Download Statistical mechanics: an intermediate course by Giuseppe Morandi PDF

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By Giuseppe Morandi

Discussing the principles of either classical and quantum statistical mechanics, this e-book goals to bridge a spot that exists among general textbooks at the topic and extra complex books. it's devised for a one-semester direction on statistical mechanics on the graduate point. Its prerequisite is hence a extra basic path at the comparable topic. Emphasis is laid at the geometrical points of classical thermodynamics, at the foundational difficulties, and on chosen functions, ordinarily to spin platforms, the which means of quantum information, section transitions, severe phenomena and the renormalization workforce.

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20) we then have ea,a:sin2e + + e22cos20 = 0. 194), pp 231 and 234. For long wavelengths kcpfo « ΩΕ or rL < λ (small Larmor radius, see p 233), -ehe argument kxcx/Q,E of the Bessel function is small. For exact parallel propagation 485 PLASMA INSTABILITIES (θ = 0/ kx = kI = 0 ) , the argument is zero. So we have for long wavelengths ^ethE <<: ω^ o r f o r P a r a l " lei propagation J n (0) = 0 for n > 0, see p 234. ö|. - ω - Ω„> de For 5Ό0 = 0 or θ = 0 one comes back t o ( 9 . i) ? 9) it is easy to see that the necessary and sufficient stability condition for /0(£||) is that Ψ (OH) have a minimum.

2 are modified. 4. 8. 67/. These electrostatic (longitudinal) modes are however not influenced by the magnetic field Bo, if they propagate in the direction parallel to ~ÈQ, see p 196. If they do not propagate exactly in the direction of B0, one has a coupling between the longitudinal and transverse waves. 17/. For the electrostatic approximation (2 + «>) the coupling goes to zero, but the electrostatic modes are still modified, see p 197 (volume 1 ) . 11) or that of Kahn for electromagnetic modes, see p 480.

T results in instability. ^ " The results obtained so far may be specified as follows. e. an Alfvên wave (Alfvèn wave . 90)/ see p 197. 101)f which means a whistler or helicon (whistler instability, helicon instability). 68) or Pn = LJ™ \fJ Cuàc, s } os 11 Ml s J the dispersion relation ω 2 ' k 2 = °A f—2 (P\ "Pll 2 p . 85) P A 1+^/δ2\ P^ / see p 214. We see that a hydromagnetic instability (fire-hose instability, garden-hose hose-instability) occurs, if P H - ρλ > QCA. 86) Let us say some words regarding this family of instabilities.

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