scholarly journals Itinerancy of Quasiequilibria in One-Dimensional Gravitating Systems

1996 ◽  
Vol 174 ◽  
pp. 385-386
Author(s):  
T. Tsuchiya ◽  
N. Gouda ◽  
T. Konishi
Keyword(s):  
Surface Density ◽  
Mass Density ◽  
Gravitational Attraction ◽  
Many Body ◽  
One Dimensional ◽  
Many Body Systems ◽  
Gravitating Systems ◽  
Image Position

One-dimensional self-gravitating many-body systems consist of N identical parallel sheets which have uniform mass density m and infinite in extent in the (y, z) plane. We call the sheets particles in this paper. The particles are free to move along x axis and accelerate as a result of their mutual gravitational attraction. The Hamiltonian of this system has a form of where m, vi, and xi are the mass (surface density), velocity, and position of ith particle respectively.

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 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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