A stochastic-geometric theory of open quantum systems

We present a stochastic-geometric framework for finite-dimensional open quantum systems, based on Langevin–Smoluchowski dynamics supplemented by Hamiltonian circulation on projective Hilbert space. The framework provides an analytically semi-tractable description of dissipative quantum dynamics directly on the space of physical pure states.

By projecting the dynamics onto scalar observables, and assuming that the relevant thermodynamic functions factor through the chosen observable, we derive closed stochastic differential equations that make first-hitting-time problems analytically accessible. In the absence of continuous measurement, we show that the average time required for a bounded observable to first reach the ε-neighbourhood of the maximum diverges algebraically: τ(ε) ~ ε^−α, where the exponent is determined by the endpoint behaviour of the Haar distribution of the observable.

For a system of N qubits, this leads to two different scaling laws. For observables whose maximum corresponds to a unique physical state, the exponent grows as α ∝ 2^N, reflecting the exponential growth of Hilbert-space dimension. In contrast, when the target consists of a family of absolutely maximally entangled states, we find α ∝ N. These results illustrate how the geometry and measure concentration of quantum state space can directly control dynamical time scales in open quantum systems.

Short Bio

• 2004 - M.Sc. in Engineering Physics (Budapest University of Technology and Economics, Hungary)
• 2012 - Ph.D. in Physical Sciences (Budapest University of Technology and Economics, Hungary)
• 2012-2014 - postdoctoral research fellow of the Hungarian Academy of Science (Wigner Research Centre for Physics, Hungary)
• 2014-2017 - VISTA postdoctoral research fellow of the Norwegian Academy of Science and Letters (University of Bergen, Norway)
• 2017-2023 - lecturer in Applied Mathematics (Loughborough University, UK)
• 2023 senior lecturer in Applied Mathematics (same)

Research areas and expertise: computational material science, classical statistical mechanics, pattern formation and phase transitions in classical systems, classical density functional and phase-field theory, parallel programming of HPC devices, stochastic processes and applied mathematics (since 2017)