Stochastic perturbation theory: a prequel to Reptation Quantum Monte Carlo

• URL: http://arxiv.org/abs/2209.02799v2
• Date: Sun, 11 Sep 2022 14:47:24 GMT
• Title: Stochastic perturbation theory: a prequel to Reptation Quantum Monte Carlo
• Authors: Stefano Baroni
• Abstract summary: I present a different approach to Rayleigh-Schr"o theory, based on Laplacedinger theory, yielding an iterative expression for the perturbative expansion of the energy of the non-degenerate ground state of a quantum system. A resummation scheme that is equivalent to Reptation Quantum Monte Carlo provides the original motivation to its development in the late nineties.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: I present a different approach to Rayleigh-Schr\"odinger perturbation theory, based on Laplace transforms and polynomial theory, yielding an iterative expression for the perturbative expansion of the energy of the non-degenerate ground state of a quantum system, which easily lends itself to symbolic computation. A stochastic interpretation of the various perturbative corrections naturally leads to a re-summation scheme that is equivalent to Reptation Quantum Monte Carlo and that actually provided the original motivation to its development in the late nineties.

Related papers

• Non-Hermitian Generalization of Rayleigh-Schrödinger Perturbation Theory [8.493769586495345]
  We generalize the Rayleigh-Schr"odinger perturbation theory to the non-Hermitian regime by employing a geometric formalism. We find that the perturbation method proposed in this paper reduces to the standard Rayleigh-Schr"odinger perturbation theory in the Hermitian regime.
  arXiv  Detail & Related papers  (2024-12-06T16:30:19Z)
• A Note on the Relativistic Transformation Properties of Quantum Stochastic Calculus [0.0]
  We argue that for uniformly accelerated open systems, the formalism must breakdown as we move from a Fock representation of the quantum noise to a unitarily inequivalent non-Fock representation. The unitary inequivalence ultimately being a consequence of the underlying flat noise spectrum approximation for the fundamental quantum processes.
  arXiv  Detail & Related papers  (2024-11-12T16:45:50Z)
• On reconstruction of states from evolution induced by quantum dynamical semigroups perturbed by covariant measures [50.24983453990065]
  We show the ability to restore states of quantum systems from evolution induced by quantum dynamical semigroups perturbed by covariant measures. Our procedure describes reconstruction of quantum states transmitted via quantum channels and as a particular example can be applied to reconstruction of photonic states transmitted via optical fibers.
  arXiv  Detail & Related papers  (2023-12-02T09:56:00Z)
• Generalised linear response theory for the full quantum work statistics [0.3277163122167433]
  We study a quantum system driven out of equilibrium via a small Hamiltonian perturbation. We find that all information about the distribution can be encoded in a single quantity.
  arXiv  Detail & Related papers  (2023-07-04T19:06:50Z)
• Demonstrating Quantum Microscopic Reversibility Using Coherent States of Light [58.8645797643406]
  We propose and experimentally test a quantum generalization of the microscopic reversibility when a quantum system interacts with a heat bath. We verify that the quantum modification for the principle of microscopic reversibility is critical in the low-temperature limit.
  arXiv  Detail & Related papers  (2022-05-26T00:25:29Z)
• Role of the electromagnetic vacuum in the transition from classical to quantum mechanics [0.0]
  We revisit the nonrelativistic problem of a bound, charged particle subject to the random zero-point radiation field (ZPF) We reveal the mechanism that takes it from the initially classical description to the final quantum-mechanical one.
  arXiv  Detail & Related papers  (2022-03-21T23:57:52Z)
• Dissipative quantum dynamics, phase transitions and non-Hermitian random matrices [0.0]
  We work in the framework of the dissipative Dicke model which is archetypal of symmetry-breaking phase transitions in open quantum systems. We establish that the Liouvillian describing the quantum dynamics exhibits distinct spectral features of integrable and chaotic character. Our approach can be readily adapted for classifying the nature of quantum dynamics across dissipative critical points in other open quantum systems.
  arXiv  Detail & Related papers  (2021-12-10T19:00:01Z)
• Quantum Simulation of Chiral Phase Transitions [62.997667081978825]
  We construct a quantum simulation for the $(+1)$ dimensional NJL model at finite temperature and finite chemical potential. We observe consistency among digital quantum simulation, exact diagonalization, and analytical solution, indicating further applications of quantum computing in simulating QCD thermodynamics.
  arXiv  Detail & Related papers  (2021-12-07T19:04:20Z)
• Quantum Simulation of Conformal Field Theory [77.34726150561087]
  We describe a quantum algorithm to simulate the dynamics of conformal field theories. A full analysis of the approximation errors suggests near-term applicability.
  arXiv  Detail & Related papers  (2021-09-29T06:44:33Z)
• Open-system approach to nonequilibrium quantum thermodynamics at arbitrary coupling [77.34726150561087]
  We develop a general theory describing the thermodynamical behavior of open quantum systems coupled to thermal baths. Our approach is based on the exact time-local quantum master equation for the reduced open system states.
  arXiv  Detail & Related papers  (2021-09-24T11:19:22Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)

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.