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In biological and engineering systems, structure, function and dynamics are highly coupled. Such interactions can be naturally and compactly captured via tensor based state space dynamic representations. However, such representations are…
Topological insulators insulate in the bulk but exhibit robust conducting edge states protected by the topology of the bulk material. Here, we design a colloidal topological insulator and demonstrate experimentally the occurrence of edge…
Nonlinear systems, whose outputs are not directly proportional to their inputs, are well known to exhibit many interesting and important phenomena which have profoundly changed our technological landscape over the last 50 years. Recently…
For spinful systems with spin 1/2, it is generally believed that P and T invariant strong and second-order topologies exist in four band and eight band system, respectively. Here, by using periodic driving, we find it is possible to have…
The ability to efficiently simulate a variety of interacting quantum systems on a single device is an overarching goal for digital and analog quantum simulators. In circuit quantum electrodynamical systems, strongly nonlinear…
Three-dimensional topological insulators are characterized by insulating bulk state and metallic surface state involving Dirac fermions that behave as massless relativistic particles. These Dirac fermions are responsible for achieving a…
Multi--stability in the response of a ferrimagnetic spin resonator to an externally applied driving is experimentally studied. The observed multi--stability cannot be derived from any master equation that linearly depends on the spins'…
We establish the existence of a topological classification of many-particle quantum systems undergoing unitary time evolution. The classification naturally inherits phenomenology familiar from equilibrium -- it is robust against disorder…
Topological insulators are new class of materials which are characterized by a bulk band gap like ordinary band insulator but have protected conducting states on their edge or surface. These states emerge out due to the combination of…
Many-body physics is one very well suited field for testing quantum algorithms and for finding working heuristics on present quantum computers. We have investigated the non-equilibrium dynamics of one- and two-electron systems, which are…
The congregation of topological quantum and classical systems with the ideas of non-Hermitian physics has generated enormous research interest in the last few years. While the concepts associated to non-trivial topological aspects have…
This paper proposes an approach to addresses the control challenges posed by a fault-induced uncertainty in both the dynamics and control input effectiveness of a class of hierarchical nonlinear systems in which the high-level dynamics is…
We investigate the emergence of anti-ferromagnetic ordering and its effect on the helical edge states in a quantum spin Hall insulator, in the presence of strong Coulomb interaction. Using dynamical mean-field theory, we show that the…
Starting from the Dirac equation, the relativistic quantum hydrodynamic equations for Dirac electrons on a surface of a three dimensional-topological insulator (TI) are derived and numerically solved to study the spin plasmons. The surface…
A hybrid structure combining the advantages of topological insulator (TI), dielectric ferromagnet (FM), and graphene is investigated to realize the electrically controlled correlation between electronic and magnetic subsystems for…
Topological concepts have been employed to understand the ground states of many strongly correlated systems, but it is still quite unclear if and how topology manifests itself in the relaxation dynamics. Here we uncover emergent topological…
The discovery of topological matter has revolutionized the field of condensed matter physics giving rise to many interesting phenomena, and fostering the development of new quantum technologies. In this thesis we study the quantum dynamics…
Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…
Topological insulators interacting with magnetic impurities have been reported to host several unconventional effects. These phenomena are described within the framework of gapping Dirac quasiparticles due to broken time-reversal symmetry.…
The incoherent dynamical properties of open quantum systems are generically attributed to an ongoing correlation between the system and its environment. Here, we propose a novel way to assess the nature of these system-environment…