Knots in Physics

After Dirac introduced the monopole, topological objects have played increasingly important roles in physics. In this review we discuss the role of the knot, the most sophisticated topological object in physics, and related topological objects in various areas in physics. In particular, we discuss how the knots appear in Maxwell's theory, Skyrme theory, and multi-component condensed matter physics.Comment: arXiv admin note: substantial text overlap with arXiv:1704.0597

Quantum Friction of Micromechanical Resonators at Low Temperatures

Dissipation of micro- and nano-scale mechanical structures is dominated by quantum-mechanical tunneling of two-level defects intrinsically present in the system. We find that at high frequencies--usually, for smaller, micron-scale structures--a novel mechanism of phonon pumping of two-level defects gives rise to weakly temperature-dependent internal friction, $Q^{-1}$, concomitant to the effects observed in recent experiments. Due to their size, comparable to or shorter than the emitted phonon wavelength, these structures suffer from superradiance-enhanced dissipation by the collective relaxation of a large number of two-level defects contained within the wavelength.Comment: To apear in Phys. Rev. Let

Integration over the quantum diagonal subgroup and associated Fourier-like algebras

By analogy with the classical construction due to Forrest, Samei and Spronk we associate to every compact quantum group $\mathbb{G}$ a completely contractive Banach algebra $A_\Delta(\mathbb{G})$, which can be viewed as a deformed Fourier algebra of $\mathbb{G}$. To motivate the construction we first analyse in detail the quantum version of the integration over the diagonal subgroup, showing that although the quantum diagonal subgroups in fact never exist, as noted earlier by Kasprzak and So{\l}tan, the corresponding integration represented by a certain idempotent state on $C(\mathbb{G})$ makes sense as long as $\mathbb{G}$ is of Kac type. Finally we analyse as an explicit example the algebras $A_\Delta(O_N^+)$, $N\ge 2$, associated to Wang's free orthogonal groups, and show that they are not operator weakly amenable.Comment: Minor updates; Remark 5.7 has been added; 31 page

Electrochemical electron beam lithography: Write, read, and erase metallic nanocrystals on demand.

We develop a solution-based nanoscale patterning technique for site-specific deposition and dissolution of metallic nanocrystals. Nanocrystals are grown at desired locations by electron beam-induced reduction of metal ions in solution, with the ions supplied by dissolution of a nearby electrode via an applied potential. The nanocrystals can be "erased" by choice of beam conditions and regrown repeatably. We demonstrate these processes via in situ transmission electron microscopy using Au as the model material and extend to other metals. We anticipate that this approach can be used to deposit multicomponent alloys and core-shell nanostructures with nanoscale spatial and compositional resolutions for a variety of possible applications

Density functional theory of the phase diagram of maximum density droplets in two-dimensional quantum dots in a magnetic field

We present a density-functional theory (DFT) approach to the study of the phase diagram of the maximum density droplet (MDD) in two-dimensional quantum dots in a magnetic field. Within the lowest Landau level (LLL) approximation, analytical expressions are derived for the values of the parameters $N$ (number of electrons) and $B$ (magnetic field) at which the transition from the MDD to a ``reconstructed'' phase takes place. The results are then compared with those of full Kohn-Sham calculations, giving thus information about both correlation and Landau level mixing effects. Our results are also contrasted with those of Hartree-Fock (HF) calculations, showing that DFT predicts a more compact reconstructed edge, which is closer to the result of exact diagonalizations in the LLL.Comment: ReVTeX 3.

Phase transitions and noise crosscorrelations in a model of directed polymers in a disordered medium

We show that effective interactions mediated by disorder between two directed polymers can be modelled as the crosscorrelation of noises in the Kardar-Parisi-Zhang (KPZ) equations satisfied by the respective free energies of these polymers. When there are two polymers, disorder introduces attractive interactions between them. We analyze the phase diagram in details and show that these interactions lead to new phases in the phase diagram. We show that, even in dimension $d=1$, the two directed polymers see the attraction only if the strength of the disorder potential exceeds a threshold value. We extend our calculations to show that if there are $m$ polymers in the system then $m$-body interactions are generated in the disorder averaged effective free energy.Comment: To appear in Phys. Rev. E(2000

Pembagian Harta Bersama Akibat Dari Perceraian (Studi Kasus Di Pengadilan Agama Kota Surakarta)

Penelitian ini bertujuan : 1) Untuk mengetahui pembagian harta bersama setelah perceraian menurut hukum Islam, hukum adat, dan hukum perdata, 2) Untuk mengetahui pertimbangan hakim dalam menentukan pembagian harta bersama setelah dinyatakan putusan cerai di Pengadilan Agama Surakarta. Jenis penelitian yang digunakan sesuai dengan pokok masalah yang akan diteliti yaitu jenis penelitian hukum normative. Metode pendekatan digunakan dalam penelitian ini adalah pendekatan yuridis normative. Sumber data dalam penelitian ini berupa data sekunder dan primer. Metode analisa data yang digunakan dalam penelitian ini adalah penelitian kepustakaan meliputi peraturan, literatur, dan yurisprudensi. Hasil penelitian dapat disimpulkan bahwa: 1)Pembagian harta bersama setelah perceraian menurut hukum Islam, hukum adat, dan hukum perdata: a) Pembagian harta bersama setelah perceraian menurut hukum Islam didasarkan pada Kompilasi Hukum Islam (KHI) khususnya pada Pasal 96 dan 97 KHI, yang menyebutkan bahwa pembagian harta bersama baik cerai hidup maupun cerai mati ini, masing-masing mendapat setengah dari harta bersama tersebut. b) Pembagian harta bersama setelah perceraian menurut hukum adat adalah menurut adat Jawa. Hukum adat Jawa di Surakarta menganut sistem kekerabatan Parental / Bilateral, yaitu sistem keturunan yang ditarik menurut garis orang tua, atau menurut garis dua sisi (bapak- ibu), dimana kedudukan pria dan wanita tidak dibedakan dalam pewarisan. Apabila perkawinan itu sudah lebih dari 5 tahun maka harta bawaan / harta asal sudah bercampur dengan harta bersama / harta gono gini, sehingga pembagiannya masing-masing suami istri mendapatkan ½ bagian dari harta bersama / harta gono gini tersebut. c) Pembagian harta bersama setelah perceraian menurut hukum perdata diatur dalam Kitab Undang-Undang Hukum Perdata, khususnya pada Pasal 119-138 KUH Perdata. Untuk ketentuan mengenai pengaturan atas pembagian serta besaran porsi perolehan masing-masing suami dan istri dari harta bersama apabila terjadi perceraian, baik cerai hidup maupun cerai mati atau cerai hidup dijumpai pada pasal 128 KUH Perdata: Setelah bubarnya harta bersama, kekayaan bersama mereka dibagi dua antara suami dan isteri, atau antara para ahli waris mereka, tanpa mempesoalkan dari pihak mana asal barang-barang itu. 2) Pertimbangan yang digunakan hakim dalam menetapkan putusan pembagian harta bersama adalah sebagai berikut: a) Pertimbangan yang mengacu pada alat bukti. Penggugat mengajukan bukti tulisan sehingga dapat memberikan keterangan dan keyakinan bagi hakim untuk menjatuhkan putusan yang menguntungkannya. Sedangkan Tergugat tidak dapat membantahnya. b) Pertimbangan yang mengacu pada Pasal 35 UUP No. 1 tahun 1974 yaitu harta benda yang diperoleh selama perkawinan menjadi harta bersama, sehingga pada saat terjadinya perceraian harta bersama tersebut dibagi sama rata antara bekas suami isteri. c) Pertimbangan yang mengacu pada Pasal 88 Kompilasi Hukum Islam, mengatur bahwa bila terdapat sengketa atas harta bersama, maka akan diserahkan kepada Pengadilan Agama yang berwenang. d) Pertimbangan yang mengacu pada Pasal 97 Kompilasi Hukum Islam mengenai presentase pembagian harta bersama. Sesuai dengan Putusan Pengadilan menetapkan pembagian harta bersama tersebut ½ (seperdua) bagian untuk penggugat dan ½ (seperdua) bagian untuk tergugat

Cytotoxic Complexes of Sodium Oleate with β-Lactoglobulin

pre-printA complex of α-lactalbumin and oleic acid has previously been shown to induce apoptosis in cancer cells in a number of in vitro and in vivo trials. This complex is called HAMLET or BAMLET, depending on the origin of α-la (human/bovine alpha-lactalbumin made lethal to tumour cells). In the current study, it was shown that bovine β-lactoglobulin (β-lg), upon binding sodium oleate (NaOle), the salt of oleic acid, also acquires cytotoxicity towards tumour cells (human monocytic cells U937), analogously to HAMLET/BAMLET complexes. The properties of the complex were characterized using FIR spectroscopy, HPLC and SDS-PAGE. It was shown that the level of covalent oligomerization (dimers and trimers) of β-lg increased with increasing the molar ratio of sodium oleate NaOle:β-lg in the preparation procedure. At the same time, increasing the molar ratio of NaOle:β-lg increased the cytotoxicity of the complex. The increase in cytotoxicity appeared to be dependent on the amount of bound NaOle in the complex, but not on the content of multimeric forms of β-lg. The NaOle/β-lg complex also showed similarity with BAMLET in penetrating the cell membrane and co-localizing with the cell nucleus. Furthermore, DNA fragmentation studies suggested that tumour cells (U937) treated with the complex died by apoptosis, as in the case of BAMLET, and healthy cells appeared to be less affected by treatment, as shown with model rat adrenal pheochromocytoma cells PC12. In conclusion, β-lg and NaOle can form complexes with apoptosis-inducing qualities comparable to those of BAMLET.The work was funded by the Irish Dairy Research Trust and The Department of Agriculture (Food Institutional Research Measure – FIRM project 08RDTMFRC650) under the National Development Plan 2007-2013. K. Lišková was funded under the TeagascWalsh Fellowship Scheme

Parity Effects in Stacked Nanoscopic Quantum Rings

The ground state and the dielectric response of stacked quantum rings are investigated in the presence of an applied magnetic field along the ring axis. For odd number $N$ of rings and an electric field perpendicular to the axis, a linear Stark effect occurs at distinct values of the magnetic field. At those fields energy levels cross in the absence of electric field. For even values of $N$ a quadratic Stark effect is expected in all cases, but the induced electric polarization is discontinuous at those special magnetic fields. Experimental consequences for related nanostructures are discussed.Comment: typos corrected, to appear Phys. Rev. B (Rapid Communication) 15 Au