scholarly journals Exactly Solvable Many-Body Systems and Pseudo-Hermitian Point Interactions

2004 ◽  
Vol 54 (1) ◽  
pp. 43-49 ◽  
Author(s):  
Shao-Ming Fei
Keyword(s):  
Many Body ◽  
Point Interactions ◽  
Exactly Solvable ◽  
Many Body Systems

scholarly journals A REMARK ON ONE-DIMENSIONAL MANY-BODY PROBLEMS WITH POINT INTERACTIONS

2000 ◽  
Vol 14 (07) ◽  
pp. 721-727 ◽  
Author(s):  
SERGIO ALBEVERIO ◽  
LUDWIK DABROWSKI ◽  
SHAO-MING FEI
Keyword(s):  
Singular Point ◽  
Bound States ◽  
Quantum Mechanical ◽  
Contact Interactions ◽  
Many Body ◽  
Point Interactions ◽  
One Dimensional ◽  
Integrable Quantum ◽  
Scattering Matrices ◽  
Many Body Systems

The integrability of one-dimensional quantum mechanical many-body problems with general contact interactions is extensively studied. It is shown that besides the pure (repulsive or attractive) δ-function interaction there is another singular point interactions which gives rise to a new one-parameter family of integrable quantum mechanical many-body systems. The bound states and scattering matrices are calculated for both bosonic and fermionic statistics.

Erweiterung der Neuen Tamm-Dancoff-Methode auf Phasen- übergänge in Vielteilchensystemen / Extension of the New Tamm-Dancoff Method to Phase Transitions in Many-Body Systems

1975 ◽  
Vol 30 (2) ◽  
pp. 142-157
Author(s):  
A. Friederich ◽  
W. Gerling ◽  
K. Bleuler
Keyword(s):  
Function Method ◽  
Many Body ◽  
Quasi Particle ◽  
First Order ◽  
Hartree Fock ◽  
Bogoliubov Theory ◽  
Lipkin Model ◽  
Exactly Solvable ◽  
Intermediate States ◽  
Many Body Systems

Abstract We extend the New Tamm-Dancoff method by introducing intermediate states. In this way we are able to treat with the Green's function method the effect of nearby levels in many-body systems. We formulate the η-and the ζ-function method with intermediate states. Aldready in first order, the ζ-function method yields a whole series of new approximations in addition to known theories such as the Hartree-Fock theory and the Hartree-Bogoliubov theory. As an example we study intensively "the Hartree-Fock theory with intermediate states". The ζ-function method which is based on the η-function method yields in first order in addition to RPA, quasi-particle RPA and other approximations "RPA with intermediate states". We apply the Hartree-Fock theory with intermediate states and RPA with intermediate states to the exactly solvable Lipkin model.

scholarly journals Page curve from non-Markovianity

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Kaixiang Su ◽  
Pengfei Zhang ◽  
Hui Zhai
Keyword(s):  
Many Body ◽  
Thermal Entropy ◽  
Initial Stage ◽  
Environment Temperature ◽  
Exactly Solvable ◽  
Long Time ◽  
Kitaev Model ◽  
Many Body Systems ◽  
Near Future ◽  
System Entropy

Abstract In this paper, we use the exactly solvable Sachdev-Ye-Kitaev model to address the issue of entropy dynamics when an interacting quantum system is coupled to a non-Markovian environment. We find that at the initial stage, the entropy always increases linearly matching the Markovian result. When the system thermalizes with the environment at a sufficiently long time, if the environment temperature is low and the coupling between system and environment is weak, then the total thermal entropy is low and the entanglement between system and environment is also weak, which yields a small system entropy in the long-time steady state. This manifestation of non-Markovian effects of the environment forces the entropy to decrease in the later stage, which yields the Page curve for the entropy dynamics. We argue that this physical scenario revealed by the exact solution of the Sachdev-Ye-Kitaev model is universally applicable for general chaotic quantum many-body systems and can be verified experimentally in near future.

REGULAR STRUCTURE OF LOW-LYING STATES FOR ATOMIC NUCLEI UNDER RANDOM INTERACTIONS

2008 ◽  
Vol 17 (supp01) ◽  
pp. 304-317
Author(s):  
Y. M. ZHAO
Keyword(s):  
Ground State ◽  
Collective Motion ◽  
Regular Structure ◽  
Positive Parity ◽  
Many Body ◽  
Random Interactions ◽  
Atomic Nuclei ◽  
Many Body Systems

In this paper we review regularities of low-lying states for many-body systems, in particular, atomic nuclei, under random interactions. We shall discuss the famous problem of spin zero ground state dominance, positive parity dominance, collective motion, odd-even staggering, average energies, etc., in the presence of random interactions.

scholarly journals Emergence of a Renormalized 1/N Expansion in Quenched Critical Many-Body Systems

2021 ◽  
Vol 126 (11) ◽  
Author(s):  
Benjamin Geiger ◽  
Juan Diego Urbina ◽  
Klaus Richter
Keyword(s):  
Many Body ◽  
Many Body Systems

scholarly journals Interaction between Different Kinds of Quantum Phase Transitions

2021 ◽  
Vol 3 (2) ◽  
pp. 253-261
Author(s):  
Angel Ricardo Plastino ◽  
Gustavo Luis Ferri ◽  
Angelo Plastino
Keyword(s):  
Phase Transitions ◽  
Nuclear Physics ◽  
Body Problem ◽  
Quantum Phase Transitions ◽  
Quantum Phase ◽  
Exactly Solvable Models ◽  
Solvable Models ◽  
Many Body ◽  
Pairing Interaction ◽  
Exactly Solvable

We employ two different Lipkin-like, exactly solvable models so as to display features of the competition between different fermion–fermion quantum interactions (at finite temperatures). One of our two interactions mimics the pairing interaction responsible for superconductivity. The other interaction is a monopole one that resembles the so-called quadrupole one, much used in nuclear physics as a residual interaction. The pairing versus monopole effects here observed afford for some interesting insights into the intricacies of the quantum many body problem, in particular with regards to so-called quantum phase transitions (strictly, level crossings).

scholarly journals Continuous Phase Transition without Gap Closing in Non-Hermitian Quantum Many-Body Systems

2020 ◽  
Vol 125 (26) ◽  
Author(s):  
Norifumi Matsumoto ◽  
Kohei Kawabata ◽  
Yuto Ashida ◽  
Shunsuke Furukawa ◽  
Masahito Ueda
Keyword(s):  
Phase Transition ◽  
Continuous Phase ◽  
Many Body ◽  
Continuous Phase Transition ◽  
Many Body Systems ◽  
Gap Closing
Sign in / Sign up

Export Citation Format

Share Document