Capturing non-Markovian polaron dressing with the master equation formalism

• URL: http://arxiv.org/abs/2407.10744v1
• Date: Mon, 15 Jul 2024 14:17:58 GMT
• Title: Capturing non-Markovian polaron dressing with the master equation formalism
• Abstract summary: We extend the validity of the polaron master equation (PME) to capture the impact of non-Markovian polaron dressing. We introduce correction terms that provide an accurate description of observables that do not commute with the transformation. We demonstrate the significance of the correction terms in two cases, the canonical spin-boson model and a dissipative time-dependent Landau-Zener protocol.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Understanding the dynamics of open quantum systems in strong coupling and non-Markovian regimes remains a formidable theoretical challenge. One popular and well-established method of approximation in these circumstances is provided by the polaron master equation (PME). In this work we reevaluate and extend the validity of the PME to capture the impact of non-Markovian polaron dressing, induced by non-equilibrium open system dynamics. By comparing with numerically exact techniques, we confirm that while the standard PME successfully predicts the dynamics of system observables that commute with the polaron transformation (e.g. populations in the Pauli z-basis), it can struggle to fully capture those that do not (e.g. coherences). This limitation stems from the mixing of system and environment degrees of freedom inherent to the polaron transformation, which affects the accuracy of calculated expectation values within the polaron frame. Employing the Nakajima-Zwanzig projection operator formalism, we introduce correction terms that provide an accurate description of observables that do not commute with the transformation. We demonstrate the significance of the correction terms in two cases, the canonical spin-boson model and a dissipative time-dependent Landau-Zener protocol, where they are shown to impact the system dynamics on both short and long timescales.

Related papers

• Floquet-Resolved Dissipation Selects Entanglement Beyond Population Spectroscopy [41.99844472131922]
  We show that two dissipative descriptions of the same parametrically coupled qubits can yield closely similar period-averaged populations.<n>Both retain the complete periodically driven Hamiltonian, the same microscopic bath couplings, and the same physical observables.
  arXiv  Detail & Related papers  (2026-08-12T15:33:26Z)
• Fluctuations of path-dependent thermodynamic quantities in open quantum systems via two-point system-only measurements [39.146761527401424]
  We propose a method to evaluate general thermodynamic fluctuations in open quantum systems.<n>Our approach allows one to obtain exact equalities for fluctuations of path-dependent thermodynamic quantities such as work and heat.<n>We look explicitly at the shape and size of the correction factors to Jarzynski's equality for a qubit undergoing phase covariant dynamics.
  arXiv  Detail & Related papers  (2026-04-29T16:23:44Z)
• Beyond the Quantum Regression Theorem in Variational Polaron Master Equations with Low-Dimensional Baths [0.0]
  The quantum regression theorem (QRT) is the standard tool for computing multi-time correlation functions in open quantum systems.<n>We derive an extension to the QRT that explicitly incorporates correlation-induced corrections.<n>Our approach broadens the reach of analytic master equations to strong-coupling regimes.
  arXiv  Detail & Related papers  (2026-04-15T06:44:37Z)
• Polaron Transformed Canonically Consistent Quantum Master Equation [0.0]
  We develop a polaron-transformed version of the canonically consistent quantum master equation (CCQME)<n>The CCQME extends beyond standard weak-coupling approaches while retaining the same numerical complexity as conventional quantum master equations.<n>We predict an initial-state-independent slowing down of thermalization in the strong-coupling regime of the spin-boson model.
  arXiv  Detail & Related papers  (2026-04-03T04:49:43Z)
• Unveiling coherent dynamics in non-Markovian open quantum systems: exact expression and recursive perturbation expansion [44.99833362998488]
  We introduce a systematic framework to derive the effective Hamiltonian governing the coherent dynamics of non-Markovian open quantum systems.<n>Applying our framework to paradigmatic spin systems, we reveal how environmental correlations influence energy shifts and eigenbasis rotations.
  arXiv  Detail & Related papers  (2025-06-04T15:55:22Z)
• Universal dissipators for driven open quantum systems and the correction to linear response [0.0]
  We show that the dissipator characterizing the dynamics of a reduced system is universal.<n>We also derive the linear response correction due to memory-mediated environmental effects in driven-dissipative systems.
  arXiv  Detail & Related papers  (2025-05-25T18:33:51Z)
• Theory of the correlated quantum Zeno effect in a monitored qubit dimer [41.94295877935867]
  We show how the competition between two measurement processes give rise to two distinct Quantum Zeno (QZ) regimes.<n>We develop a theory based on a Gutzwiller ansatz for the wavefunction that is able to capture the structure of the Hilbert phase diagram.<n>We show how the two QZ regimes are intimately connected to the topology of the flow of the underlying non-Hermitian Hamiltonian governing the no-click evolution.
  arXiv  Detail & Related papers  (2025-03-28T19:44:48Z)
• Dissipative quantum phase transitions monitored by current fluctuations [0.0]
  Dissipative phase transitions (DPT) are defined by sudden changes in the physical properties of nonequilibrium open quantum systems. Here, we consider the $textitoutput current$, defined as the average total quantum jumps per unit time between the open quantum system and the environment. We propose that output current fluctuations, and in particular their dynamical correlations, their power spectrum, and their characteristic timescale can provide valuable information about DPT.
  arXiv  Detail & Related papers  (2025-02-03T08:08:08Z)
• Time-dependent Neural Galerkin Method for Quantum Dynamics [42.81677042059531]
  We introduce a classical computational method for quantum dynamics that relies on a global-in-time variational principle.<n>Our scheme computes the entire state trajectory over a finite time window by minimizing a loss function that enforces the Schr"odinger's equation.<n>We showcase the method by simulating global quantum quenches in the paradigmatic Transverse-Field Ising model in both 1D and 2D.
  arXiv  Detail & Related papers  (2024-12-16T13:48:54Z)
• Parametric approximation as open quantum systems problem [0.0]
  We consider the Jaynes-Cummings model with dissipation, assuming that the field is in the regime close to the parametric approximation with depletion. We obtain non-unitary corrections to the parametric approximation and additional dynamical Lamb-shift contributions to it. And we show that even after depletion, initial non-Markovian behaviour contributes to the dynamics via laser-induced polishing of the density matrix.
  arXiv  Detail & Related papers  (2024-10-04T14:54:17Z)
• Observing Time-Dependent Energy Level Renormalisation in an Ultrastrongly Coupled Open System [37.69303106863453]
  We show how strong coupling and memory effects influence the energy levels of open quantum systems. Measurements reveal a time-dependent shift in the system's energy levels of up to 15% of the bare system frequency. Our findings provide direct evidence of dynamic energy level renormalisation in strongly coupled open quantum systems.
  arXiv  Detail & Related papers  (2024-08-28T16:40:55Z)
• Open quantum systems with non-commuting coupling operators: An analytic approach [0.0]
  We present an analytic approach to treat open quantum systems strongly coupled to multiple environments via noncommuting system operators. For a spin impurity coupled to both dissipative and decoherring environments, the effective Hamiltonian predicts the suppression of relaxation by decoherence.
  arXiv  Detail & Related papers  (2024-08-03T20:56:35Z)
• Dynamical invariant based shortcut to equilibration in open quantum systems [0.0]
  We propose using the Lewis-Riesenfeld invariant to speed-up the equilibration of a driven open quantum system. We show that our protocol can achieve a high-fidelity control in shorter timescales than simple non-optimized protocols.
  arXiv  Detail & Related papers  (2024-01-22T02:32:27Z)
• Combining critical and quantum metrology [0.0]
  We introduce an approach combining two methodologies into a unified protocol applicable to closed and driven-dissipative systems. We provide analytical expressions for the quantum and classical Fisher information in such a setup, elucidating as well a straightforward measurement approach. We showcase these results by focusing on the squeezing Hamiltonian, which characterizes the thermodynamic limit of Dicke and Lipkin-Meshkov-Glick Hamiltonians.
  arXiv  Detail & Related papers  (2023-11-28T04:21:39Z)
• Emergence of fluctuating hydrodynamics in chaotic quantum systems [47.187609203210705]
  macroscopic fluctuation theory (MFT) was recently developed to model the hydrodynamics of fluctuations. We perform large-scale quantum simulations that monitor the full counting statistics of particle-number fluctuations in boson ladders. Our results suggest that large-scale fluctuations of isolated quantum systems display emergent hydrodynamic behavior.
  arXiv  Detail & Related papers  (2023-06-20T11:26:30Z)
• 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)
• 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)
• On optimization of coherent and incoherent controls for two-level quantum systems [77.34726150561087]
  This article considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schr"odinger equation with coherent control. The open system's dynamics is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation.
  arXiv  Detail & Related papers  (2022-05-05T09:08:03Z)
• Assessment of weak-coupling approximations on a driven two-level system under dissipation [58.720142291102135]
  We study a driven qubit through the numerically exact and non-perturbative method known as the Liouville-von equation with dissipation. We propose a metric that may be used in experiments to map the regime of validity of the Lindblad equation in predicting the steady state of the driven qubit.
  arXiv  Detail & Related papers  (2020-11-11T22:45:57Z)
• Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations [77.34726150561087]
  The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems. Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations. Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.
  arXiv  Detail & Related papers  (2020-07-20T18:00:02Z)
• Dissipative dynamics of an interacting spin system with collective damping [1.3980986259786221]
  Hamiltonian and Lindblad dynamics in quantum systems give rise to non-equillibrium phenomena. In this paper, we investigate this interplay of dynamics in infinite range Heisenberg model coupled to a non-Markovian bath.
  arXiv  Detail & Related papers  (2018-03-03T14:13:28Z)

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.