TY  - JOUR
A1  - Prosen, Tomaz
T1  - Complexity and nonseparability of classical Liouvillian dynamics
JF  - Physical review : E, Statistical, nonlinear and soft matter physics
N2  - We propose a simple complexity indicator of classical Liouvillian dynamics, namely the separability entropy, which determines the logarithm of an effective number of terms in a Schmidt decomposition of phase space density with respect to an arbitrary fixed product basis. We show that linear growth of separability entropy provides a stricter criterion of complexity than Kolmogorov-Sinai entropy, namely it requires that the dynamics be exponentially unstable, nonlinear, and non-Markovian.
Y1  - 2011
U6  - https://doi.org/10.1103/PhysRevE.83.031124
SN  - 1539-3755
VL  - 83
IS  - 3
PB  - American Physical Society
CY  - College Park
ER  - 
TY  - JOUR
A1  - Zunkovic, Bojan
A1  - Prosen, Tomaz
T1  - Explicit solution of the Lindblad equation for nearly isotropic boundary driven XY spin 1/2 chain
N2  - Explicit solution for the two-point correlation function in a non-equilibrium steady state of a nearly isotropic boundary driven open XY spin 1/2 chain in the Lindblad formulation is provided. A non-equilibrium quantum phase transition from exponentially decaying correlations to long range order is discussed analytically. In the regime of long range order a new phenomenon of correlation resonances is reported, where the correlation response of the system is unusually high for certain discrete values of the external bulk parameter, e.g. the magnetic field.
Y1  - 2010
UR  - http://iopscience.iop.org/1742-5468/
U6  - https://doi.org/10.1088/1742-5468/2010/08/P08016
SN  - 1742-5468
ER  - 
TY  - JOUR
A1  - Prosen, Tomaz
A1  - Ilievski, Enej
T1  - Nonequilibrium phase transition in a periodically driven XY spin chain
JF  - Physical review letters
N2  - We present a general formulation of Floquet states of periodically time-dependent open Markovian quasifree fermionic many-body systems in terms of a discrete Lyapunov equation. Illustrating the technique, we analyze periodically kicked XY spin-1/2 chain which is coupled to a pair of Lindblad reservoirs at its ends. A complex phase diagram is reported with reentrant phases of long range and exponentially decaying spin-spin correlations as some of the system's parameters are varied. The structure of phase diagram is reproduced in terms of counting nontrivial stationary points of Floquet quasiparticle dispersion relation.
Y1  - 2011
U6  - https://doi.org/10.1103/PhysRevLett.107.060403
SN  - 0031-9007
VL  - 107
IS  - 6
PB  - American Physical Society
CY  - College Park
ER  -