Identical particles and the helium atom

“Identical particles and the helium atom” introduces bosons and fermions. Fermion states are expressed in terms of Slater determinants and the Pauli Principle. Helium is presented in such a way as to show what properties are and are not due to electron identity. Quantum states are described according as the space wave function is symmetric or antisymmetric under interchange of labels attached to the electrons. These in turn form singlet and triplet spin states when the electrons’ fermion identity is taken into account. Helium is an example of LS coupling, but a rather stunted example.

On the Nature of Bonding in the Photochemical Addition of Two Ethylenes: C-C Bond Formation in the Excited State?

<div><p>In this work, the 2s+2s (face-to-face) prototypical example of a photochemical reaction has been re-examined to characterize the evolution of chemical bonding. The analysis of the electron localization function (as an indirect measure of the Pauli principle) along the minimum energy path provides strong evidence in support that CC bond formation occurs not in the excited state but at the ground electronic state after crossing the rhombohedral S₁/S₀ conical intersection. </p></div><br>

On the Nature of Bonding in the Photochemical Addition of Two Ethylenes: C-C Bond Formation in the Excited State?

<div><p>In this work, the 2s+2s (face-to-face) prototypical example of a photochemical reaction has been re-examined to characterize the evolution of chemical bonding. The analysis of the electron localization function (as an indirect measure of the Pauli principle) along the minimum energy path provides strong evidence in support that CC bond formation occurs not in the excited state but at the ground electronic state after crossing the rhombohedral S₁/S₀ conical intersection. </p></div><br>

Transport of pseudothermal photons through an anharmonic cavity

Under nonequilibrium conditions, quantum optical systems reveal unusual properties that might be distinct from those in condensed matter. The fundamental reason is that photonic eigenstates can have arbitrary occupation numbers, whereas in electronic systems these are limited by the Pauli principle. Here, we address the steady-state transport of pseudothermal photons between two waveguides connected through a cavity with Bose–Hubbard interaction between photons. One of the waveguides is subjected to a broadband incoherent pumping. We predict a continuous transition between the regimes of Lorentzian and Gaussian chaotic light emitted by the cavity. The rich variety of nonequilibrium transport regimes is revealed by the zero-frequency noise. There are three limiting cases, in which the noise-current relation is characterized by a power-law, $$S\propto J^\gamma$$ S ∝ J γ . The Lorentzian light corresponds to Breit-Wigner-like transmission and $$\gamma =2$$ γ = 2 . The Gaussian regime corresponds to many-body transport with the shot noise ($$\gamma =1$$ γ = 1 ) at large currents; at low currents, however, we find an unconventional exponent $$\gamma =3/2$$ γ = 3 / 2 indicating a nontrivial interplay between multi-photon transitions and incoherent pumping. The nonperturbative solution for photon dephasing is obtained in the framework of the Keldysh field theory and Caldeira-Leggett effective action. These findings might be relevant for experiments on photon blockade in superconducting qubits, thermal states transfer, and photon statistics probing.

The Exact Theory of the Stern–Gerlach Experiment and Why it Does Not Imply that a Fermion Can Only Have Its Spin Up or Down

The Stern–Gerlach experiment is notoriously counter-intuitive. The official theory is that the spin of a fermion remains always aligned with the magnetic field. Its directions are thus quantized: It can only be spin-up or spin-down. However, that theory is based on mathematical errors in the way it (mis)treats spinors and group theory. We present here a mathematically rigorous theory for a fermion in a magnetic field, which is no longer counter-intuitive. It is based on an understanding of spinors in SU(2) which is only Euclidean geometry. Contrary to what Pauli has been reading into the Stern–Gerlach experiment, the spin directions are not quantized. The new corrected paradigm, which solves all conceptual problems, is that the fermions precess around the magnetic-field just as Einstein and Ehrenfest had conjectured. Surprisingly, this leads to only two energy states, which should be qualified as precession-up and precession-down rather than spin-up and spin-down. Indeed, despite the presence of the many different possible angles θ between the spin axis s and the magnetic field B, the fermions can only have two possible energies m0c2±μB. The values ±μB thus do not correspond to the continuum of values −μ·B Einstein and Ehrenfest had conjectured. The energy term V=−μ·B is a macroscopic quantity. It is a statistical average over a large ensemble of fermions distributed over the two microscopic states with energies ±μB, and as such not valid for individual fermions. The two fermion states with energy ±μB are not potential-energy states. We also explain the mathematically rigorous meaning of the up and down spinors. They represent left-handed and right-handed reference frames, such that now everything is intuitively clear and understandable in simple geometrical terms. The paradigm shift does not affect the Pauli principle.

Super time and the Pauly principle

The connection between the Pauli principle and the nontrivial structure of the fermionic supertime is demonstrated. When supersymmetry is localized in the manner of supergravity, fields of carriers of gravitational and exchange interactions arise. The quantum of the exchange interaction of free fermions, which is a superpartner of the graviton (gravitino), is interpreted as «paulino» - the particle responsible for the effect of «mutual avoidance» of identical fermions.