Dimensionality dependence of dynamical correlations: exact results from a quantum many body system

1993 ◽  
Vol 441 (1911) ◽  
pp. 169-179 ◽  
Keyword(s):  
Low Temperatures ◽  
Relaxation Function ◽  
Mean Field ◽  
Exact Results ◽  
Body System ◽  
Many Body ◽  
Many Body Systems

Using one of the simplest model interacting quantum many body systems it is shown that the relaxation function behaves remarkably differently at low temperatures depending upon whether the lattice dimensionality of the system, D < ∞ or → ∞. The results illustrate the possible limitations of mean-field descriptions of dynamics at T < T c in quantum many body systems.

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.

ON STRONGLY NONLINEAR AUTOREGRESSIVE MODELS: IMPLICATIONS FOR THE THEORY OF TRANSIENT AND STATIONARY RESPONSES OF MANY-BODY SYSTEMS

2013 ◽  
Vol 12 (04) ◽  
pp. 1350022 ◽  
Author(s):  
T. D. FRANK ◽  
S. MONGKOLSAKULVONG
Keyword(s):  
Evolution Equations ◽  
Mean Field Theory ◽  
Mean Field ◽  
Ar Model ◽  
Many Body ◽  
Response Dynamics ◽  
Process Mean ◽  
Stationary Response ◽  
Strongly Nonlinear ◽  
Many Body Systems

Two widely used concepts in physics and the life sciences are combined: mean field theory and time-discrete time series modeling. They are merged within the framework of strongly nonlinear stochastic processes, which are processes whose stochastic evolution equations depend self-consistently on process expectation values. Explicitly, a generalized autoregressive (AR) model is presented for an AR process that depends on its process mean value. Criteria for stationarity are derived. The transient dynamics in terms of the relaxation of the first moment and the stationary response to fluctuations in terms of the autocorrelation function are discussed. It is shown that due to the stochastic feedback via the process mean, transient and stationary responses may exhibit qualitatively different temporal patterns. That is, the model offers a time-discrete description of many-body systems that in certain parameter domains feature qualitatively different transient and stationary response dynamics.

scholarly journals Thermalization of Finite Many-Body Systems by a Collision Model

Entropy ◽  
2019 ◽  
Vol 21 (12) ◽  
pp. 1182 ◽  
Author(s):  
Onat Arısoy ◽  
Steve Campbell ◽  
Özgür E. Müstecaplıoğlu
Keyword(s):  
Weak Coupling ◽  
Target System ◽  
Model Description ◽  
Body System ◽  
Weak Coupling Regime ◽  
Many Body ◽  
Collision Model ◽  
System Transition ◽  
Many Body Systems ◽  
Thermal States

We construct a collision model description of the thermalization of a finite many-body system by using careful derivation of the corresponding Lindblad-type master equation in the weak coupling regime. Using the example of a two-level target system, we show that collision model thermalization is crucially dependent on the various relevant system and bath timescales and on ensuring that the environment is composed of ancillae which are resonant with the system transition frequencies. Using this, we extend our analysis to show that our collision model can lead to thermalization for certain classes of many-body systems. We establish that for classically correlated systems our approach is effective, while we also highlight its shortcomings, in particular with regards to reaching entangled thermal states.

scholarly journals Self-consistent effective Hamiltonian theory for fermionic many-body systems

2020 ◽  
pp. 2150019
Author(s):  
Xindong Wang ◽  
Hai-Ping Cheng
Keyword(s):  
Hubbard Model ◽  
Order Parameter ◽  
Cooper Pair ◽  
Effective Hamiltonian ◽  
Two Dimensional ◽  
Body System ◽  
Many Body ◽  
Hamiltonian Theory ◽  
Self Consistent ◽  
Many Body Systems

Using a separable many-body variational wavefunction, we formulate a self-consistent effective Hamiltonian theory for fermionic many-body system. The theory is applied to the two-dimensional (2D) Hubbard model as an example to demonstrate its capability and computational effectiveness. Most remarkably for the Hubbard model in 2D, a highly unconventional quadruple-fermion non-Cooper pair order parameter is discovered.

Calculation of the propagation amplitude in the case of a Coulomb interaction via time-independent mean-field theory

2007 ◽  
Vol 85 (7) ◽  
pp. 787-796
Author(s):  
R Yekken ◽  
F Mekideche
Keyword(s):  
Coulomb Interaction ◽  
Mean Field Theory ◽  
Mean Field ◽  
Numerical Comparison ◽  
Many Body ◽  
Field Equations ◽  
Range Interaction ◽  
Approximate Methods ◽  
Mean Field Equations ◽  
Many Body Systems

The exact study of many-body microscopic systems is impossible when the number of particles is large (N ≥ 3). Approximate methods are then used. The time-independent mean-field (TIMF) approximation has been proposed for the description of collisions in many-body systems. Collision amplitudes are derived by the use of a variational principle and the choice of trial functions as products of single-particle orbitals. Resulting mean-field equations with a nonvanishing right-hand side turn out to be a generalization of the traditional Hartree or Hatree–Fock type equations. These TIMF equations are successfully solved numerically for the case of short-range forces. In this paper, we test the validity of this theory for the Coulomb interaction between two particles, that is, a long-range interaction. A numerical comparison between the exact and the mean-field solutions is conducted PACS Nos.: 31.15.Ne, 31.15.Pf, 21.45.+v,25.10.-i

scholarly journals Quantum versus mean-field collapse in a many-body system

2015 ◽  
Vol 92 (4) ◽  
Author(s):  
G. E. Astrakharchik ◽  
B. A. Malomed
Keyword(s):  
Mean Field ◽  
Body System ◽  
Many Body

scholarly journals From dynamical localization to bunching in interacting Floquet systems

2018 ◽  
Vol 5 (2) ◽  
Author(s):  
Yuval Baum ◽  
Everard van Nieuwenburg ◽  
Gil Refael
Keyword(s):  
Hubbard Model ◽  
Dynamical Localization ◽  
Body System ◽  
Many Body ◽  
Many Body Systems

We show that a quantum many-body system may be controlled by means of Floquet engineering, i.e., their properties may be controlled and manipulated by employing periodic driving. We present a concrete driving scheme that allows control over the nature of mobile units and the amount of diffusion in generic many-body systems. We demonstrate these ideas for the Fermi-Hubbard model, where the drive renders doubly occupied sites (doublons) the mobile excitations in the system. In particular, we show that the amount of diffusion in the system and the level of fermion-pairing may be controlled and understood solely in terms of the doublon dynamics. We find that under certain circumstances the diffusion in 11D systems may be eliminated completely for extremely long times. We conclude our work by generalizing these ideas to generic many-body systems.

Mean Field Approaches to Many-Body Systems

2012 ◽  
pp. 1285-1285
Author(s):  
Gabriela Juarez-Martinez ◽  
Alessandro Chiolerio ◽  
Paolo Allia ◽  
Martino Poggio ◽  
Christian L. Degen ◽  
...  
Keyword(s):  
Mean Field ◽  
Many Body ◽  
Many Body Systems ◽  
Field Approaches
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