Transport in the sine-Gordon field theory: from generalized hydrodynamics to semiclassics

The semiclassical approach introduced by Sachdev and collaborators proved to be extremely successful in the study of quantum quenches in massive field theories, both in homogeneous and inhomogeneous settings. While conceptually very simple, this method allows one to obtain analytic predictions for several observables when the density of excitations produced by the quench is small. At the same time, a novel generalized hydrodynamic (GHD) approach, which captures exactly many asymptotic features of the integrable dynamics, has recently been introduced. Interestingly, also this theory has a natural interpretation in terms of semiclassical particles and it is then natural to compare the two approaches. This is the objective of this work: we carry out a systematic comparison between the two methods in the prototypical example of the sine-Gordon field theory. In particular, we study the "bipartitioning protocol" where the two halves of a system initially prepared at different temperatures are joined together and then left to evolve unitarily with the same Hamiltonian. We identify two different limits in which the semiclassical predictions are analytically recovered from GHD: a particular non-relativistic limit and the low temperature regime. Interestingly, the transport of topological charge becomes sub-ballistic in these cases. Away from these limits we find that the semiclassical predictions are only approximate and, in contrast to the latter, the transport is always ballistic. This statement seems to hold true even for the so-called "hybrid" semiclassical approach, where finite time DMRG simulations are used to describe the evolution in the internal space.Comment: 30 pages, 6 figure

Integrable Matrix Product States from boundary integrability

We consider integrable Matrix Product States (MPS) in integrable spin chains and show that they correspond to "operator valued" solutions of the so-called twisted Boundary Yang-Baxter (or reflection) equation. We argue that the integrability condition is equivalent to a new linear intertwiner relation, which we call the "square root relation", because it involves half of the steps of the reflection equation. It is then shown that the square root relation leads to the full Boundary Yang-Baxter equations. We provide explicit solutions in a number of cases characterized by special symmetries. These correspond to the "symmetric pairs" $(SU(N),SO(N))$ and $(SO(N),SO(D)\otimes SO(N-D))$, where in each pair the first and second elements are the symmetry groups of the spin chain and the integrable state, respectively. These solutions can be considered as explicit representations of the corresponding twisted Yangians, that are new in a number of cases. Examples include certain concrete MPS relevant for the computation of one-point functions in defect AdS/CFT.Comment: 33 pages, v2: minor corrections, references added, v3: minor modifications, v4: minor modification

Land Use Change Impacts of Biofuels: Near-VAR Evidence from the US

The present paper studies the land use change impacts of fuels and biofuels. We test the theoretical hypothesis, which says that changes in fuel prices cause changes in land use both directly and indirectly and, because of price inter-dependencies, biofuels reinforce the land use change impacts. Our data consists of yearly observations extending from 1950 to 2007 for the US, to which we apply time-series analytical mechanisms of five major traded agricultural commodities, the area of cultivated agricultural land and crude oil price. The empirical findings confirm that markets for crude oil and cultivated agricultural land are interdependent: an increase in oil price by 1 dollar/barrel increases land use between 54 and 68 thousand hectares. We also find that the rise of bioenergy sector accelerates land use change in the US.Near-VAR, energy, bioenergy, prices, land use, biofuel support policies.

Exact dynamics in dual-unitary quantum circuits

We consider the class of dual-unitary quantum circuits in 1 + 1 dimensions and introduce a notion of “solvable” matrix product states (MPSs), defined by a specific condition which allows us to tackle their time evolution analytically. We provide a classification of the latter, showing that they include certain MPSs of arbitrary bond dimension, and study analytically different aspects of their dynamics. For these initial states, we show that while any subsystem of size l reaches infinite temperature after a time t ∝ l, irrespective of the presence of conserved quantities, the light cone of two-point correlation functions displays qualitatively different features depending on the ergodicity of the quantum circuit, defined by the behavior of infinite-temperature dynamical correlation functions. Furthermore, we study the entanglement spreading from such solvable initial states, providing a closed formula for the time evolution of the entanglement entropy of a connected block. This generalizes recent results obtained in the context of the self-dual kicked Ising model. By comparison, we also consider a family of nonsolvable initial mixed states depending on one real parameter β, which, as β is varied from zero to infinity, interpolate between the infinite-temperature density matrix and arbitrary initial pure product states. We study analytically their dynamics for small values of β, and highlight the differences from the case of solvable MPSs

Nonequilibrium Quantum States of Matter

Among the few lessons that Physics teaches us on a daily basis, one in particular is hard to miss: thermalization processes are ubiquitous. With the same degree of certainty, one can predict an apple to fall onto the ground if its stalk is cut, or a cup of tea to be found cold if left on the table for too long. In this respect, generic classical and quantum mechanical systems seem to behave in the same way. This is also one of the main difficulties in the experimental observation of the bizarre effects predicted from the quantum theory, as several of these are known to disappear at finite temperatures. It has been known for a long time that thermalization is associated with \u201cchaotic\u201d behavior at the microscopic level, but recently systematic efforts, both theoretical and experimental, have allowed us to understand its mechanisms at an unprecedented level of accuracy. Indeed, it has been realized that thermalization generally occurs also in isolated systems, where the absence of interactions with the environment allows for first principle theoretical investigations1. In this case thermalization takes place locally, as the whole system acts as a thermal bath for its own subsystems. Theoretical research has been motivated and paralleled by exciting experimental progress in cold-atom physics, which has provided robust, nearly ideal realizations of several theoretical models2. As an established piece of knowledge, recent research has now confirmed that two outstanding exceptions actually exist in the quantum realm, where thermalization is prevented to occur. These are many-body localized systems3, where disorder plays a crucial role, and integrable ones, which are protected by the existence of higher conservation laws. By their own nature, these systems display exceptional non-equilibrium features, which are not washed out by the onset of thermalization as relaxation occurs. At the core of the present thesis lie the remarkable properties of integrable systems out of equilibrium, with a special attention to physical effects which could be observed in cold-atom realizations. The work collected here is part of a large theoretical effort4 which in the past decade has focused on the study of relatively simple protocols to bring a quantum system out of equilibrium, such as the so-called quantum quench. In these \u201ctheoretical laboratories\u201d it has been possible to provide quantitative predictions which helped us to develop an intuition on general questions regarding non-equilibrium and thermalization processes. Furthermore, in some cases these studies have highlighted interesting physical effects which could be directly probed experimentally within cold-atom settings. The contribution of the present thesis is two-fold. On the one hand, we have developed new technical tools for the study of integrable systems out of equilibrium, and for the computation of measurable physical quantities such as correlation functions. The techniques employed are mainly analytical and rooted within the mathematical structures of integrability. On the other hand, we have singled out physically relevant nonequilibrium situations where exotic, non-thermal states of matter emerge after relaxation occurs, and provided quantitative analytical predictions in these cases. A comprehensive discussion of the motivations and results of our work will be presented in Chapter 1, where we provide a complete overview of this thesis and discuss the organization of its content

Scrambling in Random Unitary Circuits: Exact Results

We study the scrambling of quantum information in local random unitary circuits by focusing on the tripartite information proposed by Hosur et al. We provide exact results for the averaged R\'enyi-$2$ tripartite information in two cases: (i) the local gates are Haar random and (ii) the local gates are dual-unitary and randomly sampled from a single-site Haar-invariant measure. We show that the latter case defines a one-parameter family of circuits, and prove that for a "maximally chaotic" subset of this family quantum information is scrambled faster than in the Haar-random case. Our approach is based on a standard mapping onto an averaged folded tensor network, that can be studied by means of appropriate recurrence relations. By means of the same method, we also revisit the computation of out-of-time-ordered correlation functions, re-deriving known formulae for Haar-random unitary circuits, and presenting an exact result for maximally chaotic random dual-unitary gates.Comment: 29 pages, 7 figure

Nesting of the loggerhead turtle (Caretta caretta) in the southeast Adriatic confirmed

The nesting of sea turtles in Eastern Adriatic has not been previously reported, even though the possible nesting of the loggerhead turtle in Albania has been hypothesized. Data for nesting activities have been collected since 2002 along the Albanian coastline. Anecdotal evidence assembled over the years has provided important information regarding the possibility of the nesting of the loggerhead turtle in Albania. This study confirms the nesting of the loggerhead turtle in Albania. Although sporadic, it takes place along the entire Adriatic coast of Albania. This information shifts the border of nesting known so far from the northeast Ionian (Greece) to the southeast Adriatic Sea (Albania)

Nesting of the loggerhead turtle (Caretta caretta) in the southeast Adriatic confirmed

The nesting of sea turtles in Eastern Adriatic has not been previously reported, even though the possible nesting of the loggerhead turtle in Albania has been hypothesized. Data for nesting activities have been collected since 2002 along the Albanian coastline. Anecdotal evidence assembled over the years has provided important information regarding the possibility of the nesting of the loggerhead turtle in Albania. This study confirms the nesting of the loggerhead turtle in Albania. Although sporadic, it takes place along the entire Adriatic coast of Albania. This information shifts the border of nesting known so far from the northeast Ionian (Greece) to the southeast Adriatic Sea (Albania)

Stabilizer entropies and nonstabilizerness monotones

We study different aspects of the stabilizer entropies (SEs) and compare them against known nonstabilizerness monotones such as the min-relative entropy and the robustness of magic. First, by means of explicit examples, we show that, for R\'enyi index $0\leq n<2$, the SEs are not monotones with respect to stabilizer protocols which include computational-basis measurements, not even when restricting to pure states (while the question remains open for $n\geq 2$). Next, we show that, for any R\'enyi index, the SEs do not satisfy a strong monotonicity condition with respect to computational-basis measurements. We further study SEs in different classes of many-body states. We compare the SEs with other measures, either proving or providing numerical evidence for inequalities between them. Finally, we discuss exact or efficient tensor-network numerical methods to compute SEs of matrix-product states (MPSs) for large numbers of qubits. In addition to previously developed exact methods to compute the R\'enyi SEs, we also put forward a scheme based on perfect MPS sampling, allowing us to compute efficiently the von Neumann SE for large bond dimensions.Comment: 14 pages, 5 figure

Land use analysis for slope classes in watershed using GIS analysis

The objective of this work was to survey the land use at Limoeiro watershed placed on the Presidente Prudente and Álvares Machado counties in the West of the São Paulo State. The related survey was effected using an image of TM sensor of the satellite Landsat 7 and the Geographic Information System Idrisi. The result of the survey was statistically analyzed through the kappa index. After that, it was digitalized the level curves of the watershed which were interpolated to supply the slope classes of all the studied area. Subsequently, the slope spaces were crossed with the land use with the purpose of verifying the main land uses in each slope class. It was observed that cattle and the urban area are the main ground occupations in the watershed. It was still observed that the predominant slope spaces in the studied area are those between 3 and 12 percent.El objetivo de este trabajo fue la evaluación del uso del suelo en la cuenca de arroyo Limoeiro ubicados en las ciudades de Presidente Prudente y Álvarez Machado en el oeste de Sao Paulo. Esta evaluación se realizó mediante un sensor de imagen del Landsat TM 7 y el Sistema de Información Geográfica Idrisi. A continuación, las curvas de nivel de la cuenca fueran digitalizados y interpolados para obtener las clases de pendiente del área de estudio. Después, las clases pendiente fueran correlacionadas con el uso de la tierra con el fin de identificar los principales usos de la tierra en cada clase de pendiente. Se observó que la exploración agropecuaria y urbana son las principales ocupaciones de tierras en la cuenca. También se observó que las clases pendiente predominantes en la área de estudio son entre el 3 y 12 por ciento.O objetivo deste trabalho foi o levantamento do uso da terra na microbacia hidrográfica do Córrego Limoeiro situada nos municípios de Presidente Prudente e Álvares Machado no Oeste do Estado de São Paulo. O referido levantamento foi efetuado utilizando-se uma imagem do sensor TM do satélite Landsat 7 e o Sistema de Informações Geográficas Idrisi. O resultado do levantamento foi analisado estatisticamente através do índice kappa. Em seguida, digitalizaram-se as curvas de nível da microbacia que foram interpoladas para fornecer as classes de declive de toda a área estudada. Depois disso, cruzou-se as classes de declive com o uso da terra com a finalidade de verificar os principais usos da terra em cada classe de declive. Observou-se que a pecuária e a área urbanizada são as principais ocupações do solo na microbacia. Observou-se ainda que as classes de declive predominantes na área estudada são aquelas entre 3 e 12 por cento