# fizinfo AT lists.kfki.hu

## [Fizinfo] Termo Tea

• From: Van Peter <vpet AT phyndi.fke.bme.hu>
• To: fizinfo AT sunserv.kfki.hu
• Cc:
• Subject: [Fizinfo] Termo Tea
• Date: Fri, 12 Mar 2004 14:08:03 +0100
• List-archive: <http://sunserv.kfki.hu/pipermail/fizinfo>

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2004, marcius 25. csutortok, 15.00

BME, Kemiai Fizika Tanszek, F ep. III lcsh. I em., jobbra

A. Yahalom and R. Englman (College of Judea and Samaria and
Department of Physics and Applied Mathematics, Soreq NRC, Yavne,
Israel):

"Square-root" Method in Dissipative Quantum Dynamics

The authors have earlier proposed a variational formulation to
study the time evolution of the density matrix, for situations
including both Hamiltonian ($H$)and dissipative ($L$) processes
\cite {EnglmanY2004}. This was based on a time ($t$)-dependent
density matrix of the form $\rho(t)=\gb(t)\cdot\gcrb(t)$,
originally devised in {\cite {Reznik} and developed by
\cite{SGS}, in which the equations of motion are set up for the
$\gamma(t)$ factors in the density matrix. The method has
provided justification for the extremization of the Dissipation
Function in the Onsager-Machlup formulation of non-equilibrium
processes.

In the present talk we shall illustrate the variational procedure
and further investigate quantum trajectories by expressing the
Liouville-von Neumann-Lindblad equations $\dot{\rho}=-i[H,\rho(t)] +(2L\rho L^+ - L^+ L\rho-\rho L^+L)$ in
the "square root" formalism. Results are then obtained (both by
solving the rate equations for the $\gamma(t)$ factor and
variationally) for the time evolution of state occupation in a
periodically driven two-state model near their level degeneracies
(\cite {Kayanuma},\cite {RauW}). The decoherences occurring in a
Landau-Zener transition and around the more frequent conical
intersections in the potential surfaces are illustrated both for
individual systems and for the ensemble averaged density matrix.

Additional applications of the method include non-Markovian
quantum state diffusion of Diosi et al,\cite {DiosiGS}, for which
good agreement is found with previous, exact results. The
Born-rule in quantum jumps completes the list of illustrations.

(Hivatkozasok a honlapunkon.)

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