scholarly journals Feynman diagrams and rooted maps

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 149-167 ◽  
Author(s):  
Andrea Prunotto ◽  
Wanda Maria Alberico ◽  
Piotr Czerski
Keyword(s):  
Single Particle ◽  
Feynman Diagram ◽  
Feynman Diagrams ◽  
Topological Properties ◽  
Many Body ◽  
Perturbative Order ◽  
Original Definition ◽  
Many Body Systems ◽  
Definition Of ◽  
Particle Propagator

Abstract The rooted maps theory, a branch of the theory of homology, is shown to be a powerful tool for investigating the topological properties of Feynman diagrams, related to the single particle propagator in the quantum many-body systems. The numerical correspondence between the number of this class of Feynman diagrams as a function of perturbative order and the number of rooted maps as a function of the number of edges is studied. A graphical procedure to associate Feynman diagrams and rooted maps is then stated. Finally, starting from rooted maps principles, an original definition of the genus of a Feynman diagram, which totally differs from the usual one, is given.

A SOLVABLE MODEL OF INTERACTING MANY BODY SYSTEMS EXHIBITING A BREAKDOWN OF THE BOLTZMANN EQUATION

2014 ◽  
Vol 28 (03) ◽  
pp. 1450046
Author(s):  
B. H. J. McKELLAR
Keyword(s):  
Boltzmann Equation ◽  
Time Dependence ◽  
Single Particle ◽  
Density Operator ◽  
Particle Density ◽  
Solvable Model ◽  
Many Body ◽  
Single Particle Density ◽  
The Boltzmann Equation ◽  
Many Body Systems

In a particular exactly solvable model of an interacting system, the Boltzmann equation predicts a constant single particle density operator, whereas the exact solution gives a single particle density operator with a nontrivial time dependence. All of the time dependence of the single particle density operator is generated by the correlations.

Discrete Time Crystals

2020 ◽  
Vol 11 (1) ◽  
pp. 467-499 ◽  
Author(s):  
Dominic V. Else ◽  
Christopher Monroe ◽  
Chetan Nayak ◽  
Norman Y. Yao
Keyword(s):  
Discrete Time ◽  
Quantum Dynamics ◽  
Many Body ◽  
Time Translation ◽  
Translation Symmetry ◽  
Interesting Class ◽  
Many Body Systems ◽  
Definition Of ◽  
Many Body Interactions ◽  
Time Crystals

Experimental advances have allowed for the exploration of nearly isolated quantum many-body systems whose coupling to an external bath is very weak. A particularly interesting class of such systems is those that do not thermalize under their own isolated quantum dynamics. In this review, we highlight the possibility for such systems to exhibit new nonequilibrium phases of matter. In particular, we focus on discrete time crystals, which are many-body phases of matter characterized by a spontaneously broken discrete time-translation symmetry. We give a definition of discrete time crystals from several points of view, emphasizing that they are a nonequilibrium phenomenon that is stabilized by many-body interactions, with no analog in noninteracting systems. We explain the theory behind several proposed models of discrete time crystals, and compare several recent realizations, in different experimental contexts.

THE UNIVERSAL EQUATIONS OF MOTION FOR NONLINEAR FIELDS IN DIFFERENT BASES DESCRIBING STRONGLY INTERACTING MANY-BODY SYSTEMS WITH TWO-BODY INTERACTIONS

1995 ◽  
Vol 09 (13n14) ◽  
pp. 1611-1637 ◽  
Author(s):  
J.M. DIXON ◽  
J.A. TUSZYŃSKI
Keyword(s):  
Plane Wave ◽  
Coherent Structures ◽  
Equations Of Motion ◽  
Quantum Field ◽  
Many Body ◽  
Field Equations ◽  
Strongly Interacting ◽  
Highly Nonlinear ◽  
Many Body Systems ◽  
Definition Of

A brief account of the Method of Coherent Structures (MCS) is presented using a plane-wave basis to define a quantum field. It is also demonstrated that the form of the quantum field equations, obtained by MCS, although highly nonlinear for many-body systems with two-body interactions, is independent of the basis of states used for the definition of the field.

The definition of the velocity field in many body systems

1969 ◽  
Vol 29 (10) ◽  
pp. 610-611 ◽  
Author(s):  
B.B. Varga ◽  
S.G. Eckstein
Keyword(s):  
Velocity Field ◽  
Many Body ◽  
Many Body Systems ◽  
Definition Of

Single-Particle Self-Energy in Many-Body Systems at Finite Temperature

2000 ◽  
Vol 283 (2) ◽  
pp. 308-333 ◽  
Author(s):  
N. Giovanardi ◽  
P. Donati ◽  
P.F. Bortignon ◽  
R.A. Broglia
Keyword(s):  
Single Particle ◽  
Finite Temperature ◽  
Many Body ◽  
Self Energy ◽  
Many Body Systems

THE SURPRISING PHENOMENON OF LEVEL MERGING IN FINITE FERMI SYSTEMS

2008 ◽  
Vol 22 (25n26) ◽  
pp. 4452-4463
Author(s):  
JOHN W. CLARK ◽  
VICTOR A. KHODEL ◽  
HAOCHEN LI ◽  
MIKHAIL V. ZVEREV
Keyword(s):  
Single Particle ◽  
Energy Levels ◽  
Fermi System ◽  
Particle Energy ◽  
Particle Spectrum ◽  
Many Body ◽  
Occupation Numbers ◽  
Inherent Feature ◽  
Wide Range ◽  
Many Body Systems

When applied to a finite Fermi system having a degenerate single-particle spectrum, the Landau-Migdal Fermi-liquid approach leaves room for the possibility that different single-particle energy levels merge with one another. It will be argued that the opportunity for this behavior exists over a wide range of strongly interacting quantum many-body systems. An inherent feature of the mergence phenomenon is the presence of nonintegral quasiparticle occupation numbers, which implies a radical modification of the standard quasiparticle picture. Consequences of this alteration are surveyed for nuclear, atomic, and solid-state systems.

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