Boson-fermion algebraic mapping in second quantization

• URL: http://arxiv.org/abs/2409.17271v1
• Date: Wed, 25 Sep 2024 18:37:34 GMT
• Title: Boson-fermion algebraic mapping in second quantization
• Authors: F. Lingua, D. M. Peñafiel, L. Ravera, S. Salgado,
• Abstract summary: We present a method to derive the structure at the basis of the mapping of bosonic algebras of creation and operators into fermionic algebras. The structure corresponds to a deformed Grassmann algebra, involving anticommuting Grassmann-type variables.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We present an algebraic method to derive the structure at the basis of the mapping of bosonic algebras of creation and annihilation operators into fermionic algebras, and vice versa, introducing a suitable identification between bosonic and fermionic generators. The algebraic structure thus obtained corresponds to a deformed Grassmann algebra, involving anticommuting Grassmann-type variables. The role played by the latter in the implementation of gauge invariance in second quantization within our procedure is then discussed, together with the application of the mapping to the case of the bosonic and fermionic harmonic oscillator Hamiltonians.

Related papers

• Equivalence of dynamics of disordered quantum ensembles and semi-infinite lattices [44.99833362998488]
  We develop a formalism for mapping the exact dynamics of an ensemble of disordered quantum systems onto the dynamics of a single particle propagating along a semi-infinite lattice. This mapping provides a geometric interpretation on the loss of coherence when averaging over the ensemble and allows computation of the exact dynamics of the entire disordered ensemble in a single simulation.
  arXiv  Detail & Related papers  (2024-06-25T18:13:38Z)
• Quantum Random Walks and Quantum Oscillator in an Infinite-Dimensional Phase Space [45.9982965995401]
  We consider quantum random walks in an infinite-dimensional phase space constructed using Weyl representation of the coordinate and momentum operators. We find conditions for their strong continuity and establish properties of their generators.
  arXiv  Detail & Related papers  (2024-06-15T17:39:32Z)
• Exceptional points and quantum phase transition in a fermionic extension of the Swanson oscillator [8.84834042985207]
  We propose a fermionic extension of a non-Hermitian quantum system consisting of a general representation of a quadratic Hamiltonian. The model admits a quantum phase transition - we discuss the two phases and also demonstrate that the ground-state entanglement entropy exhibits a discontinuous jump.
  arXiv  Detail & Related papers  (2024-01-30T17:20:34Z)
• 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)
• Mapping Molecular Hamiltonians into Hamiltonians of Modular cQED Processors [50.893896302254944]
  We introduce a general method to map the Hamiltonian of an arbitrary model system into the Hamiltonian of a circuit Quantum Electrodynamics (cQED) processor. The method is illustrated as applied to quantum dynamics simulations of the Fenna-Matthews-Olson complex and the spin-boson model of charge transfer.
  arXiv  Detail & Related papers  (2023-06-10T04:52:58Z)
• Dynamical symmetry of a semiconfined harmonic oscillator model with a position-dependent effective mass [0.0]
  We have found three basis elements of this algebra. The algebra defined through those basis elements is a $mathfraksuleft (1,1 right)$ Heisenberg-Lie algebra.
  arXiv  Detail & Related papers  (2023-05-19T14:30:04Z)
• Isomorphism between the Bialynicki-Birula and the Landau-Peierls Fock space quantization of the electromagnetic field in position representation [0.0]
  We first present a summary of the quantization of the electromagnetic field in position space representation. We use two main approaches: the Landau-Peierls approach in the Coulomb gauge and the Bialynicki-Birula approach. We show that the two approches are completly equivalent.
  arXiv  Detail & Related papers  (2022-12-12T12:26:12Z)
• Quantum quenches in a pseudo-Hermitian Chern insulator [1.0093662416275693]
  We show the bulk-surface duality of the pseudo-Hermitian phases, then build a concrete relation between the static band topology and quench dynamics. We propose a possible scheme to realize the seemingly challenging model in a bilayer lattice and detect the dynamics with a double-quench protocol.
  arXiv  Detail & Related papers  (2022-09-30T03:20:45Z)
• Particle on the sphere: group-theoretic quantization in the presence of a magnetic monopole [0.0]
  We consider the problem of quantizing a particle on a 2-sphere. We construct the Hilbert space directly from the symmetry algebra. We show how the Casimir invariants of the algebra determine the bundle topology.
  arXiv  Detail & Related papers  (2020-11-10T04:42:08Z)
• 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.