RESUMEN
We present a detailed analysis of the connection between chaos and the onset of thermalization in the spin-boson Dicke model. This system has a well-defined classical limit with two degrees of freedom, and it presents both regular and chaotic regions. Our studies of the eigenstate expectation values and the distributions of the off-diagonal elements of the number of photons and the number of excited atoms validate the diagonal and off-diagonal eigenstate thermalization hypothesis (ETH) in the chaotic region, thus ensuring thermalization. The validity of the ETH reflects the chaotic structure of the eigenstates, which we corroborate using the von Neumann entanglement entropy and the Shannon entropy. Our results for the Shannon entropy also make evident the advantages of the so-called "efficient basis" over the widespread employed Fock basis when investigating the unbounded spectrum of the Dicke model. The efficient basis gives us access to a larger number of converged states than what can be reached with the Fock basis.
RESUMEN
We present an analysis of chaos and regularity in the open Dicke model, when dissipation is due to cavity losses. Due to the infinite Liouville space of this model, we also introduce a criterion to numerically find a complex spectrum which approximately represents the system spectrum. The isolated Dicke model has a well-defined classical limit with two degrees of freedom. We select two case studies where the classical isolated system shows regularity and where chaos appears. To characterize the open system as regular or chaotic, we study regions of the complex spectrum taking windows over the absolute value of its eigenvalues. Our results for this infinite-dimensional system agree with the Grobe-Haake-Sommers (GHS) conjecture for Markovian dissipative open quantum systems, finding the expected 2D Poisson distribution for regular regimes, and the distribution of the Ginibre unitary ensemble (GinUE) for the chaotic ones, respectively.
RESUMEN
By employing Husimi quasiprobability distributions, we show that a bounded portion of an unbounded phase space induces a finite effective dimension in an infinite-dimensional Hilbert space. We compare our general expressions with numerical results for the spin-boson Dicke model in the chaotic energy regime, restricting its unbounded four-dimensional phase space to a classically chaotic energy shell. This effective dimension can be employed to characterize quantum phenomena in infinite-dimensional systems, such as localization and scarring.
RESUMEN
In a classically chaotic system that is ergodic, any trajectory will be arbitrarily close to any point of the available phase space after a long time, filling it uniformly. Using Born's rules to connect quantum states with probabilities, one might then expect that all quantum states in the chaotic regime should be uniformly distributed in phase space. This simplified picture was shaken by the discovery of quantum scarring, where some eigenstates are concentrated along unstable periodic orbits. Despite that, it is widely accepted that most eigenstates of chaotic models are indeed ergodic. Our results show instead that all eigenstates of the chaotic Dicke model are actually scarred. They also show that even the most random states of this interacting atom-photon system never occupy more than half of the available phase space. Quantum ergodicity is achievable only as an ensemble property, after temporal averages are performed.
RESUMEN
In order to have optimum results in oncological patients, precise evaluation, diagnosis and staging of the patient is necessary. Positron emission tomography (PET) yields a high negative predictive value through exploration of the entire body. It diagnoses the benign or malignant state of a neoplasm that has been detected by other imaging methods and establishes an extensive diagnosis previous to therapeutic treatment of a known cancer. It identifies residual tumor and changes produced after surgery, chemotherapy or radiotherapy and locates suspicious residual tumor clinically or by elevation of the tumor markers. It allows for a new extension study or re-staging after diagnosis of recurrence and permits early evaluation of response to a therapeutic regime and permits the search for a primary tumor in patients with metastasis of unknown origin. PET leads to a molecular functional imaging of cancer in the entire body.
Asunto(s)
Neoplasias/diagnóstico , Tomografía de Emisión de Positrones , Tomografía Computarizada por Rayos X , HumanosRESUMEN
En oncología es necesario el diagnóstico y estadificación precisos del paciente con cáncer, para tener resultados óptimos en su tratamiento. La tomografía por emisión de positrones (PET) tiene alto valor predictivo negativo mediante la exploración del cuerpo entero. Diagnostica la benignidad o malignidad de una neoplasia detectada por otros métodos de imagen; establece el diagnóstico de extensión previo al planteamiento terapéutico de un cáncer conocido; identifica tumor residual y cambios producidos poscirugía, quimio o radioterapia; localiza recidivas tumorales sospechosas clínicamente o por elevación de marcadores tumorales; permite hacer un nuevo estudio de extensión o reestadificación tras el diagnóstico de una recurrencia; permite valorar tempranamente la respuesta a un esquema terapéutico y la búsqueda del tumor primario en pacientes con metástasis de origen desconocido. PET conduce a una imagenología molecular funcional del cáncer en el cuerpo entero.
In order to have optimum results in oncological patients, precise evaluation, diagnosis and staging of the patient is necessary. Positron emission tomography (PET) yields a high negative predictive value through exploration of the entire body. It diagnoses the benign or malignant state of a neoplasm that has been detected by other imaging methods and establishes an extensive diagnosis previous to therapeutic treatment of a known cancer. It identifies residual tumor and changes produced after surgery, chemotherapy or radiotherapy and locates suspicious residual tumor clinically or by elevation of the tumor markers. It allows for a new extension study or re-staging after diagnosis of recurrence and permits early evaluation of response to a therapeutic regime and permits the search for a primary tumor in patients with metastasis of unknown origin. PET leads to a molecular functional imaging of cancer in the entire body.