Open quantum systems are traditionally described by decomposing the total Hilbert space into a system and an external environment, linked by an explicit interaction Hamiltonian. We propose an alternative framework in which the environment is not introduced as an independent sector a priori, but instead emerges from the dynamical activation of constraints in an initially constrained quantum system. Within Dirac quantization, the physical degrees of freedom define the system, whereas the constraint sector, once promoted to carry its own dynamics, functions as an environment. In this picture, the system-environment coupling is not added through a separate interaction term, but is encoded directly in the constraint structure. As an example, we study a quantum particle coupled to a Brownian-oscillator environment and show how the resulting environmental influence can be formulated in this constraint-based setting. Our results provide a new perspective on the origin of quantum environments and point toward a general framework for open quantum systems rooted in constrained quantization.Open quantum systems are traditionally described by decomposing the total Hilbert space into a system and an external environment, linked by an explicit interaction Hamiltonian. We propose an alternative framework in which the environment is not introduced as an independent sector a priori, but instead emerges from the dynamical activation of constraints in an initially constrained quantum system. Within Dirac quantization, the physical degrees of freedom define the system, whereas the constraint sector, once promoted to carry its own dynamics, functions as an environment. In this picture, the system-environment coupling is not added through a separate interaction term, but is encoded directly in the constraint structure. As an example, we study a quantum particle coupled to a Brownian-oscillator environment and show how the resulting environmental influence can be formulated in this constraint-based setting. Our results provide a new perspective on the origin of quantum environments and point toward a general framework for open quantum systems rooted in constrained quantization.

quant-pharXiv:2603.29489Apr 1, 20260 citations

Dynamics of Open Quantum Systems

Ángel S. Sanz, Salvador Miret-Artés

Lecture notes in physicsJan 1, 20121 citation

Lindbladian quantization of mechanical systems with nonholonomic constraints

Daniel Schubring, Sriram Ganeshan

Nonholonomic mechanics describes systems subject to non-integrable velocity constraints, such as rolling bodies and skating motion. These systems generally lack a canonical Hamiltonian formulation, obstructing standard quantization methods. Here we quantize nonholonomic systems as Markovian open quantum systems, with the nonholonomic constraint appearing in a large-dissipation limit. We find explicit Lindblad superoperators that reproduce the classical dynamics of the Chaplygin sleigh and the Suslov problem in the semiclassical limit. The master equation is numerically simulated, and the covariance is shown to satisfy a relation predicted by the theory of metastability in open quantum systems.Nonholonomic mechanics describes systems subject to non-integrable velocity constraints, such as rolling bodies and skating motion. These systems generally lack a canonical Hamiltonian formulation, obstructing standard quantization methods. Here we quantize nonholonomic systems as Markovian open quantum systems, with the nonholonomic constraint appearing in a large-dissipation limit. We find explicit Lindblad superoperators that reproduce the classical dynamics of the Chaplygin sleigh and the Suslov problem in the semiclassical limit. The master equation is numerically simulated, and the covariance is shown to satisfy a relation predicted by the theory of metastability in open quantum systems.

quant-pharXiv:2607.26146Jul 30, 20260 citations

Third-quantized master equations as a classical Ornstein-Uhlenbeck process

Léonce Dupays

Third quantization is used in open quantum systems to construct a superoperator basis in which quadratic Lindbladians can be turned into a normal form. From it follows the spectral properties of the Lindbladian, including eigenvalues and eigenvectors. However, the connection between third quantization and the semiclassical representations usually employed to obtain the dynamics of open quantum systems remains opaque. We introduce an alternative basis for third quantization that bridges this gap between third quantization and the $Q$ representation by projecting the master equation onto a superoperator coherent-state basis. The equation of motion reduces to a multidimensional complex Ornstein-Uhlenbeck process.Third quantization is used in open quantum systems to construct a superoperator basis in which quadratic Lindbladians can be turned into a normal form. From it follows the spectral properties of the Lindbladian, including eigenvalues and eigenvectors. However, the connection between third quantization and the semiclassical representations usually employed to obtain the dynamics of open quantum systems remains opaque. We introduce an alternative basis for third quantization that bridges this gap between third quantization and the $Q$ representation by projecting the master equation onto a superoperator coherent-state basis. The equation of motion reduces to a multidimensional complex Ornstein-Uhlenbeck process.

arXiv:2408.11893Physical Review ANov 6, 20251 citation

Dynamics of Open Quantum Systems

Gernot Schaller

Lecture notes in physicsJan 1, 20143 citations

Q

representation by projecting the master equation onto a superoperator coherent-state basis. The equation of motion reduces to a multidimensional complex Ornstein-Uhlenbeck process.