Bootstrapping Euclidean Two-point Correlators

• URL: http://arxiv.org/abs/2511.08560v1
• Date: Wed, 12 Nov 2025 02:04:57 GMT
• Title: Bootstrapping Euclidean Two-point Correlators
• Abstract summary: We develop a bootstrap approach to Euclidean two-point correlators in the thermal or ground state of quantum mechanical systems.<n>We derive rigorous bounds on continuous-time two-point correlators using a finite-dimensional semidefinite bootstrap program.
• Score: 1.4680035572775534
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We develop a bootstrap approach to Euclidean two-point correlators, in the thermal or ground state of quantum mechanical systems. We formulate the problem of bounding the two-point correlator as a semidefinite programming problem, subject to the constraints of reflection positivity, the Heisenberg equations of motion, and the Kubo-Martin-Schwinger condition or ground-state positivity. In the dual formulation, the Heisenberg equations of motion become "inequalities of motion" on the Lagrange multipliers that enforce the constraints. This enables us to derive rigorous bounds on continuous-time two-point correlators using a finite-dimensional semidefinite or polynomial matrix program. We illustrate this method by bootstrapping the two-point correlators of the ungauged one-matrix quantum mechanics, from which we extract the spectrum and matrix elements of the low-lying adjoint states. Along the way, we provide a new derivation of the energy-entropy balance inequality and establish a connection between the high-temperature two-point correlator bootstrap and the matrix integral bootstrap.

Related papers

• Double-Bracket Master Equations: Phase-Space Representation and Classical Limit [0.0]
  We investigate the classical limit of quantum master equations featuring double-bracket dissipators.<n>For both classes of double-bracket equations, we provide a gradient-flow representation of the dynamics.<n>We conclude by extending our analysis to generalized master equations involving higher-order nested brackets.
  arXiv  Detail & Related papers  (2026-01-28T19:00:00Z)
• Disentanglement by deranking and by suppression of correlation [0.0]
  The spontaneous disentanglement hypothesis is motivated by some outstanding issues in standard quantum mechanics.<n>Disentanglement is formulated using a nonlinear operator, which can be used to modify both the Schrdinger equation for the quantum state vector, and the master equation for the density operator.<n>It is shown that limit cycle steady state solutions, which are excluded by standard quantum mechanics, become possible in the presence of disentanglement.
  arXiv  Detail & Related papers  (2026-01-18T10:33:09Z)
• Construction of the Jaynes-Cummings interaction over the finite two-dimensional oscillator [51.56484100374058]
  The construction of the coupling between the degenerate energy states of the finite oscillator and the two levels of the atom allows the identification of excitation-conserved eigenbasis.<n>A dynamical approach to the evolution of mean values of the fields mediated by the atom is shown in the interaction picture.
  arXiv  Detail & Related papers  (2025-09-08T20:49:16Z)
• 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)
• Exact finite-time correlation functions for multi-terminal setups: Connecting theoretical frameworks for quantum transport and thermodynamics [11.061707876645764]
  Transport in open quantum systems can be explored through various theoretical frameworks, including the quantum master equation, scattering matrix, and Heisenberg equation of motion. Existing literature treats these approaches independently, lacking a unified perspective. Our work addresses this gap by clarifying the role and status of these approaches using a minimal single-level quantum dot model in a two-terminal setup.
  arXiv  Detail & Related papers  (2023-12-22T21:09:18Z)
• Low-depth unitary quantum circuits for dualities in one-dimensional quantum lattice models [0.0]
  We show how to turn dualities in (1+1)d quantum lattice models into unitary linear depth quantum circuits. The resulting circuits can for instance be used to efficiently prepare short- and long-range entangled states.
  arXiv  Detail & Related papers  (2023-11-02T17:53:38Z)
• Unconditional Wigner-negative mechanical entanglement with linear-and-quadratic optomechanical interactions [62.997667081978825]
  We propose two schemes for generating Wigner-negative entangled states unconditionally in mechanical resonators. We show analytically that both schemes stabilize a Wigner-negative entangled state that combines the entanglement of a two-mode squeezed vacuum with a cubic nonlinearity. We then perform extensive numerical simulations to test the robustness of Wigner-negative entanglement attained by approximate CPE states stabilized in the presence of thermal decoherence.
  arXiv  Detail & Related papers  (2023-02-07T19:00:08Z)
• Bootstrapping the gap in quantum spin systems [0.7106986689736826]
  We use the equations of motion to develop an analogue of the conformal block expansion for matrix elements. The method can be applied to any quantum mechanical system with a local Hamiltonian.
  arXiv  Detail & Related papers  (2022-11-07T19:07:29Z)
• Lifting the Convex Conjugate in Lagrangian Relaxations: A Tractable Approach for Continuous Markov Random Fields [53.31927549039624]
  We show that a piecewise discretization preserves better contrast from existing discretization problems. We apply this theory to the problem of matching two images.
  arXiv  Detail & Related papers  (2021-07-13T12:31:06Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)
• Operator-algebraic renormalization and wavelets [62.997667081978825]
  We construct the continuum free field as the scaling limit of Hamiltonian lattice systems using wavelet theory. A renormalization group step is determined by the scaling equation identifying lattice observables with the continuum field smeared by compactly supported wavelets.
  arXiv  Detail & Related papers  (2020-02-04T18:04:51Z)

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.