equivalence of ensembles
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Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 420
Author(s):  
Jakub Rembieliński ◽  
Paweł Caban

In this paper we consider deterministic nonlinear time evolutions satisfying so called convex quasi-linearity condition. Such evolutions preserve the equivalence of ensembles and therefore are free from problems with signaling. We show that if family of linear non-trace-preserving maps satisfies the semigroup property then the generated family of convex quasi-linear operations also possesses the semigroup property. Next we generalize the Gorini-Kossakowski-Sudarshan-Lindblad type equation for the considered evolution. As examples we discuss the general qubit evolution in our model as well as an extension of the Jaynes-Cummings model. We apply our formalism to spin density matrix of a charged particle moving in the electromagnetic field as well as to flavor evolution of solar neutrinos.



2020 ◽  
Vol 24 ◽  
pp. 341-373
Author(s):  
Younghak Kwon ◽  
Georg Menz

We consider a one-dimensional lattice system of unbounded, real-valued spins with arbitrary strong, quadratic, finite-range interaction. We show that the canonical ensemble (ce) satisfies a uniform logarithmic Sobolev inequality (LSI). The LSI constant is uniform in the boundary data, the external field and scales optimally in the system size. This extends a classical result of H.T. Yau from discrete to unbounded, real-valued spins. It also extends prior results of Landim et al. or Menz for unbounded, real-valued spins from absent- or weak- to strong-interaction. We deduce the LSI by combining two competing methods, the two-scale approach and the Zegarlinski method. Main ingredients are the strict convexity of the coarse-grained Hamiltonian, the equivalence of ensembles and the decay of correlations in the ce.





2017 ◽  
Vol 168 (4) ◽  
pp. 707-730 ◽  
Author(s):  
Nicoletta Cancrini ◽  
Stefano Olla


2017 ◽  
Vol 27 (2) ◽  
pp. 883-916 ◽  
Author(s):  
Christine Fricker ◽  
Danielle Tibi






2006 ◽  
Vol 47 (7) ◽  
pp. 073303 ◽  
Author(s):  
Wojciech De Roeck ◽  
Christian Maes ◽  
Karel Netočný




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