Complement to the Rayleigh-Ritz principle for the energy spectrum of a system composed of identical particles

1979 ◽  
Vol 20 (3) ◽  
pp. 1155-1160 ◽  
Author(s):  
Richard L. Hall
Keyword(s):  
Energy Spectrum ◽  
Identical Particles

STATISTICS IN ONE DIMENSION

1991 ◽  
Vol 06 (26) ◽  
pp. 4721-4751 ◽  
Author(s):  
C. ANEZIRIS ◽  
A.P. BALACHANDRAN ◽  
DIPTIMAN SEN
Keyword(s):  
Energy Spectrum ◽  
Boundary Conditions ◽  
Time Reversal ◽  
Wave Functions ◽  
Physical Models ◽  
One Dimension ◽  
Identical Particles ◽  
Wave Numbers ◽  
Points Of Coincidence ◽  
Vector Valued

We show that there are novel generalizations of statistics for identical particles in one dimension. These arise due to possible boundary conditions on wave functions, or equivalently due to δ-function interactions, at points of coincidence of particle coordinates. Special choices of these boundary conditions describe bosons, fermions or paraparticles. The general solution for the boundary conditions involves vector-valued wave functions and statistics with non-Abelian features, even though the classical configuration space has an Abelian fundamental group. Physical models leading to such non-Abelian statistics, involving for example δ-function interactions of spins, are constructed. Properties under parity and time reversal of the new boundary conditions are studied. It is shown that the Bethe ansatz does not always give eigenstates of energy. When it does, the wave numbers in the ansatz for three or more particles must satisfy a weaker form of the Yang-Baxter equations and certain additional equations. The energy spectrum and wave functions for identical particles on R1 or S1 are discussed in some simple cases. Our work generalizes the previous work of Lieb and Liniger, Lieb, Yang and Leinaas and Myrheim.

The electronic energy spectrum of zero-gap semiconductors

1976 ◽  
Vol 120 (11) ◽  
pp. 337 ◽  
Author(s):  
B.L. Gel'mont ◽  
V.I. Ivanov-Omskii ◽  
I.M. Tsidil'kovskii
Keyword(s):  
Energy Spectrum ◽  
Electronic Energy ◽  
Electronic Energy Spectrum

Acquisition and Evaluation of Gamma-ray Energy Spectrum with CsPbBr3

2019 ◽  
Author(s):  
Lei R. Cao ◽  
Lei Pan ◽  
Yuanxiang Feng ◽  
Praneeth Kandlakunta ◽  
Jinsong Huang
Keyword(s):  
Energy Spectrum ◽  
Gamma Ray

Energy Spectrum of Acoustic Emission Signals in Coupled Continuous Media

2019 ◽  
Vol 11 (3) ◽  
pp. 03028-1-03028-7 ◽  
Author(s):  
V. V. Marasanov ◽  
◽  
A. V. Sharko ◽  
A. A. Sharko ◽  
◽  
...  
Keyword(s):  
Acoustic Emission ◽  
Energy Spectrum ◽  
Continuous Media

Peculiarities of Stark-phonon Resonance in Two-dimensional Superlattices with Non-additive Energy Spectrum

2016 ◽  
Vol 8 (1) ◽  
pp. 01019-1-01019-3
Author(s):  
D. V. Zav’yalov ◽  
◽  
S. V. Kruchkov ◽  
E. S. Ionkina ◽  
◽  
...  
Keyword(s):  
Energy Spectrum ◽  
Two Dimensional ◽  
Additive Energy

Identical Particles and Second Quantization: Occupation Number Representation

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.

Strong Coupling of Electron and Nuclear Spins: Outlook and Prospects

2018 ◽  
Author(s):  
M. M. Glazov
Keyword(s):  
Energy Spectrum ◽  
Charge Carrier ◽  
Strong Coupling ◽  
Nuclear Spin ◽  
Spin Dynamics ◽  
Spin Polaron ◽  
Nuclear Spins ◽  
Deep Impurity ◽  
Impurity Centers ◽  
Ordered State

In this chapter, some prospects in the field of electron and nuclear spin dynamics are outlined. Particular emphasis is put ona situation where the hyperfine interaction is so strong that it leads to a qualitative rearrangement of the energy spectrum resulting in the coherent excitation transfer between the electron and nucleus. The strong coupling between the spin of the charge carrier and of the nucleus is realized, for example in the case of deep impurity centers in semiconductors or in isotopically purified systems. We also discuss the effect of the nuclear spin polaron, that is ordered state, formation at low enough temperatures of nuclear spins, where the orientation of the carrier spin results in alignment of the spins of nucleus interacting with the electron or hole.

Sign in / Sign up

Export Citation Format

Share Document