scholarly journals Time evolution of a quantum lattice system

1973 ◽  
Vol 30 (2) ◽  
pp. 83-98 ◽  
Author(s):  
M. Pulvirenti ◽  
B. Tirozzi
Keyword(s):  
Time Evolution ◽  
Lattice System ◽  
Quantum Lattice ◽  
Quantum Lattice System

Time Evolution of a Two-Dimensional Classical Lattice System

1973 ◽  
Vol 31 (5) ◽  
pp. 276-279 ◽  
Author(s):  
J. Hardy ◽  
Y. Pomeau ◽  
O. de Pazzis
Keyword(s):  
Time Evolution ◽  
Lattice System ◽  
Two Dimensional ◽  
Classical Lattice ◽  
Classical Lattice System

Perturbation Dynamics of the Infinite Dicke Model

1993 ◽  
Vol 48 (11) ◽  
pp. 1043-1053 ◽  
Author(s):  
Reinhard Honegger ◽  
Alfred Rieckers ◽  
Thomas Unnerstall
Keyword(s):  
Time Evolution ◽  
Atomic System ◽  
Mean Field ◽  
Interaction Strength ◽  
Product Formula ◽  
Collective Behaviour ◽  
Evolution Operators ◽  
Quantum Lattice ◽  
Theoretical Methods ◽  
Dicke Model

Abstract By means of operator algebraic methods the dynamics of the Dicke model is investigated in the limit where the number of the two-level atoms goes to infinity and the interaction strength remains on a finite level. The infinite atomic system is treated as a mean field quantum lattice system. It is shown that the limiting dynamics is essentially determined by the collective behaviour of the atoms. With Trotter's product formula and perturbation theoretical methods we obtain explicit expressions for the unitary time evolution operators in the uncoupled representation.

scholarly journals On the size of the space spanned by a nonequilibrium state in a quantum spin lattice system

2019 ◽  
Vol 6 (5) ◽  
Author(s):  
Maurizio Fagotti
Keyword(s):  
Time Evolution ◽  
Time Window ◽  
Error Function ◽  
Nonequilibrium State ◽  
Quantum Spin ◽  
Lattice System ◽  
Spin Lattice

We consider the time evolution of a state in an isolated quantum spin lattice system with energy cumulants proportional to the number of the sites L^dLd. We compute the distribution of the eigenvalues of the time averaged state over a time window [t_0,t_0+t][t0,t0+t] in the limit of large L. This allows us to infer the size of a subspace that captures time evolution in [t_0,t_0+t][t0,t0+t] with an accuracy 1-\epsilon1−ϵ. We estimate the size to be \frac{\sqrt{2{\mathfrak e}_2}}{\pi}erf^{-1}(1-\epsilon) L^{\frac{d}{2}}t2𝔢2πerf−1(1−ϵ)Ld2t, where {\mathfrak e}_2𝔢2 is the energy variance per site, and erf^{-1}erf−1 is the inverse error function.

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