Extreme Temporal Correlations in Non-Unitary Quantum Dynamics

Paul, Sourav (2026) Extreme Temporal Correlations in Non-Unitary Quantum Dynamics. PhD thesis, Indian Institute of Science Education and Research Kolkata.

Text (PhD thesis of Sourav Paul (20RS034)) 20RS034.pdf - Submitted Version Restricted to Repository staff only Download (29MB)

Abstract

Quantum systems interacting with an external environment undergo non-unitary evolution characterized by decoherence, dissipation, measurement back-action, and stochastic state reduction. In realistic physical settings, complete isolation of a quantum system from its surroundings is unattainable, and therefore the idealized framework of closed-system unitary dynamics becomes insufficient for describing experimentally accessible quantum phenomena. Environmental coupling leads to irreversible loss of coherence, continuous exchange of information and energy, and conditional evolution driven by measurements and post-selection. Consequently, the dynamics of open quantum systems must be described using generalized frameworks such as completely positive trace-preserving maps, stochastic quantum trajectories, and non-Hermitian effective Hamiltonians. These processes fundamentally alter the geometric structure of the quantum state space and give rise to phenomena absent in purely unitary evolution, including nonlinear state amplification, exceptional-point singularities, measurement-induced transitions, and anomalous temporal correlations. This thesis investigates non-unitary quantum dynamics in both discrete-time and continuous-time settings, with particular emphasis on the emergence of non-classical temporal correlations and their connection to conformal geometry, stochastic evolution, and post-selected quantum dynamics. The central objective is to develop a unified geometric and dynamical framework capable of characterizing diverse classes of non-unitary evolution and identifying the physical mechanisms responsible for the enhancement and breakdown of temporal quantum correlations beyond the conventional limits imposed by standard unitary quantum mechanics.

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