Reduced Density Matrix Functional Theory for Bosons

• URL: http://arxiv.org/abs/2002.06943v1
• Date: Mon, 17 Feb 2020 13:13:50 GMT
• Title: Reduced Density Matrix Functional Theory for Bosons
• Authors: Carlos L. Benavides-Riveros, Jakob Wolff, Miguel A. L. Marques, Christian Schilling
• Abstract summary: We propose a ground state theory for bosonic quantum systems. The exact functionals for this $N$-boson Hubbard dimer and general Bogoliubov-approximated systems are determined. The gradient forces are found to diverge in the regime of Bose-Einstein condensation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Based on a generalization of Hohenberg-Kohn's theorem, we propose a ground state theory for bosonic quantum systems. Since it involves the one-particle reduced density matrix $\gamma$ as a natural variable but still recovers quantum correlations in an exact way it is particularly well-suited for the accurate description of Bose-Einstein condensates. As a proof of principle we study the building block of optical lattices. The solution of the underlying $v$-representability problem is found and its peculiar form identifies the constrained search formalism as the ideal starting point for constructing accurate functional approximations: The exact functionals for this $N$-boson Hubbard dimer and general Bogoliubov-approximated systems are determined. The respective gradient forces are found to diverge in the regime of Bose-Einstein condensation, $\nabla_{\gamma} \mathcal{F} \propto 1/\sqrt{1-N_{\mathrm{BEC}}/N}$, providing a natural explanation for the absence of complete BEC in nature.

Related papers

• Scattering Neutrinos, Spin Models, and Permutations [42.642008092347986]
  We consider a class of Heisenberg all-to-all coupled spin models inspired by neutrino interactions in a supernova with $N$ degrees of freedom. These models are characterized by a coupling matrix that is relatively simple in the sense that there are only a few, relative to $N$, non-trivial eigenvalues.
  arXiv  Detail & Related papers  (2024-06-26T18:27:15Z)
• Quantum tomography of helicity states for general scattering processes [55.2480439325792]
  Quantum tomography has become an indispensable tool in order to compute the density matrix $rho$ of quantum systems in Physics. We present the theoretical framework for reconstructing the helicity quantum initial state of a general scattering process.
  arXiv  Detail & Related papers  (2023-10-16T21:23:42Z)
• Deriving density-matrix functionals for excited states [0.0]
  We first study the symmetric Hubbard dimer, constituting the building block of the Hubbard model, for which we execute the Levy-Lieb constrained search. We demonstrate three conceptually different approaches for deriving the universal functional in a homogeneous Bose gas for arbitrary pair interaction in the Bogoliubov regime. Remarkably, in both systems the gradient of the functional is found to diverge repulsively at the boundary of the functional's domain, extending the recently discovered Bose-Einstein condensation force to excited states.
  arXiv  Detail & Related papers  (2022-09-29T17:03:08Z)
• Reduced Density Matrix Functional Theory for Bosons: Foundations and Applications [0.0]
  This thesis aims to initiate and establish a bosonic RDMFT for both ground state and excited state energy calculations. Motivated by the Onsager and Penrose criterion, we derive the universal functional for a homogeneous Bose-Einstein condensates (BECs) in the Bogoliubov regime. In the second part of the thesis, we propose and work out an ensemble RDMFT targeting excitations in bosonic quantum systems.
  arXiv  Detail & Related papers  (2022-05-05T13:28:18Z)
• An exact one-particle theory of bosonic excitations: From a generalized Hohenberg-Kohn theorem to convexified N-representability [0.0]
  We propose a functional theory for targeting low-lying excitation energies of bosonic quantum systems through the one-particle picture. We employ an extension of the Rayleigh-Ritz variational principle to ensemble states with spectrum $boldsymbolw$ and prove a corresponding generalization of the Hohenberg-Kohn theorem. Remarkably, this reveals a complete hierarchy of bosonic exclusion principle constraints in conceptual analogy to Pauli's exclusion principle for fermions.
  arXiv  Detail & Related papers  (2022-04-27T06:02:22Z)
• Classical analog of qubit logic based on a magnon Bose-Einstein condensate [52.77024349608834]
  We present a classical version of several quantum bit (qubit) functionalities using a two-component magnon Bose-Einstein condensate. The macroscopic wavefunctions of these two condensates serve as orthonormal basis states that form a system being a classical counterpart of a single qubit.
  arXiv  Detail & Related papers  (2021-11-12T16:14:46Z)
• Annihilating Entanglement Between Cones [77.34726150561087]
  We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied. Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
  arXiv  Detail & Related papers  (2021-10-22T15:02:39Z)
• Repulsively diverging gradient of the density functional in the Reduced Density Matrix Functional Theory [0.0]
  We show that the existence of the Bose-Einstein condensation force is completely universal for any type of pair-interaction. We also show the existence of an analogous repulsive gradient in the fermionic RDMFT for the $N$-fermion singlet sector.
  arXiv  Detail & Related papers  (2021-03-29T11:04:30Z)
• Qubit regularization of asymptotic freedom [35.37983668316551]
  Heisenberg-comb acts on a Hilbert space with only two qubits per spatial lattice site. We show that the model reproduces the universal step-scaling function of the traditional model up to correlation lengths of 200,000 in lattice units. We argue that near-term quantum computers may suffice to demonstrate freedom.
  arXiv  Detail & Related papers  (2020-12-03T18:41:07Z)
• Functional Theory for Bose-Einstein Condensates [0.0]
  One-particle reduced density matrix functional theory would potentially be the ideal approach for describing Bose-Einstein condensates. We eventually initiate and establish this novel theory by deriving the respective universal functional $mathcalF$ for general homogeneous Bose-Einstein condensates.
  arXiv  Detail & Related papers  (2020-10-13T18:56:20Z)
• Sub-bosonic (deformed) ladder operators [62.997667081978825]
  We present a class of deformed creation and annihilation operators that originates from a rigorous notion of fuzziness. This leads to deformed, sub-bosonic commutation relations inducing a simple algebraic structure with modified eigenenergies and Fock states. In addition, we investigate possible consequences of the introduced formalism in quantum field theories, as for instance, deviations from linearity in the dispersion relation for free quasibosons.
  arXiv  Detail & Related papers  (2020-09-10T20:53:58Z)

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.