A Lindbladian From Feynman-Vernon

• URL: http://arxiv.org/abs/2312.16454v1
• Date: Wed, 27 Dec 2023 07:48:12 GMT
• Title: A Lindbladian From Feynman-Vernon
• Authors: Jose A. Magpantay
• Abstract summary: I derive a Lindbladian in a mechanical example, a point particle interacting with a bath of harmonic oscillators. I also point out the causes of these terms, the Markov Lindbladian from the very local interaction of the point particle with the classical solutions.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The effective dynamics of a system interacting with a bath or environment is presented in two ways, (1) the (LGKS) replacement of the von Neuman equation for the density matrix and (2) the Feynman-Vernon path-integral derivation, by integrating out the bath degree of freedom, to arrive at a system's density matrix. In this paper, I connect the two methods by deriving a Lindbladian in a mechanical example, a point particle interacting with a bath of harmonic oscillators, previously considered by Feynman and Vernon (FV) and expounded on later by Caldeira and Leggett (CL). But the (FV)/(CL) results only in non-Markov effect, memory terms from the bath interaction. To derive a Lindbladian, I changed the interaction term they considered to take into account the point particle interacting with the bath harmonic oscillators to something more realistic. From the resulting path-integral expression of the system's propagator for the density matrix, the Lindbladian and non-Markov terms are read for this simple problem. I also point out the causes of these terms, the Markov Lindbladian from the very local interaction of the point particle with the classical solutions of the harmonic oscillator and the non-Markov term from the global interaction of the point particle with the fluctuation of the classical solutions.

Related papers

• 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)
• A minimal tensor network beyond free fermions [39.847063110051245]
  This work proposes a minimal model extending the duality between classical statistical spin systems and fermionic systems. A Jordan-Wigner transformation applied to a two-dimensional tensor network maps the partition sum of a classical statistical mechanics model to a Grassmann variable integral. The resulting model is simple, featuring only two parameters: one governing spin-spin interaction and the other measuring the deviation from the free fermion limit.
  arXiv  Detail & Related papers  (2024-12-05T14:49:39Z)
• Measurement-induced transitions for interacting fermions [43.04146484262759]
  We develop a field-theoretical framework that provides a unified approach to observables characterizing entanglement and charge fluctuations. Within this framework, we derive a replicated Keldysh non-linear sigma model (NLSM) By using the renormalization-group approach for the NLSM, we determine the phase diagram and the scaling of physical observables.
  arXiv  Detail & Related papers  (2024-10-09T18:00:08Z)
• Dirac Brackets $\leftrightarrow$ Lindblad Equation: A Correspondence [0.0]
  We study the time evolution of an open quantum system governed by the Gorini-Kossakowski-Sudarshan-Lindlad equation. In a similar fashion, the time evolution of a physical observable in a classically constrained dynamical system is governed by a generalization of the Liouville equation. We derive an intriguing, but precise classical-quantum correspondence between the aforementioned situations which connects the Lindblad operators to the constraints.
  arXiv  Detail & Related papers  (2024-05-04T04:42:15Z)
• Observation of Nonlinear Response and Onsager Regression in a Photon Bose-Einstein Condensate [34.82692226532414]
  The quantum regression theorem states that the correlations of a system at two different times are governed by the same equations of motion as the temporal response of the average values. Here we experimentally demonstrate that the two-time particle number correlations in a photon Bose-Einstein condensate inside a dye-filled microcavity exhibit the same dynamics as the response of the condensate to a sudden perturbation of the dye molecule bath. This confirms the regression theorem for a quantum gas and, moreover, establishes a test of this relation in an unconventional form where the perturbation acts on the bath and only the condensate response is monitored.
  arXiv  Detail & Related papers  (2024-03-07T17:59:58Z)
• Effective field theory of particle mixing [10.985518406776766]
  We study emphindirect mixing of two fields induced by their couplings to a common decay channel in a medium. The analysis reveals subtle caveats in the description of mixing in terms of the widely used non-Hermitian effective Hamiltonian.
  arXiv  Detail & Related papers  (2023-10-26T00:23:34Z)
• 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)
• Lindbladian approximation beyond ultra-weak coupling [0.0]
  Lindblad-type equations provide the most general class of Markovian MEs. Lindblad-type MEs are commonly derived from the Born-Markov-Redfield equation via a rotating-wave approximation (RWA) Here we derive an alternative Lindbladian approximation to the Redfield equation, which does not rely on ultra-weak system-bath coupling.
  arXiv  Detail & Related papers  (2020-12-28T12:18:02Z)
• Non-Markovian decoherence of a two-level system in a Lorentzian bosonic reservoir and a stochastic environment with finite correlation time [0.0]
  We investigate non-Markovian evolution of a two-level system (qubit) in a bosonic bath under influence of an external classical environment.
  arXiv  Detail & Related papers  (2020-06-24T21:16:52Z)
• Localization of Rung Pairs in Hard-core Bose-Hubbard Ladder [13.46516066673]
  We study the rung-pair localization of the Bose-Hubbard ladder model without quenched disorder. In the hard-core limit, there exists a rung-pair localization both at the edges and in the bulk. Our results reveal another interesting type of disorder-free localization related to a zero-energy flat band.
  arXiv  Detail & Related papers  (2020-05-18T08:40:40Z)
• Dynamics of quantum correlations in a Qubit-Oscillator system interacting via a dissipative bath [0.0]
  We study the entanglement dynamics in a bipartite system consisting of a qubit and a harmonic oscillator interacting only through their coupling with the same bath. Based on the Kossakowski Matrix, we show that non-classical correlations including entanglement can be generated by the considered dynamics.
  arXiv  Detail & Related papers  (2020-02-11T02:29:27Z)
• Feynman Propagator for a System of Interacting Scalar Particles in the Fokker Theory [62.997667081978825]
  The functional integral on the generalized phase space is defined as the initial one in quantum theory. The measure of integration in the generalized configuration space of world particle lines is determined. A modification of the propagator is proposed, in which the role of independent time parameters is taken by the time coordinates of the particles in Minkowski space.
  arXiv  Detail & Related papers  (2020-02-10T09:09:45Z)
• 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.