Importance of cluster formation in quantum critical systems

Emil Edipovich Lin

N. G. Antoniou, Yiannis Contoyiannis, F. Κ. Diakonos

We investigate the geometry of a critical system undergoing a second-order thermal phase transition. Using a local description for the dynamics characterizing the system at the critical point T=T(c), we reveal the formation of clusters with fractal geometry, where the term cluster is used to describe regions with a nonvanishing value of the order parameter. We show that, treating the cluster as an open subsystem of the entire system, new instanton-like configurations dominate the statistical mechanics of the cluster. We study the dependence of the resulting fractal dimension on the embedding dimension and the scaling properties (isothermal critical exponent) of the system. Taking into account the finite-size effects, we are able to calculate the size of the critical cluster in terms of the total size of the system, the critical temperature, and the effective coupling of the long wavelength interaction at the critical point. We also show that the size of the cluster has to be identified with the correlation length at criticality. Finally, within the framework of the mean field approximation, we extend our local considerations to obtain a global description of the system.

Giovanni Battimelli, Giovanni Ciccotti, Pietro Greco

K. Esler

After describing these advancements in methodology, we apply our new technology to fluid sodium near its liquid-vapor critical point. In particular, we explore the microscopic mechanisms which drive the continuous change from a dense metallic liquid to an expanded insulating vapor above the critical temperature. We show that the dynamic aggregation and dissociation of clusters of atoms play a significant role in determining the conductivity and that the formation of these clusters is highly density and temperature dependent. Finally, we suggest several avenues for research to further improve our simulations.

L. De Cesare, Dimo I. Uzunov

Rupam Bhagawati

In this internet and digitalization age, information in any form is very important to perform a digital task. The processing of any information to obtain the desired results requires a specific medium and sometimes to accomplish various tasks related to that set of information like browsing, searching, sorting, retrieval and management. In order to perform those tasks on the information, which are present on various acquaintances, we need to analyze the information by performing an unsupervised clustering in the realm of quantum computation. Quantum clustering is the core technique used in quantum computation to perform clustering of information with several algorithms that have been introduced and studied till date to analyze the cluster for increasing the efficiency of information exploration, information retrieval, information management and browsing system. Hence, introducing a quantum clustering technique to form clusters which would include sentences from a set of informative data set and the formation of clusters would be carried out by performing Semantic Analysis.