Random non-Hermitian Hamiltonian framework for symmetry breaking dynamics
arXiv:2410.04333 · doi:10.1103/rkdn-j6hy
Abstract
We propose random non-Hermitian Hamiltonians to model the generic stochastic nonlinear dynamics of a quantum state in Hilbert space. Our approach features an underlying linearity in the dynamical equations, ensuring the applicability of techniques used for solving linear systems. Additionally, it offers the advantage of easily incorporating statistical symmetry, a generalization of explicit symmetry to stochastic processes. To demonstrate the utility of our approach, we apply it to describe real-time dynamics, starting from an initial symmetry-preserving state and evolving into a randomly distributed, symmetry-breaking final state. Our model serves as a quantum framework for the transition process, from disordered states to ordered ones, where symmetry is spontaneously broken.
16 pages, 11 figures. Published version
References in corpus (38)
- Making Sense of Non-Hermitian Hamiltonians
- Edge states and topological invariants of non-Hermitian systems
- Exceptional Topology of Non-Hermitian Systems
- Topological phases of non-Hermitian systems
- Symmetry and Topology in Non-Hermitian Physics
- Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
- Models of Wave-function Collapse, Underlying Theories, and Experimental Tests
- Quantum trajectories and open many-body quantum systems
- Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
- Non-Hermitian Topological Sensors
- Symmetry-protected nodal phases in non-Hermitian systems
- Simulation methods for open quantum many-body systems
- Observation of non-Bloch parity-time symmetry and exceptional points
- Dynamical phases and intermittency of the dissipative quantum Ising model
- Underground test of gravity-related wave function collapse
- Non-Hermitian Edge Burst
- Upper bounds on spontaneous wave-function collapse models using millikelvin-cooled nanocantilevers
- Present status and future challenges of non-interferometric tests of collapse models
- Improved noninterferometric test of collapse models using ultracold cantilevers
- Amoeba Formulation of Non-Bloch Band Theory in Arbitrary Dimensions
- Room temperature test of the Continuous Spontaneous Localization model using a levitated micro-oscillator
- Collapse models with non-white noises
- Narrowing the parameter space of collapse models with ultracold layered force sensors
- High-density quantum sensing with dissipative first order transitions
- Robustness of exceptional-point-based sensors against parametric noise: The role of Hamiltonian and Liouvillian degeneracies
- An ultra-narrow line width levitated nano-oscillator for testing dissipative wavefunction collapse
- Testing Linearity of Quantum Theory with a Thermometer
- Testing the foundations of quantum physics in space Interferometric and non-interferometric tests with Large Particles
- Spatial correlations of one dimensional driven-dissipative systems of Rydberg atoms
- Relativistically Invariant Markovian Dynamical Collapse Theories Must Employ Nonstandard Degrees of Freedom
- Atto-Nm Torque Sensing with a Macroscopic Optomechanical Torsion Pendulum
- Collapse models with non-white noises II: particle-density coupled noises
- Neutron star heating constraints on wave-function collapse models
- Driven-dissipative criticality within the discrete truncated Wigner approximation
- Mass-coupled relativistic spontaneous collapse models
- Quantum Dynamics with Stochastic Non-Hermitian Hamiltonians
- On the (im)possibility of extending the GRW model to relativistic particles
- Relativistic quantum field theory of stochastic dynamics in the Hilbert space