# Erratum

I have found the following errors in my book (I will change these to Latex format once I have managed to install the appropriate plugin):

• Page 6, Fig. 1.5. The scale bar in the inset figure should be 20 nm, not 20 micrometers!
• Page 9, three lines below eqn (1.7): I should have talked about “finite band mass”, since bilayer graphene still does not have a mass in the relativistic sense (see footnote 13).
• Page 13, eqn (1.14): replace \epsilon inside the cosh^2()-function by E.
• Page 18, above eqn (2.5): the total energy is of course the sum, not the difference of the kinetic energy and the potential energy. Note that the equations should be gauge invariant, i.e., adding a constant to the potential does not matter. Here the convention is so that epsilon=0 corresponds to the Fermi level, adding the potentials thus means that in the reservoirs we must have functions f(E,mu,T).
• Page 20, eqn (2.13): the delta-function appearing in the first form should be retained for the second form so that the dimensions are correct.
• Page 21, eqn (2.16): the last form for 1/tau does not make sense: it should have the concentration of impurities, and U_imp should be evaluated at the same absolute value of momentum as 1/tau. I should also have explained how to get rid of the delta-function appearing in eqn (2.13) (it can be used to get rid of the part of the sum related to the sum over absolute values of momenta).
• Page 25, eqn (2.34b): the first term should be T^2(x), not T(x).
• Page 26, last line: 2D kappa should have a prefactor 1/hbar^2, similarly to the 1D and 3D kappas.
• Page 27, second line: replace small-case omega by capital Omega.
• Page 28, below eqn (2.40): alpha should contain 1/v_S^3 in the first form.
• Page 31, eqn (2.49): it should be a second derivative instead of the first.
• Page 53, footnote 28 is wrong: the dynamic phase in fact depends on the difference E-epsilon_n, as it originates from the k_z-coordinate in eqn (3.3). For a single-mode case, this just means a constant shift of the energy, but in the many-mode case these shifts are dependent on the mode index. This means that the resonances for the different modes take place at different energies.
• Page 56, eqn (3.75): the last term should have V_beta V_gamma, i.e., the second V is missing.
• Page 71, eqn (4.44): the last terms in the sum should be p” and p”’, and also inside the summands we should replace the second p’ by p” and p” by p”’.
• Page 72, eqn (4.48): the dimensionless prefactor c is not defined. It should be replaced by (2/15)beta^(-2), and the squared conductance in brackets should be (2e^2/h)^2 to follow the discussion on the top of the page.
• Page 73, two lines above eqn (4.52): V=\dot \Phi has the wrong sign, as it should read V=-\dot \Phi (time derivative of the flux gives a negative voltage by the second Maxwell’s equation).
• Page 75, eqn (4.57): there should be a minus in front of the nabla^2 term.
• Page 77, Exercise (4.2), case c: it should be r_L=t_L and r_R=t_R, which completely specifies the scattering matrices.
• Page 77, Exercise (4.7): it is a Science paper, not a Nature paper!
• Page 78, eqn (5.1): field operators should be capitalized to conform what follows
• Page 82, Example 5.1: the phase of \Delta in the beginning is \varphi, at the end \phi. These should be the same.
• Page 83, Fig. 5.3 vertical axis label: it should be N_S(E)/N_F instead of N_S(E)/N(0), as N(0) is not really defined in the text.
• Page 88, eqn (5.36) and page 91, eqn (5.44): there should be a square root of the expression in square brackets
• Page 88, eqn (5.37): replace tau by tau_p and add the sum over the channel index p.
• Page 90, eqn (5.42): alpha is not defined, it is alpha=exp(-i arccos(E/Delta)), i.e., the phase one obtains in eqn (5.34).
• Page 92, eqn (5.45) in Exercise (5.3): replace N(0) by N_F.
• Page 93, eqn (5.47) in Exercise (5.4): the sum should start from -infinity
• Page 95, eqns (6.5) and (6.6): to get correct dimensions, we should multiply both of these equations by some time scale tau. In this particular problem, there is no such time scale, because we did not get the delta-function from a limiting procedure.
• Page 100, eqns (6.20) and (6.21): replace 4 in the prefactor by 2.
• Page 112, eqn (6.68), the argument of S_{f_x} should be divided by hbar.
• Page 119, Ex. (6.6), add factor 2 before <delta I(omega) delta I(-omega)>.
• Page 123, below the un-numbered equation: the potential of the island should be
U=(-ne+C_G V_G)/(C_J+C_G) instead of -(ne+C_G V_G)(C_J+C_G).
• Page 124, 8th line: the equation for E_ch(n,Q_G) should be (ne-Q_G)^2/(2C), i.e., the factor 2 was missing from the denominator.
• Page 161, eqn (9.5) and first line below it: the symbols “E” inside N_L/I(E) should be replaced by \epsilon_k, \epsilon_q, and \epsilon, respectively
• Page 167, first line in Sec. 9.3.1: replace “previous chapter” by “Ch. 5″.
• Page 169, Fig. 9.19 caption: replace \varphi’ by \dot \varphi: this is the first time derivative, i.e., the velocity.
• Page 188, eqn (10.16): the lower left part of this matrix should be transposed, i.e., the elements (3,2) and (4,1) should be interchanged.
• Page 190, eqn (10.21): the first column on the second row should have gamma_1 sigma_down instead of t sigma_down
• Page 191, eqn (10.23): there is  “=” missing in the second term.
• Page 192, footnote 13: it should be “… normalized at k -> 0″ instead of “… p->0″
• Page 192, eqn (10.29): the limits should be k->0 instead of p->0 (although they are the same thing, but this ensures uniform notation)
• Page 192, eqn (10.32): the second term (psi_B) should contain a minus, not a plus between the two eigenstates
• Page 199, first and second lines: it should be “y=0″ and “y=W”.
• Page 200, eqn (10.55) is valid for all x, so x could be added to the functions for uniform notation.
• Exercise 10.2a, the equation should be (10.8), not (10.6).
• Page 221, second line below eqns (11.66): the in-line equation should read phi(t)^2 \approx phi_0(t)^2+2phi_0(t) \delta phi(t).
• Page 233, eqn (A.26), add a unit matrix to satisfy the initial condition
• Page 235, eqn (A.34), the first two lines should come with a minus sign. The third line is then correct.
• Page 235, eqn (A.34), extra closing \rangle on the second line
• Page 237, eqn (A.46): replace \phi by q\varphi
• Page 239, eqn (A.57), extra e \phi(\vec{r}) in the intermediate result
• Page 240, eqn (A.61): multiply the last result by 2 (anticommutator of a Pauli matrix with itself gives two times the unit matrix)
• Page 246, in eqn (C.5), the lower limit in the integral of the first line should be t_0, the first term on the second line should have A_iI^0(t) (i.e., the 0 was missing). After the equation I should have stated: “In what follows, we take the initial time to minus infinity by extending the definition of $f(t<t_0)=0$.”

Other typos:

• Page 4, “Figs. 1.2″ should be “Fig. 1.2″
• Page 41, last paragraph before the example: additional “of” in the beginning of the paragraph.
• Page 49, the equation number in eqn (3.53a) should not contain the a

Some improvements:

• On page 1, middle of the second paragraph: “A metallic wire which is smaller…” would be better to rephrase as “A conducting wire which is smaller…”. Doped semiconductors are also conducting!
• On page 6, middle of the second paragraph: “… can be controlled in situ by attaching metal gates on top of the heterostructure” Add “, and tuning the voltage on these metal gates”. Attaching metals is of course not in situ control, but varying the voltage is!
• On page 20, after Sec. 2.4 heading, it would be good to remind that we are describing collision integrals for electrons that are fermions. This is why the form is what it is. For phonons or other bosons, the (1-f) factor in the collision integral would be (1+n), directly resulting from the commutation relations.
• On page 23, eqn (2.28), first line: it would be better to replace the nabla by \partial_x.
• On page 27, reference to Kaminski and Glazman should have brackets only around the year.
• On page 83, above eqn (5.2) ,the text after “For example” could be changed to “around an interface between a superconductor and a normal metal where superconductivity is suppressed, this is the length scale within which the order parameter regains its bulk value inside the superconductor”.
• On page 83, second paragraph of Sec. 5.3: replace “transverse dimension is low” by “transverse size is small”.
• Page 170, fourth line in Sec. 9.3.4: replace “it jumps” by “the average voltage across it jumps”.

Please let me know (by email) if you find more.