Generalized quantum geometric tensor for excited states using the path integral approach

The quantum geometric tensor, composed of the quantum metric tensor and Berry curvature, fully encodes the parameter space geometry of a physical system. We first provide a formulation of the quantum geometrical tensor in the path integral formalism that can handle both the ground and excited states, making it useful to characterize excited state quantum phase transitions (ESQPT). In this setting, we also generalize the quantum geometric tensor to incorporate variations of the system parameters and the phase-space coordinates. This gives rise to an alternative approach to the quantum covariance matrix, from which we can get information about the quantum entanglement of Gaussian states through tools such as purity and von Neumann entropy. Second, we demonstrate the equivalence between the formulation of the quantum geometric tensor in the path integral formalism and other existing methods. Furthermore, we explore the geometric properties of the generalized quantum metric tensor in depth by calculating the Ricci tensor and scalar curvature for several quantum systems, providing insight into this geometric information

Relativistic Runge-Lenz vector: from N=4{\cal N}=4 SYM to SO(4) scalar field theory

Starting from ${\cal N}=4$ SYM and using an appropriate Higgs mechanism we reconsider the construction of a scalar field theory non-minimally coupled to a Coulomb potential with a relativistic SO(4) symmetry and check for scalar field consistency conditions. This scalar field theory can also be obtained from a relativistic particle Lagrangian with a proper implementation of the non-minimal coupling. We provide the generalization of the non-relativistic construction of the Runge-Lenz vector to the relativistic case and show explicitly that this new vector generates the SO(4) algebra. Using the power of the SO(4) symmetry, we calculate the relativistic hydrogen atom spectrum. We provide a generalization of the Kustaanheimo-Stiefel transformation to the relativistic case and relate our results with the corresponding relativistic oscillator. Finally, in the light of these results, we reconsider the calculation of the hydrogen atom spectrum from the cusp anomalous dimension given in [2].Comment: 17 pages. Enhaced version matching the published JHEP version. Typos corrected. The argument of concistence at the end of section 2 was correcte

Galoisian Approach to Supersymmetric Quantum Mechanics

This thesis is concerning to the Differential Galois Theory point of view of the Supersymmetric Quantum Mechanics. The main object considered here is the non-relativistic stationary Schr\"odinger equation, specially the integrable cases in the sense of the Picard-Vessiot theory and the main algorithmic tools used here are the Kovacic algorithm and the \emph{algebrization method} to obtain linear differential equations with rational coefficients. We analyze the Darboux transformations, Crum iterations and supersymmetric quantum mechanics with their \emph{algebrized} versions from a Galoisian approach. Applying the algebrization method and the Kovacic's algorithm we obtain the ground state, the set of eigenvalues, eigenfunctions, the differential Galois groups and eigenrings of some Schr\"odinger equation with potentials such as exactly solvable and shape invariant potentials. Finally, we introduce one methodology to find exactly solvable potentials: to construct other potentials, we apply the algebrization algorithm in an inverse way since differential equations with orthogonal polynomials and special functions as solutions.Comment: Phd Dissertation, Universitat Politecnica de Catalunya, 200

The scattering of SH waves by a finite crack with a superposition based diffraction technique

The problem of diffraction of cylindrical and plane SH waves by a finite crack is revisited -- We construct an approximate solution by the addition of independent diffracted terms -- We start with the derivation of the fundamental case of a semi-infinite crack obtained as a degenerate case of generalized wedge -- This building block is then used to compute the diffraction of the main incident waves -- The interaction between the opposite edges of the crack is then considered one term at a time until a desired tolerance is reached -- We propose a recipe to determine the number of required interactions as a function of frequency -- The solution derived with the superposition technique can be applied at low and high frequencie

Chyloperitoneum in peritoneal dialysis : a case report and review of literature

El quiloperitoneo es una condicion infrecuente que se asocia a dialisis peritoneal; en la mayoria de los casos se puede confundir con peritonitis bacteriana, aunque puede ser la consecuencia de esta infeccion. Se reporta el desarrollo espontaneo de quiloperitoneo en un paciente de 54 anos con enfermedad renal cronica secundaria a nefropatia diabetica, en dialisis peritoneal manual desde hacia 5 anos. El tratamiento consistio en suspension temporal de la dialisis peritoneal, reposo intestinal, suministro de una dieta con alto contenido de acidos grasos de cadena media e infusion de octreotide, con lo cual a los 10 dias el paciente mostro mejoria, y se reinicio la dialisis peritoneal. Una busqueda sistematica de la literatura encontro 16 casos publicados (11 mujeres), con edades desde neonato hasta 88 anos.Revisión de la literatura115-11

Oral History Interview with John Niland: Conceptualising SMU

This is an abridged version of the original interview. Please contact the Library at [email protected] for access to the full version of the transcript and/or audio recording.</p