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 TMF, 1991, Volume 88, Number 2, Pages 247–259 (Mi tmf5806)

Invariant states for time dynamics of one-dimensional lattice quantum fermi systems

N. E. Ratanov, Yu. M. Sukhov

Abstract: A study is made of the problem of describing the set of invariant states for the time dynamics corresponding to a (formal) Hamiltonian $H_0$ of a one-dimensional lattice quantum Fermi system. Assuming that the invariant state $\varphi$ is a KMS state for some “Hamiltonian” $H$, we prove that $H$ is proportional to $H_0$, i.e., that $\varphi$ is a KMS state for $\beta H_0$. As a consequence, in the considered situation every “natural” invariant state is an equilibrium Gibbs state. Use is made here of the condition that $H_0$ is not a quadratic form in the creation and annihilation operators. In such a case the time dynamics admits a much richer set of invariant states. If all terms in $H_0$ except the quadratic ones are diagonal, it can be shown that $H=\beta H_0+N$. Here, $N$ is an arbitrary diagonal quadratic form.

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English version:
Theoretical and Mathematical Physics, 1991, 88:2, 849–858

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Citation: N. E. Ratanov, Yu. M. Sukhov, “Invariant states for time dynamics of one-dimensional lattice quantum fermi systems”, TMF, 88:2 (1991), 247–259; Theoret. and Math. Phys., 88:2 (1991), 849–858

Citation in format AMSBIB
\Bibitem{RatSuk91} \by N.~E.~Ratanov, Yu.~M.~Sukhov \paper Invariant states for time dynamics of one-dimensional lattice quantum fermi systems \jour TMF \yr 1991 \vol 88 \issue 2 \pages 247--259 \mathnet{http://mi.mathnet.ru/tmf5806} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1137941} \transl \jour Theoret. and Math. Phys. \yr 1991 \vol 88 \issue 2 \pages 849--858 \crossref{https://doi.org/10.1007/BF01019111} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1991HK96400005} 

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This publication is cited in the following articles:
1. N. E. Ratanov, Yu. M. Sukhov, “Invariant states for the time dynamics of a class of multidimensional lattice quantum Fermi systems”, Theoret. and Math. Phys., 94:1 (1993), 55–60
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