A technique to identify solvable dynamical systems, and a solvable generalization of the goldfish many-body problem

2004 ◽  
Vol 45 (6) ◽  
pp. 2266-2279 ◽  
Author(s):  
Francesco Calogero
Keyword(s):  
Dynamical Systems ◽  
Body Problem ◽  
Many Body ◽  
Solvable Dynamical Systems

The Nuclear Many-Body Problem

1980 ◽  
Author(s):  
Peter Ring ◽  
Peter Schuck
Keyword(s):  
Body Problem ◽  
Many Body

Many body dynamics

2018 ◽  
Author(s):  
Joseph F. Boudreau ◽  
Eric S. Swanson
Keyword(s):  
Statistical Mechanics ◽  
Body Problem ◽  
Many Body ◽  
Complex Objects ◽  
Constrained Dynamics ◽  
Gravitational Systems ◽  
Body Dynamics ◽  
System Temperature ◽  
Speed Up ◽  
Gravitating Systems

Specialized techniques for solving the classical many-body problem are explored in the context of simple gases, more complicated gases, and gravitating systems. The chapter starts with a brief review of some important concepts from statistical mechanics and then introduces the classic Verlet method for obtaining the dynamics of many simple particles. The practical problems of setting the system temperature and measuring observables are discussed. The issues associated with simulating systems of complex objects form the next topic. One approach is to implement constrained dynamics, which can be done elegantly with iterative methods. Gravitational systems are introduced next with stress on techniques that are applicable to systems of different scales and to problems with long range forces. A description of the recursive Barnes-Hut algorithm and particle-mesh methods that speed up force calculations close out the chapter.

QLB for Quantum Many-Body and Quantum Field Theory

2018 ◽  
Author(s):  
Sauro Succi
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Quantum Computing ◽  
Single Particle ◽  
Body Problem ◽  
Three Dimensions ◽  
Quantum Field ◽  
Many Body ◽  
Quantum Particles

Chapter 32 expounded the basic theory of quantum LB for the case of relativistic and non-relativistic wavefunctions, namely single-particle quantum mechanics. This chapter goes on to cover extensions of the quantum LB formalism to the overly challenging arena of quantum many-body problems and quantum field theory, along with an appraisal of prospective quantum computing implementations. Solving the single particle Schrodinger, or Dirac, equation in three dimensions is a computationally demanding task. This task, however, pales in front of the ordeal of solving the Schrodinger equation for the quantum many-body problem, namely a collection of many quantum particles, typically nuclei and electrons in a given atom or molecule.

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).

A new method in the many-body problem: II

1996 ◽  
Vol 29 (1) ◽  
pp. 133-142
Author(s):  
I V Krasovsky ◽  
V I Peresada
Keyword(s):  
Body Problem ◽  
New Method ◽  
Many Body ◽  
The Many

An Algebraic Framework for the Many-Body Problem

1996 ◽  
pp. 357-399
Author(s):  
Werner O. Amrein ◽  
Anne Boutet Monvel ◽  
Vladimir Georgescu
Keyword(s):  
Body Problem ◽  
Many Body ◽  
Algebraic Framework ◽  
The Many
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