scholarly journals Reverse engineering in many-body quantum physics: Correspondence between many-body systems and effective single-particle equations

2009 ◽  
Vol 79 (3) ◽  
Author(s):  
J. P. Coe ◽  
K. Capelle ◽  
I. D’Amico
Keyword(s):  
Reverse Engineering ◽  
Single Particle ◽  
Quantum Physics ◽  
Many Body ◽  
Many Body Systems

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.

scholarly journals Quantum echo dynamics in the Sherrington-Kirkpatrick model

2020 ◽  
Vol 9 (2) ◽  
Author(s):  
Silvia Pappalardi ◽  
Anatoli Polkovnikov ◽  
Alessandro Silva
Keyword(s):  
Quantum Physics ◽  
Transverse Field ◽  
Many Body ◽  
Initial State ◽  
Large N ◽  
Semiclassical Dynamics ◽  
Long Time ◽  
Kirkpatrick Model ◽  
Ehrenfest Time ◽  
Many Body Systems

Understanding the footprints of chaos in quantum-many-body systems has been under debate for a long time. In this work, we study the echo dynamics of the Sherrington-Kirkpatrick (SK) model with transverse field under effective time reversal. We investigate numerically its quantum and semiclassical dynamics. We explore how chaotic many-body quantum physics can lead to exponential divergence of the echo of observables and we show that it is a result of three requirements: i) the collective nature of the observable, ii) a properly chosen initial state and iii) the existence of a well-defined chaotic semi-classical (large-N) limit. Under these conditions, the echo grows exponentially up to the Ehrenfest time, which scales logarithmically with the number of spins N. In this regime, the echo is well described by the semiclassical (truncated Wigner) approximation. We also discuss a short-range version of the SK model, where the Ehrenfest time does not depend on N and the quantum echo shows only polynomial growth. Our findings provide new insights on scrambling and echo dynamics and how to observe it experimentally.

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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