Many-body quantum mechanics as a symplectic dynamical system

1980 ◽  
Vol 22 (6) ◽  
pp. 2362-2373 ◽  
Author(s):  
D. J. Rowe ◽  
A. Ryman ◽  
G. Rosensteel
Keyword(s):  
Dynamical System ◽  
Quantum Mechanics ◽  
Many Body

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.

Using Quantum Agent-Based Simulation to Model Social Networks

2011 ◽  
pp. 42-54
Author(s):  
C. Bisconti ◽  
A. Corallo ◽  
M. De Maggio ◽  
F. Grippa ◽  
S. Totaro
Keyword(s):  
Social Networks ◽  
Quantum Mechanics ◽  
Quantum Physics ◽  
Business Processes ◽  
Social Dynamics ◽  
Social Systems ◽  
Many Body ◽  
Agent Based ◽  
Microscopic Interactions ◽  
The Many

This research aims to apply models extracted from the many-body quantum mechanics to describe social dynamics. It is intended to draw macroscopic characteristics of organizational communities starting from the analysis of microscopic interactions with respect to the node model. In this chapter, the authors intend to give an answer to the following question: which models of the quantum physics are suitable to represent the behaviour and the evolution of business processes? The innovative aspects of the project are related to the application of models and methods of the quantum mechanics to social systems. In order to validate the proposed mathematical model, the authors intend to define an open-source platform able to model nodes and interactions within a network, to visualize the macroscopic results through a digital representation of the social networks.

Three-body Algebraic Theory

1995 ◽  
Author(s):  
F. Iachello ◽  
R. D. Levine
Keyword(s):  
Quantum Mechanics ◽  
Degrees Of Freedom ◽  
Differential Operators ◽  
Algebraic Theory ◽  
Many Body ◽  
Two Body Problem ◽  
Three Body ◽  
Schrödinger Picture ◽  
Algebraic Operators

In the previous chapter we discussed the usual realization of many-body quantum mechanics in terms of differential operators (Schrödinger picture). As in the case of the two-body problem, it is possible to formulate many-body quantum mechanics in terms of algebraic operators. This is done by introducing, for each coordinate r1,r2,... and momentum p1, p2, . . . , boson creation and annihilation operators, b†iα, biα. The index i runs over the number of relevant degrees of freedom, while the index α runs from 1 to n + 1, where n is the number of space dimensions (see note 3 of Chapter 2). The boson operators satisfy the usual commutation relations, which are for i ≠ j, . . . [biα, b†jα´] = 0, [biα, bjα´] = 0,. . . . . .[bjα, b†iα´] = 0, [b†jα, b†iα´] = 0,. . . . . . [biα, b†iα´] = ẟαα´, [biα, b†iα´] = 0, [b†iα, b†iα´] = 0. . . .

On the classical content of many-body quantum mechanics

1979 ◽  
Vol 9 (3-4) ◽  
pp. 193-215 ◽  
Author(s):  
Olaf Melsheimer
Keyword(s):  
Quantum Mechanics ◽  
Many Body

Many-Body Perturbation Theory Extended to the Quantum Mechanics/Molecular Mechanics Approach: Application to Indole in Water Solution

2009 ◽  
Vol 5 (7) ◽  
pp. 1822-1828 ◽  
Author(s):  
Adriano Mosca Conte ◽  
Emiliano Ippoliti ◽  
Rodolfo Del Sole ◽  
Paolo Carloni ◽  
Olivia Pulci
Keyword(s):  
Perturbation Theory ◽  
Quantum Mechanics ◽  
Molecular Mechanics ◽  
Water Solution ◽  
Many Body ◽  
Many Body Perturbation Theory

scholarly journals Effective quantum tunneling from a semiclassical momentous approach

2020 ◽  
Vol 34 (29) ◽  
pp. 2050271
Author(s):  
L. Aragón-Muñoz ◽  
G. Chacón-Acosta ◽  
H. Hernandez-Hernandez
Keyword(s):  
Dynamical System ◽  
Quantum Mechanics ◽  
Potential Barrier ◽  
Quantum Tunneling ◽  
Time Dependent ◽  
Tunnel Effect ◽  
Expectation Values ◽  
Effective Time ◽  
Dependent Potential ◽  
Individual Particles

In this work, we study the quantum tunnel effect through a potential barrier within a semiclassical formulation of quantum mechanics based on expectation values of configuration variables and quantum dispersions as dynamical variables. The evolution of the system is given in terms of a dynamical system for which we are able to determine numerical effective trajectories for individual particles, similar to the Bohmian description of quantum mechanics. We obtain a complete description of the possible trajectories of the system, finding semiclassical reflected, tunneled and confined paths due to the appearance of an effective time-dependent potential.

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