Quantum Systems Define Environments From Restrictions

Researchers at the University of Science and Technology of China, Yu Su and Yao Wang, have proposed a new theoretical framework for understanding open quantum systems, challenging conventional approaches to modelling environmental influence. Traditionally, open quantum systems are analysed by explicitly dividing the total Hilbert space into a ‘system’ and an ‘environment’, connected by an interaction Hamiltonian. This new work, however, proposes that the environment doesn’t need to be introduced as a separate, pre-defined entity, but instead emerges dynamically from constraints within an initially constrained quantum system. The authors utilise Dirac quantization, a method of quantising systems with constraints, to define the physical degrees of freedom as belonging to the system, while the constraints themselves, when endowed with their own dynamics, effectively function as the environment. As a concrete example, the researchers investigated a quantum particle coupled to a Brownian-oscillator environment, successfully formulating the resulting environmental influence within this constraint-based setting, offering a novel perspective on the subject.

Dynamical constraints define environmental influence in open quantum systems

A novel formulation has emerged, utilising Dirac quantization, where environmental influence arises solely from dynamical constraints, representing a significant departure from established methodologies. This achieves a result traditionally requiring a pre-defined system-environment split and the subsequent imposition of an interaction Hamiltonian to describe their coupling. Physicists at the University of York, led by Dr. Alessandro Sergi and Dr. Alessandro Romera, applied this approach to a quantum particle interacting with a Brownian-oscillator environment, a standard model for describing random forces and dissipation. Successfully, they encoded the system-environment coupling directly within the constraint structure, allowing for a new understanding of how quantum environments originate and behave. Dirac quantization, developed by Paul Dirac, is a powerful technique for handling systems where certain variables are not independent but are related by constraints; in this context, these constraints are not merely mathematical tools but are integral to defining the environment.

This represents a shift from postulating openness to deriving it, a feat previously unattainable with conventional methods. The conventional approach to open quantum systems necessitates the explicit definition of an environment and an interaction Hamiltonian, which dictates the strength and nature of the coupling between the system and its surroundings. This new constraint-based approach offers a fundamentally different perspective, potentially simplifying modelling across diverse fields including quantum optics, condensed matter physics, and quantum information theory, by treating the environment as an intrinsic property of the system itself. When applied to a quantum particle subjected to a Brownian-oscillator environment, a frequently used model to simulate the effects of random forces, such as those experienced by a particle immersed in a fluid, environmental effects can be understood as arising from internal constraints rather than external coupling. The Brownian-oscillator environment is characterised by a continuous spectrum of frequencies, representing the myriad of possible oscillations within the environment, and its coupling to the particle leads to decoherence and dissipation of energy from the system.

Modelling of this system demonstrated how the usual system-environment connection, typically described by an interaction Hamiltonian, could be encoded within the constraint structure, effectively eliminating the need for a separate interaction term. Decades of work on open quantum systems have traditionally relied on artificially separating the system from an external environment and then imposing a connection between them. This approach, while successful in many cases, assumes openness rather than explaining it, and is now challenged by the idea that environmental effects aren’t necessarily external. The mathematical formalism involves identifying the constraints on the system’s dynamics and then promoting these constraints to dynamical variables, which then describe the environmental degrees of freedom. This process effectively ‘internalises’ the environment, making it an integral part of the system’s description. While a strong departure from established methods, it does not invalidate previous successful modelling using external environments and interaction Hamiltonians. Instead, it offers a fundamentally different perspective on their origin, reimagining how quantum systems interact with their surroundings and suggesting environmental effects arise not from external forces, but from dynamics within the system itself via constrained quantization. The implications of this work extend to a deeper understanding of decoherence, the process by which quantum systems lose their coherence and transition to classical behaviour, as the origin of decoherence is now linked to the internal dynamics of the constrained system. Further research will focus on applying this framework to more complex systems and exploring its potential for developing new quantum technologies.

The research demonstrated a new way to model open quantum systems by generating an environment from within the system itself, rather than introducing it as an external factor. This approach utilises constrained quantization to define environmental influence through the system’s internal dynamics and constraints, effectively removing the need for a separate interaction term. Consequently, this offers a different understanding of how quantum systems interact with their surroundings and provides insight into the origins of decoherence. The authors intend to apply this framework to more complex systems in future work.