Nonequilibrium Phase Transitions in Large $N$ Matrix Quantum Mechanics

• URL: http://arxiv.org/abs/2508.04764v1
• Date: Wed, 06 Aug 2025 18:00:00 GMT
• Title: Nonequilibrium Phase Transitions in Large $N$ Matrix Quantum Mechanics
• Authors: Minjae Cho,
• Abstract summary: We investigate the planar limit of large $N$ one-matrix quantum mechanics obeying the Lindblad master equation with dissipative jump terms.<n>We study nonequilibrium phase transitions in planar ungauged matrix quantum mechanics.<n>We find evidence of nonequilibrium phase transitions analogous to those recently reported in the quantum optics literature for driven-dissipative Kerr resonators.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: It is believed that the theory of quantum gravity describing our universe is unitary. Nonetheless, if we only have access to a subsystem, its dynamics is described by nonequilibrium physics. Motivated by this, we investigate the planar limit of large $N$ one-matrix quantum mechanics obeying the Lindblad master equation with dissipative jump terms, focusing on the existence, uniqueness, and properties of steady states. After showing that Lindblad dissipation is absent in the gauged model at large $N$, we study nonequilibrium phase transitions in planar ungauged matrix quantum mechanics. In the first class of examples, where potentials are unbounded from below, we study nonequilibrium critical points above which strong dissipation allows for the existence of normalizable steady states that would otherwise not exist. In the second class of examples, termed matrix quantum optics, we find evidence of nonequilibrium phase transitions analogous to those recently reported in the quantum optics literature for driven-dissipative Kerr resonators. Preliminary results on two-matrix quantum mechanics are also presented. We implement bootstrap methods to obtain concrete and rigorous results for the nonequilibrium steady states of matrix quantum mechanics in the planar limit.

Related papers

• Stable infinite-temperature eigenstates in SU(2)-symmetric nonintegrable models [0.0]
  A class of nonintegrable bond-staggered models is endowed with a large number of zero-energy eigenstates and possesses a non-Abelian internal symmetry.<n>We show that few-magnon zero-energy states have an exact analytical description, allowing us to build a basis of low-entangled fixed-separation states.
  arXiv  Detail & Related papers  (2024-07-16T17:48:47Z)
• Quantum electrodynamics under a quench [0.0]
  We investigate the nonequilibrium regime of quantum electrodynamics following a global quantum quench. Specifically, a massive Dirac fermion is quenched to a gapless state with an interaction with gauge bosons. In stark contrast to equilibrium (3+1)-dimensional QED with gapless Dirac fermions, where the coupling is marginally irrelevant, we identify a nonequilibrium fixed point characterized by nonFermi liquid behavior.
  arXiv  Detail & Related papers  (2023-12-21T02:21:29Z)
• Real-time dynamics of false vacuum decay [49.1574468325115]
  We investigate false vacuum decay of a relativistic scalar field in the metastable minimum of an asymmetric double-well potential. We employ the non-perturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion.
  arXiv  Detail & Related papers  (2023-10-06T12:44:48Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Topological extension including quantum jump [4.681851642601744]
  We study the Su-Schrieffer-Heeger model with collective loss and gain from a topological perspective. Our study provides a qualitative analysis of the impact of quantum jumping terms and reveals their unique role in quantum systems.
  arXiv  Detail & Related papers  (2022-11-08T13:26:57Z)
• Canonically consistent quantum master equation [68.8204255655161]
  We put forth a new class of quantum master equations that correctly reproduce the state of an open quantum system beyond the infinitesimally weak system-bath coupling limit. Our method is based on incorporating the knowledge of the reduced steady state into its dynamics.
  arXiv  Detail & Related papers  (2022-05-25T15:22:52Z)
• Non-normal Hamiltonian dynamics in quantum systems and its realization on quantum computers [0.0]
  We study the dynamics driven by the non-normal matrix (Hamiltonian) realized as a continuous quantum trajectory of the Lindblad master equation in open quantum systems. We formulate the transient suppression of the decay rate of the norm due to the pseudospectral behavior and derive a non-Hermitian/non-normal analog of the time-energy uncertainty relation.
  arXiv  Detail & Related papers  (2021-07-18T13:29:28Z)
• Non-equilibrium stationary states of quantum non-Hermitian lattice models [68.8204255655161]
  We show how generic non-Hermitian tight-binding lattice models can be realized in an unconditional, quantum-mechanically consistent manner. We focus on the quantum steady states of such models for both fermionic and bosonic systems.
  arXiv  Detail & Related papers  (2021-03-02T18:56:44Z)
• Subdiffusive dynamics and critical quantum correlations in a disorder-free localized Kitaev honeycomb model out of equilibrium [0.0]
  Disorder-free localization has recently emerged as a mechanism for ergodicity breaking in homogeneous lattice gauge theories. In this work we show that this mechanism can lead to unconventional states of quantum matter as the absence of thermalization lifts constraints imposed by equilibrium statistical physics.
  arXiv  Detail & Related papers  (2020-12-10T15:39:17Z)
• Quantum Non-equilibrium Many-Body Spin-Photon Systems [91.3755431537592]
  dissertation concerns the quantum dynamics of strongly-correlated quantum systems in out-of-equilibrium states. Our main results can be summarized in three parts: Signature of Critical Dynamics, Driven Dicke Model as a Test-bed of Ultra-Strong Coupling, and Beyond the Kibble-Zurek Mechanism.
  arXiv  Detail & Related papers  (2020-07-23T19:05:56Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• Entropic Uncertainty Relations and the Quantum-to-Classical transition [77.34726150561087]
  We aim to shed some light on the quantum-to-classical transition as seen through the analysis of uncertainty relations. We employ entropic uncertainty relations to show that it is only by the inclusion of imprecision in our model of macroscopic measurements that we can prepare a system with two simultaneously well-defined quantities.
  arXiv  Detail & Related papers  (2020-03-04T14:01:17Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.