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The transformer architecture, known for capturing long-range dependencies and intricate patterns, has extended beyond natural language processing. Recently, it has attracted significant attention in quantum information and condensed matter…
For a network of discrete states with a periodically driven Markovian dynamics, we develop an inference scheme for an external observer who has access to some transitions. Based on waiting-time distributions between these transitions, the…
In the spectrum of systems showing chaos-assisted tunneling, three-state crossings are formed when a chaotic singlet intersects a tunnel doublet. We study the dissipative quantum dynamics in the vicinity of such crossings. A harmonically…
We investigate an M/M/1 queue operating in two switching environments, where the switch is governed by a two-state time-homogeneous Markov chain. This model allows to describe a system that is subject to regular operating phases alternating…
Flowgraph models provide an alternative approach in modeling a multi-state stochastic process. One of the most widely used stochastic processes that have many real-world applications especially in actuarial models is the Markov jump process…
In this work, we characterise the statistics of Markov chains by constructing an associated sequence of periodic differential operators. Studying the density of states of these operators reveals the absolutely continuous invariant measure…
A Markovian single-server queue is studied in an interactive random environment. The arrival and service rates of the queue depend on the environment, while the transition dynamics of the random environment depends on the queue length. We…
For continuous-time Markov jump processes on irreducible networks with time-independent rate constants, we employ a transition-based formalism to express the long-time precision of a single integrated current over an observable channel in…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
The simulation of fluid flows is computationally expensive due to the complexity of its governing partial differential equations. Machine learning models offer a potential surrogate, enabling learning from simulations and significantly…
We propose dynamical schemes to engineer coherent states of a mechanical resonator coupled to an ancillary, superconducting flux qubit. The flux qubit, when repeatedly projected on to its ground state drives the mechanical resonator in to a…
Well-mixed chemical reaction networks (CRNs) contain many distinct chemical species with copy numbers that fluctuate in correlated ways. While those correlations are typically monitored via Monte Carlo sampling of stochastic trajectories,…
Heat transfer in quantum systems is a current topic of interest due to emerging quantum technologies that attempt to miniaturize engines and examine fundamental aspects of thermodynamics. In this work, we consider heat transfer between two…
A combination of a steady-state preserving operator splitting method and a semi-implicit integration scheme is proposed for efficient time stepping in simulations of unsteady reacting flows, such as turbulent flames, using detailed chemical…
We introduce stochastic models for the transport of heat in systems described by local collisional dynamics. The dynamics consists of tracer particles moving through an array of hot scatterers describing the effect of heat baths at fixed…
In the thesis we present an analytic approach towards exact description for steady state density operators of nonequilibrium quantum dynamics in the framework of open systems. We employ the so-called quantum Markovian semi-group evolution,…
In this work, we present a general method to establish properties of multi-dimensional continuous-time Markov chains representing stochastic reaction networks. This method consists of grouping states together (via a partition of the state…
This paper introduces the use of statistical distributions based on transport differential equations for clear distinction of transport modes within transient kinetic experiments. More specifically,novel techniques are developed for the…
Reactive settling denotes the process of sedimentation of small solid particles dispersed in a viscous fluid with simultaneous reactions between the components that constitute the solid and liquid phases. This process is of particular…
The long-term distributions of trajectories of a flow are described by invariant densities, i.e. fixed points of an associated transfer operator. In addition, global slowly mixing structures, such as almost-invariant sets, which partition…