Abstract
This chapter provides a brief introduction to quantum systems that are coupled to large reservoirs. It aims to remind the reader of well-known concepts necessary for the understanding of the book and does not claim to provide a self-contained introduction. It starts with a brief summary of the conventions used in the book and then introduces master equations with some examples. This also requires us to introduce the density matrix: among other things, we discuss its evolution in a closed system and under measurements. To connect to system-reservoir theories, we also review the definition of the tensor product and the partial trace. Finally, we introduce the Lindblad form of a quantum master equation and discuss its properties before closing with some remarks on the superoperator representation of master equations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
P.W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26, 1484 (1997)
L.K. Grover, Fixed-point quantum search. Phys. Rev. Lett. 95, 150501 (2005)
R.P. Feynman, Simulating physics with computers. Int. J. Theor. Phys. 21, 467 (1982)
S. Lloyd, Universal quantum simulators. Science 273, 1073 (1996)
M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000)
H.-P. Breuer, F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002)
M. Schlosshauer, Decoherence and the Quantum-to-Classical Transition (Springer, Berlin, 2007)
L.M.K. Vandersypen, M. Steffen, G. Breyta, C.S. Yannoni, M.H. Sherwood, I.L. Chuang, Experimental realization of Shor’s quantum factoring algorithm using nuclear magnetic resonance. Nature 414, 883 (2001)
J.I. Cirac, P. Zoller, New frontiers in quantum information with atoms and ions. Phys. Today 57, 38 (2004)
J. Du, N. Xu, X. Peng, P. Wang, S. Wu, D. Lu, NMR implementation of a molecular hydrogen quantum simulation with adiabatic state preparation. Phys. Rev. Lett. 104, 030502 (2010)
R. Coldea, D.A. Tennant, E.M. Wheeler, E. Wawrzynska, D. Prabhakaran, M. Telling, K. Habicht, P. Smeibidl, K. Kiefer, Quantum criticality in an Ising chain: experimental evidence for emergent e 8 symmetry. Science 327, 177 (2010)
R. Sánchez, M. Buttiker, Optimal energy quanta to current conversion. Physical Review B 83, 085428 (2011)
N. Linden, S. Popescu, P. Skrzypczyk, How small can thermal machines be? The smallest possible refrigerator. Phys. Rev. Lett. 105, 130401 (2010)
V.M. Bastidas, C. Emary, G. Schaller, A. Gómez-León, G. Platero, T. Brandes, Floquet topological quantum phase transitions in the transverse Wen-plaquette model (2013). arXiv:1302.0781
J. Dziarmaga, Dynamics of a quantum phase transition: exact solution of the quantum Ising model. Phys. Rev. Lett. 95, 245701 (2005)
E. Barnes, S. Das Sarma, Analytically solvable driven time-dependent two-level quantum systems. Phys. Rev. Lett. 109, 060401 (2012)
N. Linden, S. Popescu, A.J. Short, A. Winter, Quantum mechanical evolution towards thermal equilibrium. Phys. Rev. E 79, 061103 (2009)
K. Kraus, Effects and Operations: Fundamental Notions of Quantum Theory (Springer, Berlin, 1983)
G. Lindblad, On the generators of quantum dynamical semigroups. Commun. Math. Phys. 48, 119 (1976)
M. Esposito, S. Mukamel, Fluctuation theorems for quantum master equations. Phys. Rev. E 73, 046129 (2006)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Schaller, G. (2014). Dynamics of Open Quantum Systems. In: Open Quantum Systems Far from Equilibrium. Lecture Notes in Physics, vol 881. Springer, Cham. https://doi.org/10.1007/978-3-319-03877-3_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-03877-3_1
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03876-6
Online ISBN: 978-3-319-03877-3
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)