scholarly journals Stochastic Variational Approach to Small Atoms and Molecules Coupled to Quantum Field Modes in Cavity QED

2021 ◽  
Vol 127 (27) ◽  
Author(s):  
Alexander Ahrens ◽  
Chenhang Huang ◽  
Matt Beutel ◽  
Cody Covington ◽  
Kálmán Varga
Keyword(s):  
Cavity Qed ◽  
Variational Approach ◽  
Quantum Field ◽  
Atoms And Molecules

scholarly journals The principle of stationary variance in quantum field theory

2014 ◽  
Vol 29 (05) ◽  
pp. 1450026 ◽  
Author(s):  
Fabio Siringo
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Mechanics ◽  
Quantum System ◽  
Quantum Electrodynamics ◽  
Best Approximation ◽  
Variational Approach ◽  
Heisenberg Model ◽  
Gauge Theories ◽  
Quantum Field

The principle of stationary variance is advocated as a viable variational approach to quantum field theory (QFT). The method is based on the principle that the variance of energy should be at its minimum when the state of a quantum system reaches its best approximation for an eigenstate. While not too much popular in quantum mechanics (QM), the method is shown to be valuable in QFT and three special examples are given in very different areas ranging from Heisenberg model of antiferromagnetism (AF) to quantum electrodynamics (QED) and gauge theories.

A variational approach to quantum field theory

1992 ◽  
Vol 287 (1-3) ◽  
pp. 133-137 ◽  
Author(s):  
Henri Verschelde ◽  
Marnix Coppens
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Variational Approach ◽  
Quantum Field

scholarly journals A NOVEL VARIATIONAL APPROACH FOR QUANTUM FIELD THEORY: EXAMPLE OF STUDY OF THE GROUND STATE AND PHASE TRANSITION IN NONLINEAR SIGMA MODEL

2005 ◽  
Vol 20 (15) ◽  
pp. 3488-3494 ◽  
Author(s):  
YURIY MISHCHENKO ◽  
CHUENG-RYONG JI
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Ground State ◽  
Variational Approach ◽  
Sigma Model ◽  
Fock Space ◽  
Nonlinear Sigma Model ◽  
Quantum Field ◽  
Expectation Values ◽  
Optimization Under Constraints

We discuss a novel form of the variational approach in Quantum Field Theory in which the trial quantum configuration is represented directly in terms of relevant expectation values rather than, e.g., increasingly complicated structure from Fock space. The quantum algebra imposes constraints on such expectation values so that the variational problem is formulated here as an optimization under constraints. As an example of application of such approach we consider the study of ground state and critical properties in a variant of nonlinear sigma model.

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