Gaussian phase-space representations for fermions

Abstract

We introduce a positive phase-space representation for fermions, using the most general possible multi-mode Gaussian operator basis. The representation generalizes previous bosonic quantum phase-space methods to Fermi systems. We derive equivalences between quantum and stochastic moments, as well as operator correspondences that map quantum operator evolution onto stochastic processes in phase space. The representation thus enables first-principles quantum dynamical or equilibrium calculations in many-body Fermi systems. Potential applications are to strongly interacting and correlated Fermi gases, including coherent behaviour in open systems and nanostructures described by master equations. Examples of an ideal gas and the Hubbard model are given, as well as a generic open system, in order to illustrate these ideas.

More references and examples. Much less mathematical material

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Cited by in corpus (41)

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• Superconductivity in a Hubbard-Froehlich Model and in cuprates
• Quasiprobability representation of quantum coherence
• Quasiprobability distributions for quantum-optical coherence and beyond
• Semiclassical approach to Dynamics of Interacting Fermions
• Gaussian-Basis Monte Carlo Method for Numerical Study on Ground States of Itinerant and Strongly Correlated Electron Systems
• Q-functions as models of physical reality
• Positive-P phase space method simulation in superradiant emission from a cascade atomic ensemble
• Pairing mean-field theory for the dynamics of dissociation of molecular Bose-Einstein condensates
• Probabilistic Q-function distributions in fermionic phase-space
• Systematic errors in Gaussian Quantum Monte Carlo and a systematic study of the symmetry projection method
• Quantum dynamics in ultra-cold atomic physics
• Teleporting quantum information encoded in fermionic modes
• Time evolution with symmetric stochastic action
• Linear entropy in quantum phase space
• Gaussian phase-space representation of Fermion dynamics; Beyond the time-dependent-Hartree-Fock approximation
• Complexity of Fermionic Dissipative Interactions and Applications to Quantum Computing
• Phase space methods for Majorana fermions
• Scalable quantum field simulations of conditioned systems
• Atom-atom correlations and relative number squeezing in dissociation of spatially inhomogeneous molecular condensates
• Objective quantum fields, retrocausality and ontology
• First-principles quantum dynamics for fermions: Application to molecular dissociation
• Grassmann Phase Space Methods for Fermions. II. Field Theory
• Stochastic simulations of fermionic dynamics with phase-space representations
• Initial states and apodisation for quantum field simulations in phase-space
• Directional spatial structure of dissociated elongated molecular condensates
• Grassmann phase-space methods for fermions: uncovering classical probability structure
• Resolution of unity for fermionic Gaussian operators
• The Nonequilibrium Many-Body Problem as a paradigm for extreme data science
• Quantum dynamics in phase space: From coherent states to the Gaussian representation
• Work extraction using Gaussian operations in non-interacting fermionic systems
• Quantum many-body simulations using Gaussian phase-space representations
• Phaseless quantum Monte-Carlo approach to strongly correlated superconductors with stochastic Hartree-Fock-Bogoliubov wavefunctions
• Stochastic correction to the Maxwell-Bloch equations via the positive $P$ representation
• Simulations of quantum dynamics with fermionic phase-space representations using numerical matrix factorizations as stochastic gauges
• Algorithm for initializing a generalized fermionic Gaussian state on a quantum computer
• Correlated quantum dynamics of graphene
• Theory of light-matter interactions in cascade and diamond type atomic ensembles
• Fermion quadrature bases for Wigner functionals