Related papers: Operator growth and spread complexity in open quan…
The fine grained energy spectrum of quantum chaotic systems is widely believed to be described by random matrix statistics. A basic scale in such a system is the energy range over which this behavior persists. We define the corresponding…
Entanglement is one of the most important concepts in quantum physics. We review recent progress in understanding the quantum entanglement in many-body systems using large-$N$ solvable models: the Sachdev-Ye-Kitaev (SYK) model and its…
We use the spread complexity of a time evolved state after a sudden quantum quench in the Lipkin-Meshkov-Glick (LMG) model prepared in the ground state as a probe of quantum phase transition when the system is quenched towards the critical…
Entanglement growth and out-of-time-order correlators (OTOC) are used to assess the propagation of information in isolated quantum systems. In this work, using large scale exact time-evolution we show that for weakly disordered…
Realistic quantum devices are inherently open and often involve environments with memory. Here, we investigate quantum resource generation in two classes of random circuits, namely, memoryless open and memoryful open random circuits, and…
Studying the implications and characterizations of the excited state quantum phase transitions (ESQPTs) would enable us to understand various phenomena observed in quantum many body systems.In this work, we delve into the affects and…
The entropy production rate for an open quantum system with a classically chaotic limit has been previously argued to be independent of $\hbar$ and $D$, the parameter denoting coupling to the environment, and to be equal to the sum of…
The complexity of representation of operators in quantum mechanics can be characterized by the operator space entanglement entropy (OSEE). We show that in the homogeneous Heisenberg XY spin 1/2 chains the OSEE for initial local operators…
Krylov complexity is considered to provide a measure of the growth of operators evolving under Hamiltonian dynamics. The main strategy is the analysis of the structure of Krylov subspace $\mathcal{K}_M(\mathcal{H},\eta)$ spanned by the…
The dynamical spreading of quantum information through a many-body system, typically called scrambling, is a complex process that has proven to be essential to describe many properties of out-of-equilibrium quantum systems. Scrambling can,…
Quantum information scrambling refers to the spread of the initially stored information over many degrees of freedom of a quantum many-body system. Information scrambling is intimately linked to the thermalization of isolated quantum…
This Thesis explores the notion of Krylov complexity as a probe of quantum chaos and as a candidate for holographic complexity. The first Part is devoted to presenting the fundamental notions required to conduct research in this area.…
Quantum information scrambling has attracted much attention amid the effort to reconcile the conflict between quantum-mechanical unitarity and the thermalizaiton-irreversibility in many-body systems. Here we propose an unconventional…
We study growth quenches, which are local quenches that may gradually destabilize a false vacuum in certain kinetic constrained quantum lattice models, such as the East-West model. We point out a formal analogy with the dynamics of a local…
We study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process quantum…
Entropy generation in quantum sytems is tied to the existence of a nonclassical environment (heat bath or other) with which the system interacts. The continuous `measuring' of the open system by its environment induces decoherence of its…
Statistical mechanics is founded on the assumption that all accessible configurations of a system are equally likely. This requires dynamics that explore all states over time, known as ergodic dynamics. In isolated quantum systems, however,…
Characterizing the work statistics of driven complex quantum systems is generally challenging because of the exponential growth with the system size of the number of transitions involved between different energy levels. We consider the…
We study quantum information scrambling in spin models with both long-range all-to-all and short-range interactions. We argue that a simple global, spatially homogeneous interaction together with local chaotic dynamics is sufficient to give…
Non-local connections, i. e. long-range space-time correlations intrinsic to the observed subatomic dynamics of quantum systems is also exhibited by macro-scale dynamical systems as selfsimilar fractal space-time fluctuations and is…