Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Inversion of operators represented in a coherent-state basis

Shlomo Ruschin

Published Apr 1, 1984• 0 citations
Publisher

Abstract

A method is presented for inverting operators in the coherent-states $R$ representation. The method is equivalent to the solution of an ordinary differential equation. The equation is presented in an explicit general form. Some simple nontrivial examples are illustrated. Applications suggested are calculations of resolvents in phase space and semiclassical expansions.

DOI
10.1103/physreva.29.2218

Related papers

Mapping of operator equations into C -number differential form and the atomic coherent-state representation

Luigi Lugiato, Lorenzo M. Narducci, M. Gronchi

The mapping of operator equations into $C$-number differential form by means of the atomic coherent-state representation leads to mathematical difficulties that have no counterpart in the case of the Glauber-Sudarshan representation for Bose systems. We give sufficient conditions for the solutions of $C$-number equations in the atomic coherent-state representation to be physically meaningful.

Physical Review A•Mar 1, 1977•4 citations

Differential-Form Relations Between Density Operators and Their P -Representations in Coherent State Basis

Hong-Yi Fan, Zhongxi Zhang

By virtue of the technique of integration within an ordered product of operators, we derive differential-form relations between density operators and their P -representations in the coherent state basis. Some applications of these new relations in normally ordering operators are given.

Communications in Theoretical Physics•Apr 30, 1996•0 citations

Gaussian phase-space representations for fermions

Joel Frederick Corney, P. D. Drummond

We introduce a positive phase-space representation for fermions, using the most general possible multimode 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 behavior 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.

arXiv:cond-mat/0411712•Physical Review B•Mar 22, 2006•66 citations

Inverse operators in Fock space studied via a coherent-state approach

Fan Hong‐Yi

The Fock representation of the inverse of harmonic-oscillator creation and annihilation operators [see, e.g., C. L. Mehta, Anil K. Roy, and G. M. Saxena, Phys. Rev. A 46, 1565 (1992)] are naturally derived via a coherent-state approach. The completeness relation of Fock space is reexpressed by the inverse operators. Applications of the inverse operators in studying the phase operators and in normally ordering some operators are given.

Physical Review A•May 1, 1993•29 citations

Bosonic Encodings for Hermite-Galerkin Discretizations of High-Dimensional PDEs and Bayesian Inverse Problems

Alice Barthe

The Koopman-von Neumann framework has been proposed to design quantum algorithms for non-linear dynamics. It maps a non-linear ordinary differential equation to a linear partial differential equation (PDE) governing a probability amplitude. Previous works represents this amplitude in the Hermite-function basis, equivalently as a bosonic state, and truncates the total Hermite degree to obtain a representation over $Θ(m\log N)$ qubits, where $N$ is the number of variables and $m$ the truncation order. We extend this approach to a broader class of linear PDEs whose differential operators have a structured polynomial form. We prove convergence of the truncation for both time-dependent dynamics and gapped ground-state problems under explicit regularity and stability assumptions. We then introduce a qubit encoding that supports efficient block encodings of the truncated operators. Finally, we apply the framework to Bayesian inverse problems with Gaussian priors and observation noise, reducing posterior-state preparation to the preparation of a structured Hamiltonian's ground state.

quant-pharXiv:2608.26268•Aug 28, 2026•0 citations

Features of Moyal Trajectories

Nuno Costa Dias, João Nuno Prata

We study the Moyal evolution of the canonical position and momentum variables. We compare it with the classical evolution and show that, contrary to what is commonly found in the literature, the two dynamics do not coincide. We prove that this divergence is quite general by studying Hamiltonians of the form $p^2 /2m + V(q)$. Several alternative formulations of Moyal dynamics are then suggested. We introduce the concept of starfunction and use it to reformulate the Moyal equations in terms of a system of ordinary differential equations on the noncommutative Moyal plane. We then use this formulation to study the semiclassical expansion of Moyal trajectories, which is cast in terms of a (order by order in $\\hbar$) recursive hierarchy of i) first order partial differential equations as well as ii) systems of first order ordinary differential equations. The latter formulation is derived independently for analytic Hamiltonians as well as for the more general case of smooth local integrable ones. We present various examples illustrating these results.

•Apr 22, 2006•14 citations
A method is presented for inverting operators in the coherent-states RRR representation. The method is equivalent to the solution of an ordinary differential equation. The equation is presented in an explicit general form. Some simple nontrivial examples are illustrated. Applications suggested are calculations of resolvents in phase space and semiclassical expansions.
The mapping of operator equations into CCC-number differential form by means of the atomic coherent-state representation leads to mathematical difficulties that have no counterpart in the case of the Glauber-Sudarshan representation for Bose systems. We give sufficient conditions for the solutions of CCC-number equations in the atomic coherent-state representation to be physically meaningful.
We introduce a positive phase-space representation for fermions, using the most general possible multimode 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 behavior 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.
The Koopman-von Neumann framework has been proposed to design quantum algorithms for non-linear dynamics. It maps a non-linear ordinary differential equation to a linear partial differential equation (PDE) governing a probability amplitude. Previous works represents this amplitude in the Hermite-function basis, equivalently as a bosonic state, and truncates the total Hermite degree to obtain a representation over Θ(mlog⁡N)Θ(m\log N)Θ(mlogN) qubits, where NNN is the number of variables and mmm the truncation order. We extend this approach to a broader class of linear PDEs whose differential operators have a structured polynomial form. We prove convergence of the truncation for both time-dependent dynamics and gapped ground-state problems under explicit regularity and stability assumptions. We then introduce a qubit encoding that supports efficient block encodings of the truncated operators. Finally, we apply the framework to Bayesian inverse problems with Gaussian priors and observation noise, reducing posterior-state preparation to the preparation of a structured Hamiltonian's ground state.
We study the Moyal evolution of the canonical position and momentum variables. We compare it with the classical evolution and show that, contrary to what is commonly found in the literature, the two dynamics do not coincide. We prove that this divergence is quite general by studying Hamiltonians of the form p2/2m+V(q)p^2 /2m + V(q)p2/2m+V(q). Several alternative formulations of Moyal dynamics are then suggested. We introduce the concept of starfunction and use it to reformulate the Moyal equations in terms of a system of ordinary differential equations on the noncommutative Moyal plane. We then use this formulation to study the semiclassical expansion of Moyal trajectories, which is cast in terms of a (order by order in hbar\\hbarhbar) recursive hierarchy of i) first order partial differential equations as well as ii) systems of first order ordinary differential equations. The latter formulation is derived independently for analytic Hamiltonians as well as for the more general case of smooth local integrable ones. We present various examples illustrating these results.