Lindblad Dissipation Enables Steady States in Nonequilibrium Planar Matrix Mechanics

The fundamental laws governing the universe are thought to preserve information, yet any isolated part of it inevitably experiences energy loss and change. Minjae Cho from the University of Chicago’s Leinweber Institute for Theoretical Physics, along with colleagues, investigates how these changes affect the behaviour of complex quantum systems. Their work explores the dynamics of ‘matrix mechanics’, a theoretical framework aiming to describe the fundamental building blocks of reality, when subjected to energy loss. The team demonstrates that, under certain conditions, these systems undergo distinct phase transitions, exhibiting behaviours previously observed in optical experiments with microscopic resonators, and crucially, revealing the possibility of stable states that would otherwise be impossible. This research provides new insights into how complex quantum systems evolve and establishes a rigorous mathematical approach to understanding their behaviour in realistic, non-isolated conditions.

The research investigates the master equation with dissipative jump terms, concentrating on the existence, uniqueness, and properties of steady states. After demonstrating that Lindblad dissipation is absent in the gauged model at large N, the study explores nonequilibrium phase transitions in planar ungauged matrix quantum mechanics.

Bootstrapping Open Quantum Many-Body Systems

This paper addresses the challenging problem of solving open quantum systems, those interacting with their environment, and many-body systems, containing a large number of interacting particles. Researchers employ a powerful mathematical technique called bootstrapping to determine the properties of these complex systems, relying on fundamental constraints and analytic continuation to extend predictable behaviour. The bootstrapping method involves solving optimization problems using techniques like linear and semidefinite programming, identifying the best solutions satisfying imposed constraints. This process is often implemented as a hierarchy, starting with a simple approximation and iteratively refining it for greater accuracy, and is applied to frameworks including Lindbladian dynamics and symmetry protected topological order. Researchers demonstrate the effectiveness of this method by applying it to examples such as Kerr resonators and the Sachdev-Ye-Kitaev model, also testing it using c=1 string theory. This work presents a new approach to solving open quantum systems, offering applications to diverse problems in quantum physics and establishing connections between quantum physics and mathematical physics, particularly in matrix models and string theory.

Nonequilibrium Criticality in Open Quantum Systems

Researchers are investigating the behaviour of matrix quantum mechanics, a theoretical system expected to mirror aspects of quantum gravity, when it interacts with an external environment. This interaction introduces dissipation, leading to a state far from equilibrium, and the team focuses on understanding the stable configurations, termed ‘steady states’, the system settles into. The research demonstrates the existence of critical points within this open quantum system, points at which the system’s behaviour undergoes a dramatic shift. Above these critical points, dissipation can allow for the existence of stable steady states that would otherwise be impossible, effectively stabilizing the system, suggesting that dissipation can play a constructive role in establishing order.

The team utilizes rigorous mathematical techniques, termed ‘bootstrap methods’, to obtain concrete results for these steady states. In one set of experiments, researchers examined a simplified theory with potentials unbounded from below, discovering that strong dissipation can create stable states even in seemingly unstable scenarios. Furthermore, the team explored scenarios with external forces, finding evidence of nonequilibrium phase transitions analogous to those observed in optical resonators. These transitions represent a fundamental change in the system’s behaviour, akin to shifting between distinct phases of matter. The findings suggest that nonequilibrium phase transitions can arise in open quantum gravity theories, offering a new perspective on the behaviour of black holes and other complex quantum systems interacting with their environment, and establishing a framework for investigating these transitions.

Dissipation Drives Nonequilibrium Phase Transitions in Matrices

This research investigates nonequilibrium physics within the framework of matrix quantum mechanics, exploring the existence and properties of steady states in systems subject to dissipation. The team demonstrates the presence of genuine nonequilibrium phase transitions, specifically in planar ungauged matrix mechanics and in a system termed ‘matrix optics’, analogous to those observed in driven-dissipative optical resonators. These transitions are evidenced by non-analytic behaviours in bootstrap bounds obtained through numerical methods, suggesting changes in the system’s fundamental properties as dissipation varies. The study acknowledges limitations in the convergence of these bounds and highlights the need for further investigation with additional constraints to definitively confirm the existence of these phase transitions. Future work should focus on incorporating more complex constraints, including nonlinear terms, to strengthen the numerical results and potentially determine whether a unique steady state exists across all dissipation strengths.