New Phase Space Formulations and Quantum Dynamics Approaches

Abstract

We report recent progress on the phase space formulation of quantum mechanics with coordinate-momentum variables, focusing more on new theory of (weighted) constraint coordinate-momentum phase space for discrete-variable quantum systems. This leads to a general coordinate-momentum phase space formulation of composite quantum systems, where conventional representations on infinite phase space are employed for continuous variables. It is convenient to utilize (weighted) constraint coordinate-momentum phase space for representing the quantum state and describing nonclassical features. Various numerical tests demonstrate that new trajectory-based quantum dynamics approaches derived from the (weighted) constraint phase space representation are useful and practical for describing dynamical processes of composite quantum systems in gas phase as well as in condensed phase.

References in corpus (23)

• Reconstruction of non-classical cavity field states with snapshots of their decoherence
• Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques
• Direct Fidelity Estimation from Few Pauli Measurements
• Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space
• Reduced hierarchical equations of motion in real and imaginary time: Correlated initial states and thermodynamic quantities
• Wigner function negativity and contextuality in quantum computation on rebits
• Real-Time and Imaginary-Time Quantum Hierarchal Fokker-Planck Equations
• Generalized spin mapping for quantum-classical dynamics
• Observation of Entanglement Between Itinerant Microwave Photons and a Superconducting Qubit
• Exact quantum statistics for electronically nonadiabatic systems using continuous path variables
• Capturing Vacuum Fluctuations and Photon Correlations in Cavity Quantum Electrodynamics with Multi-Trajectory Ehrenfest Dynamics
• Analysis of the quantum-classical Liouville equation in the mapping basis
• Visualizing operators of coupled spin systems
• Unified Formulation of Phase Space Mapping Approaches for Nonadiabatic Quantum Dynamics
• Benchmarking Semiclassical and Perturbative Methods for Real-time Simulations of Cavity-Bound Emission and Interference
• Dynamics of correlations in two-dimensional quantum spin models with long-range interactions: A phase-space Monte-Carlo study
• Overview of the phase space formulation of quantum mechanics with application to quantum technologies
• Quasiprobability distribution functions for periodic phase-spaces: I. Theoretical Aspects
• Nonequilibrium dynamics of spin-boson models from phase space methods
• Negative Zero-Point-Energy Parameter in the Meyer-Miller Mapping Model for Nonadiabatic Dynamics
• Commutator Matrix in Phase Space Mapping Models for Nonadiabatic Quantum Dynamics
• Measurement of complete and continuous Wigner functions for discrete atomic systems
• Semi-Classical Discretization and Long-Time Evolution of Variable Spin Systems