Operator definition and derivation of collisional energy and momentum loss in relativistic plasmas

Tis chapter explains the famous equation E = mc2 as part of a wider relationship between energy, mass, and momentum. We start by defning energy and momentum in the everyday sense. We then build on the stretching‐triangle picture of spacetime vectors developed in Chapter 11 to see how energy, mass, and momentum have a deep relationship that is not obvious at everyday low speeds. When momentum is zero (a mass is at rest) this energy‐momentum relation simplifes to E = mc2, which implies that mass at rest quietly stores tremendous amounts of energy. Te energymomentum relation also implies that traveling near the speed of light (e.g., to take advantage of time dilation for interstellar journeys) will require tremendous amounts of energy. Finally, we look at the simplifed form of the energy‐momentum relation when the mass is zero. Tis gives us insight into the behavior of massless particles such as the photon.

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Possible Mass and Angular Momentum Loss in Algol-Type Binaries. II. TT Delphini, BO Monocerotis, and Y Piscium

The Astronomical Journal ◽

10.1086/301412 ◽

2000 ◽

Vol 119 (6) ◽

pp. 3064-3070 ◽

Cited By ~ 29

Author(s):

Shengbang Qian

Keyword(s):

Angular Momentum ◽

Momentum Loss ◽

Angular Momentum Loss

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Scattering in Terms of Bohmian Conditional Wave Functions for Scenarios with Non-Commuting Energy and Momentum Operators

Entropy ◽

10.3390/e23040408 ◽

2021 ◽

Vol 23 (4) ◽

pp. 408

Author(s):

Matteo Villani ◽

Guillermo Albareda ◽

Carlos Destefani ◽

Xavier Cartoixà ◽

Xavier Oriols

Keyword(s):

Single Particle ◽

Degrees Of Freedom ◽

Single Photon ◽

Open Quantum Systems ◽

Wave Functions ◽

Practical Application ◽

Light Matter Interaction ◽

Pure States ◽

Energy And Momentum ◽

Full Quantum

Without access to the full quantum state, modeling quantum transport in mesoscopic systems requires dealing with a limited number of degrees of freedom. In this work, we analyze the possibility of modeling the perturbation induced by non-simulated degrees of freedom on the simulated ones as a transition between single-particle pure states. First, we show that Bohmian conditional wave functions (BCWFs) allow for a rigorous discussion of the dynamics of electrons inside open quantum systems in terms of single-particle time-dependent pure states, either under Markovian or non-Markovian conditions. Second, we discuss the practical application of the method for modeling light–matter interaction phenomena in a resonant tunneling device, where a single photon interacts with a single electron. Third, we emphasize the importance of interpreting such a scattering mechanism as a transition between initial and final single-particle BCWF with well-defined central energies (rather than with well-defined central momenta).

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Four-dimensional vibrational spectroscopy for nanoscale mapping of phonon dispersion in BN nanotubes

Nature Communications ◽

10.1038/s41467-021-21452-5 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Ruishi Qi ◽

Ning Li ◽

Jinlong Du ◽

Ruochen Shi ◽

Yang Huang ◽

...

Keyword(s):

Boron Nitride ◽

Energy Loss ◽

Phonon Dispersion ◽

Hexagonal Boron Nitride ◽

Real Space ◽

Boron Nitride Nanotubes ◽

Detection Sensitivity ◽

Optical Modes ◽

Optical And Mechanical Properties ◽

Energy And Momentum

AbstractDirectly mapping local phonon dispersion in individual nanostructures can advance our understanding of their thermal, optical, and mechanical properties. However, this requires high detection sensitivity and combined spatial, energy and momentum resolutions, thus has been elusive. Here, we demonstrate a four-dimensional electron energy loss spectroscopy technique, and present position-dependent phonon dispersion measurements in individual boron nitride nanotubes. By scanning the electron beam in real space while monitoring both the energy loss and the momentum transfer, we are able to reveal position- and momentum-dependent lattice vibrations at nanometer scale. Our measurements show that the phonon dispersion of multi-walled nanotubes is locally close to hexagonal-boron nitride crystals. Interestingly, acoustic phonons are sensitive to defect scattering, while optical modes are insensitive to small voids. This work not only provides insights into vibrational properties of boron nitride nanotubes, but also demonstrates potential of the developed technique in nanoscale phonon dispersion measurements.

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