Continuum tensor network field states, path integral representations and spatial symmetries

A natural way to generalize tensor network variational classes to quantum field systems is via a continuous tensor contraction. This approach is first illustrated for the class of quantum field states known as continuous matrix-product states (cMPS). As a simple example of the path-integral representation we show that the state of a dynamically evolving quantum field admits a natural representation as a cMPS. A completeness argument is also provided that shows that all states in Fock space admit a cMPS representation when the number of variational parameters tends to infinity. Beyond this, we obtain a well-behaved field limit of projected entangled-pair states (PEPS) in two dimensions that provide an abstract class of quantum field states with natural symmetries. We demonstrate how symmetries of the physical field state are encoded within the dynamics of an auxiliary field system of one dimension less. In particular, the imposition of Euclidean symmetries on the physical system requires that the auxiliary system involved in the class' definition must be Lorentz-invariant. The physical field states automatically inherit entropy area laws from the PEPS class, and are fully described by the dissipative dynamics of a lower dimensional virtual field system. Our results lie at the intersection many-body physics, quantum field theory and quantum information theory, and facilitate future exchanges of ideas and insights between these disciplines.

Stochastic and infinite dimensional analysis

This volume presents a collection of papers covering applications from a wide range of systems with infinitely many degrees of freedom studied using techniques from stochastic and infinite dimensional analysis, e.g. Feynman path integrals, the statistical mechanics of polymer chains, complex networks, and quantum field theory. Systems of infinitely many degrees of freedom create their particular mathematical challenges which have been addressed by different mathematical theories, namely in the theories of stochastic processes, Malliavin calculus, and especially white noise analysis. These proceedings are inspired by a conference held on the occasion of Prof. Ludwig Streit’s 75th birthday and celebrate his pioneering and ongoing work in these fields.

Láser Q-Switched en el manejo de ocronosis exógena: revisión sistemática de la literatura

Antecedentes: La ocronosis Exógena (OE) es una enfermedad subdiagnosticada y de difícil manejo (1). El láser Q-Switched (QS) surge como una alternativa para el tratamiento de esta (2). Objetivo: Describir las características de los pacientes, del láser QS y los desenlaces en el tratamiento de OE. Métodos: Se realizó una búsqueda de la literatura en las bases PubMed, Embase, PMC, Scielo, Elselvier, BMJ Case Reports, Journal of Medical Case Reports, Cases Journal e International Medical Case Reports Journal, desde enero del 2000 a marzo del 2016, pacientes con ocronosis exógena, 18 a 70 años, tratados con láser QS. Los artículos fueron evaluados mediante la herramienta de evaluación de validez y valor educativo de reportes de caso descrito por Pierson (3). Resultados: Se encontraron 256 artículos, 63 fueron seleccionados: 28 repetidos y 31 no cumplieron criterios de inclusión. Se escogieron 4 artículos que reportan 12 casos de pacientes con ocronosis exógena diagnosticada mediante estudio histopatológico y tratada con láser QS. Discusión: Hay poca experiencia con el láser QS en OE. En la práctica clínica se usa para tatuajes y patologías pigmentarias dérmicas con resultados satisfactorios. El pigmento dérmico en OE y la corta duración de pulso de láser QS, podrían ser el pilar de tratamiento para OE. Conclusión: El láser QS puede ser útil para el tratamiento en OE, con nivel de evidencia 3 y grado de recomendación D. Se sugiere realizar estudios clínicos con mayor grado de evidencia.

From the Humpata Plateau to Namibe Desert, SW Angola

After the Congress, a six-day field trip, will be held through three southwestern provinces of Angola (Huíla, Namibe and Cunene), every day starting and ending in the city of Lubango, for overnight stay in Lubango, with the purpose to observe some of the main sites of geological interest in this zone of Angola. The itinerary of this field trip presents the geologic history of Southwestern Angola and its evolution in the scope of the Congo Craton, through a trip that begins in the first excursion days by the oldest geologic formations and phenomena until the recent geologic formations and phenomena on the last excursion days. On the first and second excursion days, September 5th and September 6th, the field trip will go along the Kunene Anorthosite Complex of Angola (KAC), to observe some petrographic features of the KAC that are important to understand the emplacement of this huge igneous massif of the early Kibarean age. These days of the field trip allow the observation of Earthen Construction, because this region of Cunene is privileged to appreciate a kind of Eco-construction, made of raw earth and in wattle and daub, built with ancient techniques, which constitute a real GeoHeritage. On September 7th, in the morning, the destination will be Tundavala, to visit Tundavala Gap, a huge escarpment of more than 1,000 m high cutted in Neo-Archean and Paleo-Proterozoic igneous rocks, the Ruins of Tundavala (quartzite blocks with sedimentary structures) and Tundavala Waterfalls on a quartzitic scarp. After lunch, the field trip continues towards Humpata plateau to observe the panoramic view over Lubango city from the Statue of Cristo Rei, then the outcrops of dolomitic limestones with stromatolites and dolerites and finally the Leba passage, a huge escarpment and one of the most spectacular parts of the Serra da Chela, traversed by a mountain road built in the early 70s of the last century, that can be observed from the belvedere of the Serra da Chela. On September 8th, the destination is the carbonatite complexes of Tchivira and Bonga, belonging to the Mesozoic alkaline massifs of ultrabasic rocks, a rift valley system that occurs during the Early Cretaceous. In this forth excursion day, due to the huge dimensions of these two carbonatite structures it will be visited, only, the Complex of Bonga, namely the outcrops of the northern part of the structure and secondary deposits on the boundary on the southern part of the of the Complex. The last two excursion days, September 9th and September 10th, are to observe the Cretaceous Basin of Namibe. On September 9th, the northern part of Namibe Basin will be visited to observe the volcanic basic rocks of Namibe as well as the interesting paleontological site of Bentiaba. On September 10th, the destination is the southern and more recent part of Namibe Basin, where on the Namib Desert, the exotic plant Welwitschia mirabilis can be observed, as well as Arco, an oasis in the desert. This last excursion day, ends up at the dunes of Tombwa near the mouth of Curoca river and the beautiful bay of Tombwa, where can be observed heavy minerals in their beach sands.

Gli integrali di cammino

Normalmente la meccanica quantistica non relativistica è ricavata a partire dal fatto che una particella al tempo t non può essere descritta da una posizione $x$ definita, ma piuttosto è descritta da una funzione, chiamata funzione d'onda, per cui vale l'equazione differenziale di Schr\"odinger, e il cui modulo quadro in $x$ viene interpretato come la probabilità di rilevare la particella in tale posizione. Quindi grazie all'equazione di Schr\"odinger si studia la dinamica della funzione d'onda, la sua evoluzione temporale. Seguendo quest'approccio bisogna quindi abbandonare il concetto classico di traiettoria di una particella, piuttosto quello che si studia è la "traiettoria" della funzione d'onda nei vari casi di campi di forze che agiscono sulla particella. In questa tesi si è invece scelto di studiare un approccio diverso, ma anch'esso efficace nel descrivere i fenomeni della meccanica quantistica non relativistica, formulato per la prima volta negli anni '50 del secolo scorso dal dott. Richard P. Feynman. Tale approccio consiste nel considerare una particella rilevata in posizione $x_a$ nell'istante $t_a$, e studiarne la probabilità che questa ha, nelle varie configurazioni dei campi di forze in azione, di giungere alla posizione $x_b$ ad un successivo istante $t_b$. Per farlo si associa ad ogni percorso che congiunge questi due punti spazio-temporali $a$ e $b$ una quantità chiamata ampiezza di probabilità del percorso, e si sviluppa una tecnica che permette di sommare le ampiezze relative a tutti gli infiniti cammini possibili che portano da $a$ a $b$, ovvero si integra su tutte le traiettorie $x(t)$, questo tipo di integrale viene chiamato integrale di cammino o più comunemente path integral. Il modulo quadro di tale quantità darà la probabilità che la particella rilevata in $a$ verrà poi rilevata in $b$.