Single-particle propagator in the many-body system

2005 ◽  
pp. 115-140
Keyword(s):  
Single Particle ◽  
Body System ◽  
Many Body ◽  
The Many ◽  
Particle Propagator

scholarly journals Using Matrix-Product States for Open Quantum Many-Body Systems: Efficient Algorithms for Markovian and Non-Markovian Time-Evolution

Entropy ◽  
2020 ◽  
Vol 22 (9) ◽  
pp. 984
Author(s):  
Regina Finsterhölzl ◽  
Manuel Katzer ◽  
Andreas Knorr ◽  
Alexander Carmele
Keyword(s):  
Time Evolution ◽  
Nearest Neighbor ◽  
Matrix Product ◽  
Body System ◽  
Many Body ◽  
Initial State ◽  
Matrix Product States ◽  
Open Quantum ◽  
Many Body Systems ◽  
The Many

This paper presents an efficient algorithm for the time evolution of open quantum many-body systems using matrix-product states (MPS) proposing a convenient structure of the MPS-architecture, which exploits the initial state of system and reservoir. By doing so, numerically expensive re-ordering protocols are circumvented. It is applicable to systems with a Markovian type of interaction, where only the present state of the reservoir needs to be taken into account. Its adaption to a non-Markovian type of interaction between the many-body system and the reservoir is demonstrated, where the information backflow from the reservoir needs to be included in the computation. Also, the derivation of the basis in the quantum stochastic Schrödinger picture is shown. As a paradigmatic model, the Heisenberg spin chain with nearest-neighbor interaction is used. It is demonstrated that the algorithm allows for the access of large systems sizes. As an example for a non-Markovian type of interaction, the generation of highly unusual steady states in the many-body system with coherent feedback control is demonstrated for a chain length of N=30.

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.

Observable Many-Body Effects of the Two-Body Unobservable Potential

1972 ◽  
Vol 50 (14) ◽  
pp. 1614-1618 ◽  
Author(s):  
N. N. Wong ◽  
M. Razavy
Keyword(s):  
Perturbation Theory ◽  
Phase Shift ◽  
Nuclear Matter ◽  
Particle Scattering ◽  
Body System ◽  
Many Body ◽  
Many Body Effects ◽  
Transparent Potential ◽  
The Many

A two-body transparent potential, which produces no observable phase shift in two-particle scattering, is constructed explicitly. This potential is used to calculate the energy of infinite nuclear matter by applying the perturbation theory and its effects on the many-body system are investigated.

Review Lecture. Calculations of nuclear structure

1972 ◽  
Vol 326 (1565) ◽  
pp. 199-213 ◽  
Keyword(s):  
Field Theory ◽  
Nuclear Structure ◽  
Single Particle ◽  
Transition Probabilities ◽  
Energy Levels ◽  
Nucleon Nucleon ◽  
Body System ◽  
Many Body ◽  
Nucleon Scattering ◽  
Body Interaction

The field theory of elementary particles has so far failed to predict the detailed form of the interaction between neutrons and protons (nucleons), but the nucleon-nucleon scattering experiments are now sufficiently complete that for most purposes the interaction may be taken as known. At the same time a wealth of data concerning energy levels, transition probabilities and so on is available for literally hundreds of nuclei. Such measurements reveal that nuclei have an extremely rich structure, with both single-particle and collective properties, illustrating almost every feature of a many-body system. It is the purpose of this talk to review the extent to which we are able to understand these properties on the basis of the known two-body interaction. It will be shown how some features may be understood quite readily while others still pose fascinating problems.

Wave equation for dissipative motion

1991 ◽  
Vol 69 (10) ◽  
pp. 1225-1232 ◽  
Author(s):  
M. Razavy
Keyword(s):  
Wave Equation ◽  
Single Particle ◽  
Equations Of Motion ◽  
Dissipative System ◽  
Heat Bath ◽  
Initial Position ◽  
Time Dependent ◽  
Reduced Form ◽  
Body System ◽  
Many Body

From a quantized many-body system a wave equation for the motion of a particle linearly coupled to a heat bath is derived. The effective Hamiltonian describing the motion of the single particle is explicitly time dependent, and for a quadratic potential, has a simple dependence on the initial position and momentum of the particle. For the case of dissipative harmonic motion, a time-dependent wave equation is derived and the ground-state wave function is determined. It is also shown that if the equations of motion for the many-body system is Galilean invariant, the reduced form of equation of motion for the single particle is not. However a generalized form of transformation for the position and momentum operators, to a coordinate system moving with constant velocity, is obtained, which reduces to the Galilean transformation when the coupling to the dissipative system is turned off.

scholarly journals Analytical and numerical analysis of the complete Lipkin–Meshkov–Glick Hamiltonian

2018 ◽  
Vol 27 (05) ◽  
pp. 1850039 ◽  
Author(s):  
Giampaolo Co’ ◽  
Stefano De Leo
Keyword(s):  
Lower Energy ◽  
Energy Gap ◽  
Energy Levels ◽  
Body System ◽  
Many Body ◽  
Energy Eigenvalues ◽  
Lower Energy Level ◽  
First Excited State ◽  
Text Interaction ◽  
The Many

The Lipkin–Meshkov–Glick is a simple, but not trivial, model of a quantum many-body system which allows us to solve the many-body Schrödinger equation without making any approximation. The model, which in its unperturbed case is composed only by two energy levels, includes two interacting terms. A first one, the [Formula: see text] interaction, which promotes or degrades pairs of particles, and a second one, the [Formula: see text] interaction, which scatters one particle in the upper and another in the lower energy level. In comparing this model with other approximation methods, the [Formula: see text] term interaction is often set to zero. In this paper, we show how the presence of this interaction changes the global structure of the system, generates degeneracies between the various eigenstates and modifies the energy eigenvalues structure. We present analytical solutions for systems of two and three particles and, for some specific cases, also for four, six and eight particles. The solutions for systems with more than eight particles are only numerical but their behavior can be well understood by considering the extrapolations of the analytical results. Of particular interest is the study of how the [Formula: see text] interaction affects the energy gap between the ground state and the first-excited state.

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