On global dynamics for damped driven Jaynes-Cummings equations

• URL: http://arxiv.org/abs/2603.17562v1
• Date: Wed, 18 Mar 2026 10:09:57 GMT
• Title: On global dynamics for damped driven Jaynes-Cummings equations
• Abstract summary: The article concerns damped driven Jaynes-Cummings equation which quantised one-mode Maxwell coupled to a two-level molecule.<n>We consider a broad class of pumping which are damping and trace operators, and their structures correspond to the theory of completely positive and trace generators.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The article concerns damped driven Jaynes-Cummings equation which describes quantised one-mode Maxwell field coupled to a two-level molecule. We consider a broad class of damping and pumping which are polynomial in the creation and annihilation operators, and their structures correspond to the theory of completely positive and trace preserving generators (CPTP) of Lindblad and Kossakowski & al. Our main result is the construction of global generalised solutions with values in the Hilbert space of nonnegative Hermitian Hilbert-Schmidt operators in the case of time-dependent pumping. The proofs rely on finite-dimensional approximations of the annihilation and creation operators.

Related papers

• Path integral formulation of finite-dimensional quantum mechanics in discrete phase space [0.0]
  We develop a path integral representation for the dynamics of quantum systems with a finite-dimensional Hilbert space.<n>For Hamiltonians linear in the phase-space coordinates, we show that the fluctuation sum factorizes.<n>We show explicitly that the full entanglement dynamics requires the coherent contribution of all fluctuation sectors of the action.
  arXiv  Detail & Related papers  (2026-04-22T17:04:10Z)
• On dynamical semigroup for damped driven Jaynes-Cummings equations [0.0]
  The article addresses the damped driven Jaynes-Cummings for quantised one-mode Maxwell field coupled to a two-level molecule.<n>We consider a broad class of pumping which are damping in the creation and Hilbert-Schmidt operators.<n>All trajectories of the semigroup are generalised solutions to the Jaynes-Cummings equations.
  arXiv  Detail & Related papers  (2026-03-18T10:01:49Z)
• Approximate Reduced Lindblad Dynamics via Algebraic and Adiabatic Methods [0.0]
  We show that projecting a Lindblad generator on its center manifold yields an exact reduced quantum dynamical semigroup whose dynamics is unitary.<n>For analytics of a Lindblad generator with a tractable center manifold, we propose a perturbative reduction that keeps the reduced space fixed at the unperturbed center manifold.
  arXiv  Detail & Related papers  (2026-03-12T14:34:19Z)
• Symmetry-protected topology and deconfined solitons in a multi-link $\mathbb{Z}_2$ gauge theory [45.88028371034407]
  We study a $mathbbZ$ lattice gauge theory defined on a multi-graph with links that can be visualized as great circles of a spherical shell.<n>We show that this leads to state-dependent tunneling amplitudes underlying a phenomenon analogous to the Peierls instability.<n>By performining a detailed analysis based on matrix product states, we prove that charge deconfinement emerges as a consequence of charge-fractionalization.
  arXiv  Detail & Related papers  (2026-03-02T22:59:25Z)
• State Space Decomposition of Quantum Dynamical Semigroups [0.0]
  Mean evolution of an open quantum system in continuous time is described by a time continuous semigroup of quantum channels.<n>We apply this decomposition to a class of open quantum random walks and to quantum trajectories, where we study its uniqueness.
  arXiv  Detail & Related papers  (2025-06-05T17:28:22Z)
• Reproducing Kernel Hilbert Space Approach to Non-Markovian Quantum Stochastic Models [0.0]
  We give a derivation of the non-Markovian quantum state diffusion equation of Di'osi and Strunz. We show that the complex trajectories arises as a consequence of using the Bargmann-Segal representation of the bath.
  arXiv  Detail & Related papers  (2024-07-09T21:10:54Z)
• Continuous percolation in a Hilbert space for a large system of qubits [58.720142291102135]
  The percolation transition is defined through the appearance of the infinite cluster. We show that the exponentially increasing dimensionality of the Hilbert space makes its covering by finite-size hyperspheres inefficient. Our approach to the percolation transition in compact metric spaces may prove useful for its rigorous treatment in other contexts.
  arXiv  Detail & Related papers  (2022-10-15T13:53:21Z)
• The frustration-free fully packed loop model [4.965221313169878]
  We consider a quantum fully packed loop model on the square lattice with a frustration-free projector Hamiltonian and ring-exchange interactions acting on plaquettes. We discuss how the boundary term fractures the Hilbert space into Krylov subspaces, and we prove that the Hamiltonian is ergodic within each subspace. We show that the spectrum is shown to be gapless in the thermodynamic limit with a trial state constructed by adding a twist to the ground state superposition.
  arXiv  Detail & Related papers  (2022-06-03T18:00:04Z)
• General Solution and Canonical Quantization of the Conic Path Constrained Second-Class System [0.0]
  We consider the problem of constrained motion along a conic path under a given external potential function. We perform the canonical quantization in a consistent way in terms of the corresponding Dirac brackets. The complete Dirac brackets algebra in phase space as well as its physical realization in terms of differential operators is explicitly obtained.
  arXiv  Detail & Related papers  (2022-02-15T13:46:56Z)
• Conformal field theory from lattice fermions [77.34726150561087]
  We provide a rigorous lattice approximation of conformal field theories given in terms of lattice fermions in 1+1-dimensions. We show how these results lead to explicit error estimates pertaining to the quantum simulation of conformal field theories.
  arXiv  Detail & Related papers  (2021-07-29T08:54:07Z)
• Entanglement and Complexity of Purification in (1+1)-dimensional free Conformal Field Theories [55.53519491066413]
  We find pure states in an enlarged Hilbert space that encode the mixed state of a quantum field theory as a partial trace. We analyze these quantities for two intervals in the vacuum of free bosonic and Ising conformal field theories.
  arXiv  Detail & Related papers  (2020-09-24T18:00:13Z)
• 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)
• A refinement of Reznick's Positivstellensatz with applications to quantum information theory [72.8349503901712]
  In Hilbert's 17th problem Artin showed that any positive definite in several variables can be written as the quotient of two sums of squares. Reznick showed that the denominator in Artin's result can always be chosen as an $N$-th power of the squared norm of the variables.
  arXiv  Detail & Related papers  (2019-09-04T11:46:26Z)

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.