CONDENSED MATTER PHYSICS: IV Mexican Meeting on Experimental and Theoretical Physics: Symposium on Condensed Matter Physics
1319(2010); http://dx.doi.org/10.1063/1.3536611View Description Hide Description
Many textbooks on Quantum Mechanics are not very precise as to the meaning of making a measurement: as a consequence, they frequently make assertions which are not based on a dynamical description of the measurement process. A model proposed by von Neumann allows a dynamical description of measurement in Quantum Mechanics, including the measuring instrument in the formalism.
In this article we apply von Neumann’s model to illustrate the measurement of an observable by means of a measuring instrument and show how various results, which are sometimens postulated without a dynamical basis, actually emerge.
We also investigate the more complex, intriguing and fundamental problem of two successive measurements in Quantum Mechanics, extending von Neumann’s model to two measuring instruments. We present a description which allows obtaining, in a unified way, various results that have been given in the literature.
1319(2010); http://dx.doi.org/10.1063/1.3536609View Description Hide Description
We review a series of works discussing how the scattering approach to quantum transport developed by Landauer and Buttiker for one body elastic scatterers can be extended to the case where electron‐electron interactions act inside the scattering region and give rise to many body scattering. Firstly, we give an exact numerical result showing that at zero temperature a many body scatterer behaves as an effective one body scatterer, with an interaction dependent transmission. Secondly, we underline that this effective scatterer depends on the presence of external scatterers put in its vicinity. The implications of this non local scattering are illustrated studying the conductance of a quantum point contact where electrons interact with a scanning gate microscope. Thirdly, using the numerical renormalization group developed by Wilson for the Kondo problem, we study a double dot spinless model with an inter‐dot interaction U and inter‐dot hopping coupled to leads by hopping terms We show that the quantum conductance as a function of is given by a universal function, independently of the values of U and if one measures in units of a characteristic scale Mapping the double dot system without spin onto a single dot Anderson model with spin and magnetic field, we show that where is the Kondo temperature of the Anderson model.
Statistical Properties of the Conductance of Disordered Wires: From atomic‐scale contacts to macroscopically long nanowires1319(2010); http://dx.doi.org/10.1063/1.3536610View Description Hide Description
In this work, we review some statistical properties of the conductance of disordered wires. Random Matrix Theory is used to analyze the results of extensive numerical calculations for both surface and bulk disordered wires. This approach, macroscopic in nature, has been applied successfully to study different transport properties all the way from localization to quasiballistic transport and even to the limit of atomic‐scale metallic contacts. The evolution of the conductance statistical distribution in the transition from diffusion (Gaussian statistics) to localization (log normal statistics) is also discussed.
1319(2010); http://dx.doi.org/10.1063/1.3536612View Description Hide Description
We study numerically the conductance statistics of the one‐dimensional (1D) Anderson model with random long‐range hoppings described by the Power‐law Banded Random Matrix (PBRM) model. Within a scattering approach to electronic transport, we consider two scattering setups in absence and presence of direct processes: 2M single‐mode leads attached to one side and to opposite sides of 1D circular samples. For both setups we show that (i) the probability distribution of the logarithm of the conductance T behaves as for for both the critical and the non‐critical samples; and (ii) at criticality there is a smooth crossover from localized‐like to delocalized‐like behavior in the transport properties of the PBRM model by decreasing the fractality of its eigenstates.
Statistical scattering of waves in disordered waveguides: The limiting macroscopic statistics in the ballistic regime1319(2010); http://dx.doi.org/10.1063/1.3536613View Description Hide Description
In this work, we present a theoretical study of the statistical properties of wave scattering in a disordered ballistic waveguide of length L; we have called this system the “building block”. The building block is interesting as a physical system because its statistical properties could be studied experimentally in the laboratory.
In order to study the building block, as a physical system in itself, we have developed a perturbative method based on Born series. This method is valid only in the ballistic regime, when the length of the system L is smaller than the mean free path ℓ, and in the short‐wave‐length approximation, when the the wave number k and the mean free path ℓ satisfy This method has allowed to find, analytically, the behavior of quantities of interest that we have not been able to find from the diffusion equation. In contrast with the diffusion equation method, which takes into account approximately the contribution of closed channels, this method takes them explicitly. In earlier works numerical evidence was found that the expectation values of some interesting quantities are insensitive to the number of closed channels that were used on the calculations; with this method, we could show that closed channels are relevant for the expectation values of amplitudes but irrelevant for the intensities and conductance expectation values. The results of this method show a good agreement with numerical simulations.
1319(2010); http://dx.doi.org/10.1063/1.3536614View Description Hide Description
The motion of a free charge subjected to a harmonic electromagnetic wave with transients is analyzed. The two central features of a charge—field interaction with a time dependent wave envelope are the drift or remnant velocity and the charge displacement. The former phenomenon has been observed in above threshold ionization and plasma residual‐current density generation by few‐cycle laser pulses. The particle shift is a feature that may prove useful for coherent manipulation. Analytical expressions in order to obtain the extrema for the velocity and displacement for a finite gating time are presented.
1319(2010); http://dx.doi.org/10.1063/1.3536615View Description Hide Description
Using one dimensional rods with different configurations classical analogs of quantum mechanical systems frequently used in solid state physics can be obtained. Among this analogs we have recently discussed locally periodic rods which lead to band spectra; the effect of a topological defect, and the Wannier Stark ladders. In this paper, we present an elastic analog of the diatomic chain and show how the acoustical and optical bands emerge, as well of the nature of the wave amplitudes.
1319(2010); http://dx.doi.org/10.1063/1.3536616View Description Hide Description
Recent results on the scattering of waves by chaotic systems with losses and direct processes are discussed. We start by showing the results without direct processes nor absorption. We then discuss systems with direct processes and lossy systems separately. Finally the discussion of systems with both direct processes and loses is given. We will see how the regimes of strong and weak absorption are modified by the presence of the direct processes.
1319(2010); http://dx.doi.org/10.1063/1.3536617View Description Hide Description
There are many systems that present losses or gains, like optic cavities and random lasers. In this work we study a system that consists on an impenetrable barrier and an imaginary delta potential to simulate a cavity in one dimension. Contrary to the case of an Hermitean Hamiltonian the flux is not conserved; we find that the scattering matrix moves on the circle whose radius is different than one, and displaced from the origin, as a function of energy. We determine the “time” the scattering matrix spend in an certain region in the space of scattering matrices.
1319(2010); http://dx.doi.org/10.1063/1.3536618View Description Hide Description
We apply Poynting’s theorem to the dielectric‐conductor interface to determine the intensity of the absorbing mode (parasitic channel), when plane waves incide with an angle of incidence. By applying boundary conditions we are able to describes the scattering at the interface by means of a subunitary scattering matrix. The energy balance equation allows to determine the lack of unitarity (absorbance) as a function of the frequency and the angle of incidence. Also, it allows to write a unitary scattering matrix which contains the subunitary one and a single parasitic channel with transmission intensity given by the absorbance.
1319(2010); http://dx.doi.org/10.1063/1.3536600View Description Hide Description
We demonstrate the existence of absorbing “parasitic channels” by experimental measurement of the reflection coefficient R of a frustrated waveguide, at several microwave frequencies. Assuming equivalent parasitic channels, we quantify the number of parasitic channels by the ratio of the total absorbance in our system, and the absorbance of a single parasitic channel that was recently calculated in the current literature.
1319(2010); http://dx.doi.org/10.1063/1.3536602View Description Hide Description
Using the scattering matrix approach and Poynting’s theorem in the form of an energy balance equation we determine the total power that is dissipated by a thin metal film. We are able to demonstrate the existence of two absorbing modes that are correlated as well as non equivalent, contrary to what happens in more complex systems. Also, we show the dependence of the total absorption on the width of the film, as well as a function of the frequency.
1319(2010); http://dx.doi.org/10.1063/1.3536603View Description Hide Description
π‐conjugated organic molecules and polymers are of great importance in physics, chemistry, material science and engineering. It is expected that, in the near future, organic materials will find widespread use in many technological applications. In the case of organic opto‐electronic systems, the list of devices includes light emitting diodes (OLEDs), photovoltaic cells (OPVs), field‐effect transistors (OFET), photorefractive materials for light manipulation, among others. These materials are also used for photonic applications: all‐optical switching, modulators, optical correlators, plastic waveguides, all polymeric integrated circuits, solid‐state lasers, and for biophotonic applications as in the case of the development of organic labels for multiphoton microscopy and photodynamic therapy. The advances in the developing of organic compounds with better mechanical, electrical, and optical (linear and non‐linear) characteristics are of a great importance for this field. Here, we present the research on this area carried out at the Centro de Investigaciones en Óp‐tica (CIO), in collaboration with Chemistry Departments of different institutions. This work focuses on the optical characterization of materials through several techniques such as TOF, FWM, TBC, THG Maker Fringes, HRS, Z‐scan, and TPEF. Additionally, some applications, such as dynamic holography by using photorefractive polymers, and OPVs cells will be discussed.
1319(2010); http://dx.doi.org/10.1063/1.3536604View Description Hide Description
A brief review of the application of Monte Carlo and Molecular Dynamics methods to the study of the phase behavior of condensed‐matter systems is given, focusing on the binary symmetric Lennard‐Jones mixture as an example. Phase transitions of fluids are conveniently studied by Monte Carlo simulation, applying a statistical ensemble which allows the sampling of the order parameter distribution, analysis of which is done by finite‐size scaling methods. Having located the critical point with very good accuracy by the cumulant intersection method, the expected Ising critical behavior is confirmed. Analysis of the order parameter distribution in the two‐phase coexistence region allows to extract the interface tension of both flat interfaces and of spherical droplets. Using well equilibrated configurations from the Monte Carlo runs as initial states for microcanonical Molecular Dynamics runs, also the dynamic critical behavior can be successfully analyzed.
1319(2010); http://dx.doi.org/10.1063/1.3536605View Description Hide Description
The strength of the cage of neighbours in a quasi‐hard spheres colloidal system is measured by means of active microrheology up to densities close to the glass transition. An external parabolic trap is imposed to one single particle in the system, and its dynamics is analysed. The long time limit of the mean squared displacement provides information about the strength of the cage of the particle (due to the external force and neighbours), and the temperature. Assuming that both strengths are additive, the strength of the cage of neighbours is calculated. The power spectrum (Laplace transform) of the mean squared displacement is also presented.
1319(2010); http://dx.doi.org/10.1063/1.3536606View Description Hide Description
Expanded ensembles were used to obtain the association free energy, in which the number of ideal basepair contacts formed served as the order parameter, for DNA oligonucleotides of varying composition, chain length, and ionic strength. Although free energy profiles are unique to each sequence, all exhibit a pronounced response for low contact numbers dominated largely by an increase in system entropy. Short oligonucleotides with sequence periodicity exhibit a rather smooth free energy profile that increases in complexity as chain length increases. The complexity in non‐periodic sequences arises even in short oligonucleotides. Taking intact dsDNA with an extent of reaction the maximum of the free energy profile appears at representing two to four basepair contacts. In terms of chain length, the free energy barrier of longer oligonucleotides is higher and slightly narrower, due to the ensuant sharpness of the single‐to‐double stranded transition. Low ionic strength conditions induce an instability along the sugar‐phosphate backbone of DNA, resulting in a decrease of the free energy barrier toward molecular dissociation.
1319(2010); http://dx.doi.org/10.1063/1.3536607View Description Hide Description
We present a model for the calculation of the third virial coefficient in binary mixtures of non‐polar molecules, using as effective potentials approximate non‐conformal (ANC) binary interactions and the Axilrod‐Teller‐Muto (ATM) ternary potential. We propose suitable combination rules to obtain the parameters for the cross‐interaction ANC and ATM potentials from the pure‐interaction ones, so that the model includes no free parameters. Comparison of the results with available experimental data show good agreement and a more regular, smooth behavior of the features of the cross‐interaction coefficients than that obtained with currently available models based on geometrical averages of the pure‐interaction coefficients.
1319(2010); http://dx.doi.org/10.1063/1.3536608View Description Hide Description
Characterization of two crystalline phases (δ and ε) of syndiotactic polystyrene using molecular modeling are discussed. These two polymorphs present nanoporosity, being able to adsorb molecules of low molecular weight in their cavities (δ) or in their channels (ε). By means of Grand Canonical Monte Carlo molecular simulations, adsorption isotherms of nitrogen and hydrogen were calculated, exploring the possible utilization of these materials with storage purposes. Molecular Dynamics simulations were performed to determine self diffusion behavior of light gases and these results combined with a geometric method are being employed to measure the size of the nanochannels of the e polymorph.