72,728 research outputs found

    Lagrange multipliers for evolution problems with constraints on the derivatives

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    We prove the existence of generalized Lagrange multipliers for a class of evolution problems for linear differential operators of different types subject to constraints on the derivatives. Those Lagrange multipliers and the respective solutions are stable for the vanishing of the coercive parameter and are naturally associated with evolution variational inequalities with time-dependent convex sets of gradient type. We apply these results to the sandpile problem, to superconductivity problems, to flows of thick fluids, to problems with the biharmonic operator, and to first order vector fields of subelliptic type.The research of A. Azevedo and L. Santos was partially supported by the Research Centre of Mathematics of the University of Minho with the Portuguese Funds from the “Fundação para a Ciência e a Tecnologia,” through the Project UID/MAT/00013/2013, and the one by J. F. Rodrigues was done partially in the framework of the Project PTDC/MAT-PUR/28686/2017

    Tensor network approach to the fully frustrated XY model on a kagome lattice with a fractional vortex-antivortex pairing transition

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    We have developed a tensor network approach to the two-dimensional fully frustrated classical XY spin model on the kagome lattice, and clarified the nature of the possible phase transitions of various topological excitations.We find that the standard tensor network representation for the partition function does not work due to the strong frustrations in the low temperature limit. To avoid the direct truncation of the Boltzmann weight, based on the duality transformation, we introduce a new representation to build the tensor network with local tensors lying on the centers of the elementary triangles of the kagome lattice. Then the partition function is expressed as a product of one-dimensional transfer matrix operators, whose eigen-equation can be solved by the variational uniform matrix product state algorithm accurately. The singularity of the entanglement entropy for the one-dimensional quantum operator provides a stringent criterion for the possible phase transitions. Through a systematic numerical analysis of thermodynamic properties and correlation functions in the thermodynamic limit, we prove that the model exhibits a single Berezinskii-Kosterlitz-Thouless phase transition only, which is driven by the unbinding of 1/31/3 fractional vortex-antivortex pairs determined at Tc0.075J1T_{c}\simeq 0.075J_{1} accurately. The absence of long-range order of chirality or quasi-long range order of integer vortices has been verified in the whole finite temperature range. Thus the long-standing controversy about the phase transitions in this fully frustrated XY model on the kagome lattice is solved rigorously, which provides a plausible way to understand the charge-6e superconducting phase observed experimentally in the two-dimensional kagome superconductors.Comment: 14 pages, 13 figures, submitted version for publicatio

    Conceptual Design of a Liquid Helium Vertical Test-Stand for 2m long Superconducting Undulator Coils

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    Superconducting Undulators (SCUs) can produce higher photon flux and cover a wider photon energy range compared to permanent magnet undulators (PMUs) with the same vacuum gap and period length. To build the know-how to implement superconducting undulators for future upgrades of the European XFEL facility, the test stand SUNDAE1 for the characterization of SCU is being developed. The purpose of SUNDAE1 is the training, tuning and development of new SCU coils by means of precise magnetic field measurements. The experimental setup will allow the characterization of magnets up to 2m in length. These magnets will be immersed in a Helium bath at 4K or 2K temperature. In this article, we describe the experimental setup and highlight its expected performances

    Engineering anomalous Floquet Majorana modes and their time evolution in helical Shiba chain

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    We theoretically explore the Floquet generation of Majorana end modes~(MEMs) (both regular 00- and anomalous π\pi-modes) implementing a periodic sinusoidal modulation in chemical potential in an experimentally feasible setup based on one-dimensional chain of magnetic impurity atoms having spin spiral configuration fabricated on the surface of most common bulk ss-wave superconductor. We obtain a rich phase diagram in the parameter space, highlighting the possibility of generating multiple 00-/π\pi-MEMs localized at the end of the chain. We also study the real-time evolution of these emergent MEMs, especially when they start to appear in the time domain. These MEMs are topologically characterized by employing the dynamical winding number. We also discuss the possible experimental parameters in connection to our model. Our work paves the way to realize the Floquet MEMs in a magnet-superconductor heterostructure.Comment: 7.5 Pages + 5 PDF figures (Main Text), 4 Pages + 3 PDF figures (Supplementary Material), Comments are welcom

    Similarities and Differences in the Fermiology of Kagome Metals AV3_{3}Sb5_{5} (A=K, Rb, Cs) Revealed by Shubnikov-de Haas Oscillations

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    Materials with AV3_3Sb5_5 (A=K, Rb, Cs) stoichiometry are recently discovered kagome superconductors with the electronic structure featuring a Dirac band, van Hove singularities and flat bands. These systems undergo anomalous charge-density-wave (CDW) transitions at TCDWT_{\rm CDW}~80-100 K, resulting in the reconstruction of the Fermi surface from the pristine phase. Although comprehensive investigations of the electronic structure via quantum oscillations (QOs) have been performed on the sister compounds CsV3_3Sb5_5 and RbV3_3Sb5_5, a detailed QO study of KV3_3Sb5_5 is so far absent. Here, we report the Shubnikov-de Haas QO study in KV3_3Sb5_5. We resolve a large number of new frequencies with the highest frequency of 2202 T (occupying ~54% of the Brillouin zone area in the kxk_x-kyk_y plane). The Lifshitz-Kosevich analysis further gives relatively small cyclotron effective masses, and the angular dependence study reveals the two-dimensional nature of the frequencies with a sufficient signal-to-noise ratio. Finally, we compare the QO spectra for all three AV3_3Sb5_5 compounds collected under the same conditions, enabling us to point out the similarities and differences across these systems. Our results fill in the gap of the QO study in KV3_3Sb5_5 and provide valuable data to understand the band structure of all three members of AV3_3Sb5_5.Comment: 8 pages, 4 figure

    Bipolar thermoelectricity in S/I/NS and S/I/SN superconducting tunnel junctions

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    Recent studies have shown the potential for bipolar thermoelectricity in superconducting tunnel junctions with asymmetric energy gaps. The thermoelectric performance of these systems is significantly impacted by the inverse proximity effects present in the normal-superconducting bilayer, which is utilized to adjust the gap asymmetry in the junction. Here, we identify the most effective bilayer configurations, and we find that directly tunnel-coupling the normal metal side of the bilayer with the other superconductor is more advantageous compared to the scheme used before. By utilizing quasiclassical equations, we examined the nonlinear thermoelectric junction performance as a function of the normal metal film thickness and the quality of the normal-superconducting interface within the bilayer, thereby determining the optimal design to observe and maximize this nonequilibrium effect. Our results offer a roadmap to achieve improved thermoelectric performance in superconducting tunnel junctions, with promising implications for a number of applications.Comment: 5 pages, 3 figure

    Dynamic dielectric function and phonon self-energy from electrons strongly correlated with acoustic phonons in 2D Dirac crystals

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    The unique structure of two-dimensional (2D) Dirac crystals, with electronic bands linear in the proximity of the Brillouin-zone boundary and the Fermi energy, creates anomalous situations where small Fermi-energy perturbations are known to critically affect the electron-related lattice properties of the system. The Fermi-surface nesting (FSN) conditions determining such effects via electron-phonon interaction, require accurate estimates of the crystal's response function (χ)(\chi) as a function of the phonon wavevector q for any values of temperature. Numerous analytical estimates of χ(q)\chi(q) for 2D Dirac crystals beyond the Thomas-Fermi approximation have been so far carried out only in terms of dielectric response function χ(q,ω)\chi(q,\omega), for photon and optical-phonon perturbations, due to relative ease of incorporating a q-independent oscillation frequency in their calculation. However, models accounting for Dirac-electron interaction with ever-existing acoustic phonons, for which ω\omega does depend on q and is therefore dispersive, are essential to understand many critical crystal properties. The lack of such models has often led to assume that the dielectric response function χ(q)\chi(q) in these systems can be understood from free-electron behavior. Here, we show that, different from free-electron systems, χ(q)\chi(q) calculated from acoustic phonons in 2D Dirac crystals using the Lindhard model, exhibits a cuspidal point at the FSN condition. Strong variability of χq\frac{\partial\chi}{\partial q} persists also at finite temperatures, while χ(q)\chi(q) may tend to infinity in the dynamic case even where the speed of sound is small, albeit nonnegligible, over the Dirac-electron Fermi velocity. The implications of our findings for electron-acoustic phonon interaction and transport properties such as the phonon line width derived from the phonon self energy will also be discussed

    Resonant and polarization effects in the processes of quantum electrodynamics in a strong magnetic field

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    The monograph considers resonance and polarization effects in quantum electrodynamics processes that take place in a strong external magnetic field. A method for analyzing spin-polarization effects has been developed. The factorization of process cross sections in resonant conditions and the representation of these cross sections in the form of Breit-Wigner are considered. The possibility of testing these effects in modern international projects to test quantum electrodynamics in strong fields is shown.Comment: 283 pages, 24 figures, monograp

    Scanning tunneling microscopy and spectroscopy study of layered transition metal chalcogenide thin films tuned by thickness, structural phase, and heterostructure

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    Layered transition metal chalcogenides (TMCs) have a long and fruitful history, exhibiting diverse properties and interesting quantum phenomena, such as superconductivity, charge density wave (CDW), and non-trivial topological states. Since the discovery that layered materials can be exfoliated to two-dimensional (2D) sheets, such as graphene, 2D TMCs have attracted vast interest for both fundamental study and technological development. More often than not, the thin film samples behave differently from the corresponding bulk single crystals. For example, monolayer WTe2 is a quantum spin Hall insulator, a novel phase of quantum matter, while bulk WTe2 is a Weyl semimetal. Moreover, the electronic and magnetic properties of thin films are able to be tuned by various methods, including chemically doping, electrically gating, varying the structural phase, changing the sample thickness, constructing heterostructures with other 2D materials, and mechanically manipulation. This thesis presents experimental results on the effect of the number of layers, lattice structure, and heterostructure in several thin-film systems. To synthesize the high-quality samples, a home-built molecular beam epitaxy system was utilized to precisely control the thickness and structural phase. The films were characterized by scanning tunneling microscopy and spectroscopy. Our finds are the following. The 1T-VSe2 samples, grown at low temperatures, display different CDW patterns on the first and second layers. In contrast, a novel phase, i.e. distorted 1T, is obtained in the second layer by elevating the growth temperature by 250 C. No CDW is observed in this phase. The same phase engineering strategy was adopted for NbSe2 growth. While monolayer 1H-NbSe2 is demonstrated to host unconventional superconductivity, the Mott insulating ground state and strong evidence for the presence of spinon Fermi surface are disclosed in metastable 1T-NbSe2 monolayers. Besides, thin films of FeSexTe(1-x) grown on single-crystal Bi2Te3$ were systematically investigated under a low-temperature scanning tunneling microscope. Three different heterostructures coexist in the sample. At 0.3 K, the superconductivity appears in all three kinds of FeSexTe(1-x) islands, but with strikingly different gap sizes and depths. The data analysis from the phase-sensitive quasiparticle interference technique implies an odd-parity s+- pairing in superconducting states.LimitedAuthor requested closed access (OA after 2yrs) in Vireo ETD syste

    The passage of time and top-down causation

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    It is often claimed that the fundamental laws of physics are deterministic and time-symmetric and that therefore our experience of the passage of time is an illusion. This paper will critically discuss these claims and show that they are based on the misconception that the laws of physics are an exact and complete description of nature. I will argue that all supposedly fundamental deterministic and time-symmetric laws have their limitations and are supplemented by stochastic and irreversible elements. In fact, a deterministic description of a system is valid only as long as interactions with the rest of the world can be ignored. The most famous example is the quantum measurement process that occurs when a quantum system interacts with a macroscopic environment such as a measurement apparatus. This environment determines in a top-down way the possible outcomes of the measurement and their probabilities. I will argue that more generally the possible events that can occur in a system and their probabilities are the result of top-down influences from the wider context. In this way the microscopic level of a system is causally open to influences from the macroscopic environment. In conclusion, indeterminism and irreversibility are the result of a system being embedded in a wider context.Comment: This paper is based on a talk given at the MG16 conference in July 2021, and it appeared this year in the proceedings of this conference (online, open access, and print