Teleportation via Multi-Qubit Channels

We investigate the problem of teleporting an unknown qubit state to a recipient via a channel of 2L qubits. In this procedure a protocol is employed whereby L Bell state measurements are made and information based on these measurements is sent via a classical channel to the recipient. Upon receiving this information the recipient determines a local gate which is used to recover the original state. We find that the 2(2L)-dimensional Hilbert space of states available for the channel admits a decomposition into four subspaces. Every state within a given subspace is a perfect channel, and each sequence of Bell measurements projects 2L qubits of the system into one of the four subspaces. As a result, only two bits of classical information need be sent to the recipient for them to determine the gate. We note some connections between these four subspaces and ground states of many-body Hamiltonian systems, and discuss the implications of these results towards understanding entanglement in multi-qubit systems.

Magnetic properties and Spin dynamics in magnetic Molecular Rings

Molecular nanomagnets are spin clusters whose topology and magnetic interactions can be modulated at the level of the chemical synthesis. They are formed by a small number of transition metal ions coupled by the Heisenberg's exchange interactions. Each cluster is magnetically isolated from its neighbors by organic ligands, making each unit not interacting with the others. Therefore, we can investigate the magnetic properties of an isolated molecular nanomagnet by bulk measurements. The present thesis has been mostly devoted to the experimental investigation of the magnetic properties and spin dynamics of different classes of antiferromagnetic (AF) molecular rings. This study has been exploiting various techniques of investigations, such as Nuclear Magnetic Resonance (NMR), muon spin relaxation (muSR) and SQUiD magnetometry. We investigate the magnetic properties and the phonon-induced relaxation dynamics of the first regular Cr9 antiferromagnetic (AF) ring, which represents a prototype frustrated AF ring. The magnetically-open AF rings like Cr8Cd are model systems for the study of the microscopic magnetic behaviour of finite AF Heisenberg chains. In this type of system the different magnetic behaviour depends length and on the parity of the chain (odd or even). In order to study the local spin densities on the Cr sites, the Cr-NMR spectra was collected at low temperature. The experimental result confirm the theoretical predictions for the spin configuration. Finally, the study of Dy6, the first rare-earth based ring that has been ever synthesized, has been performed by AC-SQuID and muSR measurements. We found that the dynamics is characterized by more than one characteristic correlation time, whose values depend strongly on the applied field.

The 'hard problem' and the quantum physicists. Part 1:the first generation

All four of the most important figures in the early twentieth-century development of quantum physics-Niels Bohr, Erwin Schroedinger, Werner Heisenberg and Wolfgang Pauli-had strong interests in the traditional mind-brain, or 'hard,' problem. This paper reviews their approach to this problem, showing the influence of Bohr's complementarity thesis, the significance of Schroedinger's small book, 'What is life?,' the updated Platonism of Heisenberg and, perhaps most interesting of all, the interaction of Carl Jung and Wolfgang Pauli in the latter's search for a unification of mind and matter. © 2005 Elsevier Inc. All rights reserved.

The synthesis of a ferromagnetic polymer

The aim of this study was to prepare a ferromagnetic polymer using the design elements of molecular magnets. This involved the preparation of co-polyradicals of phenylacetylenes bearing nitronyl nitroxides and nitro/cyano groups. The magnetic properties of the materials were determined using a SQUID magnetometer. A novel rhodium catalyst, Rh(NBD)(NH3)Cl, was prepared in order to obtain good yields of polymerisation. A wide range of substituted phenylacetylenes were first homopolymerised in order to assess the efficiency of the catalyst. Yields were generally high, between 75% and 98%, and the time of polymerisation was short (one hour). SEC analysis revealed that the Mw of the polymers were in the range of 200,000 and 250,000. The discovery that phenylboronic acid acts a co-catalyst for the polymerisation served to increase the yields by 10% to 20% but the Mw of the polymers was reduced to approximately 100,000. Co-polyradicals were prepared in good to excellent yield using the new catalyst. The magnetic properties in the temperature range of 300K to 1.8K were investigated by SQUID, which revealed a spin glass system, antiferromagnets and possible dipolar magnets. Short-range ferromagnetic interactions between 300K and 100K were found in a co-polyradical containing nitronyl nitroxide and cyano substituted monomers. The magnetic properties were dependent upon both the type of monomers utilised and the ratio between them. The effects of ring substituents on the terminal alkyne have been studied by carbon-13 NMR. There was no correlation however, between the chemical shift of terminal alkyne and the polymerisability of the monomer.

On Maximal Function on the Laguerre Hypergroup

2000 Mathematics Subject Classification: 42B20, 42B25, 42B35

Nonexistence Results of Solutions of Semilinear Differential Inequalities with Temperal Fractional Derivative on the Heinsenberg Group

2000 Mathematics Subject Classification: 26A33, 33C60, 44A15, 35K55

The Variety of Leibniz Algebras Defined by the Identity x(y(zt)) ≡ 0

2000 Mathematics Subject Classification: Primary: 17A32; Secondary: 16R10, 16P99, 17B01, 17B30, 20C30

Nonlinear quantum transport in low-dimensional electronic devices

The study of transport processes in low-dimensional semiconductors requires a rigorous quantum mechanical treatment. However, a full-fledged quantum transport theory of electrons (or holes) in semiconductors of small scale, applicable in the presence of external fields of arbitrary strength, is still not available. In the literature, different approaches have been proposed, including: (a) the semiclassical Boltzmann equation, (b) perturbation theory based on Keldysh's Green functions, and (c) the Quantum Boltzmann Equation (QBE), previously derived by Van Vliet and coworkers, applicable in the realm of Kubo's Linear Response Theory (LRT). ^ In the present work, we follow the method originally proposed by Van Wet in LRT. The Hamiltonian in this approach is of the form: H = H 0(E, B) + λV, where H0 contains the externally applied fields, and λV includes many-body interactions. This Hamiltonian differs from the LRT Hamiltonian, H = H0 - AF(t) + λV, which contains the external field in the field-response part, -AF(t). For the nonlinear problem, the eigenfunctions of the system Hamiltonian, H0(E, B), include the external fields without any limitation on strength. ^ In Part A of this dissertation, both the diagonal and nondiagonal Master equations are obtained after applying projection operators to the von Neumann equation for the density operator in the interaction picture, and taking the Van Hove limit, (λ → 0, t → ∞, so that (λ2 t)n remains finite). Similarly, the many-body current operator J is obtained from the Heisenberg equation of motion. ^ In Part B, the Quantum Boltzmann Equation is obtained in the occupation-number representation for an electron gas, interacting with phonons or impurities. On the one-body level, the current operator obtained in Part A leads to the Generalized Calecki current for electric and magnetic fields of arbitrary strength. Furthermore, in this part, the LRT results for the current and conductance are recovered in the limit of small electric fields. ^ In Part C, we apply the above results to the study of both linear and nonlinear longitudinal magneto-conductance in quasi one-dimensional quantum wires (1D QW). We have thus been able to quantitatively explain the experimental results, recently published by C. Brick, et al., on these novel frontier-type devices. ^

Nonlinear quantum transport in low-dimensional electronic devices

The study of transport processes in low-dimensional semiconductors requires a rigorous quantum mechanical treatment. However, a full-fledged quantum transport theory of electrons (or holes) in semiconductors of small scale, applicable in the presence of external fields of arbitrary strength, is still not available. In the literature, different approaches have been proposed, including: (a) the semiclassical Boltzmann equation, (b) perturbation theory based on Keldysh's Green functions, and (c) the Quantum Boltzmann Equation (QBE), previously derived by Van Vliet and coworkers, applicable in the realm of Kubo's Linear Response Theory (LRT). In the present work, we follow the method originally proposed by Van Vliet in LRT. The Hamiltonian in this approach is of the form: H = H°(E, B) + λV, where H0 contains the externally applied fields, and λV includes many-body interactions. This Hamiltonian differs from the LRT Hamiltonian, H = H° - AF(t) + λV, which contains the external field in the field-response part, -AF(t). For the nonlinear problem, the eigenfunctions of the system Hamiltonian, H°(E, B) , include the external fields without any limitation on strength. In Part A of this dissertation, both the diagonal and nondiagonal Master equations are obtained after applying projection operators to the von Neumann equation for the density operator in the interaction picture, and taking the Van Hove limit, (λ → 0 , t → ∞ , so that (λ2 t)n remains finite). Similarly, the many-body current operator J is obtained from the Heisenberg equation of motion. In Part B, the Quantum Boltzmann Equation is obtained in the occupation-number representation for an electron gas, interacting with phonons or impurities. On the one-body level, the current operator obtained in Part A leads to the Generalized Calecki current for electric and magnetic fields of arbitrary strength. Furthermore, in this part, the LRT results for the current and conductance are recovered in the limit of small electric fields. In Part C, we apply the above results to the study of both linear and nonlinear longitudinal magneto-conductance in quasi one-dimensional quantum wires (1D QW). We have thus been able to quantitatively explain the experimental results, recently published by C. Brick, et al., on these novel frontier-type devices.

A Experiência como ordenação da realidade: uma estratégia orgânica para a educação científica

Knowledge is understanding. According to the philosopher Gaston Bachelard our immediate contact with the reality is only worth as confusing and provisional data. This phenomenological contact requires inventory and classification. For this reason our first reading on any phenomenon is limited to a basic levels of reality. Elements such as dynamics, functioning or detailed characteristics of what is observed can only be accessed at higher levels of reality, explains the physicist Werner Heisenberg. The ideas woven by these two great intellectuals oxygenates the notion that a well-made thinking does not require only observation and description of the nature, but assigns value and meaning to the knowledge. Based on these ideas and on the cognitive horizon brought by the complexity sciences, this research aims to nurture a reflection on our understanding of the world built from a rational perspective of experience, as an organic sequence of research. This arguments, over the study, describes how the experience is able to oxygenate a well-made thinking, as the concept created by Edgar Morin and expanded by Conceição Almeida. I argue that the experience as a path of investigative research allows one to ventures in the shadows of the unknown to access upper layers of reality. The experience is, therefore, an organic strategy for a well-made thinking - A nutritious mud that oxygenates, regulates, repairs and configures the quality of understanding. As a thread to discuss this ideas I've used my professional journey over a year and a half as a Natural Sciences' teacher on the Federal University of Rio Grande do Norte, where I could see how experiences helped on breaking a simplified understanding of the world. I chose to work with the research problems developed by 398 students over these three semesters. The problems were essential to the questioning of the phenomena that once seemed obvious or uninteresting, bringing out operational reasons and dynamics of the observed structures. Experience, in this sense, is the founder of dynamic thinking, as the need to deconstruct the phenomena's first impressions, assigning value and meaning to gestated knowledge.

Il ruolo della matematica nella meccanica quantistica in un approccio interdisciplinare per la scuola secondaria

Questo lavoro di tesi nasce all’interno del nucleo di ricerca in didattica della fisica dell’Università di Bologna, coordinato dalla professoressa Olivia Levrini e che coinvolge docenti di matematica e fisica dei Licei, assegnisti di ricerca e laureandi. Negli ultimi anni il lavoro del gruppo si è concentrato sullo studio di una possibile risposta all'evidente e pressante difficoltà di certi docenti nell'affrontare gli argomenti di meccanica quantistica che sono stati introdotti nelle indicazioni Nazionali per il Liceo Scientifico, dovuta a cause di vario genere, fra cui l'intrinseca complessità degli argomenti e l'inefficacia di molti libri di testo nel presentarli in modo adeguato. In questo contesto, la presente tesi si pone l’obiettivo di affrontare due problemi specifici di formalizzazione matematica in relazione a due temi previsti dalle Indicazioni Nazionali: il tema della radiazione di corpo nero, che ha portato Max Planck alla prima ipotesi di quantizzazione, e l’indeterminazione di Heisenberg, con il cambiamento di paradigma che ha costituito per l’interpretazione del mondo fisico. Attraverso un confronto diretto con le fonti, si cercherà quindi di proporre un percorso in cui il ruolo del protagonista sarà giocato dagli aspetti matematici delle teorie analizzate e dal modo in cui gli strumenti della matematica hanno contribuito alla loro formazione, mantenendo un costante legame con le componenti didattiche. Proprio in quest'ottica, ci si accorgerà della forte connessione fra i lavori di Planck e Heisenberg e due aspetti fondamentali della didattica della matematica: l'interdisciplinarietà con la fisica e il concetto di modellizzazione. Il lavoro finale sarà quindi quello di andare ad analizzare, attraverso un confronto con le Indicazioni Nazionali per il Liceo Scientifico e con alcune esigenze emerse dagli insegnanti, le parti e i modi in cui la tesi risponde a queste richieste.

Double Fourier analysis for Emotion Identification in Voiced Speech

We propose a novel analysis alternative, based on two Fourier Transforms for emotion recognition from speech -- Fourier analysis allows for display and synthesizes different signals, in terms of power spectral density distributions -- A spectrogram of the voice signal is obtained performing a short time Fourier Transform with Gaussian windows, this spectrogram portraits frequency related features, such as vocal tract resonances and quasi-periodic excitations during voiced sounds -- Emotions induce such characteristics in speech, which become apparent in spectrogram time-frequency distributions -- Later, the signal time-frequency representation from spectrogram is considered an image, and processed through a 2-dimensional Fourier Transform in order to perform the spatial Fourier analysis from it -- Finally features related with emotions in voiced speech are extracted and presented

Random path sampling applied to vector models of magnetism

The recently reported Monte Carlo Random Path Sampling method (RPS) is here improved and its application is expanded to the study of the 2D and 3D Ising and discrete Heisenberg models. The methodology was implemented to allow use in both CPU-based high-performance computing infrastructures (C/MPI) and GPU-based (CUDA) parallel computation, with significant computational performance gains. Convergence is discussed, both in terms of free energy and magnetization dependence on field/temperature. From the calculated magnetization-energy joint density of states, fast calculations of field and temperature dependent thermodynamic properties are performed, including the effects of anisotropy on coercivity, and the magnetocaloric effect. The emergence of first-order magneto-volume transitions in the compressible Ising model is interpreted using the Landau theory of phase transitions. Using metallic Gadolinium as a real-world example, the possibility of using RPS as a tool for computational magnetic materials design is discussed. Experimental magnetic and structural properties of a Gadolinium single crystal are compared to RPS-based calculations using microscopic parameters obtained from Density Functional Theory.

Detecting metrologically useful entanglement in the vicinity of Dicke states

We present a method to verify the metrological usefulness of noisy Dicke states of a particle ensemble with only a few collective measurements, without the need for a direct measurement of the sensitivity. Our method determines the usefulness of the state for the usual protocol for estimating the angle of rotation with Dicke states, which is based on the measurement of the second moment of a total spin component. It can also be used to detect entangled states that are useful for quantum metrology. We apply our method to recent experimental results.