Study of Classical and Quantum Open Systems

Lee Chee Kong

Home/Archive/arXiv

arXiv · 1008.0491

Study of Classical and Quantum Open Systems

Lee Chee Kong

View original source ↗Read source document ↗Export metadata ↓

Abstract

This thesis covers various aspects of open systems in classical and quantum mechanics. In the first part, we deal with classical systems. The bath-of-oscillators formalism is used to describe an open system, and the phenomenological Langevin equation is recovered. The Fokker-Planck equation is derived from its corresponding Langevin equation. The Fokker-Planck equation for a particle in a periodic potential in the high-friction limit is solved using the continued-fraction method. The equilibrium and time-dependent solutions are obtained. Under strong periodic driving, we observe significant non-linear effects in the dynamical hysteresis loops. Shapiro steps appear in the time-average of the drift velocity curves. Similar study is carried out for a dipole in an electric field. In the second part of the thesis, we begin the study of open quantum systems by re-deriving the quantum master equation using perturbation theory. The master equation is then applied to the bath-of-oscillators model. The subtleties and approximations of the master equation are discussed. We then use the master equation to solve the damped harmonic oscillator. The equilibrium solution coincides with the canonical distribution. The steady state response to DC and AC forces is also studied. Driven systems are more challenging in quantum open systems, and we manage to solve the quantum master equation with the continued-fraction method. We obtain the frequency-dependent susceptibility curves, which exhibit typical absorption and dispersion profiles.

Explore related subjects

cond-mat.stat-mech

Keep this discovery

BibTeX RIS

Lee Chee Kong. 2010-08-03. Study of Classical and Quantum Open Systems. https://arxiv.org/abs/1008.0491

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Universal sampling of spin systems across quenched disorder

Statistical physics extracts macroscopic laws by averaging over the many microscopic degrees of freedom of a system. Disordered systems demand a second and far harder average, one over the quenched randomness itself. The classic analytical routes, the replica and cavity methods, become uncontrolled outside mean-field or tree-like limits, and conventional numerical algorithms like parallel tempering require expensive, independent equilibration for every disorder realization. In this work, we introduce a universal neural variational framework that amortizes inference across the disorder ensemble, eliminating both the need for per-instance Markov chain equilibration and the cost of retraining instance-specific variational ansatzes. Built on an encoder-decoder Transformer architecture, after training once, it produces an explicit approximation to the Boltzmann distribution given previously unseen disorder realizations without further optimization. We validate this framework on 2D Edwards-Anderson models, and apply it to the random-bond Ising model, successfully capturing the Binder cumulant crossings near the Nishimori multicritical point. These results shift the object of variational inference from the single instance to the disorder ensemble, opening a route to frustrated many-body systems where instance-by-instance computation is prohibitive.

cond-mat.stat-mech↗

arXiv2026

Information-Theoretic Characterization of Macroscopic Chaos Emerging from the Chemical Master Equation

Open chemical reaction networks exhibit stochastic concentration dynamics at finite system sizes, whereas their macroscopic limit is governed by deterministic rate equations that can display chaos. In this Letter, we show theoretically that a rate of information loss constructed from two-time mutual information recovers the Kolmogorov-Sinai entropy in the deterministic limit. We verify this result through numerical simulations of a Markov jump process for a three-species system involving seven reactions.

cond-mat.stat-mech↗

arXiv2026

Orientational order on non-orientable domains

We study the statistical properties of passive and active many-body systems with orientational degrees of freedom on non-orientable domains. By rephrasing topological constraints as non-local symmetry relations on an orientable double-cover, we show that non-orientability eliminates global rotational soft modes without acting like an external field. In a passive XY model, this results in topological caging, where orientational fluctuations that exhibit conventional diffusive behavior on a torus saturate on a Klein bottle to a finite value that we compute exactly in the thermodynamic limit. In models of active self-propelled particles with orientational degrees of freedom, topological caging persists despite continuously changing interaction neighborhoods. In an active Ising spin model, non-orientability enforces the coexistence of ordered anti-parallel domains with vanishing global polar order, a state that is absent on orientable domains.

cond-mat.stat-mech↗