Search results for "Linear Algebra"
showing 10 items of 552 documents
A pedagogical approach to the Boltzmann factor through experiments and simulations
2009
The Boltzmann factor is the basis of a huge amount of thermodynamic and statistical physics, both classical and quantum. It governs the behaviour of all systems in nature that are exchanging energy with their environment. To understand why the expression has this specific form involves a deep mathematical analysis, whose flow of logic is hard to see and is not at the level of high school or college students' preparation. We here present some experiments and simulations aimed at directly deriving its mathematical expression and illustrating the fundamental concepts on which it is grounded. Experiments use easily available apparatuses, and simulations are developed in the Net-Logo environment…
Diffractive m-bonacci lenses.
2017
[EN] Fibonacci zone plates are proving to be promising candidates in image forming devices. In this letter we show that the set of Fibonacci zone plates are a particular member of a new family of diffractive lenses which can be designed on the basis of a given m-bonacci sequence. These lenses produce twin axial foci whose separation depends on the m-golden mean. Therefore, with this generalization, bifocal systems can be freely designed under the requirement at particular focal planes. Experimental results support our proposal. (C) 2017 Optical Society of America
The Hubbard model beyond the two-pole approximation: a Composite Operator Method study
2014
Within the framework of the Composite Operator Method, a three-pole solution for the two-dimensional Hubbard model is presented and analyzed in detail. In addition to the two Hubbard operators, the operatorial basis comprises a third operator describing electronic transitions dressed by nearest-neighbor spin fluctuations. These latter, compared to charge and pair fluctuations, are assumed to be preeminent in the region of model-parameter space - small doping, low temperature and large on-site Coulomb repulsion - where one expects strong electronic correlations to dominate the physics of the system. This assumption and the consequent choice for the basic field, as well as the whole analytica…
Sum Frequency Generation Spectra from Velocity–Velocity Correlation Functions
2017
We developed an expression for the calculation of the sum frequency generation spectra (SFG) of water interfaces that is based on the projection of the atomic velocities on the local normal modes. Our approach permits one to obtain the SFG signal from suitable velocity-velocity correlation functions, reducing the computational cost to that of the accumulation of a molecular dynamics trajectory, and therefore cutting the overhead costs associated with the explicit calculation of the dipole moment and polarizability tensor. Our method permits to interpret the peaks in the spectrum in terms of local modes, also including the bending region. The results for the water-air interface, obtained usi…
Teleportation of atomic states via position measurements
2007
We present a scheme for conditionally teleporting an unknown atomic state in cavity QED, which requires two atoms and one cavity mode. The translational degrees of freedom of the atoms are taken into account using the optical Stern-Gerlach model. We show that successful teleportation with probability 1/2 can be achieved through local measurements of the cavity photon number and atomic positions. Neither direct projection onto highly entangled states nor holonomous interaction-time constraints are required.
Periodic Table of the Elements, History, Education and Evaluation
2021
The periodic tables of transition metal thiophosphates MPS3, transition metal dichalcogenides MX2 and other materials, the origin of chemical elements and toxic trace elements in dried mushrooms are provided. The effective nucleus-electron attraction is proportional to the effective nuclear charge (Zeff) and inversely proportional to the effective principal quantum number (n*). The periodic arch is one of many modern visual displays that have been developed to augment the traditional periodic table of the chemical elements. The table is related to the multiparameter optimisation of N atom, nuclear magnetic resonance and everyday life. Educational activities were developed and evaluated. Se …
Validity of rate equations for Zeeman coherences for analysis of nonlinear interaction of atoms with broadband laser radiation
2004
In this paper we, to our knowledge, for the first time obtain the rate equations for Zeeman coherences in the broad line approximation and steady-state balance equations directly from optical Bloch equations without the use of the perturbation theory. The broad line approximation allows us to use the adiabatic elimination procedure in order to eliminate the optical coherences from the optical Bloch equations, but the steady-state condition allows us to derive the balance equations straightforward. We compare our approach with the perturbation theory approach as given previously and show that our approach is more flexible in analyzing various experiments. Meanwhile we also show the validity …
A direct approach to Gaussian measurement based quantum computation
2016
In this work we introduce a general scheme for measurement based quantum computation in continuous variables. Our approach does not necessarily rely on the use of ancillary cluster states to achieve its aim, but rather on the detection of a resource state in a suitable mode basis followed by digital post-processing, and involves an optimization of the adjustable experimental parameters. After introducing the general method, we present some examples of application to simple specific computations.
The physiological basis for the computation of direction selectivity in theDrosophilaOFF pathway
2021
AbstractInDrosophila, direction-selective neurons implement a mechanism of motion computation similar to cortical neurons, using contrast-opponent receptive fields with ON and OFF subunits. It is not clear how the presynaptic circuitry of direction-selective neurons in the OFF pathway supports this computation, because all major inputs are OFF-rectified neurons. Here, we reveal the biological substrate for motion computation in the OFF pathway. Three interneurons, Tm2, Tm9 and CT1, also provide information about ON stimuli to the OFF direction-selective neuron T5 across its receptive field, supporting a contrast-opponent receptive field organization. Consistent with its prominent role in mo…
Application of optical tomography for measurements of aeration parameters in large water tanks
2003
The paper presents a design and application study of a prototype optical tomograph for the detection and definition of shapes of gas bubbles moving in a liquid. In the applied method of measurements, the column is exposed to a homogeneous light beam and next the ray is detected with the use of optical waveguided detectors. Spatial reconstruction of the bubble shapes is done on the basis of the signals coming from two perpendicular systems of detectors. The bubble shape is approximated by an ellipsoid with suitably determined semi-axes and with the use of genetic algorithms based on the neuron network. Influence of the structure and dynamics of the measuring path on errors in representation …