Identical Particles and the Pauli Principle

“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.

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Identical particles and the Pauli principle

Basic quantum mechanics ◽

10.1007/978-1-349-16671-8_7 ◽

1982 ◽

pp. 135-141

Author(s):

J. M. Cassels

Keyword(s):

Pauli Principle ◽

Identical Particles

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Identical Particles and Second Quantization: Occupation Number Representation

10.1093/oso/9780198791942.003.0002 ◽

2018 ◽

Author(s):

Norman J. Morgenstern Horing

Keyword(s):

Occupation Number ◽

Annihilation Operator ◽

Pauli Exclusion Principle ◽

Exclusion Principle ◽

Number Representation ◽

Second Quantization ◽

Identical Particles ◽

Fundamental Properties ◽

Minimum Uncertainty ◽

Creation Operators

Focusing on systems of many identical particles, Chapter 2 introduces appropriate operators to describe their properties in terms of Schwinger’s “measurement symbols.” The latter are then factorized into “creation” and “annihilation” operators, whose fundamental properties and commutation/anticommutation relations are derived in conjunction with the Pauli exclusion principle. This leads to “second quantization” with the Hamiltonian, number, linear and angular momentum operators expressed in terms of the annihilation and creation operators, as well as the occupation number representation. Finally, the concept of coherent states, as eigenstates of the annihilation operator, having minimum uncertainty, is introduced and discussed in detail.

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Transport of pseudothermal photons through an anharmonic cavity

Scientific Reports ◽

10.1038/s41598-021-87536-w ◽

2021 ◽

Vol 11 (1) ◽

Author(s):

Dmitriy S. Shapiro

Keyword(s):

Pauli Principle ◽

Optical Systems ◽

Frequency Noise ◽

Continuous Transition ◽

Noise Current ◽

Nonperturbative Solution ◽

Occupation Numbers ◽

Fundamental Reason ◽

The Rich ◽

Quantum Optical

AbstractUnder 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.

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Generalized Pauli constraints in large systems: The Pauli principle dominates

Journal of Mathematical Physics ◽

10.1063/5.0031419 ◽

2021 ◽

Vol 62 (3) ◽

pp. 032204

Author(s):

Robin Reuvers

Keyword(s):

Pauli Principle ◽

Large Systems

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Decay amplitudes to three hadrons from finite-volume matrix elements

Journal of High Energy Physics ◽

10.1007/jhep04(2021)113 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

Maxwell T. Hansen ◽

Fernando Romero-López ◽

Stephen R. Sharpe

Keyword(s):

Finite Volume ◽

Decay Amplitude ◽

Weak Decay ◽

Matrix Elements ◽

Isospin Breaking ◽

Final State ◽

Identical Particles ◽

Hadron Decay ◽

Finite State ◽

Particle Decays

Abstract We derive relations between finite-volume matrix elements and infinite-volume decay amplitudes, for processes with three spinless, degenerate and either identical or non-identical particles in the final state. This generalizes the Lellouch-Lüscher relation for two-particle decays and provides a strategy for extracting three-hadron decay amplitudes using lattice QCD. Unlike for two particles, even in the simplest approximation, one must solve integral equations to obtain the physical decay amplitude, a consequence of the nontrivial finite-state interactions. We first derive the result in a simplified theory with three identical particles, and then present the generalizations needed to study phenomenologically relevant three-pion decays. The specific processes we discuss are the CP-violating K → 3π weak decay, the isospin-breaking η → 3π QCD transition, and the electromagnetic γ* → 3π amplitudes that enter the calculation of the hadronic vacuum polarization contribution to muonic g − 2.

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