Quantum linear Boltzmann equation
arXiv:0904.3911 · doi:10.1016/j.physrep.2009.06.001
Abstract
We review the quantum version of the linear Boltzmann equation, which describes in a non-perturbative fashion, by means of scattering theory, how the quantum motion of a single test particle is affected by collisions with an ideal background gas. A heuristic derivation of this Lindblad master equation is presented, based on the requirement of translation-covariance and on the relation to the classical linear Boltzmann equation. After analyzing its general symmetry properties and the associated relaxation dynamics, we discuss a quantum Monte Carlo method for its numerical solution. We then review important limiting forms of the quantum linear Boltzmann equation, such as the case of quantum Brownian motion and pure collisional decoherence, as well as the application to matter wave optics. Finally, we point to the incorporation of quantum degeneracies and self-interactions in the gas by relating the equation to the dynamic structure factor of the ambient medium, and we provide an extension of the equation to include internal degrees of freedom.
63 pages, 6 figures; v3:corresponds to published version
References in corpus (40)
- Atom Interferometers
- A Straightforward Introduction to Continuous Quantum Measurement
- Decoherence of matter waves by thermal emission of radiation
- Fundamental Aspects of Quantum Brownian Motion
- Non-Markovian generalization of the Lindblad theory of open quantum systems
- A Kapitza-Dirac-Talbot-Lau interferometer for highly polarizable molecules
- Introduction to decoherence theory
- Theory of decoherence in a matter wave Talbot-Lau interferometer
- Master equation for a quantum particle in a gas
- Stochastic pure state representation for open quantum systems
- Lindblad rate equations
- Theory and experimental verification of Kapitza-Dirac-Talbot-Lau interferometry
- Decoherence in a Talbot Lau interferometer: the influence of molecular scattering
- Not to normal order - Notes on the kinetic limit for weakly interacting quantum fluids
- On the Energy Increase in Space-Collapse Models
- On the quantum description of Einstein's Brownian motion
- Monitoring derivation of the quantum linear Boltzmann equation
- Monitoring approach to open quantum dynamics using scattering theory
- Influence of molecular temperature on the coherence of fullerenes in a near-field interferometer
- Non-Markovian dynamics for bipartite systems
- Normalization of Collisional Decoherence: Squaring the Delta Function, and an Independent Cross-Check
- Transition from diffusive to ballistic dynamics for a class of finite quantum models
- Nonexponential decoherence and momentum subdiffusion in a quantum Lévy kicked rotator
- Relaxation dynamics of a quantum Brownian particle in an ideal gas
- Absolute absorption spectroscopy based on molecule interferometry
- Quantum stochastic equation for test particle interacting with dilute Bose gas
- Master-equations for the study of decoherence
- First measurements of the index of refraction of gases for lithium atomic waves
- Thermal limitation of far-field matter-wave interference
- Kinetic Equations for Quantum Many-Particle Systems
- Index of refraction of gases for matter waves: effect of the motion of the gas particles on the calculation of the index
- Three-dimensional Monte Carlo simulations of the quantum linear Boltzmann equation
- Boltzmann equation approach to transport in finite modular quantum systems
- Frictional quantum decoherence
- A Monte Carlo Method for Modeling Thermal Damping: Beyond the Brownian-Motion Master Equation
- Recoil Free Scattering From a Free Gas
- Visibility Fringe Reduction Due to Noise-Induced Effects: Microscopic Approach to Interference Experiments
- Open quantum dynamics via environmental monitoring
- White noise approach to the low density limit of a quantum particle in a gas
- Quantum interferometry with complex molecules
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- Models of Wave-function Collapse, Underlying Theories, and Experimental Tests
- Quantum Decoherence
- Colloquium: Quantum interference of clusters and molecules
- Foundations and Measures of Quantum Non-Markovianity
- Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem
- Bounds on Collapse Models from Matter-Wave Interferometry: Calculational details
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- Gravity and the Collapse of the Wave Function: a Probe into Diósi-Penrose model
- Nonequilibrium Dynamics with Finite-Time Repeated Interactions
- A classical appraisal of quantum definitions of non-Markovian dynamics
- Rotational friction and diffusion of quantum rotors
- Work production of quantum rotor engines
- Decoherence Models for Discrete-Time Quantum Walks and their Application to Neutral Atom Experiments
- Energy-constrained discrimination of unitaries, quantum speed limits and a Gaussian Solovay-Kitaev theorem
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- Self-excited current oscillations in a resonant tunneling diode described by a model based on the Caldeira-Leggett Hamiltonian
- Wigner-Lindblad equations for quantum friction
- Pointer basis induced by collisional decoherence
- Quantum dissipation with conditional wave functions: Application to the realistic simulation of nanoscale electron devices
- Stochastic extensions of the regularized Schrödinger-Newton equation
- Thermalization induced by quantum scattering
- Quantum master equation for collisional dynamics of massive particles with internal degrees of freedom
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- Hybrid quantum-classical systems: Quasi-free Markovian dynamics
- Quantum master equations for a system interacting with quantum gas in the low density limit and for the semiclassical collision model
- Unraveling Quantum Brownian Motion: Pointer States and their Classical Trajectories
- Collisional decoherence of polar molecules
- Lindblad and Bloch equations for conversion of a neutron into an antineutron
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- Loss of coherence and coherence protection from a graviton bath
- Exact dynamics of moments and correlation functions for fermionic Poisson-type GKSL equations
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- Collisional decoherence of internal state superpositions in a trapped ultracold gas
- No thermalization without correlations
- Dynamics of moments of arbitrary order for stochastic Poisson squeezings
- Decoherence-Free Entropic Gravity: Model and Experimental Tests
- Phase-space measurements, decoherence and classicality
- Markovian master equations for quantum-classical hybrid systems
- Mean square displacement of a free quantum particle in a thermal state
- Emergence of molecular chirality due to chiral interactions in a biological environment
- Emergence of Molecular Chirality by Vibrational Raman Scattering
- Quantum control landscape for generation of and gates in an open qubit with both coherent and environmental drive
- Transition Rates for a Rydberg Atom Surrounded by a Plasma
- On the Tunneling Properties of non-Planar Molecules in a Gas Medium
- Coherent collisional decoherence
- Optimally Convergent Quantum Jump Expansion
- A Light impurity in an Equilibrium Gas
- Scale-free relaxation of a wave packet in a quantum well with power-law tails
- Stochastic simulation algorithm for the quantum linear Boltzmann equation
- Quantum linear Boltzmann equation with finite intercollision time
- Open quantum system approach for heavy quark thermalization
- Wave optics of quantum gravity for massive particles
- Neutron-Mirror Neutron conversion in Vacuum, Trap, Material and Neutron Star
- Decoherence: From Interpretation to Experiment
- General Galilei Covariant Gaussian Maps
- Decoherence and noise in open quantum system dynamics
- The Quantum State of Classical Matter II: Thermodynamic Equilibrium and Hydrodynamics
- Stability of Chiral States, Role of Intermolecular Interactions and Molecular Parity Violation
- Collisional Quantum Brownian Motion
- Suppressed dispersion for a randomly kicked quantum particle in a Dirac comb
- Comment on "Quantum linear Boltzmann equation with finite intercollision time"
- Quantum friction
- Quantum master equations for a fast particle in a gas
- Friction as a consistent quantum-mechanical concept
- Decoherence-Free Entropic Gravity for Dirac Fermion
- Numerical scheme for a spatially inhomogeneous matrix-valued quantum Boltzmann equation
- Derivation of some translation-invariant Lindblad equations for a quantum Brownian particle
- Perturbative Treatment of Quantum to Classical Transition in Chiral Molecules: Dilute Phase vs. Condensed Phase
- Diffusive limit for a quantum linear Boltzmann dynamics
- Classical and quantum: a conflict of interest
- Transverse quantum decoherence of a fast particle in a gas
- Subdynamics of fluctuations in an equilibrium classical many-particle system and generalized linear Boltzmann and Landau equations
- Optimization of Time-Dependent Decoherence Rates and Coherent Control for a Qutrit System
- Quantum kinetic theory of flux-carrying Brownian particles
- Quantum friction: environment engineering perspectives
- Non-Markovian quantum Brownian motion: a non-Hamiltonian approach
- Reply to "Comment on `Quantum linear Boltzmann equation with finite intercollision time' ''
- Thermalization of the Quantum Planar Rotor with external potential
- Optimal Superpositions for Particle Detection via Quantum Phase
- Time scale of stationary decoherence
- Collisional decoherence of a tracer particle moving in one dimension
- Decoherence of nonrelativistic bosonic quantum fields
- A ballistic motion disrupted by quantum reflections
- Impurity in a zero-temperature three-dimensional Fermi gas
- Testing eigenstate decoherence hypothesis in a model of collisional decoherence