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

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 Quantum Gross-Pitaevskii Equation

2017 ◽  
Vol 3 (1) ◽  
Author(s):  
Jutho Haegeman ◽  
Damian Draxler ◽  
Vid Stojevic ◽  
Ignacio Cirac ◽  
Tobias Osborne ◽  
...  
Keyword(s):  
Mean Field ◽  
Pitaevskii Equation ◽  
Matrix Product ◽  
Steady State Response ◽  
Body System ◽  
Many Body ◽  
One Dimensional ◽  
State Response ◽  
Quantum Liquids ◽  
Full Quantum

We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational manifold of continuous matrix product states. This allows for a full quantum description of many body system —including entanglement and correlations— and thus extends significantly beyond the usual mean-field description of the Gross-Pitaevskii equation, which is known to fail for (quasi) one-dimensional systems. By linearizing around a stationary solution, we furthermore derive an associated generalization of the Bogoliubov – de Gennes equations. This framework is applied to compute the steady state response amplitude to a periodic perturbation of the potential.

scholarly journals Derivation of the Landau–Pekar Equations in a Many-Body Mean-Field Limit

2021 ◽  
Vol 240 (1) ◽  
pp. 383-417
Author(s):  
Nikolai Leopold ◽  
David Mitrouskas ◽  
Robert Seiringer
Keyword(s):  
Mean Field ◽  
Einstein Condensate ◽  
Back Reaction ◽  
Many Body ◽  
Field Limit ◽  
Mean Field Limit ◽  
Phonon Field ◽  
Bose Einstein Condensate ◽  
Weakly Couple ◽  
Bose Einstein

AbstractWe consider the Fröhlich Hamiltonian in a mean-field limit where many bosonic particles weakly couple to the quantized phonon field. For large particle numbers and a suitably small coupling, we show that the dynamics of the system is approximately described by the Landau–Pekar equations. These describe a Bose–Einstein condensate interacting with a classical polarization field, whose dynamics is effected by the condensate, i.e., the back-reaction of the phonons that are created by the particles during the time evolution is of leading order.

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.

Equilibration of an isolated quantum many-body system

Physics Today ◽  
2013 ◽  
Vol 66 (11) ◽  
pp. 18-18
Author(s):  
Richard J. Fitzgerald
Keyword(s):  
Body System ◽  
Many Body
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