Inversion formula and Parsval theorem for complex continuous wavelet transforms studied by entangled state representation

In a preceding Letter (Opt. Lett. 32, 554 (2007)) we have proposed complex continuous wavelet transforms (CCWTs) and found Laguerre--Gaussian mother wavelets family. In this work we present the inversion formula and Parsval theorem for CCWT by virtue of the entangled state representation, which makes the CCWT theory complete. A new orthogonal property of mother wavelet in parameter space is revealed.Comment: 4 pages no figur

An Algebraic Approach to Linear-Optical Schemes for Deterministic Quantum Computing

Linear-Optical Passive (LOP) devices and photon counters are sufficient to implement universal quantum computation with single photons, and particular schemes have already been proposed. In this paper we discuss the link between the algebraic structure of LOP transformations and quantum computing. We first show how to decompose the Fock space of N optical modes in finite-dimensional subspaces that are suitable for encoding strings of qubits and invariant under LOP transformations (these subspaces are related to the spaces of irreducible unitary representations of U(N)). Next we show how to design in algorithmic fashion LOP circuits which implement any quantum circuit deterministically. We also present some simple examples, such as the circuits implementing a CNOT gate and a Bell-State Generator/Analyzer.Comment: new version with minor modification

ExTrA: Exoplanets in Transit and their Atmospheres

The ExTrA facility, located at La Silla observatory, will consist of a near-infrared multi-object spectrograph fed by three 60-cm telescopes. ExTrA will add the spectroscopic resolution to the traditional differential photometry method. This shall enable the fine correction of color-dependent systematics that would otherwise hinder ground-based observations. With both this novel method and an infrared-enabled efficiency, ExTrA aims to find transiting telluric planets orbiting in the habitable zone of bright nearby M dwarfs. It shall have the versatility to do so by running its own independent survey and also by concurrently following-up on the space candidates unveiled by K2 and TESS. The exoplanets detected by ExTrA will be amenable to atmospheric characterisation with VLTs, JWST, and ELTs and could give our first peek into an exo-life laboratory.Comment: 15 pages, 11 figures, SPIE 201

The HARPS search for southern extra-solar planets XLI. A dozen planets around the M dwarfs GJ 3138, GJ 3323, GJ 273, GJ 628, and GJ 3293

Context. Low mass stars are currently the best targets for searches for rocky planets in the habitable zone of their host star. Over the last 13 years, precise radial velocities measured with the HARPS spectrograph have identified over a dozen super-Earths and Earth-mass planets (msin i<10Mearth ) around M dwarfs, with a well understood selection function. This well defined sample informs on their frequency of occurrence and on the distribution of their orbital parameters, and therefore already constrains our understanding of planetary formation. The subset of these low-mass planets that were found within the habitable zone of their host star also provide prized targets for future atmospheric biomarkers searches. Aims. We are working to extend this planetary sample to lower masses and longer periods through dense and long-term monitoring of the radial velocity of a small M dwarf sample. Methods. We obtained large numbers of HARPS spectra for the M dwarfs GJ 3138, GJ 3323, GJ 273, GJ 628 and GJ 3293, from which we derived radial velocities (RVs) and spectroscopic activity indicators. We searched them for variabilities, periodicities, Keplerian modulations and correlations, and attribute the radial-velocity variations to combinations of planetary companions and stellar activity. Results. We detect 12 planets, of which 9 are new with masses ranging from 1.17 to 10.5 Mearth . Those planets have relatively short orbital periods (P<40 d), except two of them with periods of 217.6 and 257.8 days. Among these systems, GJ 273 harbor two planets with masses close to the one of the Earth. With a distance of 3.8 parsec only, GJ 273 is the second nearest known planetary system - after Proxima Centauri - with a planet orbiting the circumstellar habitable zone.Comment: 19 pages, 24 figures. Astronomy and Astrophysics in pres

The quantum state vector in phase space and Gabor's windowed Fourier transform

Representations of quantum state vectors by complex phase space amplitudes, complementing the description of the density operator by the Wigner function, have been defined by applying the Weyl-Wigner transform to dyadic operators, linear in the state vector and anti-linear in a fixed `window state vector'. Here aspects of this construction are explored, with emphasis on the connection with Gabor's `windowed Fourier transform'. The amplitudes that arise for simple quantum states from various choices of window are presented as illustrations. Generalized Bargmann representations of the state vector appear as special cases, associated with Gaussian windows. For every choice of window, amplitudes lie in a corresponding linear subspace of square-integrable functions on phase space. A generalized Born interpretation of amplitudes is described, with both the Wigner function and a generalized Husimi function appearing as quantities linear in an amplitude and anti-linear in its complex conjugate. Schr\"odinger's time-dependent and time-independent equations are represented on phase space amplitudes, and their solutions described in simple cases.Comment: 36 pages, 6 figures. Revised in light of referees' comments, and further references adde

Homogeneously derived transit timings for 17 exoplanets and reassessed TTV trends for WASP-12 and WASP-4

19 pages, 4 figures, 6 tables; revised manuscript submitted to MNRAS; online-only supplements are in the download archiveWe homogeneously analyse ∼3.2 × 10 5 photometric measurements for ∼1100 transit light curves belonging to 17 exoplanet hosts. The photometric data cover 16 years (2004–2019) and include amateur and professional observations. Old archival light curves were reprocessed using up-to-date exoplanetary parameters and empirically debiased limb-darkening models. We also derive self-consistent transit and radial-velocity fits for 13 targets. We confirm the nonlinear transit timing variation (TTV) trend in the WASP-12 data at a high significance, and with a consistent magnitude. However, Doppler data reveal hints of a radial acceleration of about −7.5 ± 2.2 m s −1 yr −1, indicating the presence of unseen distant companions, and suggesting that roughly 10 per cent of the observed TTV was induced via the light-travel (or Roemer) effect. For WASP-4, a similar TTV trend suspected after the recent TESS observations appears controversial and model dependent. It is not supported by our homogeneous TTV sample, including 10 ground-based EXPANSION light curves obtained in 2018 simultaneously with TESS. Even if the TTV trend itself does exist in WASP-4, its magnitude and tidal nature are uncertain. Doppler data cannot entirely rule out the Roemer effect induced by possible distant companions.Peer reviewe

…There are Parts of the World were Things are Badly Wrong...\u27: Forum Selection Clauses and Unfair Jurisdictions

This article considers the defences that may be available to judgment debtors who face enforcement actions in respect of judgments from unfair jurisdictions

…There are Parts of the World were Things are Badly Wrong...\u27: Forum Selection Clauses and Unfair Jurisdictions

This article considers the defences that may be available to judgment debtors who face enforcement actions in respect of judgments from unfair jurisdictions

Taxa Selic e a alocação de riqueza no Brasil: uma análise de títulos públicos e outros ativos

Trabalho de Conclusão de Curso (Graduação)O presente artigo examina a influência da taxa básica de juros, Selic, sobre a alocação de riqueza no Brasil, com foco em títulos públicos, mercado imobiliário, ações e bens de capital. A partir de uma abordagem pós-keynesiana, o estudo investiga como as variações da Selic afetam a demanda por diferentes ativos. O estudo sugere que, em períodos de queda da Selic, ocorre uma diversificação dos investimentos, com migração para ativos de maior risco e retorno, como ações, e aumento na demanda por imóveis devido à redução do custo de financiamento. Em contrapartida, a elevação da Selic direciona o capital para títulos públicos de menor risco. A análise empírica baseia-se em dados do Tesouro Nacional, Ibovespa, mercado imobiliário e produção de bens de capital entre 2010 e 2023. Os resultados indicam uma correlação entre a Taxa Selic e a composição do portfólio dos investidores, evidenciando o papel central da política monetária na dinâmica econômica brasileira. Conclui-se que, apesar da queda da taxa Selic no período analisado, a liquidez dos títulos públicos permanece atrativa, enquanto os bens de capital apresentam tendência de queda, mesmo com a redução da Selic a longo prazo