Phase separation in a spin-orbit coupled Bose-Einstein condensate

We study a spin-orbit (SO) coupled hyperfine spin-1 Bose-Einstein condensate (BEC) in a quasi-one-dimensional trap. For a SO-coupled BEC in a one-dimensional box, we show that in the absence of the Rabi term, any non-zero value of SO coupling will result in a phase separation among the components for a ferromagnetic BEC, like $^{87}$Rb. On the other hand, SO coupling favors miscibility in a polar BEC, like $^{23}$Na. In the presence of a harmonic trap, which favors miscibility, a ferromagnetic BEC phase separates, provided the SO-coupling strength and number of atoms are greater than some critical value. The Rabi term favors miscibility irrespective of the nature of the spin interaction: ferromagnetic or polar

Mobile vector soliton in a spin-orbit coupled spin-11 condensate

We study the formation of bound states and three-component bright vector solitons in a quasi-one-dimensional spin-orbit-coupled hyperfine spin $f=1$ Bose-Einstein condensate using numerical solution and variational approximation of a mean-field model. In the antiferromagnetic domain, the solutions are time-reversal symmetric, and the component densities have multi-peak structure. In the ferromagnetic domain, the solutions violate time-reversal symmetry, and the component densities have single-peak structure. The dynamics of the system is not Galelian invariant. From an analysis of Galelian invariance, we establish that the single-peak ferromagnetic vector solitons are true solitons and can move maintaining constant component densities, whereas the antiferromagnetic solitons cannot move with constant component densities

Vector solitons in a spin-orbit coupled spin-22 Bose-Einstein condensate

Five-component minimum-energy bound states and mobile vector solitons of a spin-orbit-coupled quasi-one-dimensional hyperfine-spin-2 Bose-Einstein condensate are studied using the numerical solution and variational approximation of a mean-field model. Two distinct types of solutions with single-peak and multi-peak density distribution of the components are identified in different domains of interaction parameters. From an analysis of Galilean invariance and time-reversal symmetry of the Hamiltonian, we establish that vector solitons with multi-peak density distribution preserve time-reversal symmetry, but cannot propagate maintaining the shape of individual components. However, those with single-peak density distribution violate time-reversal symmetry of the Hamiltonian, but can propagate with a constant velocity maintaining the shape of individual components

Spontaneous symmetry breaking in a spin-orbit coupled f=2f=2 spinor condensate

We study the ground-state density profile of a spin-orbit coupled $f=2$ spinor condensate in a quasi-one-dimensional trap. The Hamiltonian of the system is invariant under time reversal but not under parity. We identify different parity- and time-reversal-symmetry-breaking states. The time-reversal-symmetry breaking is possible for degenerate states. A phase separation among densities of different components is possible in the domain of time-reversal-symmetry breaking. Different types of parity- and time-reversal-symmetry-breaking states are predicted analytically and studied numerically. We employ numerical and approximate analytic solutions of a mean-field model in this investigation to illustrate our findings

Digital Afterlife : A General Overview

In this age of information, the means and mediums of exchanging information are adapting digital technologies that are developing at very rapid pace. Digital Afterlife can be understood as maintaining or transforming digital content of users present in the web-space according to users will in case of users deceased or incapability of operating their personal accounts which are considered to be a virtual representation of users in the web platforms. The user generated content can be termed as digital footprints in the cyberspace, the process also generates mass of internet users and wide range of issues of legalizing and transforming content right of users under social medias and web-based services. The thesis conceptualizes Digital Afterlife by stating Social Media and Web-based Services in the web space and their importance, legal issues concerning user, service providers and governing bodies and to seeking any alternative solution on the legal base to regulate Digital Afterlife. The scope of social media and web-based platform widens with increasing users population. The way of finding any alternative solution is done through a comparison of service providers applied terms and conditions for its usage and governing acts and policies related with Information and Communication Technology (ICT) in the region like United States and Europe. To produce more relevant output the thesis is conducted on recent publication regarding the thesis topic, studies and findings made on internet and professionals and intellectuals published materials. Since the Digital Afterlife is still in primitive stage a definite solution towards managing Digital Afterlife could not be obtained although a mutual initiative of all parties involved can implement the possibilities. Establishment of Digital Data Bank reforming the acts and regulations of ICT in co-operation of governing institutions was one of the alternatives that can be practiced in future to meet the objective of managing Digital Afterlife