A Dyson equation approach for averaging of classical and quantum
observables on multiple realizations of Markov processes
- URL: http://arxiv.org/abs/2004.01183v3
- Date: Thu, 6 May 2021 11:29:22 GMT
- Title: A Dyson equation approach for averaging of classical and quantum
observables on multiple realizations of Markov processes
- Authors: Simone Sturniolo
- Abstract summary: Time dependent signals are often the result of an ensemble average over many microscopical dynamical processes.
We present a numerical approach that can potentially be used to solve such time evolution problems.
We benchmark it against a Monte Carlo simulations of the same problems.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Time dependent signals in experimental techniques such as Nuclear Magnetic
Resonance (NMR) and Muon Spin Relaxation (muSR) are often the result of an
ensemble average over many microscopical dynamical processes. While there are a
number of functions used to fit these signals, they are often valid only in
specific regimes, and almost never properly describe the "spectral diffusion"
regime, in which the dynamics happen on time scales comparable to the
characteristic frequencies of the system. Full treatment of these problems
would require one to carry out a path integral over all possible realizations
of the dynamics of the time dependent Hamiltonian.
In this paper we present a numerical approach that can potentially be used to
solve such time evolution problems, and we benchmark it against a Monte Carlo
simulations of the same problems. The approach can be used for any sort of
dynamics, but is especially powerful for any dynamics that can be approximated
as Markov processes, in which the dynamics at each step only depend on the
previous state of the system. The approach is used to average both classical
and quantum observables; in the latter case, a formalism making use of
Liouvillians and density matrices is used.
Related papers
- Going beyond quantum Markovianity and back to reality: An exact master equation study [0.0]
An analytical depiction of an open quantum system is provided.
The steady-state excitation number (AEN) of the system shows rapid escalation with increasing non-Markovianity.
The Mpemba effect can be observed in the non-Markovian regime in a surprisingly super-cooling-like effect.
arXiv Detail & Related papers (2024-11-26T08:10:35Z) - Quantum Simulation of Nonlinear Dynamical Systems Using Repeated Measurement [42.896772730859645]
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations.
We apply this approach to the classic logistic and Lorenz systems in both integrable and chaotic regimes.
arXiv Detail & Related papers (2024-10-04T18:06:12Z) - Spectral chaos bounds from scaling theory of maximally efficient
quantum-dynamical scrambling [49.1574468325115]
A key conjecture about the evolution of complex quantum systems towards an ergodic steady state, known as scrambling, is that this process acquires universal features when it is most efficient.
We develop a single- parameter scaling theory for the spectral statistics in this scenario, which embodies exact self-similarity of the spectral correlations along the complete scrambling dynamics.
We establish that scaling predictions are matched by a privileged process, and serve as bounds for other dynamical scrambling scenarios, allowing one to quantify inefficient or incomplete scrambling on all timescales.
arXiv Detail & Related papers (2023-10-17T15:41:50Z) - Dynamically Emergent Quantum Thermodynamics: Non-Markovian Otto Cycle [49.1574468325115]
We revisit the thermodynamic behavior of the quantum Otto cycle with a focus on memory effects and strong system-bath couplings.
Our investigation is based on an exact treatment of non-Markovianity by means of an exact quantum master equation.
arXiv Detail & Related papers (2023-08-18T11:00:32Z) - Timescales of quantum and classical chaotic spin models evolving toward equilibrium [0.0]
We investigate quench dynamics in a one-dimensional spin model, comparing both quantum and classical descriptions.
Numerical simulations, supported by semi-analytical analysis, reveal that the relaxation of single-particle energies (global quantity) and on-site magnetization (local observable) occurs on a timescale independent of the system size $L$.
arXiv Detail & Related papers (2023-07-11T18:00:04Z) - Unbiasing time-dependent Variational Monte Carlo by projected quantum
evolution [44.99833362998488]
We analyze the accuracy and sample complexity of variational Monte Carlo approaches to simulate quantum systems classically.
We prove that the most used scheme, the time-dependent Variational Monte Carlo (tVMC), is affected by a systematic statistical bias.
We show that a different scheme based on the solution of an optimization problem at each time step is free from such problems.
arXiv Detail & Related papers (2023-05-23T17:38:10Z) - Decimation technique for open quantum systems: a case study with
driven-dissipative bosonic chains [62.997667081978825]
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.
arXiv Detail & Related papers (2022-02-15T19:00:09Z) - Influence functional of many-body systems: temporal entanglement and
matrix-product state representation [0.0]
Feynman-Vernon influence functional (IF) was originally introduced to describe the effect of a quantum environment on the dynamics of an open quantum system.
We apply the IF approach to describe quantum many-body dynamics in isolated spin systems.
arXiv Detail & Related papers (2021-03-25T10:41:15Z) - Fast and differentiable simulation of driven quantum systems [58.720142291102135]
We introduce a semi-analytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical methods.
We show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.
arXiv Detail & Related papers (2020-12-16T21:43:38Z) - Combining Floquet and Lyapunov techniques for time-dependent problems in
optomechanics and electromechanics [0.0]
Cavity optomechanics and electromechanics form an established field of research investigating the interactions between electromagnetic fields and the motion of quantum mechanical resonators.
In many applications, linearised form of the interaction is used, which allows for the system dynamics to be fully described using a Lyapunov equation for the covariance matrix of the Wigner function.
This approach is problematic in situations where the Hamiltonian becomes time dependent as is the case for systems driven at multiple frequencies simultaneously.
We show how the lengthy process of applying the Floquet formalism to the original equations of motion and deriving a Lyapunov equation from their time-
arXiv Detail & Related papers (2020-02-28T16:20:27Z)
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.