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The presence of noise or the interaction with an environment can radically change the dynamics of observables of an otherwise isolated quantum system. We derive a bound on the speed with which observables of open quantum systems evolve. This speed limit is divided into Mandelstam and Tamm’s original time-energy uncertainty relation and a time-information uncertainty relation recently derived for classical systems, and both are generalized to open quantum systems. By isolating the coherent and incoherent contributions to the system dynamics, we derive both lower and upper bounds on the speed of evolution. We prove that the latter provide tighter limits on the speed of observables than previously known quantum speed limits and that a preferred basis of speed operators serves to completely characterize the observables that saturate the speed limits. We use this construction to bound the effect of incoherent dynamics on the evolution of an observable and to find the Hamiltonian that gives the maximum coherent speedup to the evolution of an observable.

We present a very general model of epigenetic evolution unifying (neo-)Darwinian and (neo-)Lamarckian viewpoints. The evolution is represented in the form of adaptive dynamics given by the quantum(-like) master equation. This equation describes development of the information state of epigenome under the pressure of an environment. We use the formalism of quantum mechanics in the purely operational framework. (Hence, our model has no direct relation to quantum physical processes inside a cell.) Thus our model is about probabilities for observations which can be done on epigenomes and it does not provide a detailed description of cellular processes. Usage of the operational approach provides a possibility to describe by one model all known types of cellular epigenetic inheritance.

We consider a free-fermion chain undergoing dephasing, described by two different random-measurement protocols (unravelings): a quantum-state-diffusion and a quantum-jump one. Both protocols keep the state in a Slater-determinant form, allowing to address quite large system sizes. We find a bifurcation in the distribution of the measurement operators along the quantum trajectories, that’s to say, there is a point where the shape of this distribution changes from unimodal to bimodal. The value of the measurement strength where this phenomenon occurs is similar for the two unravelings, but the distributions and the transition have different properties reflecting the symmetries of the two measurement protocols. We also consider the scaling with the system size of the inverse participation ratio of the Slater-determinant components and find a power-law scaling that marks a multifractal behaviour, in both unravelings and for any nonvanishing measurement strength. Graphical abstract Position of the maxima of P n vs γ for the QSD protocol. The two maxima stem continuously and symmetrically at the bifurcation point γ QSD ∼ 0.2 , with a discontinuity of the derivative.

The quantum speed limit indicates the maximal evolution speed of the quantum system. In this work, we determine speed limits on the informational measures, namely the von Neumann entropy, maximal information, and coherence of quantum systems evolving under dynamical processes. These speed limits ascertain the fundamental limitations on the evolution time required by the quantum systems for the changes in their informational measures. Erasing of quantum information to reset the memory for future use is crucial for quantum computing devices. We use the speed limit on the maximal information to obtain the minimum time required to erase the information of quantum systems via some quantum processes of interest.

We study spread complexity and the statistics of work done for quenches in the three-spin interacting Ising model, the XY spin chain, and the Su–Schrieffer–Heeger model. We study these models without quench and for different schemes of quenches, such as sudden quench and multiple sudden quenches. We employ the Floquet operator technique to investigate all three models in the presence of time-dependent periodic driving of parameters. In contrast to the sudden quenched cases, the periodically varying parameter case clearly shows non-analytical behaviour near the critical point. We also elucidate the relation between work done and the Lanczos coefficient and how the statistics of work done behave near critical points. Graphical abstract

Coupling with an external environment inevitably affects the dynamics of a quantum system. Here, we consider how charging performances of a quantum battery, modelled as a two level system, are influenced by the presence of an Ohmic thermal reservoir. The latter is coupled to both longitudinal and transverse spin components of the quantum battery including decoherence and pure dephasing mechanisms. Charging and discharging dynamics of the quantum battery, subjected to a static driving, are obtained exploiting a proper mapping into the so-called spin-boson model. Analytic expressions for the time evolution of the energy stored in the weak coupling regime are presented relying on a systematic weak damping expansion. Here, decoherence and pure dephasing dissipative coupling are discussed in details. We argue that the former results in better charging performances, showing also interesting features reminiscent of the Lamb shift level splitting renormalization induced by the presence of the reservoir. Charging stability is also addressed, by monitoring the energy behaviour after the charging protocol has been switched off. This study presents a general framework to investigate relaxation effects, able to include also non Markovian effects, and it reveals the importance of controlling and, possibly, engineering system-bath coupling in the realization of quantum batteries.

Considering a non-Hermitian version of p -wave Kitaev chain in the presence of additional second nearest neighbour tunnelling, we study dynamical quantum phase transition (DQPT) which accounts for the vanishing Loschmidt amplitude. The locus of the Fisher’s zero traces a continuous path on the complex time plane for the Hermitian case while it becomes discontinuous for non-Hermitian cases. This further leads to the half-unit jumps in the winding number characterizing a dynamical topological aspect of DQPT for non-Hermitian Hamiltonian. Uncovering the interplay between non-Hermiticity and long-range tunnelling, we find these features to be universally present irrespective of the additional second nearest neighbour tunnelling terms as long as non-Hermiticity is preserved. Graphic abstract The upper panel depicts the discontinuity in Fisher’s zeros exactly on the imaginary axis. The lower panel demonstrates the half-qunatized jumps in the dynamical winding number corresponding to such discontinuous jump.

This short review explores the physics journey of Professor Amit Dutta, illuminating his collaborative contributions with students and peers. We mainly focus on standard approaches to understanding non-equilibrium quantum dynamics and ground-state criticality using quantum informatic measures like ground-state fidelity, the Loschmidt echo and/or the decoherence factor. Using Floquet theory as a tool, we also discuss the dynamics of hard-core bosonic chain, shedding light on the phenomenon of dynamical localization and different analytically approachable limits of Floquet theory. The review further extends to probe the physics of topological phase transitions in driven/quenched systems, where we mainly focus on the non-equilibrium response of topological systems and topological state preparation. Finally, we also discuss late-time quantum dynamics leading to the thermalization of open and closed systems, where we review contemporary approaches to the applicability of thermodynamic principles in microscopic quantum systems and the macroscopic emergence of statistical mechanics in driven/quenched ergodic systems. Throughout this memoir, Professor Amit Dutta’s important scientific contributions are mentioned for their impact on advancing our understanding of quantum dynamics and statistical mechanics. Graphic abstract

In nature, instances of synchronisation abound across a diverse range of environments. In the quantum regime, however, synchronisation is typically observed by identifying an appropriate parameter regime in a specific system. In this work we show that this need not be the case, identifying conditions which, when satisfied, guarantee that the individual constituents of a generic open quantum system will undergo completely synchronous limit cycles which are, to first order, robust to symmetry-breaking perturbations. We then describe how these conditions can be satisfied by the interplay between several elements: interactions, local dephasing and the presence of a strong dynamical symmetry-an operator which guarantees long-time non-stationary dynamics. These elements cause the formation of entanglement and off-diagonal long-range order which drive the synchronised response of the system. To illustrate these ideas we present two central examples: a chain of quadratically dephased spin-1s and the many-body charge-dephased Hubbard model. In both cases perfect phase-locking occurs throughout the system, regardless of the specific microscopic parameters or initial states. Furthermore, when these systems are perturbed, their nonlinear responses elicit long-lived signatures of both phase and frequency-locking.

The study of open quantum systems often relies on approximate master equations derived under the assumptions of weak coupling to the environment. However when the system is made of several interacting subsystems such a derivation is in many cases very hard. An alternative method, employed especially in the modeling of transport in mesoscopic systems, consists in using local master equations (LMEs) containing Lindblad operators acting locally only on the corresponding subsystem. It has been shown that this approach however generates inconsistencies with the laws of thermodynamics. In this paper we demonstrate that using a microscopic model of LMEs based on repeated collisions all thermodynamic inconsistencies can be resolved by correctly taking into account the breaking of global detailed balance related to the work cost of maintaining the collisions. We provide examples based on a chain of quantum harmonic oscillators whose ends are connected to thermal reservoirs at different temperatures. We prove that this system behaves precisely as a quantum heat engine or refrigerator, with properties that are fully consistent with basic thermodynamics.