Symposium: Scattering, quantum and classical transport
Plenary lectures (1 hour):
1.- Tsampikos Kottos (tkottos@wesleyan.edu) -- US
Time-Reversal Symmetry and its Applications: From Waveform Shaping to System Protection
Tsampikos Kottos. Wave Transport in Complex Systems Lab, Department of Physics, Wesleyan University
Time-reversal symmetry and its violation is one of the most powerful concepts in physics. It has applications in many physics subfields ranging from condensed matter, optics and atomic physics to mathematical physics and quantum field theories. In this talk, we will focus on two specific implementations of time-reversal symmetry (and its violation) in the field of electrodynamics with relevance to: (a) the design of waveforms of incident electromagnetic radiation that efficiently direct energy at focal points, with applications varying from non- invasive medical therapies and wireless telecommunications to electromagnetic warfare; and (b) the design of reflective photonic limiters used for protection of sensitive sensors from high- power/fluence incoming radiation.
We will highlight the connections between these two (at first glance diametrically different) applications while at the same time we will be placing the presented research effort within the framework of recently emerging sub-field of non-Hermitian wave transport.
2.- Rafael Méndez-Sánchez (mendez@icf.unam.mx) -- MX
Artificial Mechanical Molecules
Rafael Méndez-Sánchez. Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México
We show that it is possible emulate the pz orbitals of aromatic molecules using mechanical vibrations. This is done from the theoretical, numerical and experimental points of view. When connecting resonators through locally periodic structures, the resonances can be trapped thanks to the bandgaps of the locally periodic connectors [1,2]. This trapping yields a similar phenomenology to what happens with tightly bound electrons in quantum systems: the resonators take the role of the atoms, the connectors the role of the chemical bonds and the trapped vibrations the role of the orbitals. As a first system, a 1D chain of mechanical atoms is studied. In this case the spectrum and wave amplitudes agree with those obtained by a quantum tight-binding model, in which the frequency takes the role of the energy. With the same ideas the pz orbitals of some aromatic molecules are emulated.
3.- Barbara Dietz (dietz@lzu.edu.cn) -- CN
Quantum Chaotic Scattering Experiments with Microwave Billiards, Random Matrix Theory and their Application to Nuclear Data
Barbara Dietz. School of Physical Science and Technology, Lanzhou University
I will speak about experiments with flat microwave resonators with and without induced time-reversal invariance violation. The scattering matrix formalism for such systems is equivalent to that developed for the random matrix theory description of compound nuclear reactions. Accordingly, the extraordinary advantage of such experiments is that they render possible the experimental verification of a variety of statistical measures for the fluctuation properties in the spectra of the associated scattering matrix and thus the development of tools for the characterization of nuclear spectra. Recently, we validated analytical expressions for the distribution of the off-diagonal cross sections based on these microwave data and then applied them to excitation functions of the compound-nuclear reaction 37 Cl(p,a) 34 S. Furthermore, we studied the fluctuation properties in the energy spectra of 208 Pb. High resolution experiments have recently lead to a complete identification of the energy values, spin, and parity of 151 nuclear levels. We analyzed their fluctuation properties using random matrix theory and also the method of Bayesian inference.
4.- Luca Tessieri (tessieri@ifm.umich.mx) -- MX
Transport and localization phenomena in media with correlated disorder
Luca Tessieri. Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo
We present a review of some important results obtained in the field of propagation and localization of waves in one-dimensional models with correlated disorder. In particular, we discuss how specific correlations of the random potential can give rise to peculiar transport properties in random media. We analyze some of the techniques used to deal with correlated disorder, including the Hamiltonian map approach and the recent “ers” approximation. Finally, we discuss how the results valid for 1D models are being extended to 2D and 3D systems.
5.- Roberto Quezada (roqb@xanum.uam.mx) -- MX
Dynamics of quantum states in an energy transport model
Roberto Quezada. Departamento de Matemáticas, Universidad Autónoma Metropolitana -Iztapalapa
We will discuss the dynamics of quantum states in an energy transport model (photosynthesis) with a generator defined in terms of operators performing transitions between two mutually orthogonal subspaces, similar to birth and death transitions in classical stochastic processes or creation and annihilation operators in the quantum setting. It turns out that any stationary state has a portion supported on the first subspace and the remaining is supported on the orthogonal. Moreover, any state supported on the first subspace is transported to a state whose probability mass is concentrated on the orthogonal and there is an energy gain in the process.
6.- Emerson Sadurní (sadurni@ifuap.buap.mx) -- MX
Extended quantum particles in free fall: Analytical treatment of their diffraction
Emerson Sadurní. Instituto de Física, Benemérita Universidad Autónoma de Puebla
The diffraction of atomic and molecular beams is typically described by non-trivial solutions of the stationary Schrödinger equation. This has been done for structureless particles in the absence of external fields. In this contribution, the techniques that incorporate both internal composition and a gravitational field are presented. A derivation of the corresponding propagator is provided without approximations, identifying the center-of-mass propagation coordinate with a pseudo-time. In the paraxial regime --borrowed from optics-- it is shown that a superposition of Moshinsky functions with internal molecular states gives rise to corrected diffraction patterns in the far, intermediate and near field regions along the optical axis. The limit of small molecular radii in diatomic harmonic models is discussed. Single and multiple slit diffraction patterns are studied, displaying corrections to the emergent Talbot carpets. Implications on quantum tests of the equivalence principle are briefly reviewed in this light, showing that modified probability densities arise when small deviations from unity of the inertial-to-gravitational mass ratio are considered.
7.- Alberto Robledo (robledo@fisica.unam.mx) -- MX
Localization, a nonlinear dynamical equivalent and its presence in complex systems
Alberto Robledo. Instituto de Física and Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México
We describe a particular excursion into the study of the localization phenomenon, kept within a family of simple model systems for the scattering of a propagating wave. The models are fully solvable and suitable for revealing an analogous nonlinear dynamical problem. A recursion relation for the system-size dependence of the scattering matrix relates to a bifurcation diagram where single point and weakly chaotic attractors represent insulating and conducting regimes, and the in-between transition to chaos characterizes the mobility edge. While the simplicity of the models allows for the consideration of other localization phenomena, like those for light and sound, its mathematical description can be couched in the language of Mobius transformations in the complex plane, and this in turn can be directed to abstract number theoretical questions and properties. Finally, we sketch extensions of these studies towards the modeling of coherent collective patterns and motion in complex systems composed of living entities.
8.- Thomas Gorin (thomas.gorin@cucei.udg.mx) -- MX
Quantum predecessors of stochastic processes with an application to the Ising spin chain
Thomas Gorin. Centro Universitario de Ciencias Exactas e Ingenierías, Universidad de Guadalajara
One may think of classical stochastic processes as arising from the evolution of an open quantum system in the limit of strong decoherence. From this perspective, one would start with a quantum system, assume a coupling to the environment and eventually reach the classical stochastic process in the limit of strong decoherence. Here, we to proceed in the opposite direction: Given a discrete-time classical Markov process, we derive a description in terms of a sequence of quantum channels. We then modify these quantum channels in such a way that random "which path"-decisions are replaced by the superposition of all possible paths. This procedure is restricted by the requirement that the original classical stochastic process would be recovered, if sufficiently frequent and complete measurements were performed. As a consequence, the resulting process is typically semi-quantum, i.e. intermediate between purely quantum (i.e. unitary) and purely stochastic (i.e. classical).
We apply this procedure to the stochastic dynamics of an Ising spin chain under a high-to-zero temperature quench. We find that the resulting semi-quantum process conserves a surprisingly large amount of coherence. As compared to the classical process, we find a number of notable differences in the behavior of macroscopic variables, such as a faster equilibration time.
9.- Cecilia Noguez (cecilia@fisica.unam.mx) -- MX
Flatland: Two-dimensional heterostructures with van der Waals interactions
Cecilia Noguez. Instituto de Física, Universidad Nacional Autónoma de México
Two-dimensional (2D) van der Waals (vdW) heterostructures are a new realm of materials with potential applications and fascinating physical properties. Besides graphene (G), transition metal dichalcogenides (TMDCs) have been considered as promising building blocks in 2D vdW heterostructures with improved and new properties. The vertical stacking of at least two atomic monolayers bonded by vdW forces with different electronic behavior, i.e. G/TMDC, leads to new hybrid nanostructures. In principle, hybrids could retain the main advantages of pristine monolayers at the same time that they might achieve superior and unusual properties which cannot be obtained otherwise. In recent years, the combination of G and TMDCs, such as tungsten disulfide (WS2) and molybdenum disulfide (MoS2) have attracted increasing interest as promising building blocks for future electronics, photonics and optoelectronic devices. First, we present a general unfolding method for the electronic bands of systems with double-periodicity. Within density functional theory with atomic orbitals as basis-set, our method takes into account two symmetry operations of the primitive cell: a standard expansion and a single rotation, letting to elucidate the physical effects associated to the mutual interactions between systems with more than one periodicity. As a result, our unfolding method allows studying the electronic properties of vertically stacked homo- or heterostructures. Then, we apply our method to study G/WS2 heterostructures with different interlayer angles. Our unfolding method allows observing typical mini gaps reported in heterostructures, as well as other electronic deviations from pristine structures, impossible to distinguish without an unfolding method. We anticipate that this unfolding method can be useful to compare with experiments to elucidate the electronic properties of two-dimensional homo- or heterostructures, where the interlayer angle can be considered as an additional parameter.
10.- Oscar Rosas-Ortiz (orosas@fis.cinvestav.mx) -- MX
Supersymmetric Approach to Quantum Mechanics
Oscar Rosas-Ortiz. Centro de Investigación y Estudios Avanzados, Instituto Politécnico Nacional
The supersymmetric formulation of quantum mechanics is a subject of intense activity in contemporary physics. It is addressed to analyze the spectral properties of exactly solvable potentials as well as to construct new integrable quantum models. In this talk we revisit the progress of such formulation since the introduction of the factorization method by Dirac to the construction of non-Hermitian systems with all-real spectra that may be used to model open quantum systems with balanced gain (acceptor) and loss (donor) profile.
Short talks (30 minutes):
1.- John Franco (jofravil@ifisica.uaslp.mx)
Quantum gravimetry insensitive to external disturbances using composite light pulses
John Franco. Instituto de Física, Universidad Autónoma de San Luis Potosí
We introduce an atomic gravimetric sequence using Raman-type composite light pulses that excites a superposition of two momentum states with the same internal level. The scheme allows the suppression of common noise, making it less sensitive to external fluctuations of electromagnetic fields. The Raman beams are generated with a fiber modulator and are capable of momentum transfer in opposite directions. We obtain analytical expressions for the interference fringes in terms of three perturbative parameters that characterize the imperfections due to undesired frequencies introduced by the modulation process. We find special values of the Rabi frequency that improve the fringes visibility.
2.- Alejandro García Chung (alechung@xanum.uam.mx)
On the canonical transformations group and polymer quantum mechanics
Alejandro García Chung. Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa
Polymer quantum mechanics constitutes a theoretical lab where some of the mathematical techniques used in Loop Quantum Cosmology and Loop Quantum Gravity can be tested or better understood. On the other hand, the canonical transformations are an essential tool of the Hamiltonian formalism at both, classical and quantum level. In this talk, I will discuss the unitary representation of the canonical transformation within the polymer quantum mechanics scheme and will show some of its implications.
3.- Ángel Martínez (blitzkriegheinkel@gmail.com)
Transport studies in three-terminal microwave graphs with orthogonal, unitary, and symplectic symmetry
Ángel Martínez. Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México
The Landauer-Büttiker formalism establishes an equivalence between the electrical conduction through a device, e.g., a quantum dot, and the transmission. Guided by this analogy we perform transmission measurements through three-port microwave graphs with orthogonal, unitary, and symplectic symmetry, thus mimicking three-terminal voltage drop devices. One of the ports is placed as input and a second one as output, while a third port isused as a probe. Analytical predictions show good agreement with the measurements in the presence of orthogonal and unitary symmetries, provided that the absorption and the influence of the coupling port are taken into account.The symplectic symmetry is realized in specifically designed graphs mimicking spin-1/2 systems. Again a good agreement between experiment and theory is found. For the symplectic case the results are marginally sensitive to absorption and coupling strength of the port, in contrast to the orthogonal and unitary case.
4.- Luca Celardo (celardo@ifuap.buap.mx)
Cooperative effects and long range interactions: from Superradiance to Cooperative Shielding
Luca Celardo. Instituto de Física, Benemérita Universidad Autónoma de Puebla
Cooperative effects are at the center of interest in many systems in physics such as cold atomic clouds, light harvesting systems, and trapped ions. Cooperative effects such as Superradiance and Supertransfer induce enhanced energy transport efficiency and robustness to noise. In the first part of the talk we will review the role of Superradiance/Superabsorption in light-harvesting systems. Design of efficient devices for photon sensing and light-harvesting based on Superabsoption will be discussed. At the heart of Superradiance lies the long range of the interactions mediated by the photon field between the molecules.
The second part of the talk will be devoted to discuss the interplay of cooperativity and noise in systems with long range interaction which can be implemented in ion trapped experiments. The main focus will be on Cooperative Shielding. Contrary to the common expectation that long-range interaction should necessarily induce an instantaneous spread of information in the thermodynamic limit, we show that, as the system size increases, the dynamics can actually become more confined into invariant subspaces. In such subspaces, the dynamics is effectively shielded from long-range interaction, that is, it occurs as if that interaction was absent. Shielding is a cooperative effect, because the time over which it is effective diverges with system size.
5.- Guillermo Vázquez (gavc@xanum.uam.mx)
Reactive transport in terms of Graphical and Chemical Operads
Guillermo Vázquez. Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa
It is well known that in the reaction diffusion equation there is a term which takes into account the rate of reaction, the algebraic form of that term does depend on the mechanism of reaction which conventionally follows the classical semiotic of chemical reations in which reagents and products are considered as nodes and the chemical process in itself is represented by an arrow. In the language of chemical operads - which was inspired by the language of graphical operads - one makes the substitution of nodes per arrows and arrows per nodes. In this work one does introduce the language of graphical and chemical operads and shows with examples taken from chemistry and electrochemistry how to use this new language within the context of reactive transport. Of special interest to us is the relationship between the graphical structure of chemical operads and strange attractors (visual recognition patterns) in the phase space in which one considers coupled nonlinear kinetics.
6.- Antonio Fernández (antoniofdzm@gmail.com)
Aerogel-based metasurfaces for perfect acoustic energy absorption
Antonio Fernández. Laboratoire d'Acoustique de l'Université du Mans, LAUM
Silica aerogels are nanoporous lightweight materials the frame of which consists of an assembly of connected small cross-sections beam-like elements resulting from fused nanoparticles. This particular assembly additionally provides silica aerogel a very low elastic stiffness when compared to rigid silica structure of identical porosity. Therefore, when aerogel plates are clamped, they are excellent candidates to design acoustic metamaterials, because they exhibit subwavelength resonances and present efficient absorption capabilities. In this work we will study theoretically, numerically and experimentally a perfect absorbing metamaterial panel made of periodically arranged resonant building blocks consisting of a slit loaded by a clamped aerogel plate backed by a closed cavity. The impedance matching condition is analyzed using the Argand diagram of the reflection coefficient. The lack or excess of losses in the system can be identified via this Argand diagram in order to achieve the impedance matching condition. The results obtained show a good agreement between the analytical results and those measured experimentally.
7.- Ruth Diamant (ruth@xanum.uam.mx)
Photonic Crystals in the Amplitude and Phase Representation
Ruth Diamant. Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa
We use a classical optics approach to obtain the Bloch functions for several one-dimensional photonic crystals. To accomplish this, we choose the amplitude and phase representation, which leads us to a new procedure. These Bloch functions are based on numerical solutions to the field's amplitude equation, letting the refractive index vary continuously and periodically along one direction. Band gaps are found in the process too. Some interesting differences between electron and electromagnetic wave behavior are pointed out.
8.- Horacio Olivares (horop@xanum.uam.mx)
An analytic representation for the three-body interaction
Horacio Olivares. Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa
An analytic representation of the three-body potential for the ground state of the molecular ion $H^{++}_3$ in equilateral triangle configuration is presented. This representation is based on an adequate description of the two-body potential energy curve $V(R)$ for the diatomic molecule $H^+_2$. The accurate representation of $V(R)$ for $H^+_2$ is achieved by matching short and long distances behavior via two-point ad e approximation. In general, the approximation provides 3-4 significant digits correctly.
9.- Thomas Stegmann (stegmann@icf.unam.mx)
Electron optics in phosphorene pn junctions
Thomas Stegmann. Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México
Ballistic electrons in phosphorene pn junctions show optical-like phenomena. Phosphorene is modeled by a tight-binding Hamiltonian that describes its electronic structure at low energies, where the electrons behave in the armchair direction as massive Dirac fermions and in the orthogonal zigzag direction as Schrödinger electrons. Applying the continuum approximation, we derive the electron optics laws in phosphorene pn junctions, which show very particular and unusual properties. Due to the anisotropy of the electronic structure, these laws depend strongly on the orientation of the junction with respect to the sublattice. Negative and anomalous reflection are observed for tilted junctions, while the typical specular reflection is found only, if the junction is parallel to the zigzag or armchair edges. Moreover, omni-directional total reflection, called anti-super-Klein tunneling, is observed if the junction is parallel to the armchair edge. Applying the nonequilibrium Green's function method on the tight-binding model, we calculate numerically the current flow. The good agreement of both approaches confirms the atypical transport properties, which can be used in nano-devices to collimate and filter the electron flow, or to switch its direction.
10.- Robin Sagar (sagar@xanum.uam.mx)
Information Entropies, Correlations, and Applications in Continuous Variable Quantum Systems
Robin Sagar. Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa
A review of the tools taken from information theory and how they have been used to analyze quantum systems will be presented. Formulations of uncertainty relations in entropic terms will be discussed with emphasis on the behaviors in the position, momentum and phase-space representations. Statistical correlations between (among) particles will also be addressed.
11.- Eduardo Barrios (jebarrios@comunidad.unam.mx)
Laser-induced boundary states in graphite
Eduardo Barrios. Departamento de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México
The common classification of the electronic phases (insulator, semiconductor, semimetal, and metal) of the matter is based on spectral properties. However, the discovery of the topological insulators (TI) added a new kind of classification based on topological information carried by the eigenstates of the system. A topological insulator is a material that behaves as an insulator in the bulk and hosts conducting surface states, these surface states are like highways for electrons. The conducting surface states are weakly affected by the disorder which is an attractive characteristic for applications. One way to induce topological electronic phases in common materials is by using laser illumination. The illuminated material may host a topological state, a phase commonly known as Floquet topological insulator. In this work, we explore laser-induced effects in graphite, where we find topological boundary states, these states propagate mainly along the borders. The topological states present a 'skeleton' in the reciprocal space.
12.- José Mauricio López Romero (jm.lopez@cinvestav.mx)
Measuring with Fundamental Constants
José Mauricio López Romero. Centro de Investigación y Estudios Avanzados - Queretaro, Instituto Politécnico Nacional
The phrase “one measure for all men and all times” summarizes the ideal that would lead to the development of the International System of Units, SI. The evolution of the definitions of the SI units of measurement may be somehow considered as a series of approximations to such an ideal in which the units of measurement are invariant in time and space, immutable, and susceptible to equivalent realizations, reproducible, and accessible to be useful in measuring processes of practical, industrial, technological and scientific purposes. In the current state of the science and technology the fundamental constants appear as the last frontier to define the SI units of measurement. The abandonment of artifacts to support the definitions of SI units began in 1960 when the wavelength of a krypton 86 radiation was used to redefine the unit of length, the meter. Moreover, the time unit, defined in 1967 in terms of the separation of the ground state hyperfine levels of the Cesium- 133 atom, was another important step towards the incorporation of the fundamental constants in the SI units. In 1982, the unit of length was established in terms of the speed of light in vacuum and time measurements. This clearly illustrates how the SI evolves towards the incorporation of fundamental constants, or combinations of them, to support the units of measurement. In May 20th, 2019, the SI unit for mass, the kilogram, was redefined in terms of the Planck constant. Setting a value without uncertainty for lanck’s constant and by defining the kilogram in terms of electromagnetic forces generated in a balance, usually called “watt balance”, the definition of the kilogram is framed in the context of the quantum mechanics, since it rely experimentally on the time unit, and therefore on the hyperfine separation of the ground state of Cesium-133 atom, on the realizations of the volt in terms of the Josephson effect and on the ohm in terms of the quantum Hall effect. Also, the SI units for the electric current and temperature, the Ampere and the Kelvin, were redefined last May 20th in terms of the electric charge of the electron and the Boltzmann constant, respectively. The new definitions of the SI base units will allow the fundamental constants to be the support of the SI, that in order to provide measurement systems with a very high accuracy to pursuit the scientific and technological advances to come.
13.- Miztli Yépez (miztli.yepez@gmail.com)
Wave transport through disordered waveguides: the effective response and the statistics of the scattering matrix
Miztli Yépez. Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa
We present theoretical and numerical results for the statistical averages of the scattered waves in disordered waveguides. The theoretical results, based on a perturbative method, show that the averages scattering amplitudes of the disordered region depend only on a few characteristic lengths related to microscopic details of the disorder: the mean free paths. Theoretical average amplitudes show an excellent agreement with numerical simulations. This comparison exhibits that the average transmission amplitude is described successfully by an effective medium response; in contrast, only when the recurrent scattering contributions can be neglected, the average reflection amplitude is described satisfactorily by an effective medium. These results for the average scattering amplitudes suggest that the statistical distribution of the scattering matrix of disordered waveguides, does not satisfy the isotropic hypothesis assumed in the DMPK (Dorokhov, Mello, Pereyra and Kumar) description, where the phases of the scattering matrix are assumed equally probable. Our numerical simulations confirm that the isotropic hypothesis is not valid in general, it is suitable only for systems with lengths larger than the mean free path.
14.- Adrián Ortega (jivifair@gmail.com)
Spectral and transport properties of a simple PT -symmetric tight-binding chain with gain and loss
Adrián Ortega. Centro Universitario de Ciencias Exactas e Ingenierías, Universidad de Guadalajara
We consider a simple PT-symmetric tight-binding chain with gain and loss in
a symmetric configuration. Using the explicit expressions for the eigenvalues and
eigenvectors of the model, we obtain the values of the parameters at which exceptional points occur, and determine the behavior of the eigenvalues and eigenfunctions around these exceptional points perturbatively. These results are used to analyze transport through the chain. We find that for the eigenstates corresponding to complex eigenvalues in the broken PT -symmetric phase, transport is deficient, and the ratio of inflow and outflow is different from one, leading to an exponential increase or decrease of the density in the chain.
15.- Carlos Pineda (carlosp@fisica.unam.mx)
A quantum framework for coarse graining and fuzzy measurements
Carlos Pineda. Instituto de Física, Universidad Nacional Autónoma de México
We present a quantum framework for coarse graining and fuzzy measurements in a multiparticle system, based solely on what might be physically measured. For example the
case of coarse graining, we assume that the detectors can measure only randomly selected particles with a physically motivated distribution. For the case of fuzzy measurements, we assume that the detectors might be placed incorrectly, leading to misidentification of some particles. In the space of states, both situations induce completely positive maps that lead to a shrinking of the state space. These maps are studied in detail; physical quantities such as the measurable entanglement (and thus the ability to perform tasks such as teleportation), and purity are considered. In addition, by considering the symmetries and spectra of the maps, we calculate the shrinking rate of the space of states. Finally, we consider the many particle limit and find that only an exponentially small subset of the state space is observable if one has imperfect detectors. In the limit of infinite particles, this set coincides with the many particle coherent states, and thus we call this subset the classical space.
16.- Humberto Laguna (humlag@gmail.com)
The Wigner function of Open Quantum Systems and position-momentum correlation
Humberto Laguna. Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa
The interest in Open Quantum Systems (OQS) has increased as OQS has been applied for the study of diverse physical phenomena. In this work we study the Wigner functions of the Harmonic Oscillator (HO) and two coupled Harmonic Oscillators (the Moshinsky atom). Both models were coupled with a bath under two different coupling bath-system regimes: a) pure-dephasing without relaxation and b) relaxation without pure-dephasing. The time evolution of the phase-space functions was analyzed with the aid of information-theoretic tools (Shannon entropy and mutual information). The time evolution of the localization in phase space and of the position-momentum correlation is analyzed.
17.- Shi-Hai Dong (dongsh2@yahoo.com)
Entanglement measures for W-class states in noninertial frame
Shi-Hai Dong. Centro de Innovación y Desarrollo Tecnológico en Cómputo, Instituto Politécnico Nacional
We present the entanglement measures of a tetrapartite W-Class entangled system in noninertial frame, where the transformation between Minkowski and Rindler coordinates is applied. Two cases are considered. First, when one qubit has uniform acceleration whilst the other three remain stationary. Second, when two qubits have nonuniform accelerations and the others stay inertial. The 1-1 tangle, 1-3 tangle and whole entanglement measurements $\pi_4$ and $\Pi_4$, are studied and illustrated with graphics through their dependency on the acceleration parameter $r_d$ for the first case and $r_c$ and $r_d$ for the second case. It is found that the negativities (1-1 tangle and 1-3 tangle) and $\pi$-tangle decrease when the acceleration parameter $r_d$ or in the second case $r_c$ and $r_d$ increase, remaining a nonzero entanglement in the majority of the results. This means that the system will be always entangled except for special cases. It is shown that only the 1-1 tangle for the first case, vanishes at infinite accelerations, but for the second case the 1-1 tangle disappears completely when $r>0.472473$. It is found an analytical expression for von Neumann information entropy of the system and we notice that it increases with the acceleration parameter.
18.- Gabriela Báez (gbaez@correo.azc.uam.mx)
Elastic Metamaterial Engineering
Gabriela Báez. Departamento de Ciencias Básicas, Universidad Autónoma Metropolina-Azcapotzalco
The design of artificial materials, with emerging anomalous properties, is a very active frontier research today due to the multiple and novel applications based on new physics. These new materials, also called metamaterials, are characterized by their wave phenomenology that defies our intuition: superfocusing, invisibility and slowing down, among others.
The main challenge of metamaterials is their mass production since, so far, only samples whose anomalous emergent properties have been verified in small frequency intervals have been manufactured. The first samples manufactured successfully, at the beginning of our 21st century, were electromagnetic metamaterials, characterized by their negative refractive index. On the other hand, elastic metamaterials present a greater degree of difficulty, due to the coupling between the different polarizations of the mechanical waves, as well as the conversion between them.
In this conference we present experimental evidence of the control of mechanical waves through some structured elastic metamaterials, strategically designed and manufactured in our research group. Some emergent properties of these elastic materials are Bloch oscillations; rainbow entrapment and near-zero group speed.
This frontier research has potential applications in seismology; in the design of modern cities and in the automotive, aeronautical and aerospace industries since comfort, maintenance and mainly the safety of vehicles depend on control of elastic waves and mechanical vibrations in them.
19.- Víctor Ibarra-Sierra (dirac.iasv@gmail.com)
Method for finding effective Hamiltonian of time-driven quantum systems
Víctor Ibarra-Siera. Instituto de Física, Universidad Nacional Autónoma de México
Time-driven quantum systems are essential in many different fields of physics as cold atoms, solid-state, optics, etc. Many of their properties are encoded in the time evolution operator or the effective Hamiltonian. Finding these operators usually requires very complicated calculations that often involve some approximations. In this talk, we present a theoretical model that exploits the structure of the associated Lie group for time-periodic Hamiltonians. This method allows us to find the time evolution operator through the decomposition on each group generator and, subsequently, the effective Hamiltonian.
20.- Quetzalsin Carrasco (quetzalsin.carrasco@gmail.com)
Phenomenological model for the incoherent addition of two quantum resistors connected in series
Quetzalsin Carrasco. Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa
Ever since the creation of the integrated circuit in the late 50’s and the emergence of nanotechnology, the number of developed nanostructures has been increasing, so much so that at present, nanostructures are viewed as ideal systems for the study of electronic transport; however, a mathematical model that introduces and studies decoherence phenomena into an arbitrary mesoscopic system has not yet been created. This work focuses on studying the behavior of the total conductance of a system through the creation of a phenomenological model that allows the introduction of a local inelastic process in the transmission between two quantum resistors connected in series.
21.- Felipe de Jesús Castañeda Ramírez (felipe.castaneda.r@gmail.com)
Four-point measurements in multiprobes mesoscopic quantum wires
Felipe de Jesús Castañeda Ramírez. Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa
A four terminal device is used to determine the potential difference between two points on both sides of a chaotic quantum wire, where two terminals are used as voltage probes. Numerical simulations with random matrix theory are performed for the orthogonal, unitary and symplectic symmetries. Weak localization and antilocalization phenomena and effects of the coupling of the probes are clearly observed.
22.- José Luis López González (luisideas@gmail.com)
Presence of Avoided Crossings in Rectangular Thin Plates.
José Luis López González. Instituto de Física, Universidad Autónoma de San Luis Potosí
In this talk it is introduced the basics of Classical Plate Theory and Random Matrix Theory in order to appreciate the discovery and consequences of avoided crossings in a free vibrating rectangular elastic billiard. Mathematical, Numerical and Experimental evidences are presented.
