scholarly journals Time evolution of one-dimensional Quantum Many Body Systems

2005 ◽  
Author(s):  
Salvatore R. Manmana
Keyword(s):  
Time Evolution ◽  
Many Body ◽  
One Dimensional ◽  
Many Body Systems

scholarly journals Undecidability in quantum thermalization

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Naoto Shiraishi ◽  
Keiji Matsumoto
Keyword(s):  
Turing Machine ◽  
Thermal Equilibrium ◽  
General Theorem ◽  
Nearest Neighbour ◽  
Many Body ◽  
Initial State ◽  
One Dimensional ◽  
Universal Turing Machine ◽  
Many Body Systems ◽  
Neighbour Interaction

AbstractThe investigation of thermalization in isolated quantum many-body systems has a long history, dating back to the time of developing statistical mechanics. Most quantum many-body systems in nature are considered to thermalize, while some never achieve thermal equilibrium. The central problem is to clarify whether a given system thermalizes, which has been addressed previously, but not resolved. Here, we show that this problem is undecidable. The resulting undecidability even applies when the system is restricted to one-dimensional shift-invariant systems with nearest-neighbour interaction, and the initial state is a fixed product state. We construct a family of Hamiltonians encoding dynamics of a reversible universal Turing machine, where the fate of a relaxation process changes considerably depending on whether the Turing machine halts. Our result indicates that there is no general theorem, algorithm, or systematic procedure determining the presence or absence of thermalization in any given Hamiltonian.

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 Yang-Lee zeros of one-dimensional quantum many-body systems

1999 ◽  
Vol 59 (1) ◽  
pp. 222-227 ◽  
Author(s):  
Xian-Zhi Wang ◽  
Jai Sam Kim
Keyword(s):  
Many Body ◽  
One Dimensional ◽  
Many Body Systems

scholarly journals Quasiequilibria in one-dimensional self-gravitating many-body systems

1994 ◽  
Vol 50 (4) ◽  
pp. 2607-2615 ◽  
Author(s):  
Toshio Tsuchiya ◽  
Tetsuro Konishi ◽  
Naoteru Gouda
Keyword(s):  
Many Body ◽  
One Dimensional ◽  
Many Body Systems

scholarly journals Relaxation processes in one-dimensional self-gravitating many-body systems

1996 ◽  
Vol 53 (3) ◽  
pp. 2210-2216 ◽  
Author(s):  
Toshio Tsuchiya ◽  
Naoteru Gouda ◽  
Tetsuro Konishi
Keyword(s):  
Relaxation Processes ◽  
Many Body ◽  
One Dimensional ◽  
Many Body Systems
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