Quantum Correlations in Field Theory and Integrable Systems

In this thesis we will investigate some properties of one-dimensional quantum systems. From a theoretical point of view quantum models in one dimension are particularly interesting because they are strongly interacting, since particles cannot avoid each other in their motion, and you we can never ignore collisions. Yet, integrable models often generate new and non-trivial solutions, which could not be found perturbatively. In this dissertation we shall focus on two important aspects of integrable one- dimensional models: Their entanglement properties at equilibrium and their dynamical correlators after a quantum quench. The first part of the thesis will be therefore devoted to the study of the entanglement entropy in one- dimensional integrable systems, with a special focus on the XYZ spin-1/2 chain, which, in addition to being integrable, is also an interacting model. We will derive its Renyi entropies in the thermodynamic limit and its behaviour in different phases and for different values of the mass-gap will be analysed. In the second part of the thesis we will instead study the dynamics of correlators after a quantum quench , which represent a powerful tool to measure how perturbations and signals propagate through a quantum chain. The emphasis will be on the Transverse Field Ising Chain and the O(3) non-linear sigma model, which will be both studied by means of a semi-classical approach. Moreover in the last chapter we will demonstrate a general result about the dynamics of correlation functions of local observables after a quantum quench in integrable systems. In particular we will show that if there are not long-range interactions in the final Hamiltonian, then the dynamics of the model (non equal- time correlations) is described by the same statistical ensemble that describes its statical properties (equal-time correlations).

Monoidal categories for the physics of integrable models

Scopo di questa tesi é di evidenziare le connessioni tra le categorie monoidali, l'equazione di Yang-Baxter e l’integrabilità di alcuni modelli. Oggetto prinacipale del nostro lavoro é stato il monoide di Frobenius e come sia connesso alle C∗-algebre. In questo contesto la totalità delle dimostrazioni sfruttano la strumentazione dell'algebra diagrammatica. Nel corso del lavoro di tesi sono state riprodotte tali dimostrazioni tramite il più familiare linguaggio dell’algebra multilineare allo scopo di rendere più fruibili questi risultati ad un raggio più ampio di potenziali lettori.

The effects of aging and musical experience on the representation of tonal hierarchies

Two experiments explored the representation of the tonal hierarchy in Western music among older (aged 60 to 80) and younger (aged 15 to 22) musicians and nonmusicians. A probe tone technique was used: 4 notes from the major triad were presented, followed by 1 note chosen from the 12 notes of the chromatic scale. Whereas musicians had a better sense of the tonal hierarchy than nonmusicians, older adults were no worse than younger adults in differentiating the notes according to musical principles. However, older adults were more prone than younger adults to classify the notes by frequency proximity (pitch height) when proximity was made more salient, as were nonmusicians compared with musicians. With notes having ambiguous pitch height, pitch height effects disappeared among older adults but not nonmusicians. Older adults seem to have internalized tonal structure, but they sometimes fail to inhibit less musically relevant information.

An Analysis of Capacities, Moral Hierarchies, and the Moral Status of Non-Human Animals in Contemporary Animal Rights Work

The primary objective of this thesis is to demonstrate the pernicious impact that moral hierarchies have on our perception and subsequent treatment of non-human animals. Moral hierarchies in general are characterized by a dynamic in which one group is considered to be fundamentally superior to a lesser group. This thesis focuses specifically on the moral hierarchies that arise when humans are assumed to be superior to non-human animals in virtue of their advanced mental capabilities. The operative hypothesis of this thesis is essentially that moral hierarchies thwart the provision of justice to non-human animals in that they function as a justification for otherwise impermissible actions. When humans are assumed to be fundamentally superior to non-human animals then it becomes morally permissible for humans to kill non-human animals and utilize them as mere instrumentalities. This thesis is driven primarily by an in-depth analysis of the approaches to animal rights that are provided by Peter Singer, Tom Regan, and Gary Francione. Each of these thinkers claim that they overcome anthropocentrism and provide approaches that preclude the establishment of a moral hierarchy. One of the major findings of this thesis, however, is that Singer and Regan offer approaches that remain highly anthropocentric despite the fact that each thinker claims that they have overcome anthropocentrism. The anthropocentrism persists in these respective approaches in that each thinkers gives humans Regan and Singer have different conceptions of the criteria that are required to afford a being moral worth, but they both give preference to beings that have the cognitive ability to form desires regarding the future.. As a result, a moral hierarchy emerges in which humans are regarded to be fundamentally superior. Francione, however, provides an approach that does not foster a moral hierarchy. Francione creates such an approach by applying the principle of equal consideration of interests in a consistent manner. Moreover, Francione argues that mere sentience is both a necessary and sufficient condition for being eligible and subsequently receiving moral consideration. The upshot of this thesis is essentially that the moral treatment of animals is not compatible with the presence of a moral hierarchy. As a result, this thesis demonstrates that future approaches to animal rights must avoid the establishment of moral hierarchies. The research and analysis within this thesis demonstrates that this is not a possibility, however, unless all theories of justice that are to accommodate animals abandon the notion that cognition matters morally.

From hierarchies to well-foundedness

We highlight that the connection of well-foundedness and recursive definitions is more than just convenience. While the consequences of making well-foundedness a sufficient condition for the existence of hierarchies (of various complexity) have been extensively studied, we point out that (if parameters are allowed) well-foundedness is a necessary condition for the existence of hierarchies e.g. that even in an intuitionistic setting (Π01−CA0)α⊢wf(α)where(Π01−CA0)α stands for the iteration of Π01 comprehension (with parameters) along some ordinal α and wf(α) stands for the well-foundedness of α.

The anisotropic λ -deformed SU(2) model is integrable

The all-loop anisotropic Thirring model interpolates between the WZW model and the non-Abelian T-dual of the anisotropic principal chiral model. We focus on the SU(2) case and we prove that it is classically integrable by providing its Lax pair formulation. We derive its underlying symmetry current algebra and use it to show that the Poisson brackets of the spatial part of the Lax pair, assume the Maillet form. In this way we procure the corresponding r and s matrices which provide non-trivial solutions to the modified Yang–Baxter equation.

Generalised integrable λ- and η-deformations and their relation

We construct two-parameter families of integrable λ -deformations of two-dimensional field theories. These interpolate between a CFT (a WZW/gauged WZW model) and the non-Abelian T-dual of a principal chiral model on a group/symmetric coset space. In examples based on the SU(2) WZW model and the SU(2)/U(1) exact coset CFT, we show that these deformations are related to bi-Yang–Baxter generalisations of η-deformations via Poisson–Lie T-duality and analytic continuation. We illustrate the quantum behaviour of our models under RG flow. As a byproduct we demonstrate that the bi-Yang–Baxter σ-model for a general group is one-loop renormalisable.

All-loop anomalous dimensions in integrable λ-deformed σ-models

We calculate the all-loop anomalous dimensions of current operators in λ-deformed σ-models. For the isotropic integrable deformation and for a semi-simple group G we compute the anomalous dimensions using two different methods. In the first we use the all-loop effective action and in the second we employ perturbation theory along with the Callan–Symanzik equation and in conjunction with a duality-type symmetry shared by these models. Furthermore, using CFT techniques we compute the all-loop anomalous dimension of bilinear currents for the isotropic deformation case and a general G . Finally we work out the anomalous dimension matrix for the cases of anisotropic SU(2) and the two couplings, corresponding to the symmetric coset G/H and a subgroup H, splitting of a group G.

Integrable high order UWB pulse photonic generator based on cross phase modulation in a SOA-MZI

We propose and experimentally demonstrate a potentially integrable optical scheme to generate high order UWB pulses. The technique is based on exploiting the cross phase modulation generated in an InGaAsP Mach-Zehnder interferometer containing integrated semiconductor optical amplifiers, and is also adaptable to different pulse modulation formats through an optical processing unit which allows to control of the amplitude, polarity and time delay of the generated taps.