298 research outputs found
Efficient simulation of strong system-environment interactions
Multi-component quantum systems in strong interaction with their environment
are receiving increasing attention due to their importance in a variety of
contexts, ranging from solid state quantum information processing to the
quantum dynamics of bio-molecular aggregates. Unfortunately, these systems are
difficult to simulate as the system-bath interactions cannot be treated
perturbatively and standard approaches are invalid or inefficient. Here we
combine the time dependent density matrix renormalization group methods with
techniques from the theory of orthogonal polynomials to provide an efficient
method for simulating open quantum systems, including spin-boson models and
their generalisations to multi-component systems
A generalized multi-polaron expansion for the spin-boson model: Environmental entanglement and the biased two-state system
We develop a systematic variational coherent state expansion for the
many-body ground state of the spin-boson model, in which a quantum two-level
system is coupled to a continuum of harmonic oscillators. Energetic constraints
at the heart of this technique are rationalized in terms of polarons
(displacements of the bath states in agreement with classical expectations) and
antipolarons (counter-displacements due to quantum tunneling effects). We
present a comprehensive study of the ground state two-level system population
and coherence as a function of tunneling amplitude, dissipation strength, and
bias (akin to asymmetry of the double well potential defining the two-state
system). The entanglement among the different environmental modes is
investigated by looking at spectroscopic signatures of the bipartite
entanglement entropy between a given environmental mode and all the other
modes. We observe a drastic change in behavior of this entropy for increasing
dissipation, indicative of the entangled nature of the environmental states. In
addition, the entropy spreads over a large energy range at strong dissipation,
a testimony to the wide entanglement window characterizing the underlying Kondo
state. Finally, comparisons to accurate numerical renormalization group
calculations and to the exact Bethe Ansatz solution of the model demonstrate
the rapid convergence of our variationally-optimized multi-polaron expansion,
suggesting that it should also be a useful tool for dissipative models of
greater complexity, as relevant for numerous systems of interest in quantum
physics and chemistry.Comment: 17 pages, 14 figure
Intermediate scattering function and quantum recoil in non-Markovian quantum diffusion
Exact expressions are derived for the intermediate scattering function (ISF)
of a quantum particle diffusing in a harmonic potential and linearly coupled to
a harmonic bath. The results are valid for arbitrary strength and spectral
density of the coupling. The general, exact non-Markovian result is expressed
in terms of the classical velocity autocorrelation function, which represents
an accumulated phase during a scattering event. The imaginary part of the
exponent of the ISF is proportional to the accumulated phase, which is an
antisymmetric function of the correlation time . The expressions extend
previous results given in the quantum Langevin framework where the classical
response of the bath was taken as Markovian. For a special case of
non-Markovian friction, where the friction kernel decays exponentially in time
rather than instantaneously, we provide exact results relating to unconfined
quantum diffusion, and identify general features that allow insight to be
exported to more complex examples. The accumulated phase as a function of the t
has a universal gradient at the origin, depending only on the mass of the
diffusing system particle. At large t the accumulated phase reaches a constant
limit that depends only on the classical diffusion coefficient and is therefore
independent of the detailed memory properties of the friction kernel.
Non-Markovian properties of the friction kernel are encoded in the details of
how the accumulated phase switches from its to its
limit, subject to the constraint of the universal
gradient. When memory effects are significant, the transition from one limit to
the other becomes non-monotonic, owing to oscillations in the classical
velocity autocorrelation. The result is interpreted in terms of a solvent
caging effect, in which slowly fluctuating bath modes create transient wells
for the system particle.PT thanks the EPSRC for doctoral funding under the award reference 1363145, which enabled the majority of the present work
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