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5 Phase Transitions‣ Statistical Physics by David Tong
www.damtp.cam.ac.uk/user/tong/statphys/statmechhtml/S5.html18 Oct 2021: 5 Phase Transitions. 5 Phase Transitions. A phase transition is an abrupt, discontinuous change in the properties of a system. We’ve already seen one example of a phase transition in our discussion of Bose-Einstein condensation. In that case, we -
4 Classical Thermodynamics‣ Statistical Physics by David Tong
www.damtp.cam.ac.uk/user/tong/statphys/statmechhtml/S4.html18 Oct 2021: Figure 24:. Expressing the work as. -. d. W. =. -. p. d. V. also allows us to underline the meaning of the new symbol. -. -
3 Quantum Gases‣ Statistical Physics by David Tong
www.damtp.cam.ac.uk/user/tong/statphys/statmechhtml/S3.html18 Oct 2021: 3 Quantum Gases. 3 Quantum Gases. In this section we will discuss situations where quantum effects are important. We’ll still restrict attention to gases — meaning a bunch of particles moving around and barely interacting — but one of the -
2 Classical Gases‣ Statistical Physics by David Tong
www.damtp.cam.ac.uk/user/tong/statphys/statmechhtml/S2.html18 Oct 2021: 2 Classical Gases. 2 Classical Gases. Our goal in this section is to use the techniques of statistical mechanics to describe the dynamics of the simplest system: a gas. This means a bunch of particles, flying around in a box. Although much of the -
1 The Fundamentals of Statistical Mechanics‣ Statistical Physics by…
www.damtp.cam.ac.uk/user/tong/statphys/statmechhtml/S1.html18 Oct 2021: ρ. =. e. -. β. H. Z. (1.24). If we make a measurement described by an operator. ... In the quantum context, it is sometimes written in terms of the density matrix (1.24) as. -
3 The Renormalisation Group‣ Statistical Field Theory by David Tong
www.damtp.cam.ac.uk/user/tong/sft/sfthtml/S3.html16 Oct 2021: ζ. Δ. ϕ. ϕ. (. 𝐱. ). Figure 24: RG flows when. -
1 From Spins to Fields‣ Statistical Field Theory by David Tong
www.damtp.cam.ac.uk/user/tong/sft/sfthtml/S1.html16 Oct 2021: 1.24). Here, the notation. {. s. i. }. |. m. (. 𝐱. ). means that we sum over all configurations of spins such that the coarse graining yields. ... We will invoke one last notational flourish. We’re left in (1.24) with a sum over all possible -
dynrel
www.damtp.cam.ac.uk/user/tong/relativity/two.pdf12 Jun 2021: perpendicular to B. In the last line, we’ve used the equation (2.24). ... oscillating with frequency! = qB/m. However, because of the constraint (2.24), the. -
dynrel
www.damtp.cam.ac.uk/user/tong/relativity/six.pdf12 Jun 2021: anti-clockwise in the Southern hemisphere. Notice that the period of rotation is not 24. ... hours unless the pendulum is suspended at the poles. Instead the period is 24/ sin. -
dynrel
www.damtp.cam.ac.uk/user/tong/relativity/seven.pdf12 Jun 2021: 7. Special Relativity. Although Newtonian mechanics gives an excellent description of Nature, it is not uni-. versally valid. When we reach extreme conditions — the very small, the very heavy or. the very fast — the Newtonian Universe that
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