ibovespa in the same period in the \"12x3\" portfolios and \"9x6\" portfolios, respectively, 1.60% and 1.48%. The main contributions of this study was to adopt a rolling window for evaluating the performance of the portfolios, the extended period used in the analysis and the large number of stocks, which provides greater robustness to the results found

Neste trabalho foi medido o alargamento Doppler de uma aniquilação elétron pósitron com o uso de um filtro angular. O Filtro angular reduz, substancialmente, a detecção de fótons provenientes de aniquilações de elétrons com baixo momento, enfatizando, desta forma, a contribuição de aniquilações com elétrons fortemente ligados. Foram medidos os espectros de coincidência para os ângulos de corte de 0,28°, 0,42° e 1.2°. Os resultados obtidos mostram que, conforme se aumenta o ângulo de corte, há uma redução das aniquilações com elétrons de valência em proporção muito maior do que para elétrons fortemente ligados. Foi determinada a transmissibilidade do filtro em função do ângulo entre as direções de emissão dos gamas, levando em conta todos os elementos do arranjo experimental para cada ângulo crítico, assim como a distribuição espacial da atividade da fonte radioativa. Um modelo simples foi utilizado para estimar teoricamente a dependência da dispersão da energia em função do ângulo de corte. Este modelo permitiu calcular o alargamento Doppler da radiação de aniquilação elétron pósitron. Os resultados obtidos mostram um bom acordo com os dados experimentais. Geralmente, estudos de aniquilação de pósitrons com elétrons fortemente ligados dependem de uma modelagem detalhada do espectro de coincidência, ou da medida dos fótons provenientes da aniquilação em coincidência com elétrons Auger. O filtro angular, desenvolvido neste trabalho se coloca como uma boa alternativa a estes métodos. / This work reports the measurement of the Doppler broadening of the electron-positron annihilation radiation using an angular filter. The angular filter substantially reduces the number of detected gamma-rays from positron annihilation with low momentum electrons, therefore emphasizing the contribution of bound electron. Four coincidence measurements of the emitted gamma-rays were done with arrangements corresponding to critical angles of 0.28°, 0.42°, 1.2°. The obtained results show that the relative intensity of annihilation with valence electrons decreases as the critical angle increases. The filter transmissibility as a function of the angle between the two gamma-rays emission directions was determined taking into account all the elements of the experimental arrangement for every critical angle as well as the spatial distribution of the source activity. A simple model was used to theoretically estimate the dependence of the energy dispersion on the critical angle. The model allows us to calculate the Doppler broadening of the electron-positron annihilation radiation, and the obtained results show good agreement with the experimental data. Usually, the study of positrons annihilation with inner electrons requires good detectors\' energy resolution and depends on either sophisticated modeling and statistical analysis of the coincidence spectra or the measurement of the annihilation gamma-rays in coincidence with Auger electrons. The use of the angular filter developed in this work is a good alternative to those procedures.

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