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In this paper, we consider a mean-reverting stochastic volatility equation with regime switching, and present some sufficient conditions for the existence of global positive solution, asymptotic boundedness in pth moment, positive…
We study the behavior of an open quantum system, with an $N$--dimensional space of states, whose density matrix evolves according to a non--unitary map defined in two steps: A unitary step, where the system evolves with an evolution…
We show that the dynamics of generic quantum systems concentrate around their equilibrium value when measuring at arbitrary times. This means that the probability of finding them away from equilibrium is exponentially suppressed, with a…
One of the greatest challenges in quantum information processing is the coherent control over quantum systems with an ever increasing number of particles. Within this endeavor, the harnessing of many-body entanglement against the effects of…
The theory of controlled quantum open systems describes quantum systems interacting with quantum environments and influenced by external forces varying according to given algorithms. It is aimed, for instance, to model quantum devices which…
Towers of quantum many-body scars are sets of highly-excited eigenstates of nonintegrable Hamiltonians whose dynamics shows athermal behavior and persistent oscillations in time. The preparation of such states is, however, challenging due…
By solving the exact master equation of open quantum systems, we formulate the quantum thermodynamics from weak to strong couplings. The open quantum systems exchange matters, energies and information with their reservoirs through quantum…
A direct classical analog of the quantum dynamics of intrinsic decoherence in Hamiltonian systems, characterized by the time dependence of the linear entropy of the reduced density operator, is introduced. The similarities and differences…
A dynamical decoupling method is presented which is based on embedding a deterministic decoupling scheme into a stochastic one. This way it is possible to combine the advantages of both methods and to increase the suppression of undesired…
Discrete time crystals are related to non-equilibrium dynamics of periodically driven quantum many-body systems where the discrete time translation symmetry of the Hamiltonian is spontaneously broken into another discrete symmetry.…
We study the relaxation dynamics of strongly interacting quantum systems that display a kind of many-body localization in spite of their translation-invariant Hamiltonian. We show that dynamics starting from a random initial configuration…
A theory recently proposed by the author aims to explain decoherence and the thermodynamical behaviour of closed systems within a conservative, unitary, framework for quantum gravity by assuming that the operators tied to the gravitational…
Stochastic resetting has been a subject of considerable interest within statistical physics, both as means of improving completion times of complex processes such as searches and as a paradigm for generating nonequilibrium stationary…
In the classical stochastic resetting problem, a particle, moving according to some stochastic dynamics, undergoes random interruptions that bring it to a selected domain, and then, the process recommences. Hitherto, the resetting mechanism…
In closed generic many-body systems, unitary evolution disperses local quantum information into highly non-local objects, resulting in thermalization. Such a process is called information scrambling, whose swiftness is quantified by the…
We generalize a recently developed scheme for monitoring coherent quantum dynamics with good time-resolution and low backaction [Reuther et al., Phys. Rev. Lett. 102, 033602 (2009)] to the case of more complex quantum dynamics of one or…
The evolution of a quantum system interacting with an environment can be described as a unitary process acting on both the system and the environment. In this framework, the system's evolution can be predicted by tracing out the…
Stochastic resetting generates nonequilibrium steady states by interspersing unitary quantum dynamics with resets at random times. When the state to which the system is reset is chosen conditionally on the outcome of a global and spatially…
A new control method that considers all sources of uncertainty and noises that might affect the time evolutions of quantum physical systems is introduced. Under the proposed approach, the dynamics of quantum systems are characterised by…
Often quantum systems are not isolated and interactions with their environments must be taken into account. In such open quantum systems these environmental interactions can lead to decoherence and dissipation, which have a marked influence…