Statistical Mechanics

Causal signal transmission by quantum fields. I: Response of the harmonic oscillator

“…Our immediate goal is to clarify another important connection, namely, between the response formulation and Kubo's linear response theory [10]. The way D R was introduced into the quantum treatment in section 2.5.1 gives a misleading impression of pure luck: we just happened to notice that a particular combination of the quantum Green's functions coincides with the retaded Green's function of the classical oscillator.…”

“…Following Kubo [10], we analyse response of the oscillator by adding a source term to the Hamiltonian (1)Ĥ…”

“…In section 4.1 we introduce a response formulation of noninteracting bosons and clarify its relation to Glauber's photodetection theory [2,11,13,14]. In section 4.2 we discuss the relation between the response formulation and Kubo's linear response theory [10]. In section 4.3 we compare the concept of external c-number current in Kubo's and Schwinger's approaches.…”

“…Schwinger [9] recognised the importance of formal c-number currents in the equations for Green's functions in the quantum field theory. Kubo [10] formulated his linear response theory by adding classical source terms to quantum Hamiltonians. Glauber [11] was first to understand the relevance of phase-space concepts to macroscopic measurements.…”

Fermi energy of electrons in neutron stars with strong magnetic field and magnetars

“…We find that in almost all the literatures directly or indirectly cite the internationally popular classic statistical physics textbooks (see e. g., Refs [6] and [7]), however, in which the calculation of electronic micro state number density for a strong magnetic field is not correct. In those statistical physics textbooks, the authors used the following method to calculate the statistical weight (degeneracy) of the Landau level n: In the interval of momentum p z → p z + dp z along the magnetic field direction, the possible microscopic state number density for the electron gas is N phase (p z ) = h −2 dp x dp y = h −2 π(p 2 ⊥ ) n+1 n = 4πmμ B B/h 2 .…”