No description available.

No description available.

With the increasing demand for intelligent transportation systems (ITS), security and privacy requirements are paramount. This demand led to many proposals aimed at creating a Vehicular Public Key Infrastructure (VPKI) able to address such prerequisites. Among them, the Security Credential Management System (SCMS) is particularly promising, providing data authentication in a privacy-preserving manner and supporting the revocation of misbehaving vehicles. Namely, one of the main benefits of SCMS is its so-called butterfly key expansion process, which issues arbitrarily large batches of pseudonym certificates through a single request. Despite SCMS\'s appealing design, in this document, we show that its certificate issuing process can be improved. Namely, this protocol originally requires the vehicle to provide two separate public/private key pairs to registration authorities; we now propose an improved approach that unifies them into a single key pair. We also show that such performance gains come with no negative impact in terms of security, flexibility or scalability when compared to the original SCMS. Besides the improvement on the initial Elliptic Curve based protocol, we present a post-quantum version of the protocol using Ring Learning-with-errors (R-LWE) assumption. This new protocol has the same shape and features of the original one, but using R-LWE-based signature and encryption as underlying schemes and Lattices operation for the key issuing instead of Elliptic Curves. / Com o aumento da demanda por Sistemas de Transporte Inteligentes (ITS - intelligent transportation systems), requisitos de segurança de informação e privacidade são primordiais. Isso levou a muitas propostas visando a criação de uma infraestrutura de chave pública veicular (VPKI - Vehicular Public Key Infrastructure) capaz de atender esses requisitos. Entre estes, o Sistema de Gerenciamento de Credenciais de segurança (SCMS - Security Credential Management System) é particularmente promissor. Ele provê autenticação de dados de uma maneira a preservar a privacidade e também suporta revogação de veículos que apresentem comportamento inadequado. Especificamente, um dos principais benefícios do SCMS é o chamado processo de butterfly key expansion, que emite lotes arbitrariamente grandes de certificados para pseudônimos a partir de única requisição. Embora este protocolo originalmente exija que o veículo forneça dois pares de chaves públicas/privadas separadas para as autoridades de registro, aqui é proposta uma abordagem aprimorada que as unifica em um único par de chaves. Também é mostrado esse ganho de desempenho não causa nenhuma deterioração em termos de segurança, flexibilidade ou escalabilidade quando comparado ao SCMS original. Além das melhorias no protocolo original baseado em curvas elípticas, aqui é apresentada uma versão pós-quântica do protocolo usando a hipótese de segurança R-LWE (Ring Learning-with-errors). Este novo protocolo tem o mesmo formato e características do original, mas usa assinatura e cifração baseada em R-LWE como esquemas subjacentes e operações em reticulados para o processo de emissão de chaves em vez de curvas elípticas.

Lattice-based cryptography has generated considerable interest in the last two decades due toattractive features, including conjectured security against quantum attacks, strong securityguarantees from worst-case hardness assumptions and constructions of fully homomorphicencryption schemes. On the other hand, even though it is a crucial part of many lattice-basedschemes, Gaussian sampling is still lagging and continues to limit the effectiveness of this newcryptography. The first goal of this thesis is to improve the efficiency of Gaussian sampling forlattice-based hash-and-sign signature schemes. We propose a non-centered algorithm, with aflexible time-memory tradeoff, as fast as its centered variant for practicable size of precomputedtables. We also use the Rényi divergence to bound the precision requirement to the standarddouble precision. Our second objective is to construct Falcon, a new hash-and-sign signaturescheme, based on the theoretical framework of Gentry, Peikert and Vaikuntanathan for latticebasedsignatures. We instantiate that framework over NTRU lattices with a new trapdoor sampler.

This dissertation discusses a number of theoretical models of coupled bosonic modes, all closely related to the Bose-Hubbard dimer. In studying these models, we will repeatedly return to two unifying themes: the classical structure underlying quantum dynamics and the impact of weakly coupling a system to an environment. Or, more succinctly, semiclassical methods and open quantum systems. Our primary motivation for studying models such as the Bose-Hubbard is their relevance to ongoing ultracold atom experiments. We review these experiments, derive the Bose-Hubbard model in their context and briefly discuss its limitations in the first half of Chapter 1. In its second half, we review the theory of open quantum systems and the master equation description of the dissipative Bose-Hubbard model. This opening chapter constitutes a survey of existing results, rather than original work. In Chapter 2, we turn to the mean-field limit of the Bose-Hubbard model. After reviewing the striking localization phenomena predicted by the mean-field (and confirmed by experiment), we identify the first corrections to this picture for the dimer. The most interesting of these is the dynamical tunneling between the self-trapping points of the mean-field. We derive an accurate analytical expression for the tunneling rate using semiclassical techniques. We continue studying the dynamics near the self-trapping fixed points in Chapter 3, focusing on corrections to the mean-field that arise at larger nonlinearities and on shorter time scales than dynamical tunneling. We study the impact of dissipation on coherence and entanglement near the fixed points, and explain it in terms of the structure of the classical phase space. The last chapter of the dissertation is also devoted to a dissipative bosonic dimer model, but one arising in a very different physical context. Abandoning optical lattices, we consider the problem of formulating a quantum model of operation of the cylindrical anode magnetron, a vacuum tube crossed-field microwave amplifier. We derive an effective dissipative dimer model and study its relationship to the classical description. Our dimer model is a first step towards the analysis of solid-state analogs of such devices.

Over the past several decades, rapid progress has been made toward the accurate characterization and control of atoms, made possible largely by the development of narrow-linewidth lasers and techniques for trapping and cooling at ultracold temperatures. Extending this progress to molecules will have exciting implications for chemistry, condensed matter physics, and precision tests of physics beyond the Standard Model. These possibilities are all consequences of the richness of molecular structure, which is governed by physics substantially different from that characterizing atomic structure. This same richness of structure, however, increases the complexity of any molecular experiment manyfold over its atomic counterpart, magnifying the difficulty of everything from trapping and cooling to the comparison of theory with experiment. This thesis describes work performed over the past six years to establish the state of the art in manipulation and quantum control of ultracold molecules. Our molecules are produced via photoassociation of ultracold strontium atoms followed by spontaneous decay to a stable ground state. We describe a thorough set of measurements characterizing the rovibrational structure of very weakly bound (and therefore very large) ⁸⁸Sr₂ molecules from several different perspectives, including determinations of binding energies; linear, quadratic, and higher order Zeeman shifts; transition strengths between bound states; and lifetimes of narrow subradiant states. The physical intuition gained in these experiments applies generally to weakly bound diatomic molecules, and suggests extensive applications in precision measurement and metrology. In addition, we present a detailed analysis of the thermally broadened spectroscopic lineshape of molecules in a non-magic optical lattice trap, showing how such lineshapes can be used to directly determine the temperature of atoms or molecules in situ, addressing a long-standing problem in ultracold physics. Finally, we discuss the measurement of photofragment angular distributions produced by photodissociation, leading to an exploration of quantum-state-resolved ultracold chemistry.

Quasicrystals are long-range ordered and yet non-periodic. This interplay results in a wealth of intriguing physical phenomena, such as the inheritance of topological properties from higher dimensions, self-similarity, and the presence of non-trivial structure on all scales. The concept of aperiodic order has been extensively studied in mathematics and geometry, exemplified by the celebrated Penrose tiling. However, the understanding of physical quasicrystals (the vast majority of them are intermetallic compounds) is still incomplete owing to their complexity, regarding both growth processes and stability. Ultracold atoms in optical lattices offer an ideal, yet untested environment for investigating quasicrystals. Optical lattices, i.e. standing waves of light, allow the defect-free formation of a large variety of potential landscapes, including quasiperiodic geometries. In recent years, optical lattices have become one of the most successful tools in the large-scale quantum simulation of condensed-matter problems. This study presents the first experimental realisation of a two-dimensional quasicrystalline potential for ultracold atoms, based on an eightfold symmetric optical lattice. It is aimed at bringing together the fields of ultracold atoms and quasicrystals - and the more general concept of aperiodic order. The first part of this thesis introduces the theoretical aspects of aperiodic order and quasicrystalline structure. The second part comprises a detailed account of the newly designed apparatus that has been used to produce quantum-degenerate gases in quasicrystalline lattices. The third and final part summarises the matter-wave diffraction experiments that have been performed in various lattice geometries. These include one- and two-dimensional simple cubic lattices, one-dimensional quasiperiodic lattices, as well as two-dimensional quasicrystalline lattices. The striking self-similarity of this quasicrystalline structure has been directly observed, in close analogy to Shechtman's very first discovery of quasicrystals using electron diffraction. In addition, an in-depth study of the diffraction dynamics reveals the fundamental differences between periodic and quasicrystalline lattices, in excellent agreement with ab initio theory. The diffraction dynamics on short timescales constitutes a continuous-time quantum walk on a homogeneous four-dimensional tight-binding lattice. On the one hand, these measurements establish a novel experimental platform for investigating quasicrystals proper. On the other hand, ultracold atoms in quasicrystalline optical lattices are worth studying in their own right: Possible avenues include the observation many-body localisation and Bose glasses, as well as the creation of topologically non-trivial systems in higher dimensions.

Lu, Wenlong = 一维光格子中费米型原子混合物基态行为的玻色化研究 / 魯文龙. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (p. 70-72). / Abstract also in Chinese. / Lu, Wenlong = Yi wei guang ge zi zhong Feimi xing yuan zi hun he wu ji tai xing wei de Bose hua yan jiu / Lu Wenlong. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Cold-atom systems --- p.1 / Chapter 1.1.1 --- Optical lattices --- p.2 / Chapter 1.1.2 --- Feshbach resonance --- p.3 / Chapter 1.2 --- Outline of the thesis --- p.6 / Chapter 2 --- Bosonization method --- p.8 / Chapter 2.1 --- Special property of one-dimensional Fermion system --- p.9 / Chapter 2.2 --- Bosonization techniques --- p.13 / Chapter 2.2.1 --- Density operators as bosonic fields --- p.14 / Chapter 2.2.2 --- Bosonization Identities --- p.17 / Chapter 2.3 --- Renormalization analysis for Sine-Gordon field --- p.19 / Chapter 2.4 --- Summary --- p.25 / Chapter 3 --- Mass imbalance in the spin polarized fermion system --- p.26 / Chapter 3.1 --- Kinetic term --- p.29 / Chapter 3.2 --- Interaction term --- p.32 / Chapter 3.3 --- Phase separation --- p.38 / Chapter 3.4 --- Dominant order and pairing behavior --- p.47 / Chapter 3.5 --- Summary --- p.49 / Chapter 4 --- Mass imbalance in the strong repulsive interaction region --- p.50 / Chapter 4.1 --- Effective Hamiltonian at large U limit --- p.50 / Chapter 4.2 --- Bosonization of t-J-Jz model --- p.54 / Chapter 4.3 --- Phase separation --- p.60 / Chapter 4.4 --- Summary --- p.67 / Chapter 5 --- Conclusions --- p.68 / Bibliography --- p.70 / Chapter A --- Proofs of Bosonization --- p.73 / Chapter A.1 --- Anti-commutation relations between two branches of fermionic field operators --- p.73 / Chapter A.2 --- Bosonization-identities checking --- p.74 / Chapter B --- Diagonalization of Quadratic Hamiltonian with Two Bosonic Fields --- p.77 / Chapter C --- Correlation functions --- p.82

Yau, Chung Wah. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 55-57). / Abstracts in English and Chinese. / Acknowledgement --- p.i / Abstract --- p.ii / Table of Contents --- p.iv / Index of Compounds --- p.v / Chapter 1. --- Introduction / Chapter 1.1 --- Fundamentals of inclusion chemistry --- p.1 / Chapter 1.2 --- Hydrogen bonding in supramolecular chemistry and crystal engineering --- p.3 / Chapter 1.3 --- Hydrogen-bonded rosette system --- p.4 / Chapter 1.4 --- Research plan --- p.7 / Chapter 2. --- Descriptions of crystal structures / Chapter 2.1 --- Supramolecular rosette layer and rosette ribbon constructed from guanidinium cations and hydrogen carbonate dimers /carbonate anions / Chapter 2.1.1 --- (Et4N+)[C(NH2)3+]7(C032-)3[C3N2H2(C00-)2] (1) --- p.11 / Chapter 2.1.2 --- [(n-Bu)4N+]3[C(NH2)3+]4(HC03-)4[H+{C3N2H-(C00-)(C00H)}2] (2) --- p.14 / Chapter 2.1.3 --- [(n-Bu)4N+]2[C(NH2)3+]2(HC03-)2[NCC6H4(C00-)]2 ´Ø 2H20 (3)…… --- p.16 / Chapter 2.1.4 --- "[(n-Bu)4+]8[C(NH2)3+]8(HCO3-)8[4,4'-C12H8(C00-)2]4 ´Ø 8H20 ´″…" --- p.17 / Chapter 2.2 --- Channel- and layer-type anionic host structures constructed from benzene hexacarboxylic acid and guanidinium cation / Chapter 2.2.1 --- [C6(COO-)6][C(NH2)3]6 ´Ø H20 (5) --- p.20 / Chapter 2.2.2 --- [C6(COOH)3(COO´ؤ)3][C(NH2)3+]3 ´Ø 2H20 (6) --- p.23 / Chapter 2.2.3 --- [(n-Pr)4N+][C6(COOH)5(COO-)] ´Ø 3H20 (7) --- p.27 / Chapter 2.2.4 --- [(n-Bu)4N+]4[C6(COOH)5(COO-)]2[C6(COOH)4(COO-)2]2 [C(NH2)3+]2.8H2O(8) --- p.30 / Chapter 2.2.5 --- (Et4N+)2[C6(COOH)4(COO-)2]2[C(NH2)3+]2 ´Ø 2H20 (9) --- p.35 / Chapter 2.2.6 --- (Me4N+)[C6(COOH)3(COO-)3][C(NH2)3+]2 ´Ø H20 (10) --- p.37 / Chapter 3. --- Summary and discussion / Chapter 3.1 --- Robustness of hydrogen-bonded supramolecular rosette networks --- p.40 / Chapter 3.2 --- Versatile hydrogen bonding modes of guanidinium with mellitate anions --- p.43 / Chapter 4. --- Experimental / Chapter 4.1 --- Preparation methods --- p.48 / Chapter 4.2 --- X-ray crystallography --- p.52 / Chapter 5. --- References --- p.55 / "Appendix A: Tables of atomic coordinates, thermal parameters, bond lengths and angles and hydrogen bonds" --- p.58

abstract: In the 1980's, Gromov and Piatetski-Shapiro introduced a technique called "hybridization'' which allowed them to produce non-arithmetic hyperbolic lattices from two non-commensurable arithmetic lattices. It has been asked whether an analogous hybridization technique exists for complex hyperbolic lattices, because certain geometric obstructions make it unclear how to adapt this technique. This thesis explores one possible construction (originally due to Hunt) in depth and uses it to produce arithmetic lattices, non-arithmetic lattices, and thin subgroups in SU(2,1). / Dissertation/Thesis / Doctoral Dissertation Mathematics 2019