
Andrés F. Reyes LegaLos Andes University (Colombia) | UNIANDES · Department of Physics
Andrés F. Reyes Lega
Ph.D.
About
50
Publications
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279
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Introduction
Additional affiliations
December 2011 - March 2012
March 1997 - September 1999
January 2010 - present
Universidad de los Andes
Position
- Professor (Associate)
Publications
Publications (50)
It has been known for some years that entanglement entropy obtained from partial trace does not provide the correct entanglement measure when applied to systems of identical particles. Several criteria have been proposed that have the drawback of being different according to whether one is dealing with fermions, bosons, or distinguishable particles...
We consider the dynamics of the Sorkin-Johnston (SJ) state for a massless
scalar field in two dimensions. We conduct a study of the renormalized
stress-tensor by a subtraction procedure, and compare the results with those of
the conformal vacuum, with an important contribution from correction term. We
find a large trace anomaly and compute backreac...
Ground states of quadratic Hamiltonians for fermionic systems can be characterized in terms of orthogonal complex structures. The standard way in which such Hamiltonians are diagonalized makes use of a certain "doubling" of the Hilbert space. In this work we show that this redundancy in the Hilbert space can be completely lifted if the relevant ort...
The algebraic approach to quantum physics emphasizes the role played by the structure of the algebra of observables and its relation to the space of states. An important feature of this point of view is that subsystems can be described by subalgebras, with partial trace being replaced by the more general notion of restriction to a subalgebra. This,...
We use infinite dimensional self-dual \(\mathrm {CAR}\) \(C^{*}\)-algebras to study a \({\mathbb {Z}}_{2}\)-index, which classifies free-fermion systems embedded on \({\mathbb {Z}}^{d}\) disordered lattices. Combes–Thomas estimates are pivotal to show that the \({\mathbb {Z}}_{2}\)-index is uniform with respect to the size of the system. We additio...
An approach to renormalization of scalar fields on the Doplicher–Fredenhagen–Roberts (DFR) quantum spacetime is presented. The effective nonlocal theory obtained through the use of states of optimal localization for the quantum spacetime is reformulated in the language of (perturbative) Algebraic Quantum Field Theory. The structure of the singulari...
An algebraic approach to the study of entanglement entropy of quantum systems is reviewed. Starting with a state on a C*-algebra, one can construct a density operator describing the state in the GNS representation space. Applications of this approach to the study of entanglement measures for systems of identical particles are outlined. The ambiguit...
An approach to renormalization of scalar fields on the Doplicher-Fredenhagen-Roberts (DFR) quantum spacetime is presented. The effective non-local theory obtained through the use of states of optimal localization for the quantum spacetime is reformulated in the language of (perturbative) Algebraic Quantum Field Theory. The structure of the singular...
An algebraic approach to the study of entanglement entropy of quantum systems is reviewed. Starting with a state on a $C^*$-algebra, one can construct a density operator describing the state in the GNS representation state. Applications of this approach to the study of entanglement measures for systems of identical particles are outlined. The ambig...
We consider the generators of gauge transformations with test functions which do not vanish on the boundary of a spacelike region of interest. These are known to generate the edge degrees of freedom in a gauge theory. In this paper, we augment these by introducing the dual or magnetic analog of such operators. We then study the algebra of these ope...
Within the setting of infinite-dimensional self-dual CAR C* algebras describing fermions in the [Formula: see text] lattice, we depart from the well-known Araki–Evans [Formula: see text] index for quasi-free fermion states and rewrite it in terms of states rather than in terms of basis projections. Furthermore, we reformulate results that relate eq...
The observables associated with a quantum system S form a non-commutative algebra A S . It is assumed that a density matrix ρ can be determined from the expectation values of observables. But A S admits inner automorphisms a→uau ⁻¹ , a, u ∈ A S , u*u = uu* = 1, so that its individual elements can be identified only up to unitary transformations. So...
Within the setting of infinite dimensional self-dual $\mathrm{CAR}$ $C^{*}$-algebras describing fermions in the $\mathbb{Z}^{d}$-lattice, we depart from the well-known Araki-Evans $\sigma(P_{1},P_{2})$ $\mathbb{Z}_{2}$-index for quasi-free fermion states and rewrite it in terms of states, rather than in terms of basis projections. Furthermore, we r...
We consider the generators of gauge transformations with test functions which do not vanish on the boundary of a spacelike region of interest. These are known to generate the edge degrees of freedom in a gauge theory. In this paper, we augment these by introducing the dual or magnetic analogue of such operators. We then study the algebra of these o...
The observables associated with a quantum system $S$ form a non-commutative algebra ${\mathcal A}_S$. It is assumed that a density matrix $\rho$ can be determined from the expectation values of observables. But $\mathcal A_S$ admits inner automorphisms $a\mapsto uau^{-1},\; a,u\in {\mathcal A}_S$, $u^*u=u^*u=1$, so that its individual elements can...
We use infinite dimensional self-dual $\mathrm{CAR}$ $C^{*}$-algebras to study the existence of a $\mathbb{Z}_{2}$-index, which classifies free-fermions systems embedded on $\mathbb{Z}^{d}$ disordered lattices. Combes-Thomas estimates are pivotal to show that the $\mathbb{Z}_{2}$-index is uniform with respect to the size of the system. We additiona...
The algebraic approach to quantum physics emphasizes the role played by the structure of the algebra of observables and its relation to the space of states. An important feature of this point of view is that subsystems can be described by subalgebras, with partial trace being replaced by the more general notion of restriction to a subalgebra. This,...
The Gauss law Balachandran, A. P. a basic role in gauge theories, enforcing gauge invariance Reyes-Lega, A. F. creating edge states and superselection sectors. This article surveys these aspects of the Gauss law in QED, QCD and nonlinear G/H models. It is argued that nonabelian superselection rules are spontaneously broken. That is the case with SU...
The Gauss law plays a basic role in gauge theories, enforcing gauge invariance and creating edge states and superselection sectors. This article surveys these aspects of the Gauss law in QED, QCD and nonlinear $G/H$ models. It is argued that nonabelian superselection rules are spontaneously broken. That is the case with $SU(3)$ of colour which is s...
Ground states of quadratic Hamiltonians for fermionic systems can be characterized in terms of orthogonal complex structures. The standard way in which such Hamiltonians are diagonalized makes use of a certain "doubling" of the Hilbert space. In this work we show that this redundancy in the Hilbert space can be completely lifted if the relevant ort...
This chapter provides the reader with a general overview of the various topics discussed in this volume, emphasizing the deep relations existing between them. Following a brief historical account of the emergence of the concept of “quantization” both in physics and mathematics, a description of the main concepts and tools appearing in subsequent ch...
These notes present an overview of the lectures held by Abhay Ashtekar on the theory of quantum fields in curved space-times and its applications to cosmology at the Summer School “Geometric, topological, and algebraic methods for quantum field theory”, held at Villa de Leyva in 2015. The first part of the notes is pretty much self contained, assum...
This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics.
The opening chapter introduces the various forms of quantization and their interactions with each other...
Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the algebraic approach to quantum physics. Aspects of the representation theory of C*-algebras will be motivated and illustrated in physical terms. Particular...
Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the algebraic approach to quantum physics. Aspects of the representation theory of C*-algebras will be motivated and illustrated in physical terms. Particular...
Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the algebraic approach to quantum physics. Aspects of the representation theory of C*-algebras will be motivated and illustrated in physical terms. Particular...
A partir de la estrategia reube (Renovación de la Enseñanza Universitaria Basada en Evidencias), abordamos la problemática de la renovación didáctica del proceso de enseñanza/aprendizaje de la docencia universitaria de Física de pregrado. La estrategia de acompañamiento e innovación pedagógica reube se basa en la recolección de evidencias puntuales...
Based on the REBUT (Renovation of Evidence-Based University Teaching) strategy, this paper addresses the didactic problem of the educational renewal of teaching/learning regarding university teaching staff for undergraduate physics programs. The support strategy and pedagogical innovation of REBUT is based on the collection of evidence on the speci...
Based on lectures given at the renowned Villa de Leyva summer school, this book provides a unique presentation of modern geometric methods in quantum field theory. Written by experts, it enables readers to enter some of the most fascinating research topics in this subject. Covering a series of topics on geometry, topology, algebra, number theory me...
Based on lectures given at the renowned Villa de Leyva summer school, this book provides a unique presentation of modern geometric methods in quantum field theory. Written by experts, it enables readers to enter some of the most fascinating research topics in this subject. Covering a series of topics on geometry, topology, algebra, number theory me...
We have developed a novel approach to entanglement, suitable to be used in general quantum systems and specially in systems of identical particles. The approach is based on the GNS construction of representation of C -algebra of observables. In particular, the notion of partial trace is replaced by the more general notion of restriction of a state...
It has been known for some years that entanglement entropy obtained from partial trace does not provide the correct entanglement measure when applied to systems of identical particles. Several criteria have been proposed that have the drawback of being different according to whether one is dealing with fermions, bosons or distinguishable particles....
We present a general approach to quantum entanglement and entropy that is
based on algebras of observables and states thereon. In contrast to more
standard treatments, Hilbert space is an emergent concept, appearing as a
representation space of the observable algebra, once a state is chosen. In this
approach, which is based on the Gelfand-Naimark-S...
A novel approach to entanglement, based on the Gelfand-Naimark-Segal (GNS)
construction, is introduced. It considers states as well as algebras of
observables on an equal footing. The conventional approach to the emergence of
mixed from pure ones based on taking partial traces is replaced by the more
general notion of the restriction of a state to...
An algebraic approach to the study of quantum mechanics on configuration
spaces with a finite fundamental group is presented. It uses, in an essential
way, the Gelfand-Naimark and Serre-Swan equivalences and thus allows one to
represent geometric properties of such systems in algebraic terms. As an
application, the problem of quantum indistinguisha...
The angular momentum operators for a system of two spin-zero indistinguishable particles are constructed, using Isham’s Canonical
Group Quantization method. This mathematically rigorous method provides a hint at the correct definition of (total) angular
momentum operators, for arbitrary spin, in a system of indistinguishable particles. The connecti...
Within a geometric and algebraic framework, the structures which are related to the spin-statistics connection are discussed.
A comparison with the Berry-Robbins approach is made. The underlying geometric structure constitutes an additional support
for this approach. In our work, a geometric approach to quantum indistinguishability is introduced wh...
Using the method of canonical group quantization, we construct the angular
momentum operators associated to configuration spaces with the topology of (i)
a sphere and (ii) a projective plane. In the first case, the obtained angular
momentum operators are the quantum version of Poincare's vector, i.e., the
physically correct angular momentum operato...
The aim of this paper is to give a simple, geometric proof of Wigner’s theorem on the realization
of symmetries in quantum mechanics that clarifies its relation to projective geometry. Although several
proofs exist already, it seems that the relevance of Wigner’s theorem is not fully appreciated in general.
It is Wigner’s theorem which allows the u...
We study the relation between Chern numbers and Quantum Phase Transitions (QPT) in the XY spin-chain model. By coupling the spin chain to a single spin, it is possible to study topological invariants associated to the coupling Hamiltonian. These invariants contain global information, in addition to the usual one (obtained by integrating the Berry c...
We present results on both the intensity and phase-dynamics of the transient non-linear optical response of a single quantum dot (SQD) with and without the presence of a magnetic field. The time evolution of the Four Wave Mixing (FWM) signal on a sub-picosecond time scale is calculated, taking into account exciton-exciton correlations. The two case...
In this work we consider non-relativistic quantum mechanics, obtained from a classical configuration space Q of indistinguishable particles. Following an approach proposed by one of the authors, wave functions are regarded as elements of suitable projective modules over C(Q). We take furthermore into account the G-Theory point of view, where the ro...
We present results on both the intensity and phase-dynamics of the transient non-linear optical response of a single quantum dot (SQD). The time evolution of the Four Wave Mixing (FWM) signal on a subpicosecond time scale is dominated by biexciton effects. In particular, for the cross-polarized excitation case a biexciton bound state is found. In t...
A short survey of the theory of the Quantum Hall effect is given emphasizing topological aspects of the quantization of the conductivity and showing how topological invariants can be derived from the hamiltonian. We express these invariants in terms of Chern numbers and show in precise mathematical terms how this relates to the Kubo formula.
Ultrafast spectroscopy experiments on single quantum dot (SQD) in magnetic fields provide a variety of unexpected results, one of them being the recently reported entanglement of exciton states. In order to explore the entanglement robustness, dephasing mechanisms must be considered. By calculating the non-linear time resolved optical spectrum of a...
Recent experimental results demonstrate an exceptionally high level of control of excitons in a single quantum dot. We report on theoretical results about non-linear optical effects due to exciton-exciton correlations. Our formalism allows us to consider the fully degenerate non-linear spectrum (two laser excitations at the same frequency) as well...
The energy and wavefunction of a quasi-two-dimensional magnetic polaron in semimagnetic semiconductors are calculated by solving a non-linear Wannier equation. A self-consistent solution is presented including exactly the structure factor of the system. We found that the magnetic polaron energy is strongly dependent on temperature and well width. G...
A partir de la estrategia REUBE (Renovación de la Enseñanza UniversitariaBasada en Evidencias), abordamos la problemática de la renovación didácticadel proceso de enseñanza/aprendizaje de la docencia universitariade Física de pregrado. La estrategia de acompañamiento e innovaciónpedagógica REUBE se basa en la recolección de evidencias puntuales sob...