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We review progress towards direct simulation of quantum dynamics in many-body systems, using recently developed stochastic gauge techniques. We consider master equations, canonical ensemble calculations and reversible quantum dynamics are…
The relationship between the thermodynamic and computational characteristics of dynamical physical systems has been a major theoretical interest since at least the 19th century, and has been of increasing practical importance as the…
In mathematical psychology, decision makers are modeled using the Lindbladian equations from quantum mechanics to capture important human-centric features such as order effects and violation of the sure thing principle. We consider…
The study of density-dependent stochastic population processes is important from a historical perspective as well as from the perspective of a number of existing and emerging applications today. In more recent applications of these…
Exact generalized stochastic representation of deterministic interaction between two dynamical (quantum or classical) systems is derived which helps when considering one of them to replace another by equivalent commutative ($c$-number…
A stochastic representation of the dynamics of open quantum systems, suitable for non-perturbative system-reservoir interaction, non-Markovian effects and arbitrarily driven systems is presented. It includes the case of driving on…
We investigate the optimal control of open quantum systems, in particular, the mutual influence of driving and dissipation. A stochastic approach to open-system control is developed, using a generalized version of Krotov's iterative…
Strong-field quantum-state control is investigated, taking advantage of the full---amplitude and phase---characterization of the interaction between matter and intense ultrashort pulses via transient-absorption spectroscopy. A sequence of…
The exact quantum state evolution of a fermionic gas with binary interactions is obtained as the stochastic average of BCS-state trajectories. We find the most general Ito stochastic equations which reproduce exactly the dynamics of the…
The quantum dynamics of open many-body systems poses a challenge for computational approaches. Here we develop a stochastic scheme based on the positive P phase-space representation to study the nonequilibrium dynamics of coupled spin-boson…
In mathematical psychology, decision makers are modeled using the Lindbladian equations from quantum mechanics to capture important human-centric features such as order effects and violation of the sure thing principle. We consider…
In this thesis we study continuously observed open quantum systems from the point of view of quantum filtering theory. The conditioned state of the open system obeys a non-commutative or quantum analogue of the Kushner-Stratonovich equation…
Recent developments in quantum gas microscopy open up the possibility of real-time observation of quantum many-body systems. To understand the dynamics of atoms under such circumstances, we formulate the dynamics under a real-time spatially…
The application of a random modulation of a system parameter usually increases decoherence effects. Here we show how, employing an appropriate stochastic modulation, it is instead possible to preserve the quantum coherence of a system.
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…
The presence of algebraically decaying long-range interactions may alter the critical as well as topological behaviour of a quantum many-body systems. However, when the interaction decays at a faster rate, the short-range behaviour is…
The stochastic Kuramoto model defined on a sequence of graphs is analyzed: the emphasis is posed on the relationship between the mean field limit, the connectivity of the underlying graph and the long time behavior. We give an explicit…
Driving a quantum system periodically in time can profoundly alter its long-time dynamics and trigger topological order. Such schemes are particularly promising for generating non-trivial energy bands and gauge structures in quantum-matter…
Starting from a many-body classical system governed by a trace-form entropy we derive, in the stochastic quantization picture, a family of non linear and non-Hermitian Schroedinger equations describing, in the mean filed approximation, a…
We study long-range interacting systems driven by external stochastic forces that act collectively on all the particles constituting the system. Such a scenario is frequently encountered in the context of plasmas, self-gravitating systems,…