My research area spans stochastic processes, non-equilibrium aspects of statistical physics, including stochastic resetting, long-range spin models, the Kuramoto models, and stochastic control techniques. Recently, I have been working on open quantum systems.
Stochastic Resetting in Complex Interacting Systems: It is a mechanism in which the natural evolution of a system is intermittently interrupted and returned to a prescribed initial state or configuration at random times. This simple intervention can profoundly alter the long-time behaviour of a system, leading to phenomena such as localisation, optimum search efficiency, and the emergence of nonequilibrium steady states (NESS) that would otherwise be absent, providing an efficient way of manipulating the dynamics and stationary properties of a system without necessarily changing its underlying interactions.
My research explores how stochastic resetting can be employed to control the collective behaviour and stationary properties of interacting many-body systems. In particular, I investigate resetting protocols in globally-coupled and networked oscillator systems, as well as long-range interacting spin models. This includes subsystem resetting, in which only a subpart of the system is reset rather than the entire system. This provides a versatile means of controlling collective phenomena, including synchronization and phase transitions.
Controlling Phase Transitions: The interplay between microscopic interactions and fluctuations gives rise to qualitatively different macroscopic states, leading to phase transitions in many-body systems. E.g. the transition from a disordered (paramagnetic) to an ordered (ferromagnetic) magnetic state and the spontaneous synchronization of interacting oscillators, etc. Conventionally, such transitions are controlled by tuning system parameters, such as temperature, interaction strength, or external fields. I am interested in the question of whether one can control the emergence and nature of phase transitions by manipulating the dynamics itself, without necessarily modifying the underlying interactions.
My research explores how nonequilibrium driving and dynamical interventions may be employed to engineer phase transitions. Using protocols like stochastic resetting and modified dissipative dynamics, I study how these dynamical protocols influence collective phenomena in classical and quantum systems. To mention a few, these kinds of dynamical interventions can shift phase boundaries, induce or suppress collective ordering, and even alter the nature of phase transitions, for instance, from continuous to discontinuous transitions, and vice versa.
Open Quantum Systems: My research explores the nonequilibrium dynamics and stationary-state properties of interacting quantum many-body systems coupled to external environments. Going beyond conventional linear Lindblad dynamics, I study nonlinear modifications that account for imperfect quantum-jump processes, introducing additional parameters that control the retention of quantum jumps. I demonstrate how these modifications can drive the system into nonequilibrium steady states with properties distinct from those of conventional thermal stationary states. An important motivation is to understand how engineered dissipative processes can control stationary states in open quantum systems.