11627 9 archive 1 disk0/00/01/16/27 2008-09-14 00:31:07 2008-09-14 00:43:22 2008-09-14 00:31:07 article show 0 Zwolak Michael Zwolak-M pub cls public environmental factors, quantum theory ©2008 American Institute of Physics. Received 28 May 2008; accepted 5 August 2008; published 8 September 2008. We thank W. Zurek, G. Refael, G. Smith, F. M. Cucchietti, and P. Milonni for helpful comments. This research was supported in part by a Gordon and Betty Moore Fellowship at Caltech and by the U.S. Department of Energy through the LANL/LDRD Program. Understanding dissipative and decohering processes is fundamental to the study of quantum systems. An accurate and generic method for investigating these processes is to simulate both the system and environment, which, however, is computationally very demanding. We develop a novel approach to constructing finite representations of the environment based on the influence of different frequency scales on the system's dynamics. As an illustration, we analyze a solvable model of an optical mode decaying into a reservoir. The influence of the environment modes is constant for small frequencies, but drops off rapidly for large frequencies, allowing for a very sparse representation at high frequencies that gives a significant computational speedup in simulating the environment. This approach provides a general framework for simulating open quantum systems. 2008-09-14 published Journal of Chemical Physics 129 10 American Institute of Physics Art. No. 101101 CaltechAUTHORS:ZWOjcp08 TRUE 0021-9606 http://resolver.caltech.edu/CaltechAUTHORS:ZWOjcp08 http://dx.doi.org/10.1063/1.2976008 doi http://link.aip.org/link/?JCPSA6/129/101101/1 pub 1. U. Weiss, Quantum Dissipative Systems (World Scientific, Singapore, 1993). 2. A. J. Leggett, S. Chakravarty, A. T. Dorsey, M. P. A. Fisher, A. Garg, and W. Zwerger, Rev. Mod. Phys. 59, 1 (1987). 3. W. H. Zurek, Rev. Mod. Phys. 75, 715 (2003). 4. Y.-C. Chen and M. Di Ventra, Phys. 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Alternative measures are appropriate if one is interested in a particular observable or the relative error. 19. Since we plan to remove many modes, the spectral density of these modes must be included with the remaining modes. Another question one can ask is if we remove two modes and replace them with one, what error is incurred? This error has similar behavior to the influence in Eq. (4). 20. M. Zwolak, e-print arXiv:cond-mat/0611412; “Numerical ansatz for solving integro-differential equations with increasingly smooth memory kernels: Spin-boson model and beyond,” Computational Science and Discovery (to be published). 21. H. J. Carmichael, An Open Systems Approach to Quantum Optics (Springer-Verlag, Berlin, 1993). 22. We remove the conserved term ωo (a†a+Σkbbk) and take the system frequency ωo to be large. 23. P. W. Milonni, J. R. Ackerhalt, H. W. Galbraith, and M.-L. Shih, Phys. Rev. A 28, 32 (1983). 24. The spectral function appears with Δ as the product J(ω)Δ, suggesting a more general spacing Δo+dω^2/J(ω) (Ref. 32). 25. We set Δo=2π/2T since low frequency modes will give large recurrence errors if their spacing is larger than 2π/T. 26. An additional, numerical comparison with Δ(ω)=Δo+dω shows that the spacing [Eq. (11)] is more efficient. 27. We conjecture that including a time-dependent field within the solvable model will mimic the many-body interaction by creating a range of accessible states. Likewise, we stress that the spacing is going to be dependent on the particulars of the system, including how the environment modifies the system, e.g., whether it shifts energies, mixes states, etc. 28. G. Vidal, Phys. Rev. Lett. 91, 147902 (2003). 29. G. Vidal, Phys. Rev. Lett. 93, 040502 (2004). 30. M. Zwolak and G. Vidal, Phys. Rev. Lett. 93, 207205 (2004). 31. F. Verstraete, J. J. Garcia-Ripoll, and J. I. Cirac, Phys. Rev. Lett. 93, 207204 (2004). 32. M. Zwolak and G. Refael (unpublished). 33. There will be a corresponding reduction in computational cost for MPS simulations that is harder to assess since the effect on the MPS dimension is unclear. 34. B. M. Garraway, Phys. Rev. A 55, 4636 (1997). 35. A. Sergi, Phys. Rev. E 72, 066125 (2005). 36. A. Sergi, J. Phys. A 40, F347 (2007). You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format. Gordon and Betty Moore Foundation Department of Energy CaltechAUTHORS 12086 3 11627 1 application/pdf en public other

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