Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains

• URL: http://arxiv.org/abs/2202.07674v1
• Date: Tue, 15 Feb 2022 19:00:09 GMT
• Title: Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains
• Authors: \'Alvaro G\'omez-Le\'on and Tom\'as Ramos and Diego Porras and Alejandro Gonz\'alez-Tudela
• Abstract summary: Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics. We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
• Score: 62.997667081978825
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics, which can be radically different from closed-system scenarios. Such open quantum system dynamics is generally described by Lindblad master equations, whose dynamical and steady-state properties are challenging to obtain, especially in the many-particle regime. Here, we introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function with a real-space decimation technique. Compared to other methods, such technique enables obtaining compact analytical expressions for the dynamics and steady-state properties, such as asymptotic decays or correlation lengths. We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity, including the Hatano-Nelson model. The latter is especially illustrative because its surface and bulk dissipative behavior are linked due to its non-trivial topology, which manifests in directional amplification.

Related papers

• Tensor network methods for the Gross-Pitaevskii equation on fine grids [0.0]
  Gross-Pitaevskii equation and generalisations to dissipative and dipolar gases have been very useful in describing dynamics of cold atomic gases.<n>For some of these applications the numerically accessible grid spacing can become a limiting factor, especially in describing turbulent dynamics.<n>We explore the application of tensor networks to these systems, where (in analogy to related work in fluid and plasma dynamics) they allow for physically motivated data compression.<n>Analysing different non-equilibrium cases involving vortex formation, we find that these methods are particularly efficient.
  arXiv  Detail & Related papers  (2025-07-01T19:16:19Z)
• Weak coupling limit for quantum systems with unbounded weakly commuting system operators [50.24983453990065]
  This work is devoted to a rigorous analysis of the weak coupling limit (WCL) for the reduced dynamics of an open infinite-dimensional quantum system interacting with electromagnetic field or a reservoir formed by Fermi or Bose particles.<n>We derive in the weak coupling limit the reservoir statistics, which is determined by whose terms in the multi-point correlation functions of the reservoir are non-zero in the WCL.<n>We prove that the resulting reduced system dynamics converges to unitary dynamics with a modified Hamiltonian which can be interpreted as a Lamb shift to the original Hamiltonian.
  arXiv  Detail & Related papers  (2025-05-13T05:32:34Z)
• Restricted Monte Carlo wave function method and Lindblad equation for identifying entangling open-quantum-system dynamics [0.0]
  Our algorithm performs tangential projections onto the set of separable states, leading to classically correlated quantum trajectories. Applying this method is equivalent to solving the nonlinear master equation in Lindblad form introduced in citePAH24 for two-qubit systems. We identify the impact of dynamical entanglement in open systems by applying our approach to several correlated decay processes.
  arXiv  Detail & Related papers  (2024-12-11T19:05:34Z)
• Estimates of loss function concentration in noisy parametrized quantum circuits [0.0]
  Variational quantum computing offers a powerful framework with applications across diverse fields such as quantum chemistry, machine learning, and optimization.<n>Its scalability is hindered by the exponential concentration of the loss function, known as the barren plateau problem.<n>We introduce a novel analytical framework that enables the description of the variance in layered noisy quantum circuits with arbitrary noise channels.
  arXiv  Detail & Related papers  (2024-10-02T18:00:09Z)
• Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model [44.99833362998488]
  We analytically study the dynamical decoupling of a two-level system coupled with a structured bosonic environment. We find sufficient conditions under which dynamical decoupling works for such systems. Our bounds reproduce the correct scaling in various relevant system parameters.
  arXiv  Detail & Related papers  (2024-09-24T04:58:28Z)
• Bexcitonics: Quasi-particle approach to open quantum dynamics [0.0]
  We develop a quasiparticle approach to capture the dynamics of open quantum systems coupled to bosonic thermal baths. Bexcitonic properties offer a coarse-grained view of the correlated system-bath dynamics and its numerical convergence.
  arXiv  Detail & Related papers  (2024-01-19T22:29:13Z)
• Decoherence quantification through commutation relations decay for open quantum harmonic oscillators [2.0508733018954843]
  We consider the exponentially fast decay in the two-point commutator matrix of the system variables as a manifestation of quantum decoherence. These features are exploited as nonclassical resources in quantum computation and quantum information processing technologies.
  arXiv  Detail & Related papers  (2022-08-04T08:57:31Z)
• Structure-Preserving Learning Using Gaussian Processes and Variational Integrators [62.31425348954686]
  We propose the combination of a variational integrator for the nominal dynamics of a mechanical system and learning residual dynamics with Gaussian process regression. We extend our approach to systems with known kinematic constraints and provide formal bounds on the prediction uncertainty.
  arXiv  Detail & Related papers  (2021-12-10T11:09:29Z)
• Boundary Chaos [0.0]
  Scrambling in many-body quantum systems causes initially local observables to spread uniformly over the whole available space under unitary dynamics. We present a free quantum circuit model, in which ergodicity is induced by an impurity interaction placed on the system's boundary.
  arXiv  Detail & Related papers  (2021-12-09T18:34:08Z)
• Unification of Random Dynamical Decoupling and the Quantum Zeno Effect [68.8204255655161]
  We show that the system dynamics under random dynamical decoupling converges to a unitary with a decoupling error that characteristically depends on the convergence speed of the Zeno limit. This reveals a unification of the random dynamical decoupling and the quantum Zeno effect.
  arXiv  Detail & Related papers  (2021-12-08T11:41:38Z)
• Exact solutions of interacting dissipative systems via weak symmetries [77.34726150561087]
  We analytically diagonalize the Liouvillian of a class Markovian dissipative systems with arbitrary strong interactions or nonlinearity. This enables an exact description of the full dynamics and dissipative spectrum. Our method is applicable to a variety of other systems, and could provide a powerful new tool for the study of complex driven-dissipative quantum systems.
  arXiv  Detail & Related papers  (2021-09-27T17:45:42Z)
• 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)
• Method of spectral Green functions in driven open quantum dynamics [77.34726150561087]
  A novel method based on spectral Green functions is presented for the simulation of driven open quantum dynamics. The formalism shows remarkable analogies to the use of Green functions in quantum field theory. The method dramatically reduces computational cost compared with simulations based on solving the full master equation.
  arXiv  Detail & Related papers  (2020-06-04T09:41:08Z)
• The entanglement membrane in chaotic many-body systems [0.0]
  In certain analytically-tractable quantum chaotic systems, the calculation of out-of-time-order correlation functions, entanglement entropies after a quench, and other related dynamical observables, reduces to an effective theory of an entanglement membrane'' in spacetime. We show here how to make sense of this membrane in more realistic models, which do not involve an average over random unitaries.
  arXiv  Detail & Related papers  (2019-12-27T19:01:13Z)

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.