Study of work on a quantum harmonic oscillator

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2017, Tutor: Bruno Juliá DíazWe define the work probability distribution that is done to a quantum system during some process, from which the average work, its variance and the irreversible work can be obtained. Two limits are introduced according to whether the system evolves adiabatically or it undergoes an instantaneous quench. The time evolution of this system is obtained by solving numerically the time dependent Schrödinger equation through the Crank-Nicolson method. The two limit situations are explored for the simple case of a quantum harmonic oscillator with a time dependent Hamiltonian, as well as the intermediate regime between both limits. The results for the average work done during the process and its variance agree with the analytical expressions for the two limits. Finally, we study the work probability distribution during a shortcut to adiabacity protocol

Work analysis of one-dimensional driven quantum systems

In recent years there has been a tremendous advance in the techniques to trap and control systems of a few bosonic and fermionic atoms [1,2]. In these systems the trap properties are usually tunable, thus allowing one to study how the quantum system adapts to the new trap properties. In particular one can consider a simple scenario in which a particle is trapped in a harmonic oscillator potential which trapping frequency is varied in time with a given time dependence. This system represents a simple example where the concepts of work [3] need to be adapted to quantumWe introduce the probability distribution of work performed on a one- dimensional quantum system and study the cases of a single particle in a harmonic or finite well potential and of a Bose-Einstein condensate in a finite well potential. The irreversible work is generalised for the case of Bose-Einstein condensates, described in the mean-field theory by the Gross-Pitaevskii equation. The properties of the ground state are analysed for each case, finding two di?erent static regimes for the finite well potential (with a third one for a BEC with attractive interactions) and one for the harmonic well. Finally, the irreversible work is studied for a linear ramping protocol where the potential is widened, and a relation between the static regimes and the dynamics of the system is identified. The evolution of the system is obtained by numerically solving either the time-dependent Gross-Pitaevskii or Schrödinger equation through the Crank-Nicolson method

Shell-shaped condensates with gravitational sag: contact and dipolar interactions.

We investigate Bose-Einstein condensates in bubble trap potentials in the presence of a small gravity. In particular, we focus on thin shells and study both contact and dipolar interacting condensates. We first analyze the effects of the anisotropic nature of the dipolar interactions, which already appear in the absence of gravity and are enhanced when the polarization axis of the dipoles and the gravity are slightly misaligned. Then, in the small gravity context, we investigate the dynamics of small oscillations of these thin, shell-shaped condensates triggered either by an instantaneous tilting of the gravity direction or by a sudden change of the gravity strength. This system could be a preliminary stage for realizing a gravity sensor in space laboratories

Improving unsupervised learning with exemplarCNNs

Most recent unsupervised learning methods explore alternative objectives, often referred to as self-supervised tasks, to train convolutional neural networks without the supervision of human annotated labels. This paper explores the generation of surrogate classes as a self-supervised alternative to learn discriminative features, and proposes a clustering algorithm to overcome one of the main limitations of this kind of approach. Our clustering technique improves the initial implementation and achieves 76.4% accuracy in the STL-10 test set, surpassing the current state-of-the-art for the STL-10 unsupervised benchmark. We also explore several issues with the unlabeled set from STL-10 that should be considered in future research using this dataset

Diseño e implementación de un sistema de monitorización y control para un módem satélite a través del protocolo SNMP

Projecte final de carrera fet en col.laboració amb Indra Espacio, S.A.The present project has been done in full at the Communications and Navigation Solutions Department of the company Indra Espacio and consists in the design and implementation of a system that, using the network management protocol SNMP, allows monitoring and configuring the most relevant parameters of a satellite modem. The whole system has been implemented in C language on a Linux Red Hat operating system and is made of a communication interface in charge of sending and receiving the SNMP messages, one module that analyzes the content of these messages and another module in charge of interacting with the main application that controls the operation of the modem. The interacting mechanism between the applications is based on the use of 2 shared memories where all the different parameters to manage are stored. Both memories have its own instructions sets for reading and writing and its own access control mechanisms. The system implements authentication and privacy mechanisms to ensure a total security in the communications. This new communication system has allowed the fully integration of the modem in environments managed with the SNMP protocol. This, at the same time, has allowed the configuration and monitoring of the modem through generic SNMP tools, making easier and faster both processes. The memory of the project includes all the details of the design and implementation processes of the systems and the entire tests done to ensure its correct operation, besides the description of the most relevant concepts used in it

No anul·lació de funcions L en valors crítics i resultats d'equidistribució en aritmètica

L'objectiu del treball és revisar els principals resultats d'equidistribució en aritmètica. En primer terme es presenten i demostren el Teorema de densitat de Dirichlet i el Teorema de densitat de Chebotarev. La part central del treball és la conjectura de Sato-Tate. Per presentar aquesta conjectura es desenvolupa la teoria de Serre, que ens serveix per unificar el teorema de Chebotarev i la conjectura de Sato-Tate. Una versió parcial de la conjectura de Sato-Tate va ser resolta recentment, utilitzant resultats molt avançats de teoria de nombres, per Richard Taylor. Una de les tasques del treball consisteix a esboçar aquesta demostració. Mitjançant la teoria de Serre generalitzem la conjectura de Sato-Tate per corbes de gènere superior. A partir d'aquesta generalització reinterpretem els resultats per a corbes el·líptiques amb CM. Per finalitzar l'estudi, considerem corbes de gènere 2, de les quals s'ha suggerit una possible solució de la conjectura de Sato-Tate generalitzada. Realitzant un estudi sobre aquesta solució podrem oferir resultats per tal d'aportar més informació sobre la resolució de conjectura.. Estudiar com la no anul·lació de funcions L permet la demostració de resultats aritmetics, com per exemple el teorema de densitat de Chebotarev i la conjectura de Soto-Tate