11,776 research outputs found

    Quantum Mechanics Lecture Notes. Selected Chapters

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    These are extended lecture notes of the quantum mechanics course which I am teaching in the Weizmann Institute of Science graduate physics program. They cover the topics listed below. The first four chapter are posted here. Their content is detailed on the next page. The other chapters are planned to be added in the coming months. 1. Motion in External Electromagnetic Field. Gauge Fields in Quantum Mechanics. 2. Quantum Mechanics of Electromagnetic Field 3. Photon-Matter Interactions 4. Quantization of the Schr\"odinger Field (The Second Quantization) 5. Open Systems. Density Matrix 6. Adiabatic Theory. The Berry Phase. The Born-Oppenheimer Approximation 7. Mean Field Approaches for Many Body Systems -- Fermions and Boson

    Barren plateaus in quantum tensor network optimization

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    We analyze the barren plateau phenomenon in the variational optimization of quantum circuits inspired by matrix product states (qMPS), tree tensor networks (qTTN), and the multiscale entanglement renormalization ansatz (qMERA). We consider as the cost function the expectation value of a Hamiltonian that is a sum of local terms. For randomly chosen variational parameters we show that the variance of the cost function gradient decreases exponentially with the distance of a Hamiltonian term from the canonical centre in the quantum tensor network. Therefore, as a function of qubit count, for qMPS most gradient variances decrease exponentially and for qTTN as well as qMERA they decrease polynomially. We also show that the calculation of these gradients is exponentially more efficient on a classical computer than on a quantum computer

    Band width estimates with lower scalar curvature bounds

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    A band is a connected compact manifold X together with a decomposition ∂X = ∂−X t ∂+X where ∂±X are non-empty unions of boundary components. If X is equipped with a Riemannian metric, the pair (X, g) is called a Riemannian band and the width of (X, g) is defined to be the distance between ∂−X and ∂+X with respect to g. Following Gromov’s seminal work on metric inequalities with scalar curvature, the study of Riemannian bands with lower curvature bounds has been an active field of research in recent years, which led to several breakthroughs on longstanding open problems in positive scalar curvature geometry and to a better understanding of the positive mass theorem in general relativity In the first part of this thesis we combine ideas of Gromov and Cecchini-Zeidler and use the variational calculus surrounding so called µ-bubbles to establish a scalar and mean curvature comparison principle for Riemannian bands with the property that no closed embedded hypersurface which separates the two ends of the band admits a metric of positive scalar curvature. The model spaces we use for this comparison are warped product over scalar flat manifolds with log-concave warping functions. We employ ideas from surgery and bordism theory to deduce that, if Y is a closed orientable manifold which does not admit a metric of positive scalar curvature, dim(Y ) 6= 4 and Xn≤7 = Y ×[−1, 1], the width of X with respect to any Riemannian metric with scalar curvature ≥ n(n − 1) is bounded from above by 2π n. This solves, up to dimension 7, a conjecture due to Gromov in the orientable case. Furthermore, we adapt and extend our methods to show that, if Y is as before and Mn≤7 = Y × R, then M does not admit a metric of positive scalar curvature. This solves, up to dimension 7 a conjecture due to Rosenberg and Stolz in the orientable case. In the second part of this thesis we explore how these results transfer to the setting where the lower scalar curvature bound is replaced by a lower bound on the macroscopic scalar curvature of a Riemannian band. This curvature condition amounts to an upper bound on the volumes of all unit balls in the universal cover of the band. We introduce a new class of orientable manifolds we call filling enlargeable and prove: If Y is filling enlargeable, Xn = Y × [−1, 1] and g is a Riemannian metric on X with the property that the volumes of all unit balls in the universal cover of (X, g) are bounded from above by a small dimensional constant εn, then width(X, g) ≤ 1. Finally, we establish that whether or not a closed orientable manifold is filling enlargeable or not depends on the image of the fundamental class under the classifying map of the universal cover

    Path integrals and stochastic calculus

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    Path integrals are a ubiquitous tool in theoretical physics. However, their use is sometimes hindered by the lack of control on various manipulations -- such as performing a change of the integration path -- one would like to carry out in the light-hearted fashion that physicists enjoy. Similar issues arise in the field of stochastic calculus, which we review to prepare the ground for a proper construction of path integrals. At the level of path integration, and in arbitrary space dimension, we not only report on existing Riemannian geometry-based approaches that render path integrals amenable to the standard rules of calculus, but also bring forth new routes, based on a fully time-discretized approach, that achieve the same goal. We illustrate these various definitions of path integration on simple examples such as the diffusion of a particle on a sphere.Comment: 96 pages, 4 figures. New title, expanded introduction and additional references. Version accepted in Advandes in Physic

    A Decision Support System for Economic Viability and Environmental Impact Assessment of Vertical Farms

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    Vertical farming (VF) is the practice of growing crops or animals using the vertical dimension via multi-tier racks or vertically inclined surfaces. In this thesis, I focus on the emerging industry of plant-specific VF. Vertical plant farming (VPF) is a promising and relatively novel practice that can be conducted in buildings with environmental control and artificial lighting. However, the nascent sector has experienced challenges in economic viability, standardisation, and environmental sustainability. Practitioners and academics call for a comprehensive financial analysis of VPF, but efforts are stifled by a lack of valid and available data. A review of economic estimation and horticultural software identifies a need for a decision support system (DSS) that facilitates risk-empowered business planning for vertical farmers. This thesis proposes an open-source DSS framework to evaluate business sustainability through financial risk and environmental impact assessments. Data from the literature, alongside lessons learned from industry practitioners, would be centralised in the proposed DSS using imprecise data techniques. These techniques have been applied in engineering but are seldom used in financial forecasting. This could benefit complex sectors which only have scarce data to predict business viability. To begin the execution of the DSS framework, VPF practitioners were interviewed using a mixed-methods approach. Learnings from over 19 shuttered and operational VPF projects provide insights into the barriers inhibiting scalability and identifying risks to form a risk taxonomy. Labour was the most commonly reported top challenge. Therefore, research was conducted to explore lean principles to improve productivity. A probabilistic model representing a spectrum of variables and their associated uncertainty was built according to the DSS framework to evaluate the financial risk for VF projects. This enabled flexible computation without precise production or financial data to improve economic estimation accuracy. The model assessed two VPF cases (one in the UK and another in Japan), demonstrating the first risk and uncertainty quantification of VPF business models in the literature. The results highlighted measures to improve economic viability and the viability of the UK and Japan case. The environmental impact assessment model was developed, allowing VPF operators to evaluate their carbon footprint compared to traditional agriculture using life-cycle assessment. I explore strategies for net-zero carbon production through sensitivity analysis. Renewable energies, especially solar, geothermal, and tidal power, show promise for reducing the carbon emissions of indoor VPF. Results show that renewably-powered VPF can reduce carbon emissions compared to field-based agriculture when considering the land-use change. The drivers for DSS adoption have been researched, showing a pathway of compliance and design thinking to overcome the ‘problem of implementation’ and enable commercialisation. Further work is suggested to standardise VF equipment, collect benchmarking data, and characterise risks. This work will reduce risk and uncertainty and accelerate the sector’s emergence

    Statistical-dynamical analyses and modelling of multi-scale ocean variability

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    This thesis aims to provide a comprehensive analysis of multi-scale oceanic variabilities using various statistical and dynamical tools and explore the data-driven methods for correct statistical emulation of the oceans. We considered the classical, wind-driven, double-gyre ocean circulation model in quasi-geostrophic approximation and obtained its eddy-resolving solutions in terms of potential vorticity anomaly and geostrophic streamfunctions. The reference solutions possess two asymmetric gyres of opposite circulations and a strong meandering eastward jet separating them with rich eddy activities around it, such as the Gulf Stream in the North Atlantic and Kuroshio in the North Pacific. This thesis is divided into two parts. The first part discusses a novel scale-separation method based on the local spatial correlations, called correlation-based decomposition (CBD), and provides a comprehensive analysis of mesoscale eddy forcing. In particular, we analyse the instantaneous and time-lagged interactions between the diagnosed eddy forcing and the evolving large-scale PVA using the novel `product integral' characteristics. The product integral time series uncover robust causality between two drastically different yet interacting flow quantities, termed `eddy backscatter'. We also show data-driven augmentation of non-eddy-resolving ocean models by feeding them the eddy fields to restore the missing eddy-driven features, such as the merging western boundary currents, their eastward extension and low-frequency variabilities of gyres. In the second part, we present a systematic inter-comparison of Linear Regression (LR), stochastic and deep-learning methods to build low-cost reduced-order statistical emulators of the oceans. We obtain the forecasts on seasonal and centennial timescales and assess them for their skill, cost and complexity. We found that the multi-level linear stochastic model performs the best, followed by the ``hybrid stochastically-augmented deep learning models''. The superiority of these methods underscores the importance of incorporating core dynamics, memory effects and model errors for robust emulation of multi-scale dynamical systems, such as the oceans.Open Acces

    Towards a more just refuge regime: quotas, markets and a fair share

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    The international refugee regime is beset by two problems: Responsibility for refuge falls disproportionately on a few states and many owed refuge do not get it. In this work, I explore remedies to these problems. One is a quota distribution wherein states are distributed responsibilities via allotment. Another is a marketized quota system wherein states are free to buy and sell their allotments with others. I explore these in three parts. In Part 1, I develop the prime principles upon which a just regime is built and with which alternatives can be adjudicated. The first and most important principle – ‘Justice for Refugees’ – stipulates that a just regime provides refuge for all who have a basic interest in it. The second principle – ‘Justice for States’ – stipulates that a just distribution of refuge responsibilities among states is one that is capacity considerate. In Part 2, I take up several vexing questions regarding the distribution of refuge responsibilities among states in a collective effort. First, what is a state’s ‘fair share’? The answer requires the determination of some logic – some metric – with which a distribution is determined. I argue that one popular method in the political theory literature – a GDP-based distribution – is normatively unsatisfactory. In its place, I posit several alternative metrics that are more attuned with the principles of justice but absent in the political theory literature: GDP adjusted for Purchasing Power Parity and the Human Development Index. I offer an exploration of both these. Second, are states required to ‘take up the slack’ left by defaulting peers? Here, I argue that duties of help remain intact in cases of partial compliance among states in the refuge regime, but that political concerns may require that such duties be applied with caution. I submit that a market instrument offers one practical solution to this problem, as well as other advantages. In Part 3, I take aim at marketization and grapple with its many pitfalls: That marketization is commodifying, that it is corrupting, and that it offers little advantage in providing quality protection for refugees. In addition to these, I apply a framework of moral markets developed by Debra Satz. I argue that a refuge market may satisfy Justice Among States, but that it is violative of the refugees’ welfare interest in remaining free of degrading and discriminatory treatment

    Interference mitigation in LiFi networks

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    Due to the increasing demand for wireless data, the radio frequency (RF) spectrum has become a very limited resource. Alternative approaches are under investigation to support the future growth in data traffic and next-generation high-speed wireless communication systems. Techniques such as massive multiple-input multiple-output (MIMO), millimeter wave (mmWave) communications and light-fidelity (LiFi) are being explored. Among these technologies, LiFi is a novel bi-directional, high-speed and fully networked wireless communication technology. However, inter-cell interference (ICI) can significantly restrict the system performance of LiFi attocell networks. This thesis focuses on interference mitigation in LiFi attocell networks. The angle diversity receiver (ADR) is one solution to address the issue of ICI as well as frequency reuse in LiFi attocell networks. With the property of high concentration gain and narrow field of view (FOV), the ADR is very beneficial for interference mitigation. However, the optimum structure of the ADR has not been investigated. This motivates us to propose the optimum structures for the ADRs in order to fully exploit the performance gain. The impact of random device orientation and diffuse link signal propagation are taken into consideration. The performance comparison between the select best combining (SBC) and maximum ratio combining (MRC) is carried out under different noise levels. In addition, the double source (DS) system, where each LiFi access point (AP) consists of two sources transmitting the same information signals but with opposite polarity, is proven to outperform the single source (SS) system under certain conditions. Then, to overcome issues around ICI, random device orientation and link blockage, hybrid LiFi/WiFi networks (HLWNs) are considered. In this thesis, dynamic load balancing (LB) considering handover in HLWNs is studied. The orientation-based random waypoint (ORWP) mobility model is considered to provide a more realistic framework to evaluate the performance of HLWNs. Based on the low-pass filtering effect of the LiFi channel, we firstly propose an orthogonal frequency division multiple access (OFDMA)-based resource allocation (RA) method in LiFi systems. Also, an enhanced evolutionary game theory (EGT)-based LB scheme with handover in HLWNs is proposed. Finally, due to the characteristic of high directivity and narrow beams, a vertical-cavity surface-emitting laser (VCSEL) array transmission system has been proposed to mitigate ICI. In order to support mobile users, two beam activation methods are proposed. The beam activation based on the corner-cube retroreflector (CCR) can achieve low power consumption and almost-zero delay, allowing real-time beam activation for high-speed users. The mechanism based on the omnidirectional transmitter (ODTx) is suitable for low-speed users and very robust to random orientation

    BECOMEBECOME - A TRANSDISCIPLINARY METHODOLOGY BASED ON INFORMATION ABOUT THE OBSERVER

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    ABSTRACT Andrea T. R. Traldi BECOMEBECOME A Transdisciplinary Methodology Based on Information about the Observer The present research dissertation has been developed with the intention to provide practical strategies and discover new intellectual operations which can be used to generate Transdisciplinary insight. For this reason, this thesis creates access to new knowledge at different scales. Firstly, as it pertains to the scale of new knowledge generated by those who attend Becomebecome events. The open-source nature of the Becomebecome methodology makes it possible for participants in Becomebecome workshops, training programmes and residencies to generate new insight about the specific project they are working on, which then reinforce and expand the foundational principles of the theoretical background. Secondly, as it pertains to the scale of the Becomebecome framework, which remains independent of location and moment in time. The method proposed to access Transdisciplinary knowledge constitutes new knowledge in itself because the sequence of activities, described as physical and mental procedures and listed as essential criteria, have never been found organised 6 in such a specific order before. It is indeed the order in time, i.e. the sequence of the ideas and activities proposed, which allows one to transform Disciplinary knowledge via a new Transdisciplinary frame of reference. Lastly, new knowledge about Transdisciplinarity as a field of study is created as a consequence of the heretofore listed two processes. The first part of the thesis is designated ‘Becomebecome Theory’ and focuses on the theoretical background and the intellectual operations necessary to support the creation of new Transdisciplinary knowledge. The second part of the thesis is designated ‘Becomebecome Practice’ and provides practical examples of the application of such operations. Crucially, the theoretical model described as the foundation for the Becomebecome methodology (Becomebecome Theory) is process-based and constantly checked against the insight generated through Becomebecome Practice. To this effect, ‘information about the observer’ is proposed as a key notion which binds together Transdisciplinary resources from several studies in the hard sciences and humanities. It is a concept that enables understanding about why and how information that is generated through Becomebecome Practice is considered of paramount importance for establishing the reference parameters necessary to access Transdisciplinary insight which is meaningful to a specific project, a specific person, or a specific moment in time
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