20 research outputs found
Exact propagation of open quantum systems in a system-reservoir context
A stochastic representation of the dynamics of open quantum systems, suitable
for non-perturbative system-reservoir interaction, non-Markovian effects and
arbitrarily driven systems is presented. It includes the case of driving on
timescales comparable to or shorter than the reservoir correlation time, a
notoriously difficult but relevant case in the context of quantum information
processing and quantum thermodynamics. A previous stochastic approach is
re-formulated for the case of finite reservoir correlation and response times,
resulting in a numerical simulation strategy exceeding previous ones by orders
of magnitude in efficiency. Although the approach is based on a memory
formalism, the dynamical equations propagated in the simulations are
time-local. This leaves a wide range of choices in selecting the system to be
studied and the numerical method used for propagation. For a series of tests,
the dynamics of the spin-boson system is computed in various settings including
strong external driving and Landau-Zener transitions.Comment: 7 pages, 4 figures. v2: inset in Fig. 2 and some text added, further
references. v3: minor correction
A Variance Reduction Technique for the Stochastic Liouville-von Neuman Equation
The Stochastic Liouville-von Neumann equation provides an exact numerical
simulation strategy for quantum systems interacting with Gaussian reservoirs
[J.T. Stockburger & H. Grabert, PRL 88, 170407 (2002)]. Its scaling with the
extension of the time interval covered has recently improved dramatically
through time-domain projection techniques [J.T. Stockburger, EPL 115, 40010
(2016)]. Here we present a sampling strategy which results in a significantly
improved scaling with the strength of the dissipative interaction, based on
reducing the non-unitary terms in sample propagation through convex
optimization techniques.Comment: 9 pages, 2 figures, 2 table
Simulating spin-boson dynamics with stochastic Liouville-von Neumann equations
Based on recently derived exact stochastic Liouville-von Neumann equations,
several strategies for the efficient simulation of open quantum systems are
developed and tested on the spin-boson model. The accuracy and efficiency of
these simulations is verified for several test cases including both coherent
and incoherent dynamics, involving timescales differing by several orders of
magnitude. Using simulations with a time-dependent field, the time evolution of
coherences in the reduced density matrix is investigated. Even in the case of
weak damping, pronounced preparation effects are found. These indicate hidden
coherence in the interacting system which can only be indirectly observed in
the basis of the reduced quantum dynamics.Comment: 25 pages, 7 figures; to be published in Chemical Physic
A Dynamical Theory of Electron Transfer: Crossover from Weak to Strong Electronic Coupling
We present a real-time path integral theory for the rate of electron transfer
reactions. Using graph theoretic techniques, the dynamics is expressed in a
formally exact way as a set of integral equations. With a simple approximation
for the self-energy, the rate can then be computed analytically to all orders
in the electronic coupling matrix element. We present results for the crossover
region between weak (nonadiabatic) and strong (adiabatic) electronic coupling
and show that this theory provides a rigorous justification for the salient
features of the rate expected within conventional electron transfer theory.
Nonetheless, we find distinct characteristics of quantum behavior even in the
strongly adiabatic limit where classical rate theory is conventionally thought
to be applicable. To our knowledge, this theory is the first systematic
dynamical treatment of the full crossover region.Comment: 11 pages, LaTeX, 8 Postscript figures to be published in J. Chem.
Phy
Exact c-number Representation of Non-Markovian Quantum Dissipation
The reduced dynamics of a quantum system interacting with a linear heat bath
finds an exact representation in terms of a stochastic Schr{\"o}dinger
equation. All memory effects of the reservoir are transformed into noise
correlations and mean-field friction. The classical limit of the resulting
stochastic dynamics is shown to be a generalized Langevin equation, and
conventional quantum state diffusion is recovered in the Born--Markov
approximation. The non-Markovian exact dynamics, valid at arbitrary temperature
and damping strength, is exemplified by an application to the dissipative
two-state system.Comment: 4 pages, 2 figures. To be published in Phys. Rev. Let