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 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 Probing the edge between integrability and quantum chaos in interacting few-atom systems

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 486
Author(s):  
Thomás Fogarty ◽  
Miguel Ángel García-March ◽  
Lea F. Santos ◽  
Nathan L. Harshman
Keyword(s):  
Quantum Chaos ◽  
Cold Atoms ◽  
Quantum Systems ◽  
Particle Interactions ◽  
Body System ◽  
Many Body ◽  
One Dimensional ◽  
The Core ◽  
Emergence Of Chaos ◽  
Number Of Particles

Interacting quantum systems in the chaotic domain are at the core of various ongoing studies of many-body physics, ranging from the scrambling of quantum information to the onset of thermalization. We propose a minimum model for chaos that can be experimentally realized with cold atoms trapped in one-dimensional multi-well potentials. We explore the emergence of chaos as the number of particles is increased, starting with as few as two, and as the number of wells is increased, ranging from a double well to a multi-well Kronig-Penney-like system. In this way, we illuminate the narrow boundary between integrability and chaos in a highly tunable few-body system. We show that the competition between the particle interactions and the periodic structure of the confining potential reveals subtle indications of quantum chaos for 3 particles, while for 4 particles stronger signatures are seen. The analysis is performed for bosonic particles and could also be extended to distinguishable fermions.

On the Steady-State Response of a One-Dimensional Yielding Continuum

1970 ◽  
Vol 37 (3) ◽  
pp. 720-727 ◽  
Author(s):  
W. D. Iwan
Keyword(s):  
Steady State ◽  
Standing Wave ◽  
Steady State Response ◽  
Higher Modes ◽  
One Dimensional ◽  
State Response ◽  
Wave Response ◽  
Response Modes ◽  
Damped Systems

The steady-state or standing wave response of a bounded one-dimensional yielding continuum is investigated using an approximate analytic technique. Details of the nature of the fundamental and higher modes of response are presented. It is found that the effective damping in the higher response modes may be quite small compared to that of linear viscous damped systems.

One-Dimensional Classical Many-Body System Having a Normal Thermal Conductivity

1984 ◽  
Vol 53 (11) ◽  
pp. 1120-1120 ◽  
Author(s):  
Giulio Casati ◽  
Joseph Ford ◽  
Franco Vivaldi ◽  
William M. Visscher
Keyword(s):  
Thermal Conductivity ◽  
Body System ◽  
Many Body ◽  
One Dimensional

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.

Classical solitons for a one-dimensional many-body system with inverse-square interaction

1994 ◽  
Vol 50 (2) ◽  
pp. 888-896 ◽  
Author(s):  
Bill Sutherland ◽  
Joel Campbell
Keyword(s):  
Body System ◽  
Many Body ◽  
One Dimensional
Sign in / Sign up

Export Citation Format

Share Document