Defining stable phases of open quantum systems
- URL: http://arxiv.org/abs/2308.15495v2
- Date: Sun, 11 Feb 2024 21:51:28 GMT
- Title: Defining stable phases of open quantum systems
- Authors: Tibor Rakovszky and Sarang Gopalakrishnan and Curt von Keyserlingk
- Abstract summary: We show that uniformity is satisfied in a canonical classical cellular automaton.
We conjecture some sufficient conditions for a channel to exhibit uniformity and therefore stability.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The steady states of dynamical processes can exhibit stable nontrivial
phases, which can also serve as fault-tolerant classical or quantum memories.
For Markovian quantum (classical) dynamics, these steady states are extremal
eigenvectors of the non-Hermitian operators that generate the dynamics, i.e.,
quantum channels (Markov chains). However, since these operators are
non-Hermitian, their spectra are an unreliable guide to dynamical relaxation
timescales or to stability against perturbations. We propose an alternative
dynamical criterion for a steady state to be in a stable phase, which we name
uniformity: informally, our criterion amounts to requiring that, under
sufficiently small local perturbations of the dynamics, the unperturbed and
perturbed steady states are related to one another by a finite-time dissipative
evolution. We show that this criterion implies many of the properties one would
want from any reasonable definition of a phase. We prove that uniformity is
satisfied in a canonical classical cellular automaton, and provide numerical
evidence that the gap determines the relaxation rate between nearby steady
states in the same phase, a situation we conjecture holds generically whenever
uniformity is satisfied. We further conjecture some sufficient conditions for a
channel to exhibit uniformity and therefore stability.
Related papers
- Entanglement and localization in long-range quadratic Lindbladians [49.1574468325115]
Signatures of localization have been observed in condensed matter and cold atomic systems.
We propose a model of one-dimensional chain of non-interacting, spinless fermions coupled to a local ensemble of baths.
We show that the steady state of the system undergoes a localization entanglement phase transition by tuning $p$ which remains stable in the presence of coherent hopping.
arXiv Detail & Related papers (2023-03-13T12:45:25Z) - Spectral stabilizability [0.0]
We develop conditions for stabilizability based on the target state's eigendecomposition.
We use the spectral approach to derive upper bounds on stabilizability for a number of exemplary open system scenarios.
arXiv Detail & Related papers (2022-12-23T10:38:31Z) - Spontaneous symmetry breaking in non-steady modes of open quantum
many-body systems [0.0]
We consider spontaneous symmetry breaking in non-steady modes of an open quantum many-body system.
For a dissipative spin model, it is shown that the most coherent mode exhibits a transition from a disordered phase to a symmetry-broken ordered phase.
arXiv Detail & Related papers (2022-12-19T09:45:44Z) - Sufficient condition for gapless spin-boson Lindbladians, and its
connection to dissipative time-crystals [64.76138964691705]
We discuss a sufficient condition for gapless excitations in the Lindbladian master equation for collective spin-boson systems.
We argue that gapless modes can lead to persistent dynamics in the spin observables with the possible formation of dissipative time-crystals.
arXiv Detail & Related papers (2022-09-26T18:34:59Z) - Quantum behavior of a superconducting Duffing oscillator at the
dissipative phase transition [0.817918559522319]
We reconcile the classical and quantum descriptions in a unified picture of quantum metastability.
By engineering the lifetime of the metastable states sufficiently large, we observe a first-order dissipative phase transition.
Results reveal a smooth quantum evolution behind a sudden dissipative transition.
arXiv Detail & Related papers (2022-06-13T17:35:27Z) - Harmonic oscillator kicked by spin measurements: a Floquet-like system
without classical analogous [62.997667081978825]
The impulsive driving is provided by stroboscopic measurements on an ancillary degree of freedom.
The dynamics of this system is determined in closed analytical form.
We observe regimes with crystalline and quasicrystalline structures in phase space, resonances, and evidences of chaotic behavior.
arXiv Detail & Related papers (2021-11-23T20:25:57Z) - Observation of Time-Crystalline Eigenstate Order on a Quantum Processor [80.17270167652622]
Quantum-body systems display rich phase structure in their low-temperature equilibrium states.
We experimentally observe an eigenstate-ordered DTC on superconducting qubits.
Results establish a scalable approach to study non-equilibrium phases of matter on current quantum processors.
arXiv Detail & Related papers (2021-07-28T18:00:03Z) - 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) - Stability of quantum eigenstates and kinetics of wave function collapse
in a fluctuating environment [0.0]
The work analyzes the stability of the quantum eigenstates when they are submitted to fluctuations.
In the limit of sufficiently slow kinetics, the quantum eigenstates show to remain stationary configurations.
The work shows that the final stationary eigenstate depends by the initial configuration of the superposition of states.
arXiv Detail & Related papers (2020-11-25T10:41:53Z) - Non-equilibrium non-Markovian steady-states in open quantum many-body
systems: Persistent oscillations in Heisenberg quantum spin chains [68.8204255655161]
We investigate the effect of a non-Markovian, structured reservoir on an open Heisenberg spin chain.
We establish a coherent self-feedback mechanism as the reservoir couples frequency-dependent to the spin chain.
arXiv Detail & Related papers (2020-06-05T09:16:28Z) - Deconstructing effective non-Hermitian dynamics in quadratic bosonic
Hamiltonians [0.0]
We show that stability-to-instability transitions may be classified in terms of a suitably generalized $mathcalPmathcalT$ symmetry.
We characterize the stability phase diagram of a bosonic analogue to the Kitaev-Majorana chain under a wide class of boundary conditions.
Our analysis also reveals that boundary conditions that support Majorana zero modes in the fermionic Kitaev chain are precisely the same that support stability in the bosonic chain.
arXiv Detail & Related papers (2020-03-06T19:30:51Z)
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.