Exact solution for a class of quantum models of interacting bosons

• URL: http://arxiv.org/abs/2411.14204v1
• Date: Thu, 21 Nov 2024 15:13:03 GMT
• Title: Exact solution for a class of quantum models of interacting bosons
• Authors: Valery Shchesnovich,
• Abstract summary: In quantum optics the prime interest is the evolution of an initial state, such as the generation of optical signal modes by a strong pump mode propagating in a nonlinear medium. I propose a simple and general method of derivation of the solution to such a state evolution problem, applicable to a wide class of quantum models of interacting bosons.
• Score: 0.0
• License:
• Abstract: Quantum models of interacting bosons have wide range of applications, among them the propagation of optical modes in nonlinear media, such as the $k$-photon down conversion. Many of such models are related to nonlinear deformations of finite group algebras, thus, in this sense, they are exactly solvable. Whereas the advanced group-theoretic methods have been developed to study the eigenvalue spectrum of exactly solvable Hamiltonians, in quantum optics the prime interest is not the spectrum of the Hamiltonian, but the evolution of an initial state, such as the generation of optical signal modes by a strong pump mode propagating in a nonlinear medium. I propose a simple and general method of derivation of the solution to such a state evolution problem, applicable to a wide class of quantum models of interacting bosons. For the $k$-photon down conversion model and its generalizations, the solution to the state evolution problem is given in the form of an infinite series expansion in the powers of propagation time with the coefficients defined by a recursion relation with a single polynomial function, unique for each nonlinear model. As an application, I compare the exact solution to the parametric down conversion process with the semiclassical parametric approximation.

Related papers

• Bridging classical and quantum approaches in optical polarimetry: Predicting polarization-entangled photon behavior in scattering environments [36.89950360824034]
  We explore quantum-based optical polarimetry as a potential diagnostic tool for biological tissues. We develop a theoretical and experimental framework to understand polarization-entangled photon behavior in scattering media.
  arXiv  Detail & Related papers  (2024-11-09T10:17:47Z)
• The multi-state geometry of shift current and polarization [44.99833362998488]
  We employ quantum state projectors to develop an explicitly gauge-invariant formalism. We provide a simple expression for the shift current that resolves its precise relation to the moments of electronic polarization. We reveal its decomposition into the sum of the skewness of the occupied states and intrinsic multi-state geometry.
  arXiv  Detail & Related papers  (2024-09-24T18:00:02Z)
• Variational approach to light-matter interaction: Bridging quantum and semiclassical limits [0.0]
  We present a time-dependent variational approach to simulate the dynamics of light-matter systems. The variational approach is applicable to a variety of quantum models of light-matter interaction.
  arXiv  Detail & Related papers  (2024-07-17T00:53:33Z)
• Quench dynamics in higher-dimensional Holstein models: Insights from Truncated Wigner Approaches [41.94295877935867]
  We study the melting of charge-density waves in a Holstein model after a sudden switch-on of the electronic hopping. A comparison with exact data obtained for a Holstein chain shows that a semiclassical treatment of both the electrons and phonons is required in order to correctly describe the phononic dynamics.
  arXiv  Detail & Related papers  (2023-12-19T16:14:01Z)
• Geometric Neural Diffusion Processes [55.891428654434634]
  We extend the framework of diffusion models to incorporate a series of geometric priors in infinite-dimension modelling. We show that with these conditions, the generative functional model admits the same symmetry.
  arXiv  Detail & Related papers  (2023-07-11T16:51:38Z)
• Exact solution for quantum strong long-range models via a generalized Hubbard-Stratonovich transformation [0.0]
  We present an exact analytical solution for quantum strong long-range models in the canonical ensemble. We utilize the equivalence between generalized Dicke models and interacting quantum models as a generalization of the Hubbard-Stratonovich transformation.
  arXiv  Detail & Related papers  (2023-05-17T18:00:02Z)
• Designing Kerr Interactions for Quantum Information Processing via Counterrotating Terms of Asymmetric Josephson-Junction Loops [68.8204255655161]
  static cavity nonlinearities typically limit the performance of bosonic quantum error-correcting codes. Treating the nonlinearity as a perturbation, we derive effective Hamiltonians using the Schrieffer-Wolff transformation. Results show that a cubic interaction allows to increase the effective rates of both linear and nonlinear operations.
  arXiv  Detail & Related papers  (2021-07-14T15:11:05Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• Diagonalization of Hamiltonian for finite-sized dispersive media: Canonical quantization with numerical mode-decomposition (CQ-NMD) [3.032299122358857]
  We present a new math-physics modeling approach, called canonical quantization with numerical mode-decomposition. We provide several numerical simulations that capture the physics of full quantum effects, impossible by classical Maxwell's equations.
  arXiv  Detail & Related papers  (2021-01-28T18:47:33Z)
• Quantum limit-cycles and the Rayleigh and van der Pol oscillators [0.0]
  Self-oscillating systems are emerging as canonical models for driven dissipative nonequilibrium open quantum systems. We derive an exact analytical solution for the steady-state quantum dynamics of the simplest of these models. Our solution is a generalization to arbitrary temperature of existing solutions for very-low, or zero, temperature.
  arXiv  Detail & Related papers  (2020-11-05T08:51:51Z)
• Renormalization to localization without a small parameter [0.0]
  We study the wave function localization properties in a d-dimensional model of randomly spaced particles with isotropic hopping potential depending solely on Euclidean interparticle distances. Due to the generality of this model usually called the Euclidean random matrix model, it arises naturally in various physical contexts such as studies of vibrational modes, artificial atomic systems, liquids and glasses, ultracold gases and photon localization phenomena.
  arXiv  Detail & Related papers  (2020-01-17T19:00:06Z)

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.