Topics in classical and quantum linear stochastic systems

Alexander Mikhailovich Chebotarev

Sergio A Albeverio, Giulio Casati, D. Merlini

C Hogg (13538632)

An understanding of strongly coupled open quantum systems is crucial for the realisation of many of today’s emerging quantum technologies. However, actually simulating a quantum system that strongly interacts, or couples, with its environment is no easy task. This thesis tackles a number of topics in the field of strongly coupled open quantum systems. Given the computational challenges of solving the full open system dynamics, we first discuss how and why a quasiclassical stochastic approach can be used to simulate the dynamics of a quantum harmonic oscillator that is strongly coupled to its environment. We build upon the established analytical agreement by implementing the quasiclassical stochastic case numerically in the SpiDy.jl Julia package. Motivated by the applications to magnetic modelling, we then solve the full open quantum systems model for a single spin coupled arbitrarily strongly to multiple heat baths. In doing so, we find that the presence of multiple baths can actually increase the system-environment entanglement in the steady state. We also compare this to a fully classical approach and find that, for isotropic environmental coupling, the environment-induced effects in the equilibrium state only appear quantum mechanically. Finally, we couple these two topics together by considering the quasiclassical stochastic simulation of a single quantum spin, helping to understand the regimes of validity beyond the linear harmonic oscillator. This is with the larger aim to eventually be able to encode quantum effects into more realistic systems, such as those that describe magnetic materials.

Nikos Demopoulos

The role of randomness in physical systems remains a pivotal topic, influencing the transition from quantum mechanics to classical stability and shaping complex dynamic behaviors. This paper explores the concept of stochastic determinism, illustrating how stochastic processes contribute to order in classical and quantum systems. By integrating stochastic differential equations (SDEs), entropy-driven self-organization, and fluctuation-dissipation principles, we demonstrate that randomness is not merely an obstacle to predictability but a key mechanism for structure formation. The study further examines applications in thermodynamics, turbulence, and quantum decoherence, bridging stochasticity and determinism as complementary aspects of physical reality.

Luis de la Peña, Ana Marı́a Cetto

Gian‐Carlo Rota