From doubled Chern–Simons–Maxwell lattice gauge theory to extensions of the toric code

We regularize compact and non-compact Abelian Chern–Simons–Maxwell theories on a spatial lattice using the Hamiltonian formulation. We consider a doubled theory with gauge fields living on a lattice and its dual lattice. The Hilbert space of the theory is a product of local Hilbert spaces, each associated with a link and the corresponding dual link. The two electric field operators associated with the link-pair do not commute. In the non-compact case with gauge group R, each local Hilbert space is analogous to the one of a charged “particle” moving in the link-pair group space R2 in a constant “magnetic” background field. In the compact case, the link-pair group space is a torus U(1)2 threaded by k units of quantized “magnetic” flux, with k being the level of the Chern–Simons theory. The holonomies of the torus U(1)2 give rise to two self-adjoint extension parameters, which form two non-dynamical background lattice gauge fields that explicitly break the manifest gauge symmetry from U(1) to Z(k). The local Hilbert space of a link-pair then decomposes into representations of a magnetic translation group. In the pure Chern–Simons limit of a large “photon” mass, this results in a Z(k)-symmetric variant of Kitaev’s toric code, self-adjointly extended by the two non-dynamical background lattice gauge fields. Electric charges on the original lattice and on the dual lattice obey mutually anyonic statistics with the statistics angle . Non-Abelian U(k) Berry gauge fields that arise from the self-adjoint extension parameters may be interesting in the context of quantum information processing.

The M-theory origin of global properties of gauge theories

We show that global properties of gauge groups can be understood as geometric properties in M-theory. Different wrappings of a system of N M5-branes on a torus reduce to four-dimensional theories with AN−1 gauge algebra and different unitary groups. The classical properties of the wrappings determine the global properties of the gauge theories without the need to impose any quantum conditions. We count the inequivalent wrappings as they fall into orbits of the modular group of the torus, which correspond to the S-duality orbits of the gauge theories.

From quantum to classical dynamics: The relativistic O ( N ) model in the framework of the real-time functional renormalization group

We investigate the transition from unitary to dissipative dynamics in the relativistic O(N) vector model with the λ(φ2)2 interaction using the nonperturbative functional renormalization group in the real-time formalism. In thermal equilibrium, the theory is characterized by two scales, the interaction range for coherent scattering of particles and the mean free path determined by the rate of incoherent collisions with excitations in the thermal medium. Their competition determines the renormalization group flow and the effective dynamics of the model. Here we quantify the dynamic properties of the model in terms of the scale-dependent dynamic critical exponent z in the limit of large temperatures and in 2≤d≤4 spatial dimensions. We contrast our results to the behavior expected at vanishing temperature and address the question of the appropriate dynamic universality class for the given microscopic theory.

Room temperature absorption in laterally biased Quantum Infrared Detectors fabricated by MBE regrowth

In this paper, we show room temperature operation of a quantum well infrared photodetector (QWIP) using lateral conduction through ohmic contacts deposited at both sides of two n-doped quantum wells. To reduce the dark current due to direct conduction in the wells, we apply an electric field between the quantum wells and two pinch-off Schottky gates, in a fashion similar to a field effect device. Since the normal incidence absorption is strongly reduced in intersubband transitions in quantum wells, we first analyze the response of a detector based on quantum dots (QD). This QD device shows photocurrent signal up to 150 K when it is processed in conventional vertical detector. However, it is possible to observe room temperature signal when it is processed in a lateral structure. Finally, the room temperature photoresponse of the QWIP is demonstrated, and compared with theory. An excellent agreement between the estimated and measured characteristics of the device is found

Relational and Allegorical Semantics for Constraint Logic Programming

El cálculo de relaciones binarias fue creado por De Morgan en 1860 para ser posteriormente desarrollado en gran medida por Peirce y Schröder. Tarski, Givant, Freyd y Scedrov demostraron que las álgebras relacionales son capaces de formalizar la lógica de primer orden, la lógica de orden superior así como la teoría de conjuntos. A partir de los resultados matemáticos de Tarski y Freyd, esta tesis desarrolla semánticas denotacionales y operacionales para la programación lógica con restricciones usando el álgebra relacional como base. La idea principal es la utilización del concepto de semántica ejecutable, semánticas cuya característica principal es el que la ejecución es posible utilizando el razonamiento estándar del universo semántico, este caso, razonamiento ecuacional. En el caso de este trabajo, se muestra que las álgebras relacionales distributivas con un operador de punto fijo capturan toda la teoría y metateoría estándar de la programación lógica con restricciones incluyendo los árboles utilizados en la búsqueda de demostraciones. La mayor parte de técnicas de optimización de programas, evaluación parcial e interpretación abstracta pueden ser llevadas a cabo utilizando las semánticas aquí presentadas. La demostración de la corrección de la implementación resulta extremadamente sencilla. En la primera parte de la tesis, un programa lógico con restricciones es traducido a un conjunto de términos relacionales. La interpretación estándar en la teoría de conjuntos de dichas relaciones coincide con la semántica estándar para CLP. Las consultas contra el programa traducido son llevadas a cabo mediante la reescritura de relaciones. Para concluir la primera parte, se demuestra la corrección y equivalencia operacional de esta nueva semántica, así como se define un algoritmo de unificación mediante la reescritura de relaciones. La segunda parte de la tesis desarrolla una semántica para la programación lógica con restricciones usando la teoría de alegorías—versión categórica del álgebra de relaciones—de Freyd. Para ello, se definen dos nuevos conceptos de Categoría Regular de Lawvere y _-Alegoría, en las cuales es posible interpretar un programa lógico. La ventaja fundamental que el enfoque categórico aporta es la definición de una máquina categórica que mejora e sistema de reescritura presentado en la primera parte. Gracias al uso de relaciones tabulares, la máquina modela la ejecución eficiente sin salir de un marco estrictamente formal. Utilizando la reescritura de diagramas, se define un algoritmo para el cálculo de pullbacks en Categorías Regulares de Lawvere. Los dominios de las tabulaciones aportan información sobre la utilización de memoria y variable libres, mientras que el estado compartido queda capturado por los diagramas. La especificación de la máquina induce la derivación formal de un juego de instrucciones eficiente. El marco categórico aporta otras importantes ventajas, como la posibilidad de incorporar tipos de datos algebraicos, funciones y otras extensiones a Prolog, a la vez que se conserva el carácter 100% declarativo de nuestra semántica. ABSTRACT The calculus of binary relations was introduced by De Morgan in 1860, to be greatly developed by Peirce and Schröder, as well as many others in the twentieth century. Using different formulations of relational structures, Tarski, Givant, Freyd, and Scedrov have shown how relation algebras can provide a variable-free way of formalizing first order logic, higher order logic and set theory, among other formal systems. Building on those mathematical results, we develop denotational and operational semantics for Constraint Logic Programming using relation algebra. The idea of executable semantics plays a fundamental role in this work, both as a philosophical and technical foundation. We call a semantics executable when program execution can be carried out using the regular theory and tools that define the semantic universe. Throughout this work, the use of pure algebraic reasoning is the basis of denotational and operational results, eliminating all the classical non-equational meta-theory associated to traditional semantics for Logic Programming. All algebraic reasoning, including execution, is performed in an algebraic way, to the point we could state that the denotational semantics of a CLP program is directly executable. Techniques like optimization, partial evaluation and abstract interpretation find a natural place in our algebraic models. Other properties, like correctness of the implementation or program transformation are easy to check, as they are carried out using instances of the general equational theory. In the first part of the work, we translate Constraint Logic Programs to binary relations in a modified version of the distributive relation algebras used by Tarski. Execution is carried out by a rewriting system. We prove adequacy and operational equivalence of the semantics. In the second part of the work, the relation algebraic approach is improved by using allegory theory, a categorical version of the algebra of relations developed by Freyd and Scedrov. The use of allegories lifts the semantics to typed relations, which capture the number of logical variables used by a predicate or program state in a declarative way. A logic program is interpreted in a _-allegory, which is in turn generated from a new notion of Regular Lawvere Category. As in the untyped case, program translation coincides with program interpretation. Thus, we develop a categorical machine directly from the semantics. The machine is based on relation composition, with a pullback calculation algorithm at its core. The algorithm is defined with the help of a notion of diagram rewriting. In this operational interpretation, types represent information about memory allocation and the execution mechanism is more efficient, thanks to the faithful representation of shared state by categorical projections. We finish the work by illustrating how the categorical semantics allows the incorporation into Prolog of constructs typical of Functional Programming, like abstract data types, and strict and lazy functions.

InAs/AlGaAs quantum dot intermediate band solar cells with enlarged sub-bandgaps

In the last decade several prototypes of intermediate band solar cells (IBSCs) have been manufactured. So far, most of these prototypes have been based on InAs/GaAs quantum dots (QDs) in order to implement the IB material. The key operation principles of the IB theory are two photon sub-bandgap (SBG) photocurrent, and output voltage preservation, and both have been experimentally demonstrated at low temperature. At room temperature (RT), however, thermal escape/relaxation between the conduction band (CB) and the IB prevents voltage preservation. To improve this situation, we have produced and characterized the first reported InAs/AlGaAs QD-based IBSCs. For an Al content of 25% in the host material, we have measured an activation energy of 361 meV for the thermal carrier escape. This energy is about 250 meV higher than the energies found in the literature for InAs/GaAs QD, and almost 140 meV higher than the activation energy obtained in our previous InAs/GaAs QD-IBSC prototypes including a specifically designed QD capping layer. This high value is responsible for the suppression of the SBG quantum efficiency under monochromatic illumination at around 220 K. We suggest that, if the energy split between the CB and the IB is large enough, activation energies as high as to suppress thermal carrier escape at room temperature (RT) can be achieved. In this respect, the InAs/AlGaAs system offers new possibilities to overcome some of the problems encountered in InAs/GaAs and opens the path for QD-IBSC devices capable of achieving high efficiency at RT.

Self-organized colloidal quantum dots and metal nanoparticles for plasmon-enhanced intermediate-band solar cells

A colloidal deposition technique is presented to construct long-range ordered hybrid arrays of self-assembled quantum dots and metal nanoparticles. Quantum dots are promising for novel opto-electronic devices but, in most cases, their optical transitions of interest lack sufficient light absorption to provide a significant impact in their implementation. A potential solution is to couple the dots with localized plasmons in metal nanoparticles. The extreme confinement of light in the near-field produced by the nanoparticles can potentially boost the absorption in the quantum dots by up to two orders of magnitude. In this work, light extinction measurements are employed to probe the plasmon resonance of spherical gold nanoparticles in lead sulfide colloidal quantum dots and amorphous silicon thin-films. Mie theory computations are used to analyze the experimental results and determine the absorption enhancement that can be generated by the highly intense near-field produced in the vicinity of the gold nanoparticles at their surface plasmon resonance. The results presented here are of interest for the development of plasmon-enhanced colloidal nanostructured photovoltaic materials, such as colloidal quantum dot intermediate-band solar cells.

Key reconciliation for high performance Quantum Key Distribution

Quantum Key Distribution is carving its place among the tools used to secure communications. While a difficult technology, it enjoys benefits that set it apart from the rest, the most prominent is its provable security based on the laws of physics. QKD requires not only the mastering of signals at the quantum level, but also a classical processing to extract a secret-key from them. This postprocessing has been customarily studied in terms of the efficiency, a figure of merit that offers a biased view of the performance of real devices. Here we argue that it is the throughput the significant magnitude in practical QKD, specially in the case of high speed devices, where the differences are more marked, and give some examples contrasting the usual postprocessing schemes with new ones from modern coding theory. A good understanding of its implications is very important for the design of modern QKD devices.

Intermediate Band Solar Cell with Extreme Broadband Spectrum Quantum Efficiency

We report, for the first time, about an intermediate band solar cell implemented with InAs/AlGaAs quantum dots whose photoresponse expands from 250 to ~ 6000  nm. To our knowledge, this is the broadest quantum efficiency reported to date for a solar cell and demonstrates that the intermediate band solar cell is capable of producing photocurrent when illuminated with photons whose energy equals the energy of the lowest band gap. We show experimental evidence indicating that this result is in agreement with the theory of the intermediate band solar cell, according to which the generation recombination between the intermediate band and the valence band makes this photocurrent detectable. © 2015 American Physical Society

Fundamental finite key limits for information reconciliation in quantum key distribution

The security of quantum key distribution protocols is guaranteed by the laws of quantum mechanics. However, a precise analysis of the security properties requires tools from both classical cryptography and information theory. Here, we employ recent results in non-asymptotic classical information theory to show that information reconciliation imposes fundamental limitations on the amount of secret key that can be extracted in the finite key regime. In particular, we find that an often used approximation for the information leakage during one-way information reconciliation is flawed and we propose an improved estimate.

The vibrational energy flow transition in organic molecules: Theory meets experiment

Most large dynamical systems are thought to have ergodic dynamics, whereas small systems may not have free interchange of energy between degrees of freedom. This assumption is made in many areas of chemistry and physics, ranging from nuclei to reacting molecules and on to quantum dots. We examine the transition to facile vibrational energy flow in a large set of organic molecules as molecular size is increased. Both analytical and computational results based on local random matrix models describe the transition to unrestricted vibrational energy flow in these molecules. In particular, the models connect the number of states participating in intramolecular energy flow to simple molecular properties such as the molecular size and the distribution of vibrational frequencies. The transition itself is governed by a local anharmonic coupling strength and a local state density. The theoretical results for the transition characteristics compare well with those implied by experimental measurements using IR fluorescence spectroscopy of dilution factors reported by Stewart and McDonald [Stewart, G. M. & McDonald, J. D. (1983) J. Chem. Phys. 78, 3907–3915].

On the absorbance changes in the photocycle of the photoactive yellow protein: A quantum-chemical analysis

Spectral changes in the photocycle of the photoactive yellow protein (PYP) are investigated by using ab initio multiconfigurational second-order perturbation theory at the available structures experimentally determined. Using the dark ground-state crystal structure [Genick, U. K., Soltis, S. M., Kuhn, P., Canestrelli, I. L. & Getzoff, E. D. (1998) Nature (London) 392, 206–209], the ππ* transition to the lowest excited state is related to the typical blue-light absorption observed at 446 nm. The different nature of the second excited state (nπ*) is consistent with the alternative route detected at 395-nm excitation. The results suggest the low-temperature photoproduct PYPHL as the most plausible candidate for the assignment of the cryogenically trapped early intermediate (Genick et al.). We cannot establish, however, a successful correspondence between the theoretical spectrum for the nanosecond time-resolved x-ray structure [Perman, B., Šrajer, V., Ren, Z., Teng, T., Pradervand, C., et al. (1998) Science 279, 1946–1950] and any of the spectroscopic photoproducts known up to date. It is fully confirmed that the colorless light-activated intermediate recorded by millisecond time-resolved crystallography [Genick, U. K., Borgstahl, G. E. O., Ng, K., Ren, Z., Pradervand, C., et al. (1997) Science 275, 1471–1475] is protonated, nicely matching the spectroscopic features of the photoproduct PYPM. The overall contribution demonstrates that a combined analysis of high-level theoretical results and experimental data can be of great value to perform assignments of detected intermediates in a photocycle.

Quantum groups with invariant integrals

Quantum groups have been studied intensively for the last two decades from various points of view. The underlying mathematical structure is that of an algebra with a coproduct. Compact quantum groups admit Haar measures. However, if we want to have a Haar measure also in the noncompact case, we are forced to work with algebras without identity, and the notion of a coproduct has to be adapted. These considerations lead to the theory of multiplier Hopf algebras, which provides the mathematical tool for studying noncompact quantum groups with Haar measures. I will concentrate on the *-algebra case and assume positivity of the invariant integral. Doing so, I create an algebraic framework that serves as a model for the operator algebra approach to quantum groups. Indeed, the theory of locally compact quantum groups can be seen as the topological version of the theory of quantum groups as they are developed here in a purely algebraic context.

The operator algebra approach to quantum groups

A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory.

Polarized interacting exciton gas in quantum wells and bulk semiconductors

We develop a theory to calculate exciton binding energies of both two- and three-dimensional spin polarized exciton gases within a mean field approach. Our method allows the analysis of recent experiments showing the importance of the polarization and intensity of the excitation light on the exciton luminescence of GaAs quantum wells. We study the breaking of the spin degeneracy observed at high exciton density (5×1010 cm2). Energy level splitting between spin +1 and spin -1 is shown to be due to many-body interexcitonic exchange while the spin relaxation time is controlled by intraexciton exchange. © 1996 The American Physical Society.